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diff --git a/26495-h/26495-h.html b/26495-h/26495-h.html new file mode 100644 index 0000000..a92da00 --- /dev/null +++ b/26495-h/26495-h.html @@ -0,0 +1,22726 @@ +<?xml version="1.0" encoding="utf-8"?> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8" /><meta http-equiv="Content-Style-Type" content="text/css" /><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" /><meta name="DC.Creator" content="John Stuart Mill" /><meta name="DC.Title" content="A System Of Logic, Ratiocinative And Inductive (Vol. 1 of 2)" /><meta name="DC.Date" content="August 31, 2008" /><meta name="DC.Language" content="English" /><meta name="DC.Publisher" content="Project Gutenberg" /><meta name="DC.Identifier" content="http://www.gutenberg.org/etext/26495" /><meta name="DC.Rights" content="This text is in the public domain." /><title>The Project Gutenberg EBook of A System Of Logic, Ratiocinative And Inductive (Vol. 1 of 2) by John Stuart Mill</title><style type="text/css">/* +The Gnutenberg Press - default CSS2 stylesheet + +Any generated element will have a class "tei" and a class "tei-elem" +where elem is the element name in TEI. +The order of statements is important !!! 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You may copy it, + give it away or re-use it under the terms of the Project + Gutenberg License <a href="#pglicense" class="tei tei-ref">included with this + eBook</a> or online at <a href="http://www.gutenberg.org/license" class="tei tei-xref">http://www.gutenberg.org/license</a></p></div><pre class="pre tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em">Title: A System Of Logic, Ratiocinative And Inductive (Vol. 1 of 2) + +Author: John Stuart Mill + +Release Date: August 31, 2008 [Ebook #26495] + +Language: English + +Character set encoding: UTF-8 + + +***START OF THE PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE (VOL. 1 OF 2)*** +</pre></div> + </div> + <div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> + + </div> + + <hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.73em"><span style="font-size: 173%">A SYSTEM OF LOGIC,</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.73em"><span style="font-size: 173%">RATIOCINATIVE AND INDUCTIVE,</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">BEING A CONNECTED VIEW OF THE</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">PRINCIPLES OF EVIDENCE,</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">AND THE</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">METHODS OF SCIENTIFIC INVESTIGATION.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">by</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.73em"><span style="font-size: 173%">JOHN STUART MILL.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">In Two Volumes.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.44em"><span style="font-size: 144%">Vol. I.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">Third Edition.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">London:</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.44em"><span style="font-size: 144%">John Parker, West Strand.</span></p> + <p class="tei tei-p" style="text-align: center; margin-bottom: 1.20em"><span style="font-size: 120%">M DCCC LI.</span></p> + </div> + <hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> + <h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">Contents</span></h1> + <ul class="tei tei-index tei-index-toc"><li><a href="#toc1">PREFACE TO THE FIRST EDITION.</a></li><li><a href="#toc3">PREFACE TO THE THIRD EDITION.</a></li><li><a href="#toc5">INTRODUCTION.</a></li><li><a href="#toc7">BOOK I. OF NAMES AND PROPOSITIONS.</a></li><li style="margin-left: 2em"><a href="#toc9">CHAPTER I. OF THE NECESSITY OF COMMENCING WITH AN +ANALYSIS OF LANGUAGE.</a></li><li style="margin-left: 2em"><a href="#toc11">CHAPTER II. OF NAMES.</a></li><li style="margin-left: 2em"><a href="#toc13">CHAPTER III. OF THE THINGS DENOTED BY NAMES.</a></li><li style="margin-left: 4em"><a href="#toc15">I. Feelings, or States of Consciousness.</a></li><li style="margin-left: 4em"><a href="#toc17">II. Substances.</a></li><li style="margin-left: 4em"><a href="#toc19">III. Attributes: and, first, Qualities.</a></li><li style="margin-left: 4em"><a href="#toc21">IV. Relations.</a></li><li style="margin-left: 4em"><a href="#toc23">V. Quantity.</a></li><li style="margin-left: 4em"><a href="#toc25">VI. Attributes Concluded.</a></li><li style="margin-left: 4em"><a href="#toc27">VII. General Results.</a></li><li style="margin-left: 2em"><a href="#toc29">CHAPTER IV. OF PROPOSITIONS.</a></li><li style="margin-left: 2em"><a href="#toc31">CHAPTER V. OF THE IMPORT OF PROPOSITIONS.</a></li><li style="margin-left: 2em"><a href="#toc33">CHAPTER VI. OF PROPOSITIONS MERELY VERBAL.</a></li><li style="margin-left: 2em"><a href="#toc35">CHAPTER VII. OF THE NATURE OF CLASSIFICATION, AND THE FIVE +PREDICABLES.</a></li><li style="margin-left: 2em"><a href="#toc37">CHAPTER VIII. OF DEFINITION.</a></li><li><a href="#toc39">BOOK II. OF REASONING.</a></li><li style="margin-left: 2em"><a href="#toc41">CHAPTER I. OF INFERENCE, OR REASONING, IN GENERAL.</a></li><li style="margin-left: 2em"><a href="#toc43">CHAPTER II. OF RATIOCINATION, OR SYLLOGISM.</a></li><li style="margin-left: 2em"><a href="#toc45">CHAPTER III. OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE +SYLLOGISM.</a></li><li style="margin-left: 2em"><a href="#toc47">CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.</a></li><li style="margin-left: 2em"><a href="#toc49">CHAPTER V. OF DEMONSTRATION, AND NECESSARY TRUTHS.</a></li><li style="margin-left: 2em"><a href="#toc51">CHAPTER VI. THE SAME SUBJECT CONTINUED.</a></li><li><a href="#toc53">BOOK III. OF INDUCTION.</a></li><li style="margin-left: 2em"><a href="#toc55">CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN +GENERAL.</a></li><li style="margin-left: 2em"><a href="#toc57">CHAPTER II. OF INDUCTIONS IMPROPERLY SO CALLED.</a></li><li style="margin-left: 2em"><a href="#toc59">CHAPTER III. OF THE GROUND OF INDUCTION.</a></li><li style="margin-left: 2em"><a href="#toc61">CHAPTER IV. OF LAWS OF NATURE.</a></li><li style="margin-left: 2em"><a href="#toc63">CHAPTER V. OF THE LAW OF UNIVERSAL CAUSATION.</a></li><li style="margin-left: 2em"><a href="#toc65">CHAPTER VI. OF THE COMPOSITION OF CAUSES.</a></li><li style="margin-left: 2em"><a href="#toc67">CHAPTER VII. OF OBSERVATION AND EXPERIMENT.</a></li><li style="margin-left: 2em"><a href="#toc69">CHAPTER VIII. OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.</a></li><li style="margin-left: 2em"><a href="#toc71">CHAPTER IX. MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.</a></li><li style="margin-left: 2em"><a href="#toc73">CHAPTER X. OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE +OF EFFECTS.</a></li><li style="margin-left: 2em"><a href="#toc75">CHAPTER XI. OF THE DEDUCTIVE METHOD.</a></li><li style="margin-left: 2em"><a href="#toc77">CHAPTER XII. OF THE EXPLANATION OF LAWS OF NATURE.</a></li><li style="margin-left: 2em"><a href="#toc79">CHAPTER XIII. MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF +LAWS OF NATURE.</a></li><li><a href="#toc81">Footnotes</a></li></ul> + </div> + </div> +<div class="tei tei-body" style="margin-bottom: 6.00em; margin-top: 6.00em"> + +<span class="tei tei-pb" id="pageiii">[pg iii]</span><a name="Pgiii" id="Pgiii" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc1" id="toc1"></a> +<a name="pdf2" id="pdf2"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">PREFACE TO THE FIRST EDITION.</span></h1> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This book makes no pretence of giving to the +world a new theory of the intellectual operations. +Its claim to attention, if it possess any, is grounded +on the fact that it is an attempt not to supersede, but +to embody and systematize, the best ideas which have +been either promulgated on its subject by speculative +writers, or conformed to by accurate thinkers in their +scientific inquiries. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To cement together the detached fragments of a +subject, never yet treated as a whole; to harmonize +the true portions of discordant theories, by supplying +the links of thought necessary to connect them, and by +disentangling them from the errors with which they +are always more or less interwoven; must necessarily +require a considerable amount of original speculation. +To other originality than this, the present work lays +no claim. In the existing state of the cultivation of +the sciences, there would be a very strong presumption +against any one who should imagine that he had +effected a revolution in the theory of the investigation +of truth, or added any fundamentally new +process to the practice of it. The improvement which +remains to be effected in the methods of philosophizing +(and the author believes that they have much +<span class="tei tei-pb" id="pageiv">[pg iv]</span><a name="Pgiv" id="Pgiv" class="tei tei-anchor"></a> +need of improvement) can only consist in performing, +more systematically and accurately, operations with +which, at least in their elementary form, the human +intellect in some one or other of its employments is +already familiar. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the portion of the work which treats of Ratiocination, +the author has not deemed it necessary to +enter into technical details which may be obtained in +so perfect a shape from the existing treatises on what +is termed the Logic of the Schools. In the contempt +entertained by many modern philosophers for the +syllogistic art, it will be seen that he by no means +participates; although the scientific theory on which +its defence is usually rested appears to him erroneous: +and the view which he has suggested of the nature +and functions of the Syllogism may, perhaps, afford +the means of conciliating the principles of the art +with as much as is well grounded in the doctrines and +objections of its assailants. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The same abstinence from details could not be +observed in the First Book, on Names and Propositions; +because many useful principles and distinctions +which were contained in the old Logic, have +been gradually omitted from the writings of its later +teachers; and it appeared desirable both to revive +these, and to reform and rationalize the philosophical +foundation on which they stood. The earlier chapters +of this preliminary Book will consequently appear, to +some readers, needlessly elementary and scholastic. +But those who know in what darkness the nature of +our knowledge, and of the processes by which it is +<span class="tei tei-pb" id="pagev">[pg v]</span><a name="Pgv" id="Pgv" class="tei tei-anchor"></a> +obtained, is often involved by a confused apprehension +of the import of the different classes of Words and +Assertions, will not regard these discussions as either +frivolous, or irrelevant to the topics considered in the +later Books. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +On the subject of Induction, the task to be performed +was that of generalizing the modes of investigating +truth and estimating evidence, by which so +many important and recondite laws of nature have, +in the various sciences, been aggregated to the stock +of human knowledge. That this is not a task free +from difficulty may be presumed from the fact, that +even at a very recent period, eminent writers (among +whom it is sufficient to name Archbishop Whately, +and the author of a celebrated article on Bacon in the +<span class="tei tei-hi"><span style="font-style: italic">Edinburgh Review</span></span>) have not scrupled to pronounce it +impossible.<a id="noteref_1" name="noteref_1" href="#note_1"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">1</span></span></a> +The author has endeavoured to combat +their theory in the manner in which Diogenes confuted +the sceptical reasonings against the possibility of +motion; remembering that Diogenes' argument would +have been equally conclusive, though his individual +perambulations might not have extended beyond the +circuit of his own tub. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Whatever may be the value of what the author +<span class="tei tei-pb" id="pagevi">[pg vi]</span><a name="Pgvi" id="Pgvi" class="tei tei-anchor"></a> +has succeeded in effecting on this branch of his subject, +it is a duty to acknowledge that for much of it +he has been indebted to several important treatises, +partly historical and partly philosophical, on the generalities +and processes of physical science, which have +been published within the last few years. To these +treatises, and to their authors, he has endeavoured to do +justice in the body of the work. But as with one of +these writers, Dr. Whewell, he has occasion frequently +to express differences of opinion, it is more particularly +incumbent on him in this place to declare, that without +the aid derived from the facts and ideas contained in +that gentleman's <span class="tei tei-hi"><span style="font-style: italic">History of the Inductive Sciences</span></span>, the +corresponding portion of this work would probably not +have been written. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The concluding Book is an attempt to contribute +towards the solution of a question, which the decay of +old opinions, and the agitation that disturbs European +society to its inmost depths, render as important in the +present day to the practical interests of human life, +as it must at all times be to the completeness of our +speculative knowledge: viz. Whether moral and social +phenomena are really exceptions to the general +certainty and uniformity of the course of nature; and +how far the methods, by which so many of the laws of +the physical world have been numbered among +truths irrevocably acquired and universally assented +to, can be made instrumental to the formation of a +similar body of received doctrine in moral and political +science. +</p> + +</div> + +<span class="tei tei-pb" id="pagevii">[pg vii]</span><a name="Pgvii" id="Pgvii" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc3" id="toc3"></a> +<a name="pdf4" id="pdf4"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">PREFACE TO THE THIRD EDITION.</span></h1> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Several criticisms, of a more or less controversial +character, on this work, have appeared since the publication +of the second edition; and Dr. Whewell has +lately published a reply to those parts of it in which +some of his opinions were controverted. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I have carefully reconsidered all the points on +which my conclusions have been assailed. But I have +not to announce a change of opinion on any matter of +importance. Such minor oversights as have been +detected, either by myself or by my critics, I have, in +general silently, corrected: but it is not to be inferred +that I agree with the objections which have been made +to a passage, in every instance in which I have altered +or cancelled it. I have often done so, merely that it +might not remain a stumbling-block, when the amount +of discussion necessary to place the matter in its true +light would have exceeded what was suitable to the +occasion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To several of the arguments which have been +urged against me, I have thought it useful to reply +with some degree of minuteness; not from any taste +for controversy, but because the opportunity was +favourable for placing my own conclusions, and the +grounds of them, more clearly and completely before +<span class="tei tei-pb" id="pageviii">[pg viii]</span><a name="Pgviii" id="Pgviii" class="tei tei-anchor"></a> +the reader. Truth, on these subjects, is militant, and +can only establish itself by means of conflict. The +most opposite opinions can make a plausible show of +evidence while each has the statement of its own case; +and it is only possible to ascertain which of them is +in the right, after hearing and comparing what each +can say against the other, and what the other can urge +in its defence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Even the criticisms from which I most dissent have +been of great service to me, by showing in what places +the exposition most needed to be improved, or the +arguments strengthened. And I should have been well +pleased if the book had undergone a much greater +amount of attack; as in that case I should probably +have been enabled to improve it still more than I +believe I have now done. +</p> + +</div> + +<span class="tei tei-pb" id="page001">[pg 001]</span><a name="Pg001" id="Pg001" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc5" id="toc5"></a> +<a name="pdf6" id="pdf6"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">INTRODUCTION.</span></h1> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. There is as great diversity among authors in the +modes which they have adopted of defining logic, as in their +treatment of the details of it. This is what might naturally +be expected on any subject on which writers have availed +themselves of the same language as a means of delivering +different ideas. Ethics and jurisprudence are liable to the +remark in common with logic. Almost every writer having +taken a different view of some of the particulars which these +branches of knowledge are usually understood to include; +each has so framed his definition as to indicate beforehand +his own peculiar tenets, and sometimes to beg the question +in their favour. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This diversity is not so much an evil to be complained of, +as an inevitable and in some degree a proper result of the +imperfect state of those sciences. It is not to be expected +that there should be agreement about the definition of a +thing, until there is agreement about the thing itself. To +define a thing, is to select from among the whole of its properties +those which shall be understood to be designated and +declared by its name; and the properties must be well +known to us before we can be competent to determine which +of them are fittest to be chosen for this purpose. Accordingly, +in the case of so complex an aggregation of particulars +as are comprehended in anything which can be called a +science, the definition we set out with is seldom that which a +more extensive knowledge of the subject shows to be the +most appropriate. Until we know the particulars themselves, +we cannot fix upon the most correct and compact mode of +circumscribing them by a general description. It was not +till after an extensive and accurate acquaintance with the +<span class="tei tei-pb" id="page002">[pg 002]</span><a name="Pg002" id="Pg002" class="tei tei-anchor"></a> +details of chemical phenomena, that it was found possible to +frame a rational definition of chemistry; and the definition +of the science of life and organization is still a matter of +dispute. So long as the sciences are imperfect, the definitions +must partake of their imperfections; and if the former +are progressive, the latter ought to be so too. As much, +therefore, as is to be expected from a definition placed at the +commencement of a subject, is that it should define the scope +of our inquiries: and the definition which I am about to +offer of the science of logic, pretends to nothing more, than +to be a statement of the question which I have put to myself, +and which this book is an attempt to resolve. The reader +is at liberty to object to it as a definition of logic; but it +is at all events a correct definition of the subject of these +volumes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Logic has often been called the Art of Reasoning. +A writer<a id="noteref_2" name="noteref_2" href="#note_2"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">2</span></span></a> +who has done more than any other living person +to restore this study to the rank from which it had fallen in +the estimation of the cultivated class in our own country, has +adopted the above definition with an amendment; he has +defined Logic to be the Science, as well as the Art, of reasoning; +meaning by the former term, the analysis of the mental +process which takes place whenever we reason, and by the +latter, the rules, grounded on that analysis, for conducting +the process correctly. There can be no doubt as to the +propriety of the emendation. A right understanding of the +mental process itself, of the conditions it depends on, and +the steps of which it consists, is the only basis on which a +system of rules, fitted for the direction of the process, can +possibly be founded. Art necessarily presupposes knowledge; +art, in any but its infant state, presupposes scientific knowledge: +and if every art does not bear the name of the science +on which it rests, it is only because several sciences are often +necessary to form the groundwork of a single art. Such is +the complication of human affairs, that to enable one thing to +<span class="tei tei-pb" id="page003">[pg 003]</span><a name="Pg003" id="Pg003" class="tei tei-anchor"></a> +be <em class="tei tei-emph"><span style="font-style: italic">done</span></em>, it is often requisite to <em class="tei tei-emph"><span style="font-style: italic">know</span></em> the nature and +properties of many things. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Logic, then, comprises the science of reasoning, as well as +an art, founded on that science. But the word Reasoning, +again, like most other scientific terms in popular use, +abounds in ambiguities. In one of its acceptations, it means +syllogizing; or the mode of inference which may be called +(with sufficient accuracy for the present purpose) concluding +from generals to particulars. In another of its senses, to +reason, is simply to infer any assertion, from assertions +already admitted: and in this sense induction is as much +entitled to be called reasoning as the demonstrations of +geometry. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Writers on logic have generally preferred the former +acceptation of the term; the latter, and more extensive signification +is that in which I mean to use it. I do this by +virtue of the right I claim for every author, to give whatever +provisional definition he pleases of his own subject. But +sufficient reasons will, I believe, unfold themselves as we +advance, why this should be not only the provisional but the +final definition. It involves, at all events, no arbitrary +change in the meaning of the word; for, with the general +usage of the English language, the wider signification, I +believe, accords better than the more restricted one. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. But Reasoning, even in the widest sense of which +the word is susceptible, does not seem to comprehend all +that is included, either in the best, or even in the most +current, conception of the scope and province of our science. +The employment of the word Logic to denote the theory of +argumentation, is derived from the Aristotelian, or, as they +are commonly termed, the scholastic logicians. Yet even +with them, in their systematic treatises, argumentation was +the subject only of the third part: the two former treated of +Terms, and of Propositions; under one or other of which +heads were also included Definition and Division. Professedly, +indeed, these previous topics were introduced only +on account of their connexion with reasoning, and as a preparation +<span class="tei tei-pb" id="page004">[pg 004]</span><a name="Pg004" id="Pg004" class="tei tei-anchor"></a> +for the doctrine and rules of the syllogism. Yet +they were treated with greater minuteness, and dwelt on at +greater length, than was required for that purpose alone. +More recent writers on logic have generally understood the +term as it was employed by the able author of the Port +Royal Logic; viz. as equivalent to the Art of Thinking. Nor +is this acceptation confined to books, and scientific inquirers. +Even in ordinary conversation, the ideas connected with the +word Logic, include at least precision of language, and accuracy +of classification: and we perhaps oftener hear persons +speak of a logical arrangement, or of expressions logically +defined, than of conclusions logically deduced from premisses. +Again, a man is often called a great logician, or a man of +powerful logic, not for the accuracy of his deductions, but for +the extent of his command over premisses; because the +general propositions required for explaining a difficulty or +refuting a sophism, copiously and promptly occur to him: +because, in short, his knowledge, besides being ample, is well +under his command for argumentative use. Whether, therefore, +we conform to the practice of those who have made the +subject their particular study, or to that of popular writers +and common discourse, the province of logic will include +several operations of the intellect not usually considered to +fall within the meaning of the terms Reasoning and Argumentation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These various operations might be brought within the +compass of the science, and the additional advantage be obtained +of a very simple definition, if, by an extension of the +term, sanctioned by high authorities, we were to define logic +as the science which treats of the operations of the human +understanding in the pursuit of truth. For to this ultimate +end, naming, classification, definition, and all other operations +over which logic has ever claimed jurisdiction, are +essentially subsidiary. They may all be regarded as contrivances +for enabling a person to know the truths which are +needful to him, and to know them at the precise moment at +which they are needful. Other purposes, indeed, are also +served by these operations; for instance, that of imparting +<span class="tei tei-pb" id="page005">[pg 005]</span><a name="Pg005" id="Pg005" class="tei tei-anchor"></a> +our knowledge to others. But, viewed with regard to this +purpose, they have never been considered as within the province +of the logician. The sole object of Logic is the guidance +of one's own thoughts; the communication of those +thoughts to others falls under the consideration of Rhetoric, +in the large sense in which that art was conceived by the +ancients; or of the still more extensive art of Education. +Logic takes cognizance of our intellectual operations, only +as they conduce to our own knowledge, and to our command +over that knowledge for our own uses. If there were but one +rational being in the universe, that being might be a perfect +logician; and the science and art of logic would be the same +for that one person as for the whole human race. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. But, if the definition which we formerly examined +included too little, that which is now suggested has the opposite +fault of including too much. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Truths are known to us in two ways: some are known +directly, and of themselves; some through the medium of +other truths. The former are the subject of Intuition, or +Consciousness; the latter, of Inference. The truths known +by intuition are the original premisses from which all others +are inferred. Our assent to the conclusion being grounded +on the truth of the premisses, we never could arrive at any +knowledge by reasoning, unless something could be known +antecedently to all reasoning. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Examples of truths known to us by immediate consciousness, +are our own bodily sensations and mental feelings. I +know directly, and of my own knowledge, that I was vexed +yesterday, or that I am hungry to-day. Examples of truths +which we know only by way of inference, are occurrences +which took place while we were absent, the events recorded +in history, or the theorems of mathematics. The two former +we infer from the testimony adduced, or from the traces of +those past occurrences which still exist; the latter, from the +premisses laid down in books of geometry, under the title of +definitions and axioms. Whatever we are capable of knowing +must belong to the one class or to the other; must be in +<span class="tei tei-pb" id="page006">[pg 006]</span><a name="Pg006" id="Pg006" class="tei tei-anchor"></a> +the number of the primitive data, or of the conclusions which +can be drawn from these. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +With the original data, or ultimate premisses of our +knowledge; with their number or nature, the mode in which +they are obtained, or the tests by which they may be distinguished; +logic, in a direct way at least, has, in the sense +in which I conceive the science, nothing to do. These questions +are partly not a subject of science at all, partly that of +a very different science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Whatever is known to us by consciousness, is known +beyond possibility of question. What one sees or feels, +whether bodily or mentally, one cannot but be sure that +one sees or feels. No science is required for the purpose +of establishing such truths; no rules of art can render our +knowledge of them more certain than it is in itself. There +is no logic for this portion of our knowledge. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But we may fancy that we see or feel what we in reality +infer. Newton saw the truth of many propositions of geometry +without reading the demonstrations, but not, we may +be sure, without their flashing through his mind. A truth, +or supposed truth, which is really the result of a very rapid +inference, may seem to be apprehended intuitively. It +has long been agreed by thinkers of the most opposite +schools, that this mistake is actually made in so familiar +an instance as that of the eyesight. There is nothing of +which we appear to ourselves to be more directly conscious, +than the distance of an object from us. Yet it has long been +ascertained, that what is perceived by the eye, is at most +nothing more than a variously coloured surface; that when we +fancy we see distance, all we really see is certain variations of +apparent size, and degrees of faintness of colour; and that +our estimate of the object's distance from us is the result of +a comparison (made with so much rapidity that we are unconscious +of making it) between the size and colour of the +object as they appear at the time, and the size and colour of +the same or of similar objects as they appeared when close +at hand, or when their degree of remoteness was known by +other evidence. The perception of distance by the eye, +<span class="tei tei-pb" id="page007">[pg 007]</span><a name="Pg007" id="Pg007" class="tei tei-anchor"></a> +which seems so like intuition, is thus, in reality, an inference +grounded on experience; an inference, too, which we +learn to make; and which we make with more and more +correctness as our experience increases; though in familiar +cases it takes place, so rapidly as to appear exactly on a par +with those perceptions of sight which are really intuitive, our +perceptions of colour.<a id="noteref_3" name="noteref_3" href="#note_3"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">3</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of the science, therefore, which expounds the operations +of the human understanding in the pursuit of truth, one +essential part is the inquiry: What are the facts which are +the objects of intuition or consciousness, and what are those +which we merely infer? But this inquiry has never been +considered a portion of logic. Its place is in another and a +perfectly distinct department of science, to which the name +metaphysics more particularly belongs: that portion of mental +philosophy which attempts to determine what part of the furniture +of the mind belongs to it originally, and what part is constructed +out of materials furnished to it from without. To +this science appertain the great and much debated questions +of the existence of matter; the existence of spirit, and of a +distinction between it and matter; the reality of time and +space, as things without the mind, and distinguishable from +the objects which are said to exist <em class="tei tei-emph"><span style="font-style: italic">in</span></em> them. For in the +present state of the discussion on these topics, it is almost +universally allowed that the existence of matter or of spirit, +of space or of time, is, in its nature, unsusceptible of being +proved; and that if anything is known of them, it must be by +immediate intuition. To the same science belong the inquiries +into the nature of Conception, Perception, Memory, and +Belief; all of which are operations of the understanding in the +<span class="tei tei-pb" id="page008">[pg 008]</span><a name="Pg008" id="Pg008" class="tei tei-anchor"></a> +pursuit of truth; but with which, as phenomena of the mind, +or with the possibility which may or may not exist of analysing +any of them into simpler phenomena, the logician as such +has no concern. To this science must also be referred the +following, and all analogous questions: To what extent our +intellectual faculties and our emotions are innate—to what +extent the result of association: Whether God, and duty, +are realities, the existence of which is manifest to us +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: 'italic">à priori</span></span> +by the constitution of our rational faculty; or whether our +ideas of them are acquired notions, the origin of which we +are able to trace and explain; and the reality of the objects +themselves a question not of consciousness or intuition, but +of evidence and reasoning. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The province of logic must be restricted to that portion +of our knowledge which consists of inferences from truths +previously known; whether those antecedent data be general +propositions, or particular observations and perceptions. +Logic is not the science of Belief, but the science of Proof, +or Evidence. In so far as belief professes to be founded on +proof, the office of logic is to supply a test for ascertaining +whether or not the belief is well grounded. With the claims +which any proposition has to belief on the evidence of consciousness, +that is, without evidence in the proper sense +of the word, logic has nothing to do. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. By far the greatest portion of our knowledge, +whether of general truths or of particular facts, being avowedly +matter of inference, nearly the whole, not only of +science, but of human conduct, is amenable to the authority of +logic. To draw inferences has been said to be the great business +of life. Every one has daily, hourly, and momentary +need of ascertaining facts which he has not directly observed; +not from any general purpose of adding to his stock +of knowledge, but because the facts themselves are of importance +to his interests or to his occupations. The business of +the magistrate, of the military commander, of the navigator, +of the physician, of the agriculturist, is merely to judge of +evidence, and to act accordingly. They all have to ascertain +<span class="tei tei-pb" id="page009">[pg 009]</span><a name="Pg009" id="Pg009" class="tei tei-anchor"></a> +certain facts, in order that they may afterwards apply +certain rules, either devised by themselves, or prescribed for +their guidance by others; and as they do this well or ill, so +they discharge well or ill the duties of their several callings. +It is the only occupation in which the mind never ceases to +be engaged; and is the subject, not of logic, but of knowledge +in general. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Logic, however, is not the same thing with knowledge, +though the field of logic is coextensive with the field of +knowledge. Logic is the common judge and arbiter of all +particular investigations. It does not undertake to find +evidence, but to determine whether it has been found. Logic +neither observes, nor invents, nor discovers; but judges. It +is no part of the business of logic to inform the surgeon what +appearances are found to accompany a violent death. This +he must learn from his own experience and observation, or +from that of others, his predecessors in his peculiar pursuit. +But logic sits in judgment on the sufficiency of that observation +and experience to justify his rules, and on the sufficiency +of his rules to justify his conduct. It does not give him +proofs, but teaches him what makes them proofs, and how he +is to judge of them. It does not teach that any particular fact +proves any other, but points out to what conditions all facts +must conform, in order that they may prove other facts. To +decide whether any given fact fulfils these conditions, or +whether facts can be found which fulfil them in a given case, +belongs exclusively to the particular art or science, or to +our knowledge of the particular subject. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is in this sense that logic is, what Bacon so expressively +called it, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">ars artium</span></span>; +the science of science itself. All +science consists of data and conclusions from those data, of +proofs and what they prove: now logic points out what relations +must subsist between data and whatever can be concluded +from them, between proof and everything which it +can prove. If there be any such indispensable relations, +and if these can be precisely determined, every particular +branch of science, as well as every individual in the guidance +of his conduct, is bound to conform to those relations, under +<span class="tei tei-pb" id="page010">[pg 010]</span><a name="Pg010" id="Pg010" class="tei tei-anchor"></a> +the penalty of making false inferences, of drawing conclusions +which are not grounded in the realities of things. +Whatever has at any time been concluded justly, whatever +knowledge has been acquired otherwise than by immediate +intuition, depended on the observance of the laws which it +is the province of logic to investigate. If the conclusions +are just, and the knowledge real, those laws, whether known +or not, have been observed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. We need not, therefore, seek any farther for a solution +of the question, so often agitated, respecting the utility +of logic. If a science of logic exists, or is capable of existing, +it must be useful. If there be rules to which every +mind consciously or unconsciously conforms in every instance +in which it infers rightly, there seems little necessity +for discussing whether a person is more likely to observe +those rules, when he knows the rules, than when he is +unacquainted with them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A science may undoubtedly be brought to a certain, not +inconsiderable, stage of advancement, without the application +of any other logic to it than what all persons, who are +said to have a sound understanding, acquire empirically in +the course of their studies. Mankind judged of evidence, +and often correctly, before logic was a science, or they +never could have made it one. And they executed great +mechanical works before they understood the laws of mechanics. +But there are limits both to what mechanicians +can do without principles of mechanics, and to what thinkers +can do without principles of logic. A few individuals may, +by extraordinary genius, anticipate the results of science; +but the bulk of mankind require either to understand the +theory of what they are doing, or to have rules laid +down for them by those who have understood the theory. +In the progress of science from its easiest to its more difficult +problems, each great step in advance has usually had either +as its precursor, or as its accompaniment and necessary +condition, a corresponding improvement in the notions and +principles of logic received among the most advanced +<span class="tei tei-pb" id="page011">[pg 011]</span><a name="Pg011" id="Pg011" class="tei tei-anchor"></a> +thinkers. And if several of the more difficult sciences are +still in so defective a state; if not only so little is proved, +but disputation has not terminated even about the little +which seemed to be so; the reason perhaps is, that men's +logical notions have not yet acquired the degree of extension, +or of accuracy, requisite for the estimation of the +evidence proper to those particular departments of knowledge. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. Logic, then, is the science of the operations of the +understanding which are subservient to the estimation of +evidence: both the process itself of proceeding from known +truths to unknown, and all other intellectual operations in +so far as auxiliary to this. It includes, therefore, the operation +of Naming; for language is an instrument of thought, +as well as a means of communicating our thoughts. It includes, +also, Definition, and Classification. For, the use of +these operations (putting all other minds than one's own +out of consideration) is to serve not only for keeping our +evidences and the conclusions from them permanent and +readily accessible in the memory, but for so marshalling the +facts which we may at any time be engaged in investigating, +as to enable us to perceive more clearly what evidence there +is, and to judge with fewer chances of error whether it be +sufficient. These, therefore, are operations specially instrumental +to the estimation of evidence, and as such are within +the province of Logic. There are other more elementary +processes, concerned in all thinking, such as Conception, +Memory, and the like; but of these it is not necessary that +Logic should take any peculiar cognizance, since they have +no special connexion with the problem of Evidence, further +than that, like all other problems addressed to the understanding, +it presupposes them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Our object, then, will be to attempt a correct analysis of +the intellectual process called Reasoning or Inference, and +of such other mental operations as are intended to facilitate +this: as well as, on the foundation of this analysis, and <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">pari +</span><span class="tei tei-pb" id="page012">[pg 012]</span><a name="Pg012" id="Pg012" class="tei tei-anchor"></a><span style="font-style: italic"> +passu</span></span> with it, to bring together or frame a set of rules or +canons for testing the sufficiency of any given evidence to +prove any given proposition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +With respect to the first part of this undertaking, I do +not attempt to decompose the mental operations in question +into their ultimate elements. It is enough if the analysis as +far as it goes is correct, and if it goes far enough for the +practical purposes of logic considered as an art. The +separation of a complicated phenomenon into its component +parts, is not like a connected and interdependent chain of +proof. If one link of an argument breaks, the whole drops +to the ground; but one step towards an analysis holds good +and has an independent value, though we should never be +able to make a second. The results of analytical chemistry +are not the less valuable, though it should be discovered that +all which we now call simple substances are really compounds. +All other things are at any rate compounded of +those elements: whether the elements themselves admit of +decomposition, is an important inquiry, but does not affect +the certainty of the science up to that point. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I shall, accordingly, attempt to analyse the process of +inference, and the processes subordinate to inference, so far +only as may be requisite for ascertaining the difference between +a correct and an incorrect performance of those processes. +The reason for thus limiting our design, is evident. +It has been said by objectors to logic, that we do not learn +to use our muscles by studying their anatomy. The fact is +not quite fairly stated; for if the action of any of our +muscles were vitiated by local weakness, or other physical +defect, a knowledge of their anatomy might be very necessary +for effecting a cure. But we should be justly liable to +the criticism involved in this objection, were we, in a treatise +on logic, to carry the analysis of the reasoning process beyond +the point at which any inaccuracy which may have +crept into it must become visible. In learning bodily exercises +(to carry on the same illustration) we do, and must, +analyse the bodily motions so far as is necessary for distinguishing +<span class="tei tei-pb" id="page013">[pg 013]</span><a name="Pg013" id="Pg013" class="tei tei-anchor"></a> +those which ought to be performed from those which +ought not. To a similar extent, and no further, it is necessary +that the logician should analyse the mental processes +with which Logic is concerned. Any ulterior and +minuter analysis must be left to metaphysics; which in +this, as in other parts of our mental nature, decides what +are ultimate facts, and what are resolvable into other facts. +And I believe it will be found that the conclusions arrived +at in this work have no necessary connexion with any particular +views respecting the ulterior analysis. Logic is +common ground on which the partisans of Hartley and of +Reid, of Locke and of Kant, may meet and join hands. +Particular and detached opinions of all these thinkers will +no doubt occasionally be controverted, since all of them +were logicians as well as metaphysicians; but the field on +which their principal battles have been fought, lies beyond +the boundaries of our science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It cannot, indeed, be pretended that logical principles can +be altogether irrelevant to those more abstruse discussions; +nor is it possible but that the view we are led to take of +the problem which logic proposes, must have a tendency +favourable to the adoption of some one opinion on these controverted +subjects rather than another. For metaphysics, in +endeavouring to solve its own peculiar problem, must employ +means, the validity of which falls under the cognizance of +logic. It proceeds, no doubt, as far as possible, merely by a +closer and more attentive interrogation of our consciousness, +or more properly speaking, of our memory; and so +far is not amenable to logic. But wherever this method is +insufficient to attain the end of its inquiries, it must proceed, +like other sciences, by means of evidence. Now, the moment +this science begins to draw inferences from evidence, logic +becomes the sovereign judge whether its inferences are well-grounded, +or what other inferences would be so. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, however, constitutes no nearer or other relation +between logic and metaphysics than that which exists +between logic and all the other sciences. And I can conscientiously +<span class="tei tei-pb" id="page014">[pg 014]</span><a name="Pg014" id="Pg014" class="tei tei-anchor"></a> +affirm, that no one proposition laid down in +this work has been adopted for the sake of establishing, or +with any reference to its fitness for being employed in +establishing, preconceived opinions in any department of +knowledge or of inquiry on which the speculative world is +still undecided. +</p> + +</div> + +<span class="tei tei-pb" id="page015">[pg 015]</span><a name="Pg015" id="Pg015" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc7" id="toc7"></a> +<a name="pdf8" id="pdf8"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">BOOK I. OF NAMES AND PROPOSITIONS.</span></h1> + +<span class="tei tei-pb" id="page016">[pg 016]</span><a name="Pg016" id="Pg016" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“La scolastique, qui produisit dans la logique, comme dans la morale, et dans +une partie de la métaphysique, une subtilité, une précision d'idées, dont l'habitude +inconnue aux anciens, a contribué plus qu'on ne croit au progrès de la +bonne philosophie.”</span>—<span class="tei tei-hi"><span style="font-variant: small-caps">Condorcet</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">Vie de Turgot</span></span>. +</p> + +<span class="tei tei-pb" id="page017">[pg 017]</span><a name="Pg017" id="Pg017" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc9" id="toc9"></a> +<a name="pdf10" id="pdf10"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER I. OF THE NECESSITY OF COMMENCING WITH AN +ANALYSIS OF LANGUAGE.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. It is so much the established practice of writers +on logic to commence their treatises by a few general +observations (in most cases, it is true, rather meagre) on +Terms and their varieties, that it will, perhaps, scarcely be +required from me, in merely following the common usage, +to be as particular in assigning my reasons, as it is usually +expected that those should be who deviate from it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The practice, indeed, is recommended by considerations +far too obvious to require a formal justification. Logic is a +portion of the Art of Thinking: Language is evidently, and +by the admission of all philosophers, one of the principal +instruments or helps of thought; and any imperfection in +the instrument, or in the mode of employing it, is confessedly +liable, still more than in almost any other art, to confuse and +impede the process, and destroy all ground of confidence in +the result. For a mind not previously versed in the meaning +and right use of the various kinds of words, to attempt the +study of methods of philosophizing, would be as if some one +should attempt to make himself an astronomical observer, +having never learned to adjust the focal distance of his +optical instruments so as to see distinctly. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Since Reasoning, or Inference, the principal subject of +logic, is an operation which usually takes place by means of +words, and in complicated cases can take place in no other +way; those who have not a thorough insight into the signification +and purposes of words, will be under chances, amounting +almost to certainty, of reasoning or inferring incorrectly. And +logicians have generally felt that unless, in the very first stage, +they removed this fertile source of error; unless they taught +<span class="tei tei-pb" id="page018">[pg 018]</span><a name="Pg018" id="Pg018" class="tei tei-anchor"></a> +their pupil to put away the glasses which distort the object, +and to use those which are adapted to his purpose in such a +manner as to assist, not perplex his vision; he would not +be in a condition to practise the remaining part of their discipline +with any prospect of advantage. Therefore it is that +an inquiry into language, so far as is needful to guard against +the errors to which it gives rise, has at all times been deemed +a necessary preliminary to the study of logic. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But there is another reason, of a still more fundamental +nature, why the import of words should be the earliest subject +of the logician's consideration: because without it he cannot +examine into the import of Propositions. Now this is a +subject which stands on the very threshold of the science of +logic. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The object of logic, as defined in the Introductory Chapter, +is to ascertain how we come by that portion of our +knowledge (much the greatest portion) which is not intuitive: +and by what criterion we can, in matters not self-evident, +distinguish between things proved and things not proved, +between what is worthy and what is unworthy of belief. Of +the various questions which present themselves to our +inquiring faculties, some receive an answer from direct +consciousness, others, if resolved at all, can only be resolved +by means of evidence. Logic is concerned with these last. +But before inquiring into the mode of resolving questions, +it is necessary to inquire, what are those which offer themselves? +what questions are conceivable? what inquiries +are there, to which mankind have either obtained, or +been able to imagine it possible that they should obtain, +an answer? This point is best ascertained by a survey +and analysis of Propositions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. The answer to every question which it is possible +to frame, is contained in a Proposition, or Assertion. Whatever +can be an object of belief, or even of disbelief, must, +when put into words, assume the form of a proposition. All +truth and all error lie in propositions. What, by a convenient +misapplication of an abstract term, we call a Truth, +<span class="tei tei-pb" id="page019">[pg 019]</span><a name="Pg019" id="Pg019" class="tei tei-anchor"></a> +means simply a True Proposition; and errors are false propositions. +To know the import of all possible propositions, +would be to know all questions which can be raised, all +matters which are susceptible of being either believed or +disbelieved. How many kinds of inquiries can be propounded; +how many kinds of judgments can be made; and +how many kinds of propositions it is possible to frame with +a meaning; are but different forms of one and the same +question. Since, then, the objects of all Belief and of +all Inquiry express themselves in propositions; a sufficient +scrutiny of Propositions and of their varieties will +apprize us what questions mankind have actually asked of +themselves, and what, in the nature of answers to those +questions, they have actually thought they had grounds to +believe. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now the first glance at a proposition shows that it is +formed by putting together two names. A proposition, +according to the common simple definition, which is sufficient +for our purpose, is, <span class="tei tei-hi"><span style="font-style: italic">discourse</span></span>, <span class="tei tei-hi"><span style="font-style: italic">in which +something is affirmed or denied of something</span></span>. Thus, in the proposition, +Gold is yellow, the quality <span class="tei tei-hi"><span style="font-style: italic">yellow</span></span> is affirmed of the substance +<span class="tei tei-hi"><span style="font-style: italic">gold</span></span>. In the proposition, Franklin was not born in England, +the fact expressed by the words <span class="tei tei-hi"><span style="font-style: italic">born in England</span></span> is denied +of the man Franklin. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Every proposition consists of three parts: the Subject, +the Predicate, and the Copula. The predicate is the name +denoting that which is affirmed or denied. The subject is +the name denoting the person or thing which something is +affirmed or denied of. The copula is the sign denoting that +there is an affirmation or denial; and thereby enabling the +hearer or reader to distinguish a proposition from any other +kind of discourse. Thus, in the proposition, The earth is +round, the Predicate is the word <span class="tei tei-hi"><span style="font-style: italic">round</span></span>, which denotes the +quality affirmed, or (as the phrase is) predicated: <span class="tei tei-hi"><span style="font-style: italic">the earth</span></span>, +words denoting the object which that quality is affirmed +of, compose the Subject; the word <span class="tei tei-hi"><span style="font-style: italic">is</span></span>, which serves as +the connecting mark between the subject and predicate, to +<span class="tei tei-pb" id="page020">[pg 020]</span><a name="Pg020" id="Pg020" class="tei tei-anchor"></a> +show that one of them is affirmed of the other, is called the +Copula. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dismissing, for the present, the copula, of which more +will be said hereafter, every proposition, then, consists of at +least two names; brings together two names, in a particular +manner. This is already a first step towards what we are +in quest of. It appears from this, that for an act of belief, +<span class="tei tei-hi"><span style="font-style: italic">one</span></span> object is not sufficient; the simplest act of belief supposes, +and has something to do with, <span class="tei tei-hi"><span style="font-style: italic">two</span></span> objects: two +names, to say the least; and (since the names must be +names of something) two <span class="tei tei-hi"><span style="font-style: italic">nameable things</span></span>. A large class of +thinkers would cut the matter short by saying, two <span class="tei tei-hi"><span style="font-style: italic">ideas</span></span>. +They would say, that the subject and predicate are both of +them names of ideas; the idea of gold, for instance, and the +idea of yellow; and that what takes place (or a part of what +takes place) in the act of belief, consists in bringing (as it +is often expressed) one of these ideas under the other. But +this we are not yet in a condition to say: whether such be +the correct mode of describing the phenomenon, is an after +consideration. The result with which for the present we +must be contented, is, that in every act of belief <em class="tei tei-emph"><span style="font-style: italic">two</span></em> objects +are in some manner taken cognizance of; that there can be +no belief claimed, or question propounded, which does not +embrace two distinct (either material or intellectual) subjects +of thought; each of them capable or not of being conceived +by itself, but incapable of being believed by itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I may say, for instance, <span class="tei tei-q">“the sun.”</span> The word has a +meaning, and suggests that meaning to the mind of any one +who is listening to me. But suppose I ask him, Whether it +is true: whether he believes it? He can give no answer. +There is as yet nothing to believe, or to disbelieve. Now, +however, let me make, of all possible assertions respecting +the sun, the one which involves the least of reference to any +object besides itself; let me say, <span class="tei tei-q">“the sun exists.”</span> Here, +at once, is something which a person can say he believes. +But here, instead of only one, we find two distinct objects of +conception: the sun is one object; existence is another. +Let it not be said, that this second conception, existence, is +<span class="tei tei-pb" id="page021">[pg 021]</span><a name="Pg021" id="Pg021" class="tei tei-anchor"></a> +involved in the first; for the sun may be conceived as no +longer existing. <span class="tei tei-q">“The sun”</span> does not convey all the meaning +that is conveyed by <span class="tei tei-q">“the sun exists:”</span> <span class="tei tei-q">“my father”</span> does +not include all the meaning of <span class="tei tei-q">“my father exists,”</span> for he +may be dead; <span class="tei tei-q">“a round square”</span> does not include the +meaning of <span class="tei tei-q">“a round square exists,”</span> for it does not and +cannot exist. When I say, <span class="tei tei-q">“the sun,”</span> <span class="tei tei-q">“my father,”</span> or a +<span class="tei tei-q">“round square,”</span> I call upon the hearer for no belief or disbelief, +nor can either the one or the other be afforded me; +but if I say, <span class="tei tei-q">“the sun exists,”</span> <span class="tei tei-q">“my father exists,”</span> or <span class="tei tei-q">“a +round square exists,”</span> I call for belief; and should, in the +first of the three instances, meet with it; in the second, with +belief or disbelief, as the case might be; in the third, with +disbelief. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. This first step in the analysis of the object of belief, +which, though so obvious, will be found to be not unimportant, +is the only one which we shall find it practicable to +make without a preliminary survey of language. If we +attempt to proceed further in the same path, that is, to +analyse any further the import of Propositions; we find +forced upon us, as a subject of previous consideration, the +import of Names. For every proposition consists of two +names; and every proposition affirms or denies one of these +names, of the other. Now what we do, what passes in our +mind, when we affirm or deny two names of one another, +must depend on what they are names of; since it is with +reference to that, and not to the mere names themselves, that +we make the affirmation or denial. Here, therefore, we find +a new reason why the signification of names, and the relation +generally between names and the things signified by +them, must occupy the preliminary stage of the inquiry we +are engaged in. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It may be objected, that the meaning of names can guide +us at most only to the opinions, possibly the foolish and +groundless opinions, which mankind have formed concerning +things, and that as the object of philosophy is truth, not +opinion, the philosopher should dismiss words and look +<span class="tei tei-pb" id="page022">[pg 022]</span><a name="Pg022" id="Pg022" class="tei tei-anchor"></a> +into things themselves, to ascertain what questions can be +asked and answered in regard to them. This advice +(which no one has it in his power to follow) is in reality +an exhortation to discard the whole fruits of the labours of +his predecessors, and conduct himself as if he were the first +person who had ever turned an inquiring eye upon nature. +What does any one's personal knowledge of Things amount +to, after subtracting all which he has acquired by means of +the words of other people? Even after he has learned as +much as people usually do learn from others, will the notions +of things contained in his individual mind afford as sufficient +a basis for a <span lang="fr" class="tei tei-foreign" xml:lang="fr"><span style="font-style: italic">catalogue raisonné</span></span> +as the notions which are in the minds of all mankind? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In any enumeration and classification of Things, which +does not set out from their names, no varieties of things will +of course be comprehended but those recognised by the particular +inquirer; and it will still remain to be established, +by a subsequent examination of names, that the enumeration +has omitted nothing which ought to have been included. +But if we begin with names, and use them as our clue +to the things, we bring at once before us all the distinctions +which have been recognised, not by a single inquirer, +but by all inquirers taken together. It doubtless may, +and I believe it will, be found, that mankind have multiplied +the varieties unnecessarily, and have imagined distinctions +among things where there were only distinctions +in the manner of naming them. But we are not entitled +to assume this in the commencement. We must begin +by recognising the distinctions made by ordinary language. +If some of these appear, on a close examination, not to +be fundamental, the enumeration of the different kinds of +realities may be abridged accordingly. But to impose upon +the facts in the first instance the yoke of a theory, while the +grounds of the theory are reserved for discussion in a subsequent +stage, is not a course which a logician can reasonably +adopt. +</p> + +</div> + +<span class="tei tei-pb" id="page023">[pg 023]</span><a name="Pg023" id="Pg023" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc11" id="toc11"></a> +<a name="pdf12" id="pdf12"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER II. OF NAMES.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. <span class="tei tei-q">“A name,”</span> says Hobbes,<a id="noteref_4" name="noteref_4" href="#note_4"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">4</span></span></a> <span class="tei tei-q">“is a word taken at +pleasure to serve for a mark, which may raise in our mind a +thought like to some thought we had before, and which being +pronounced to others, may be to them a sign of what thought +the speaker had<a id="noteref_5" name="noteref_5" href="#note_5"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">5</span></span></a> +before in his mind.”</span> This simple definition +of a name, as a word (or set of words) serving the double +purpose of a mark to recall to ourselves the likeness of a +former thought, and a sign to make it known to others, appears +unexceptionable. Names, indeed, do much more than +this; but whatever else they do, grows out of, and is the +result of this: as will appear in its proper place. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Are names more properly said to be the names of things, +or of our ideas of things? The first is the expression in common +use; the last is that of some metaphysicians, who conceived +that in adopting it they were introducing a highly +important distinction. The eminent thinker, just quoted, +seems to countenance the latter opinion. <span class="tei tei-q">“But seeing,”</span> he +continues, <span class="tei tei-q">“names ordered in speech (as is defined) are +signs of our conceptions, it is manifest they are not signs of +the things themselves; for that the sound of this word <span class="tei tei-hi"><span style="font-style: italic">stone</span></span> +should be the sign of a stone, cannot be understood in any +sense but this, that he that hears it collects that he that pronounces +it thinks of a stone.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If it be merely meant that the conception alone, and not +the thing itself, is recalled by the name, or imparted to the +hearer, this of course cannot be denied. Nevertheless, there +seems good reason for adhering to the common usage, and +<span class="tei tei-pb" id="page024">[pg 024]</span><a name="Pg024" id="Pg024" class="tei tei-anchor"></a> +calling the word <span class="tei tei-hi"><span style="font-style: italic">sun</span></span> the name of the sun, and not the name +of our idea of the sun. For names are not intended only to +make the hearer conceive what we conceive, but also to inform +him what we believe. Now, when I use a name for the +purpose of expressing a belief, it is a belief concerning the +thing itself, not concerning my idea of it. When I say, <span class="tei tei-q">“the +sun is the cause of day,”</span> I do not mean that my idea of the +sun causes or excites in me the idea of day; or in other +words, that thinking of the sun makes me think of day. I +mean, that a certain physical fact, which is called the sun's +presence (and which, in the ultimate analysis, resolves itself +into sensations, not ideas) causes another physical fact, +which is called day. It seems proper to consider a word +as the <em class="tei tei-emph"><span style="font-style: italic">name</span></em> of that which we intend to be understood by +it when we use it; of that which any fact that we assert +of it is to be understood of; that, in short, concerning +which, when we employ the word, we intend to give information. +Names, therefore, shall always be spoken of in this +work as the names of things themselves, and not merely of +our ideas of things. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But the question now arises, of what things? and to +answer this it is necessary to take into consideration the +different kinds of names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. It is usual, before examining the various classes +into which names are commonly divided, to begin by distinguishing +from names of every description, those words +which are not names, but only parts of names. Among such +are reckoned particles, as <span class="tei tei-hi"><span style="font-style: italic">of</span></span>, <span class="tei tei-hi"><span style="font-style: italic">to</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">truly</span></span>, <span class="tei tei-hi"><span style="font-style: italic">often</span></span>; the inflected +cases of nouns substantive, as <span class="tei tei-hi"><span style="font-style: italic">me</span></span>, <span class="tei tei-hi"><span style="font-style: italic">him</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">John's</span></span>;<a id="noteref_6" name="noteref_6" href="#note_6"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">6</span></span></a> +and even adjectives, as <span class="tei tei-hi"><span style="font-style: italic">large</span></span>, <span class="tei tei-hi"><span style="font-style: italic">heavy</span></span>. +These words do not express things of which anything can be affirmed or denied. We +cannot say, Heavy fell, or A heavy fell; Truly, or A truly, +was asserted; Of, or An of, was in the room. Unless, indeed, +<span class="tei tei-pb" id="page025">[pg 025]</span><a name="Pg025" id="Pg025" class="tei tei-anchor"></a> +we are speaking of the mere words themselves, as when we +say, Truly is an English word, or, Heavy is an adjective. +In that case they are complete names, viz. names of those +particular sounds, or of those particular collections of written +characters. This employment of a word to denote the mere +letters and syllables of which it is composed, was termed by +the schoolmen the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">suppositio +materialis</span></span> of the word. In any +other sense we cannot introduce one of these words into the +subject of a proposition, unless in combination with other +words; as, A heavy <span class="tei tei-hi"><span style="font-style: italic">body</span></span> fell, A truly <span class="tei tei-hi"><span style="font-style: italic">important +fact</span></span> was asserted, A <span class="tei tei-hi"><span style="font-style: italic">member</span></span> of +<span class="tei tei-hi"><span style="font-style: italic">parliament</span></span> was in the room. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An adjective, however, is capable of standing by itself as +the predicate of a proposition; as when we say, Snow is +white; and occasionally even as the subject, for we may say, +White is an agreeable colour. The adjective is often said to +be so used by a grammatical ellipsis: Snow is white, instead +of Snow is a white object; White is an agreeable colour, +instead of, A white colour, or, The colour white, is agreeable. +The Greeks and Romans were allowed, by the rules of +their language, to employ this ellipsis universally in the subject +as well as in the predicate of a proposition. In English +this cannot, generally speaking, be done. We may say, +The earth is round; but we cannot say, Round is easily +moved; we must say, A round object. This distinction, however, +is rather grammatical than logical. Since there is no +difference of meaning between <span class="tei tei-hi"><span style="font-style: italic">round</span></span>, and +<span class="tei tei-hi"><span style="font-style: italic">a round object</span></span>, it +is only custom which prescribes that on any given occasion +one shall be used, and not the other. We shall therefore, +without scruple, speak of adjectives as names, whether in +their own right, or as representative of the more circuitous +forms of expression above exemplified. The other classes +of subsidiary words have no title whatever to be considered +as names. An adverb, or an accusative case, cannot under +any circumstances (except when their mere letters and syllables +are spoken of) figure as one of the terms of a proposition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Words which are not capable of being used as names, +but only as parts of names, were called by some of the +schoolmen Syncategorematic terms: from σὺν, with, and +κατηγορέω, to predicate, because it was only <em class="tei tei-emph"><span style="font-style: italic">with</span></em> some other +<span class="tei tei-pb" id="page026">[pg 026]</span><a name="Pg026" id="Pg026" class="tei tei-anchor"></a> +word that they could be predicated. A word which could +be used either as the subject or predicate of a proposition +without being accompanied by any other word, was termed +by the same authorities a Categorematic term. A combination +of one or more Categorematic, and one or more +Syncategorematic words, as, A heavy body, or A court of +justice, they sometimes called a <span class="tei tei-hi"><span style="font-style: italic">mixed</span></span> term; but this seems +a needless multiplication of technical expressions. A mixed +term is, in the only useful sense of the word, Categorematic. +It belongs to the class of what have been called many-worded +names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For, as one word is frequently not a name, but only part +of a name, so a number of words often compose one single +name, and no more. These words, <span class="tei tei-q">“the place which the +wisdom or policy of antiquity had destined for the residence +of the Abyssinian princes,”</span> form in the estimation of the +logician only one name; one Categorematic term. A mode +of determining whether any set of words makes only one +name, or more than one, is by predicating something of it, +and observing whether, by this predication, we make only +one assertion or several. Thus, when we say, John Nokes, +who was the mayor of the town, died yesterday,—by this predication +we make but one assertion; whence it appears that +<span class="tei tei-q">“John Nokes, who was the mayor of the town,”</span> is no more +than one name. It is true that in this proposition, besides +the assertion that John Nokes died yesterday, there is +included another assertion, namely, that John Nokes was +mayor of the town. But this last assertion was already +made: we did not make it by adding the predicate, <span class="tei tei-q">“died +yesterday.”</span> Suppose, however, that the words had been, +John Nokes <span class="tei tei-hi"><span style="font-style: italic">and</span></span> the mayor of the town, they would have +formed two names instead of one. For when we say, John +Nokes and the mayor of the town died yesterday, we make +two assertions; one, that John Nokes died yesterday; the +other, that the mayor of the town died yesterday. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It being needless to illustrate at any greater length the +subject of many-worded names, we proceed to the distinctions +which have been established among names, not according to +<span class="tei tei-pb" id="page027">[pg 027]</span><a name="Pg027" id="Pg027" class="tei tei-anchor"></a> +the words they are composed of, but according to their +signification. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. All names are names of something, real or imaginary; +but all things have not names appropriated to them +individually. For some individual objects we require, and +consequently have, separate distinguishing names; there is +a name for every person, and for every remarkable place. +Other objects, of which we have not occasion to speak so +frequently, we do not designate by a name of their own; +but when the necessity arises for naming them, we do so by +putting together several words, each of which, by itself, +might be and is used for an indefinite number of other +objects; as when I say, <span class="tei tei-hi"><span style="font-style: italic">this stone</span></span>: <span class="tei tei-q">“this”</span> and <span class="tei tei-q">“stone”</span> +being, each of them, names that may be used of many other objects +besides the particular one meant, although the only object +of which they can both be used at the given moment, consistently +with their signification, may be the one of which I +wish to speak. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Were this the sole purpose for which names, that are +common to more things than one, could be employed; if +they only served, by mutually limiting each other, to afford +a designation for such individual objects as have no names +of their own; they could only be ranked among contrivances +for economizing the use of language. But it is evident that +this is not their sole function. It is by their means that we +are enabled to assert <em class="tei tei-emph"><span style="font-style: italic">general</span></em> propositions; to affirm or deny +any predicate of an indefinite number of things at once. The +distinction, therefore, between <em class="tei tei-emph"><span style="font-style: italic">general</span></em> names, and +<em class="tei tei-emph"><span style="font-style: italic">individual</span></em> +or <em class="tei tei-emph"><span style="font-style: italic">singular</span></em> names, is fundamental; and may be considered +as the first grand division of names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A general name is familiarly defined, a name which is +capable of being truly affirmed, in the same sense, of each +of an indefinite number of things. An individual or singular +name is a name which is only capable of being truly affirmed, +in the same sense, of one thing. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus, <em class="tei tei-emph"><span style="font-style: italic">man</span></em> is capable of being truly affirmed of John, +Peter, George, Mary, and other persons without assignable +<span class="tei tei-pb" id="page028">[pg 028]</span><a name="Pg028" id="Pg028" class="tei tei-anchor"></a> +limit: and it is affirmed of all of them in the same sense; for +the word man expresses certain qualities, and when we predicate +it of those persons, we assert that they all possess those +qualities. But <em class="tei tei-emph"><span style="font-style: italic">John</span></em> is only capable of being truly affirmed +of one single person, at least in the same sense. For +although there are many persons who bear that name, it is +not conferred upon them to indicate any qualities, or anything +which belongs to them in common; and cannot be +said to be affirmed of them in any <em class="tei tei-emph"><span style="font-style: italic">sense</span></em> at all, consequently +not in the same sense. <span class="tei tei-q">“The present queen of England”</span> +is also an individual name. For, that there never can be +more than one person at a time of whom it can be truly +affirmed, is implied in the meaning of the words. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is not unusual, by way of explaining what is meant +by a general name, to say that it is the name of a <span class="tei tei-hi"><span style="font-style: italic">class</span></span>. +But this, though a convenient mode of expression for some +purposes, is objectionable as a definition, since it explains +the clearer of two things by the more obscure. It would be +more logical to reverse the proposition, and turn it into +a definition of the word <span class="tei tei-hi"><span style="font-style: italic">class</span></span>: <span class="tei tei-q">“A class is the indefinite +multitude of individuals denoted by a general name.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is necessary to distinguish <em class="tei tei-emph"><span style="font-style: italic">general</span></em> from <em class="tei tei-emph"><span style="font-style: italic">collective</span></em> names. +A general name is one which can be predicated of <em class="tei tei-emph"><span style="font-style: italic">each</span></em> individual +of a multitude; a collective name cannot be predicated +of each separately, but only of all taken together. <span class="tei tei-q">“The +76th regiment of foot,”</span> which is a collective name, is not a +general but an individual name; for although it can be predicated +of a multitude of individual soldiers taken jointly, +it cannot be predicated of them severally. We may say, +Jones is a soldier, and Thompson is a soldier, and Smith is +a soldier, but we cannot say, Jones is the 76th regiment, +and Thompson is the 76th regiment, and Smith is the 76th +regiment. We can only say, Jones, and Thompson, and +Smith, and Brown, and so forth, (enumerating all the +soldiers,) are the 76th regiment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“The 76th regiment”</span> is a collective name, but not a +general one: <span class="tei tei-q">“a regiment”</span> is both a collective and a general +name. General with respect to all individual regiments, of +<span class="tei tei-pb" id="page029">[pg 029]</span><a name="Pg029" id="Pg029" class="tei tei-anchor"></a> +each of which separately it can be affirmed; collective with +respect to the individual soldiers, of whom any regiment is +composed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. The second general division of names is into +<span class="tei tei-hi"><span style="font-style: italic">concrete</span></span> and <span class="tei tei-hi"><span style="font-style: italic">abstract</span></span>. A concrete name is +a name which stands for a thing; an abstract name is a name which stands +for an attribute of a thing. Thus, <span class="tei tei-hi"><span style="font-style: italic">John</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">the sea</span></span>, <span class="tei tei-hi"><span style="font-style: italic">this table</span></span>, +are names of things. <span class="tei tei-hi"><span style="font-style: italic">White</span></span>, also, is a name of a thing, or +rather of things. Whiteness, again, is the name of a quality +or attribute of those things. Man is a name of many things; +humanity is a name of an attribute of those things. <span class="tei tei-hi"><span style="font-style: italic">Old</span></span> +is a name of things; <span class="tei tei-hi"><span style="font-style: italic">old age</span></span> is a name of one of their +attributes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I have used the words concrete and abstract in the sense +annexed to them by the schoolmen, who, notwithstanding +the imperfections of their philosophy, were unrivalled in the +construction of technical language, and whose definitions, +in logic at least, though they never went more than a little +way into the subject, have seldom, I think, been altered but +to be spoiled. A practice, however, has grown up in more +modern times, which, if not introduced by Locke, has gained +currency chiefly from his example, of applying the expression +<span class="tei tei-q">“abstract name”</span> to all names which are the result of +abstraction or generalization, and consequently to all general +names, instead of confining it to the names of attributes. +The metaphysicians of the Condillac school,—whose admiration +of Locke, passing over the profoundest speculations +of that truly original genius, usually fastens with peculiar +eagerness upon his weakest points,—have gone on imitating +him in this abuse of language, until there is now some +difficulty in restoring the word to its original signification. +A more wanton alteration in the meaning of a word is rarely +to be met with; for the expression <span class="tei tei-hi"><span style="font-style: italic">general name</span></span>, the exact +equivalent of which exists in all languages I am acquainted +with, was already available for the purpose to which <span class="tei tei-hi"><span style="font-style: italic">abstract</span></span> +has been misappropriated, while the misappropriation leaves +that important class of words, the names of attributes, without +<span class="tei tei-pb" id="page030">[pg 030]</span><a name="Pg030" id="Pg030" class="tei tei-anchor"></a> +any compact distinctive appellation. The old acceptation, +however, has not gone so completely out of use, as to +deprive those who still adhere to it of all chance of being understood. +By <span class="tei tei-hi"><span style="font-style: italic">abstract</span></span>, then, I shall always mean the opposite +of <span class="tei tei-hi"><span style="font-style: italic">concrete</span></span>: by an abstract name, the name of an attribute; +by a concrete name, the name of an object. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Do abstract names belong to the class of general, or to +that of singular names? Some of them are certainly general. +I mean those which are names not of one single and definite +attribute, but of a class of attributes. Such is the word +<span class="tei tei-hi"><span style="font-style: italic">colour</span></span>, which is a name common to whiteness, redness, &c. +Such is even the word whiteness, in respect of the different +shades of whiteness to which it is applied in common; the +word magnitude, in respect of the various degrees of magnitude +and the various dimensions of space; the word weight, +in respect of the various degrees of weight. Such also is +the word <span class="tei tei-hi"><span style="font-style: italic">attribute</span></span> itself, the common name of all particular +attributes. But when only one attribute, neither variable in +degree nor in kind, is designated by the name; as visibleness; +tangibleness; equality; squareness; milkwhiteness; +then the name can hardly be considered general; for though +it denotes an attribute of many different objects, the attribute +itself is always conceived as one, not many. The +question is, however, of no moment, and perhaps the best +way of deciding it would be to consider these names as +neither general nor individual, but to place them in a class +apart. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It may be objected to our definition of an abstract name, +that not only the names which we have called abstract, but +adjectives, which we have placed in the concrete class, are +names of attributes; that <span class="tei tei-hi"><span style="font-style: italic">white</span></span>, for example, is as much the +name of the colour, as <span class="tei tei-hi"><span style="font-style: italic">whiteness</span></span> is. But (as before remarked) +a word ought to be considered as the name of that which +we intend to be understood by it when we put it to its +principal use, that is, when we employ it in predication. +When we say snow is white, milk is white, linen is white, +we do not mean it to be understood that snow, or linen, or +milk, is a colour. We mean that they are things having the +<span class="tei tei-pb" id="page031">[pg 031]</span><a name="Pg031" id="Pg031" class="tei tei-anchor"></a> +colour. The reverse is the case with the word whiteness; +what we affirm to <em class="tei tei-emph"><span style="font-style: italic">be</span></em> whiteness is not snow but the colour of +snow. Whiteness, therefore, is the name of the colour +exclusively: white is a name of all things whatever having +the colour; a name, not of the quality whiteness, but of +every white object. It is true, this name was given to all +those various objects on account of the quality; and we may +therefore say, without impropriety, that the quality forms +part of its signification; but a name can only be said to +stand for, or to be a name of, the things of which it can be +predicated. We shall presently see that all names which +can be said to have any signification, all names by applying +which to an individual we give any information respecting +that individual, may be said to <em class="tei tei-emph"><span style="font-style: italic">imply</span></em> an attribute of some +sort; but they are not names of the attribute; it has its own +proper abstract name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. This leads to the consideration of a third great +division of names, into <span class="tei tei-hi"><span style="font-style: italic">connotative</span></span> +and <span class="tei tei-hi"><span style="font-style: italic">non-connotative</span></span>, the +latter sometimes, but improperly, called <span class="tei tei-hi"><span style="font-style: italic">absolute</span></span>. This is +one of the most important distinctions which we shall have +occasion to point out, and one of those which go deepest +into the nature of language. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A non-connotative term is one which signifies a subject +only, or an attribute only. A connotative term is one which +denotes a subject, and implies an attribute. By a subject is +here meant anything which possesses attributes. Thus John, +or London, or England, are names which signify a subject +only. Whiteness, length, virtue, signify an attribute only. +None of these names, therefore, are connotative. But <span class="tei tei-hi"><span style="font-style: italic">white</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">long</span></span>, <span class="tei tei-hi"><span style="font-style: italic">virtuous</span></span>, are connotative. +The word white, denotes all white things, as snow, paper, the foam of the sea, +&c., and implies, or as it was termed by the schoolmen, +<span class="tei tei-hi"><span style="font-style: italic">connotes</span></span>,<a id="noteref_7" name="noteref_7" href="#note_7"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">7</span></span></a> the +attribute <span class="tei tei-hi"><span style="font-style: italic">whiteness</span></span>. The word white is not predicated of the +attribute, but of the subjects, snow, &c.; but when we predicate +<span class="tei tei-pb" id="page032">[pg 032]</span><a name="Pg032" id="Pg032" class="tei tei-anchor"></a> +it of them, we imply, or connote, that the attribute +whiteness belongs to them. The same may be said of the +other words above cited. Virtuous, for example, is the name +of a class, which includes Socrates, Howard, the man of +Ross, and an undefined number of other individuals, past, +present, and to come. These individuals, collectively and +severally, can alone be said with propriety to be denoted by +the word: of them alone can it properly be said to be a +name. But it is a name applied to all of them in consequence +of an attribute which they are supposed to possess in +common, the attribute which has received the name of virtue. +It is applied to all beings that are considered to possess +this attribute; and to none which are not so considered. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All concrete general names are connotative. The word +<span class="tei tei-hi"><span style="font-style: italic">man</span></span>, for example, denotes Peter, Jane, John, and an indefinite +number of other individuals, of whom, taken as a class, +it is the name. But it is applied to them, because they +possess, and to signify that they possess, certain attributes. +These seem to be, corporeity, animal life, rationality, and a +certain external form, which for distinction we call the +human. Every existing thing, which possessed all these +attributes, would be called a man; and anything which possessed +none of them, or only one, or two, or even three +of them without the fourth, would not be so called. For +example, if in the interior of Africa there were to be discovered +a race of animals possessing reason equal to that of human +beings, but with the form of an elephant, they would not be +called men. Swift's Houyhnhms were not so called. Or if +such newly-discovered beings possessed the form of man +without any vestige of reason, it is probable that some other +name than that of man would be found for them. How it +happens that there can be any doubt about the matter, will +appear hereafter. The word <span class="tei tei-hi"><span style="font-style: italic">man</span></span>, therefore, signifies all these +attributes, and all subjects which possess these attributes. +But it can be predicated only of the subjects. What we call +men, are the subjects, the individual Stiles and Nokes; not +the qualities by which their humanity is constituted. The +name, therefore, is said to signify the subjects <em class="tei tei-emph"><span style="font-style: italic">directly</span></em>, the +<span class="tei tei-pb" id="page033">[pg 033]</span><a name="Pg033" id="Pg033" class="tei tei-anchor"></a> +attributes <em class="tei tei-emph"><span style="font-style: italic">indirectly</span></em>; it <em class="tei tei-emph"><span style="font-style: italic">denotes</span></em> the subjects, and implies, or +involves, or indicates, or as we shall say henceforth, <em class="tei tei-emph"><span style="font-style: italic">connotes</span></em>, +the attributes. It is a connotative name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Connotative names have hence been also called <em class="tei tei-emph"><span style="font-style: italic">denominative</span></em>, +because the subject which they denote is denominated +by, or receives a name from, the attribute which they connote. +Snow, and other objects, receive the name white, +because they possess the attribute which is called whiteness; +James, Mary, and others receive the name man, because +they possess the attributes which are considered to constitute +humanity. The attribute, or attributes, may therefore be +said to denominate those objects, or to give them a common +name.<a id="noteref_8" name="noteref_8" href="#note_8"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">8</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It has been seen that all concrete general names are +connotative. Even abstract names, though the names only of +attributes, may in some instances be justly considered as +connotative; for attributes themselves may have attributes +ascribed to them; and a word which denotes attributes +may connote an attribute of those attributes. It is thus, +for example, with such a word as <span class="tei tei-hi"><span style="font-style: italic">fault</span></span>; equivalent to +<span class="tei tei-hi"><span style="font-style: italic">bad</span></span> or <span class="tei tei-hi"><span style="font-style: italic">hurtful quality</span></span>. This word is a +name common to many attributes, and connotes hurtfulness, an attribute of those +various attributes. When, for example, we say that slowness, +in a horse, is a fault, we do not mean that the slow +movement, the actual change of place of the slow horse, is a thing +to be avoided, but that the property or peculiarity of +the horse, from which it derives that name, the quality of +being a slow mover, is an undesirable peculiarity. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In regard to those concrete names which are not general +but individual, a distinction must be made. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Proper names are not connotative: they denote the individuals +<span class="tei tei-pb" id="page034">[pg 034]</span><a name="Pg034" id="Pg034" class="tei tei-anchor"></a> +who are called by them; but they do not indicate +or imply any attributes as belonging to those individuals. +When we name a child by the name Paul, or a dog by the +name Cæsar, these names are simply marks used to enable +those individuals to be made subjects of discourse. It may +be said, indeed, that we must have had some reason for +giving them those names rather than any others: and this is +true; but the name, once given, becomes independent of the +reason. A man may have been named John, because that +was the name of his father; a town may have been named +Dartmouth, because it is situated at the mouth of the Dart. +But is no part of the signification of the word John, that the +father of the person so called bore the same name; nor even +of the word Dartmouth, to be situated at the mouth of the +Dart. If sand should choke up the mouth of the river, or an +earthquake change its course, and remove it to a distance +from the town, the name of the town would not necessarily +be changed. That fact, therefore, can form no part of the +signification of the word; for otherwise, when the fact confessedly +ceased to be true, no one would any longer think of +applying the name. Proper names are attached to the objects +themselves, and are not dependent on the continuance of any +attribute of the object. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But there is another kind of names, which although they +are individual names, that is, predicable only of one object, +are really connotative. For, although we may give to an +individual a name utterly unmeaning, which we call a proper +name,—a word which answers the purpose of showing what +thing it is we are talking about, but not of telling anything +about it; yet a name peculiar to an individual is not necessarily +of this description. It may be significant of some +attribute, or some union of attributes, which being possessed +by no object but one, determines the name exclusively to +that individual. <span class="tei tei-q">“The sun”</span> is a name of this description; +<span class="tei tei-q">“God,”</span> when used by a monotheist, is another. These, +however, are scarcely examples of what we are now attempting +to illustrate, being, in strictness of language, general, +and not individual names: for, however they may be <em class="tei tei-emph"><span style="font-style: italic">in fact</span></em> +<span class="tei tei-pb" id="page035">[pg 035]</span><a name="Pg035" id="Pg035" class="tei tei-anchor"></a> +predicable only of one object, there is nothing in the meaning +of the words themselves which implies this: and, accordingly, +when we are imagining and not affirming, we may speak of +many suns; and the majority of mankind have believed, and +still believe, that there are many gods. But it is easy to produce +words which are real instances of connotative individual +names. It may be part of the meaning of the connotative +name itself, that there exists but one individual possessing +the attribute which it connotes; as, for instance, <span class="tei tei-q">“the <em class="tei tei-emph"><span style="font-style: italic">only</span></em> +son of John Stiles;”</span> <span class="tei tei-q">“the <em class="tei tei-emph"><span style="font-style: italic">first</span></em> emperor of Rome.”</span> Or the +attribute connoted may be a connexion with some determinate +event, and the connexion may be of such a kind as only one +individual could have; or may at least be such as only one +individual actually had; and this may be implied in the form +of the expression. <span class="tei tei-q">“The father of Socrates,”</span> is an example +of the one kind (since Socrates could not have had two +fathers); <span class="tei tei-q">“the author of the Iliad,”</span> <span class="tei tei-q">“the murderer of Henri +Quatre,”</span> of the second. For, although it is conceivable that +more persons than one might have participated in the authorship +of the Iliad, or in the murder of Henri Quatre, the +employment of the article <em class="tei tei-emph"><span style="font-style: italic">the</span></em> implies that, in fact, this was +not the case. What is here done by the word <em class="tei tei-emph"><span style="font-style: italic">the</span></em>, is done +in other cases by the context: thus, <span class="tei tei-q">“Cæsar's army”</span> is an +individual name, if it appears from the context that the +army meant is that which Cæsar commanded in a particular +battle. The still more general expressions, <span class="tei tei-q">“the Roman +army,”</span> or <span class="tei tei-q">“the Christian army,”</span> may be individualized in a +similar manner. Another case of frequent occurrence has +already been noticed; it is the following. The name, being +a many-worded one, may consist, in the first place, of a +<em class="tei tei-emph"><span style="font-style: italic">general</span></em> name, capable therefore in itself of being affirmed of +more things than one, but which is, in the second place, so +limited by other words joined with it, that the entire expression +can only be predicated of one object, consistently with +the meaning of the general term. This is exemplified in +such an instance as the following: <span class="tei tei-q">“the present prime +minister of England.”</span> Prime Minister of England is a +general name; the attributes which it connotes may be possessed +<span class="tei tei-pb" id="page036">[pg 036]</span><a name="Pg036" id="Pg036" class="tei tei-anchor"></a> +by an indefinite number of persons: in succession +however, not simultaneously; since the meaning of the word +itself imports (among other things) that there can be only +one such person at a time. This being the case, and the +application of the name being afterwards limited by the +word <em class="tei tei-emph"><span style="font-style: italic">present</span></em>, to such individuals as possess the attributes at +one indivisible point of time, it becomes applicable only to +one individual. And as this appears from the meaning of +the name, without any extrinsic proof, it is strictly an individual +name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From the preceding observations it will easily be collected, +that whenever the names given to objects convey any +information, that is, whenever they have properly any meaning, +the meaning resides not in what they <em class="tei tei-emph"><span style="font-style: italic">denote</span></em>, but in what +they <em class="tei tei-emph"><span style="font-style: italic">connote</span></em>. The only names of objects which connote nothing +are <em class="tei tei-emph"><span style="font-style: italic">proper</span></em> names; and these have, strictly speaking, no signification. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If, like the robber in the Arabian Nights, we make a mark +with chalk on a house to enable us to know it again, the +mark has a purpose, but it has not properly any meaning. The +chalk does not declare anything about the house; it does not +mean, This is such a person's house, or This is a house +which contains booty. The object of making the mark is +merely distinction. I say to myself, All these houses are +so nearly alike, that if I lose sight of them I shall not again +be able to distinguish that which I am now looking at, from +any of the others; I must therefore contrive to make the +appearance of this one house unlike that of the others, that +I may hereafter know, when I see the mark—not indeed any +attribute of the house—but simply that it is the same house +which I am now looking at. Morgiana chalked all the other +houses in a similar manner, and defeated the scheme: how? +simply by obliterating the difference of appearance between +that house and the others. The chalk was still there, but it +no longer served the purpose of a distinctive mark. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When we impose a proper name, we perform an operation +in some degree analogous to what the robber intended +in chalking the house. We put a mark, not indeed upon the +<span class="tei tei-pb" id="page037">[pg 037]</span><a name="Pg037" id="Pg037" class="tei tei-anchor"></a> +object itself, but, so to speak, upon the idea of the object. +A proper name is but an unmeaning mark which we connect +in our minds with the idea of the object, in order that whenever +the mark meets our eyes or occurs to our thoughts, we +may think of that individual object. Not being attached +to the thing itself, it does not, like the chalk, enable us to +distinguish the object when we see it; but it enables us to +distinguish it when it is spoken of, either in the records of +our own experience, or in the discourse of others; to know +that what we find asserted in any proposition of which it is +the subject, is asserted of the individual thing with which we +were previously acquainted. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When we predicate of anything its proper name; when +we say, pointing to a man, this is Brown or Smith, or pointing +to a city, that it is York, we do not, merely by so doing, +convey to the hearer any information about them, except that +those are their names. By enabling him to identify the individuals, +we may connect them with information previously +possessed by him; by saying, This is York, we may tell him +that it contains the Minster. But this is in virtue of what +he has previously heard concerning York; not by anything +implied in the name. It is otherwise when objects are spoken +of by connotative names. When we say, The town is built +of marble, we give the hearer what may be entirely new +information, and this merely by the signification of the many-worded +connotative name, <span class="tei tei-q">“built of marble.”</span> Such names +are not signs of the mere objects, invented because we have +occasion to think and speak of those objects individually; +but signs which accompany an attribute: a kind of livery in +which the attribute clothes all objects which are recognized +as possessing it. They are not mere marks, but more, that +is to say, significant marks; and the connotation is what +constitutes their significance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As a proper name is said to be the name of the one individual +which it is predicated of, so (as well from the +importance of adhering to analogy, as for the other reasons +formerly assigned) a connotative name ought to be considered +a name of all the various individuals which it is +<span class="tei tei-pb" id="page038">[pg 038]</span><a name="Pg038" id="Pg038" class="tei tei-anchor"></a> +predicable of, or in other words <em class="tei tei-emph"><span style="font-style: italic">denotes</span></em>, and not of what it +connotes. But by learning what things it is a name of, we +do not learn the meaning of the name: for to the same thing +we may, with equal propriety, apply many names, not equivalent +in meaning. Thus, I call a certain man by the name +Sophroniscus: I call him by another name, The father of +Socrates. Both these are names of the same individual, but +their meaning is altogether different; they are applied to +that individual for two different purposes; the one, merely +to distinguish him from other persons who are spoken of; the +other to indicate a fact relating to him, the fact that Socrates +was his son. I further apply to him these other expressions: +a man, a Greek, an Athenian, a sculptor, an old man, an +honest man, a brave man. All these are names of Sophroniscus, +not indeed of him alone, but of him and each of an +indefinite number of other human beings. Each of these +names is applied to Sophroniscus for a different reason, and +by each whoever understands its meaning is apprised of a +distinct fact or number of facts concerning him; but those +who knew nothing about the names except that they were +applicable to Sophroniscus, would be altogether ignorant of +their meaning. It is even conceivable that I might know +every single individual of whom a given name could be with +truth affirmed, and yet could not be said to know the meaning +of the name. A child knows who are its brothers and +sisters, long before it has any definite conception of the +nature of the facts which are involved in the signification of +those words. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In some cases it is not easy to decide precisely how much +a particular word does or does not connote; that is, we do +not exactly know (the case not having arisen) what degree of +difference in the object would occasion a difference in the +name. Thus, it is clear that the word <em class="tei tei-emph"><span style="font-style: italic">man</span></em>, besides animal +life and rationality, connotes also a certain external form; but +it would be impossible to say precisely what form; that is, +to decide how great a deviation from the form ordinarily +found in the beings whom we are accustomed to call men, +would suffice in a newly-discovered race to make us refuse +<span class="tei tei-pb" id="page039">[pg 039]</span><a name="Pg039" id="Pg039" class="tei tei-anchor"></a> +them the name of man. Rationality, also, being a quality +which admits of degrees, it has never been settled what is the +lowest degree of that quality which would entitle any creature +to be considered a human being. In all such cases, the +meaning of the general name is so far unsettled, and vague; +mankind have not come to any positive agreement about the +matter. When we come to treat of classification, we shall +have occasion to show under what conditions this vagueness +may exist without practical inconvenience; and cases will +appear, in which the ends of language are better promoted +by it than by complete precision; in order that, in natural +history for instance, individuals or species of no very marked +character may be ranged with those more strongly characterized +individuals or species to which, in all their properties +taken together, they bear the nearest resemblance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But this partial uncertainty in the connotation of names +can only be free from mischief when guarded by strict precautions. +One of the chief sources, indeed, of lax habits of +thought, is the custom of using connotative terms without a +distinctly ascertained connotation, and with no more precise +notion of their meaning than can be loosely collected from +observing what objects they are used to denote. It is in this +manner that we all acquire, and inevitably so, our first knowledge +of our vernacular language. A child learns the meaning +of the words <em class="tei tei-emph"><span style="font-style: italic">man</span></em>, or <em class="tei tei-emph"><span style="font-style: italic">white</span></em>, by hearing them applied to a +variety of individual objects, and finding out, by a process of +generalization and analysis of which he is but imperfectly +conscious, what those different objects have in common. In +the case of these two words the process is so easy as to require +no assistance from culture; the objects called human +beings, and the objects called white, differing from all others +by qualities of a peculiarly definite and obvious character. +But in many other cases, objects bear a general resemblance +to one another, which leads to their being familiarly classed +together under a common name, while, without more analytic +habits than the generality of mankind possess, it is not immediately +apparent what are the particular attributes, upon +the possession of which in common by them all, their general +<span class="tei tei-pb" id="page040">[pg 040]</span><a name="Pg040" id="Pg040" class="tei tei-anchor"></a> +resemblance depends. When this is the case, people use +the name without any recognized connotation, that is, without +any precise meaning; they talk, and consequently think, +vaguely, and remain contented to attach only the same degree +of significance to their own words, which a child three +years old attaches to the words brother and sister. The +child at least is seldom puzzled by the starting up of new +individuals, on whom he is ignorant whether or not to confer +the title; because there is usually an authority close at +hand competent to solve all doubts. But a similar resource +does not exist in the generality of cases; and new objects +are continually presenting themselves to men, women, and +children, which they are called upon to class <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">proprio motu</span></span>. +They, accordingly, do this on no other principle than that of +superficial similarity, giving to each new object the name of +that familiar object, the idea of which it most readily recalls, +or which, on a cursory inspection, it seems to them +most to resemble: as an unknown substance found in the +ground will be called, according to its texture, earth, sand, +or a stone. In this manner, names creep on from subject to +subject, until all traces of a common meaning sometimes disappear, +and the word comes to denote a number of things +not only independently of any common attribute, but which +have actually no attribute in common; or none but what is +shared by other things to which the name is capriciously refused.<a id="noteref_9" name="noteref_9" href="#note_9"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">9</span></span></a> +Even scientific writers have aided in this perversion +of general language from its purpose; sometimes because, +<span class="tei tei-pb" id="page041">[pg 041]</span><a name="Pg041" id="Pg041" class="tei tei-anchor"></a> +like the vulgar, they knew no better; and sometimes in deference +to that aversion to admit new words, which induces +mankind, on all subjects not considered technical, to attempt +to make the original small stock of names serve with but +little augmentation to express a constantly increasing number +of objects and distinctions, and, consequently, to express +them in a manner progressively more and more imperfect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To what degree this loose mode of classing and denominating +objects has rendered the vocabulary of mental and moral +philosophy unfit for the purposes of accurate thinking, is best +known to whoever has most reflected on the present condition +of those branches of knowledge. Since, however, the introduction +of a new technical language as the vehicle of speculations +on subjects belonging to the domain of daily discussion, is +extremely difficult to effect, and would not be free from +inconvenience even if effected, the problem for the philosopher, +and one of the most difficult which he has to resolve, +is, in retaining the existing phraseology, how best to alleviate +its imperfections. This can only be accomplished by +giving to every general concrete name which there is frequent +occasion to predicate, a definite and fixed connotation; in +order that it may be known what attributes, when we call an +object by that name, we really mean to predicate of the +object. And the question of most nicety is, how to give this +fixed connotation to a name, with the least possible change +in the objects which the name is habitually employed to +denote; with the least possible disarrangement, either by +adding or subtraction, of the group of objects which, in +however imperfect a manner, it serves to circumscribe and +hold together; and with the least vitiation of the truth of any +propositions which are commonly received as true. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This desirable purpose, of giving a fixed connotation +where it is wanting, is the end aimed at whenever any one +attempts to give a definition of a general name already in +use; every definition of a connotative name being an attempt +either merely to declare, or to declare and analyse, the connotation +of the name. And the fact, that no questions +which have arisen in the moral sciences have been subjects +<span class="tei tei-pb" id="page042">[pg 042]</span><a name="Pg042" id="Pg042" class="tei tei-anchor"></a> +of keener controversy than the definitions of almost all the +leading expressions, is a proof how great an extent the evil +to which we have adverted has attained. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Names with indeterminate connotation are not to be confounded +with names which have more than one connotation, +that is to say, ambiguous words. A word may have several +meanings, but all of them fixed and recognised ones; as the +word <span class="tei tei-hi"><span style="font-style: italic">post</span></span>, for example, or the word <span class="tei tei-hi"><span style="font-style: italic">box</span></span>, +the various senses of which it would be endless to enumerate. And the +paucity of existing names, in comparison with the demand +for them, may often render it advisable and even necessary +to retain a name in this multiplicity of acceptations, distinguishing +these so clearly as to prevent their being confounded +with one another. Such a word may be considered as two +or more names, accidentally written and spoken alike.<a id="noteref_10" name="noteref_10" href="#note_10"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">10</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. The fourth principal division of names, is into +<em class="tei tei-emph"><span style="font-style: italic">positive</span></em> and <em class="tei tei-emph"><span style="font-style: italic">negative</span></em>. Positive, as <em class="tei tei-emph"><span style="font-style: italic">man</span></em>, +<em class="tei tei-emph"><span style="font-style: italic">tree</span></em>, <em class="tei tei-emph"><span style="font-style: italic">good</span></em>; negative, +<span class="tei tei-pb" id="page043">[pg 043]</span><a name="Pg043" id="Pg043" class="tei tei-anchor"></a> +as <em class="tei tei-emph"><span style="font-style: italic">not-many</span></em>, <em class="tei tei-emph"><span style="font-style: italic">not-tree</span></em>, <em class="tei tei-emph"><span style="font-style: italic">not-good</span></em>. To every positive +concrete name, a corresponding negative one might be framed. After +giving a name to any one thing, or to any plurality of things, +we might create a second name which should be a name of +all things whatever except that particular thing or things. +These negative names are employed whenever we have occasion +to speak collectively of all things other than some thing +or class of things. When the positive name is connotative, +the corresponding negative name is connotative likewise; +but in a peculiar way, connoting not the presence but the +absence of an attribute. Thus, <em class="tei tei-emph"><span style="font-style: italic">not-white</span></em> denotes all things +whatever except white things; and connotes the attribute of +not possessing whiteness. For the non-possession of any +given attribute is also an attribute, and may receive a name +as such; and thus negative concrete names may obtain negative +abstract names to correspond to them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Names which are positive in form are often negative in +reality, and others are really positive though their form is +<span class="tei tei-pb" id="page044">[pg 044]</span><a name="Pg044" id="Pg044" class="tei tei-anchor"></a> +negative. The word <span class="tei tei-hi"><span style="font-style: italic">inconvenient</span></span>, for example, does not +express the mere absence of convenience; it expresses a +positive attribute, that of being the cause of discomfort or +annoyance. So the word <span class="tei tei-hi"><span style="font-style: italic">unpleasant</span></span>, notwithstanding its +negative form, does not connote the mere absence of pleasantness, +but a less degree of what is signified by the word +<span class="tei tei-hi"><span style="font-style: italic">painful</span></span>, which, it is hardly necessary to say, is positive. +<span class="tei tei-hi"><span style="font-style: italic">Idle</span></span>, on the other hand, is a word which, though positive in +form, expresses nothing but what would be signified either +by the phrase <span class="tei tei-hi"><span style="font-style: italic">not working</span></span>, or by the phrase <span class="tei tei-hi"><span style="font-style: italic">not +disposed to work</span></span>; and <span class="tei tei-hi"><span style="font-style: italic">sober</span></span>, either by <span class="tei tei-hi"><span style="font-style: italic">not +drunk</span></span> or by <span class="tei tei-hi"><span style="font-style: italic">not drunken</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is a class of names called <span class="tei tei-hi"><span style="font-style: italic">privative</span></span>. A privative +name is equivalent in its signification to a positive and a +negative name taken together; being the name of something +which has once had a particular attribute, or for some other +reason might have been expected to have it, but which has it +not. Such is the word <span class="tei tei-hi"><span style="font-style: italic">blind</span></span>, which is not equivalent to +<span class="tei tei-hi"><span style="font-style: italic">not seeing</span></span>, or to <span class="tei tei-hi"><span style="font-style: italic">not capable of seeing</span></span>, +for it would not, except by a poetical or rhetorical figure, be applied to stocks and +stones. A thing is not usually said to be blind, unless the class to +which it is most familiarly referred, or to which it is referred +on the particular occasion, be chiefly composed of things +which can see, as in the case of a blind man, or a blind +horse; or unless it is supposed for any reason that it ought +to see; as in saying of a man, that he rushed blindly into an +abyss, or of philosophers or the clergy that the greater part +of them are blind guides. The names called privative, therefore, +connote two things: the absence of certain attributes, +and the presence of others, from which the presence also of +the former might naturally have been expected. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. The fifth leading division of names is into <em class="tei tei-emph"><span style="font-style: italic">relative</span></em> +and <em class="tei tei-emph"><span style="font-style: italic">absolute</span></em>, or let us rather say, <em class="tei tei-emph"><span style="font-style: italic">relative</span></em> and +<em class="tei tei-emph"><span style="font-style: italic">non-relative</span></em>; for the word absolute is put upon much too hard duty in +metaphysics, not to be willingly spared when its services can be +dispensed with. It resembles the word <span class="tei tei-hi"><span style="font-style: italic">civil</span></span> in the language +of jurisprudence, which stands for the opposite of criminal, +the opposite of ecclesiastical, the opposite of military, the +<span class="tei tei-pb" id="page045">[pg 045]</span><a name="Pg045" id="Pg045" class="tei tei-anchor"></a> +opposite of political, in short, the opposite of any positive +word which wants a negative. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Relative names are such as father, son; ruler, subject; +like; equal; unlike; unequal; longer, shorter; cause, effect. +Their characteristic property is, that they are always given +in pairs. Every relative name which is predicated of an +object, supposes another object (or objects), of which we may +predicate either that same name or another relative name +which is said to be the <span class="tei tei-hi"><span style="font-style: italic">correlative</span></span> of the former. Thus, +when we call any person a son, we suppose other persons +who must be called parents. When we call any event a +cause, we suppose another event which is an effect. When +we say of any distance that it is longer, we suppose another +distance which is shorter. When we say of any object +that it is like, we mean that it is like some other object, +which is also said to be like the first. In this last case, both +objects receive the same name; the relative term is its own +correlative. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is evident that these words, when concrete, are, like +other concrete general names, connotative; they denote a +subject, and connote an attribute: and each of them has or +might have a corresponding abstract name, to denote the +attribute connoted by the concrete. Thus the concrete <span class="tei tei-hi"><span style="font-style: italic">like</span></span> +has its abstract <span class="tei tei-hi"><span style="font-style: italic">likeness</span></span>; the concretes, father and son, have, +or might have, the abstracts, paternity, and filiety, or filiation. +The concrete name connotes an attribute, and the abstract +name which answers to it denotes that attribute. But of +what nature is the attribute? Wherein consists the peculiarity +in the connotation of a relative name? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The attribute signified by a relative name, say some, is a +relation; and this they give, if not as a sufficient explanation, +at least as the only one attainable. If they are asked, What +then is a relation? they do not profess to be able to tell. It +is generally regarded as something peculiarly recondite and +mysterious. I cannot, however, perceive in what respect it +is more so than any other attribute; indeed, it appears to me +to be so in a somewhat less degree. I conceive, rather, that +it is by examining into the signification of relative names, +<span class="tei tei-pb" id="page046">[pg 046]</span><a name="Pg046" id="Pg046" class="tei tei-anchor"></a> +or in other words, into the nature of the attribute which they +connote, that a clear insight may best be obtained into the +nature of all attributes; of all that is meant by an attribute. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is obvious, in fact, that if we take any two correlative names, +<span class="tei tei-hi"><span style="font-style: italic">father</span></span> and <span class="tei tei-hi"><span style="font-style: italic">son</span></span>, for instance, although +the objects <span class="tei tei-hi"><span style="font-style: italic">de</span></span>noted by the names are different, they both, in a +certain sense, connote the same thing. They cannot, indeed, be +said to connote the same <em class="tei tei-emph"><span style="font-style: italic">attribute</span></em>; to be a father, is not the +same thing as to be a son. But when we call one man a +father, another his son, what we mean to affirm is a set of +facts, which are exactly the same in both cases. To predicate +of A that he is the father of B, and of B that he is the +son of A, is to assert one and the same fact in different +words. The two propositions are exactly equivalent: neither +of them asserts more or asserts less than the other. The +paternity of A and the filiety of B are not two facts, but +two modes of expressing the same fact. That fact, when +analysed, consists of a series of physical events or phenomena, +in which both A and B are parties concerned, and +from which they both derive names. What those names +really connote, is this series of events: that is the meaning, +and the whole meaning, which either of them is intended to +convey. The series of events may be said to <span class="tei tei-hi"><span style="font-style: italic">constitute</span></span> the +relation; the schoolmen called it the foundation of the relation, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum relationis</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In this manner any fact, or series of facts, in which two +different objects are implicated, and which is therefore predicable +of both of them, may be either considered as constituting +an attribute of the one, or an attribute of the other. +According as we consider it in the former, or in the latter +aspect, it is connoted by the one or the other of the two +correlative names. <span class="tei tei-hi"><span style="font-style: italic">Father</span></span> connotes the fact, regarded as +constituting an attribute of A: <span class="tei tei-hi"><span style="font-style: italic">son</span></span> connotes the same fact, +as constituting an attribute of B. It may evidently be regarded +with equal propriety in either light. And all that +appears necessary to account for the existence of relative +names, is, that whenever there is a fact in which two individuals +<span class="tei tei-pb" id="page047">[pg 047]</span><a name="Pg047" id="Pg047" class="tei tei-anchor"></a> +are concerned, an attribute grounded on that fact +may be ascribed to either of these individuals. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A name, therefore, is said to be relative, when, over and +above the object which it denotes, it implies in its signification +the existence of another object, also deriving a denomination +from the same fact which is the ground of the first +name. Or (to express the same meaning in other words) a +name is relative, when, being the name of one thing, its signification +cannot be explained but by mentioning another. +Or we may state it thus—when the name cannot be employed +in discourse, so as to have a meaning, unless the name of +some other thing than what it is itself the name of, be either +expressed or understood. These definitions are all, at +bottom, equivalent, being modes of variously expressing this +one distinctive circumstance—that every other attribute of +an object might, without any contradiction, be conceived +still to exist if all objects besides that one were annihilated;<a id="noteref_11" name="noteref_11" href="#note_11"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">11</span></span></a> +but those of its attributes which are expressed by relative +names, would on that supposition be swept away. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 8. Names have been further distinguished into <span class="tei tei-hi"><span style="font-style: italic">univocal</span></span> +and <span class="tei tei-hi"><span style="font-style: italic">æquivocal</span></span>: these, however, are not two kinds of +names, but two different modes of employing names. A +name is univocal, or applied univocally, with respect to all +things of which it can be predicated <em class="tei tei-emph"><span style="font-style: italic">in the same sense</span></em>; but it +is æquivocal, or applied æquivocally, as respects those things +of which it is predicated in different senses. It is scarcely +necessary to give instances of a fact so familiar as the double +meaning of a word. In reality, as has been already observed, +an æquivocal or ambiguous word is not one name, but two +names, accidentally coinciding in sound. <span class="tei tei-hi"><span style="font-style: italic">File</span></span> standing for an +iron instrument, and <span class="tei tei-hi"><span style="font-style: italic">file</span></span> standing for a line of soldiers, have +no more title to be considered one word, because written +<span class="tei tei-pb" id="page048">[pg 048]</span><a name="Pg048" id="Pg048" class="tei tei-anchor"></a> +alike, than <span class="tei tei-hi"><span style="font-style: italic">grease</span></span> and <span class="tei tei-hi"><span style="font-style: italic">Greece</span></span> have, because +they are pronounced alike. They are one sound, appropriated to form +two different words. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An intermediate case is that of a name used <span class="tei tei-hi"><span style="font-style: italic">analogically</span></span> +or metaphorically; that is, a name which is predicated of two +things, not univocally, or exactly in the same signification, +but in significations somewhat similar, and which being derived +one from the other, one of them may be considered the +primary, and the other a secondary signification. As when +we speak of a brilliant light, and a brilliant achievement. The +word is not applied in the same sense to the light and to the +achievement; but having been applied to the light in its original +sense, that of brightness to the eye, it is transferred to +the achievement in a derivative signification, supposed to be +somewhat like the primitive one. The word, however, is just +as properly two names instead of one, in this case, as in that +of the most perfect ambiguity. And one of the commonest +forms of fallacious reasoning arising from ambiguity, is that +of arguing from a metaphorical expression as if it were literal; +that is, as if a word, when applied metaphorically, were the +same name as when taken in its original sense: which will +be seen more particularly in its place. +</p> + +</div> + +<span class="tei tei-pb" id="page049">[pg 049]</span><a name="Pg049" id="Pg049" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc13" id="toc13"></a> +<a name="pdf14" id="pdf14"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER III. OF THE THINGS DENOTED BY NAMES.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. Looking back now to the commencement of our +inquiry, let us attempt to measure how far it has advanced. +Logic, we found, is the Theory of Proof. But proof supposes +something provable, which must be a Proposition or +Assertion; since nothing but a Proposition can be an object +of belief, or therefore of proof. A Proposition is, discourse +which affirms or denies something of some other thing. This +is one step: there must, it seems, be two things concerned in +every act of belief. But what are these Things? They can +be no other than those signified by the two names, which +being joined together by a copula constitute the Proposition. +If, therefore, we knew what all Names signify, we should +know everything which is capable either of being made a +subject of affirmation or denial, or of being itself affirmed +or denied of a subject. We have accordingly, in the preceding +chapter, reviewed the various kinds of Names, in +order to ascertain what is signified by each of them. And +we have now carried this survey far enough to be able to +take an account of its results, and to exhibit an enumeration +of all the kinds of Things which are capable of being made +predicates, or of having anything predicated of them: after +which to determine the import of Predication, that is, of +Propositions, can be no arduous task. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The necessity of an enumeration of Existences, as the +basis of Logic, did not escape the attention of the schoolmen, +and of their master, Aristotle, the most comprehensive, +if not the most sagacious, of the ancient philosophers. The +Categories, or Predicaments—the former a Greek word, the +latter its literal translation in the Latin language—were intended +by him and his followers as an enumeration of all +things capable of being named; an enumeration by the +<span class="tei tei-pb" id="page050">[pg 050]</span><a name="Pg050" id="Pg050" class="tei tei-anchor"></a> +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">summa genera</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span> the most extensive +classes into which things could be distributed; which, therefore, were so many +highest Predicates, one or other of which was supposed +capable of being affirmed with truth of every nameable +thing whatsoever. The following are the classes into which, +according to this school of philosophy, Things in general +might be reduced:— +</p> + +<table summary="This is a list." class="tei tei-list" style="margin-bottom: 1.00em; margin-top: 1.00em"><tbody><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Οὐσία, Substantia.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Ποσὸν, Quantitas.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Ποιόν, Qualitas.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Πρός τι, Relatio.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Ποιεῖν, Actio.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Πάσχειν, Passio.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Ποῦ, Ubi.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Πότε, Quando.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Κεῖσθαι, Situs.</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Εχειν, Habitus.</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The imperfections of this classification are too obvious to +require, and its merits are not sufficient to reward, a minute +examination. It is a mere catalogue of the distinctions +rudely marked out by the language of familiar life, with +little or no attempt to penetrate, by philosophic analysis, to +the <em class="tei tei-emph"><span style="font-style: italic">rationale</span></em> even of those common distinctions. Such an +analysis, however superficially conducted, would have shown +the enumeration to be both redundant and defective. Some +objects are omitted, and others repeated several times under +different heads. It is like a division of animals into men, +quadrupeds, horses, asses, and ponies. That, for instance, +could not be a very comprehensive view of the nature of Relation +which could exclude action, passivity, and local situation +from that category. The same observation applies to +the categories Quando (or position in time), and Ubi (or +position in space); while the distinction between the latter +and Situs is merely verbal. The incongruity of erecting into +a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">summum genus</span></span> +the class which forms the tenth category is +manifest. On the other hand, the enumeration takes no +notice of anything besides substances and attributes. In +what category are we to place sensations, or any other +feelings, and states of mind; as hope, joy, fear; sound, +smell, taste; pain, pleasure; thought, judgment, conception, +<span class="tei tei-pb" id="page051">[pg 051]</span><a name="Pg051" id="Pg051" class="tei tei-anchor"></a> +and the like? Probably all these would have been placed +by the Aristotelian school in the categories of <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">actio</span></span> and <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">passio</span></span>; and the relation +of such of them as are active, to +their objects, and of such of them as are passive, to their +causes, would rightly be so placed; but the things themselves, +the feelings or states of mind, wrongly. Feelings, +or states of consciousness, are assuredly to be counted +among realities, but they cannot be reckoned either among +substances or attributes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Before recommencing, under better auspices, the +attempt made with such imperfect success by the great +founder of the science of logic, we must take notice of an +unfortunate ambiguity in all the concrete names which correspond +to the most general of all abstract terms, the word +Existence. When we have occasion for a name which shall +be capable of denoting whatever exists, as contradistinguished +from non-entity or Nothing, there is hardly a word applicable +to the purpose which is not also, and even more familiarly, +taken in a sense in which it denotes only substances. But +substances are not all that exist; attributes, if such things +are to be spoken of, must be said to exist; feelings also exist. +Yet when we speak of an <em class="tei tei-emph"><span style="font-style: italic">object</span></em>, or of a <em class="tei tei-emph"><span style="font-style: italic">thing</span></em>, we are almost +always supposed to mean a substance. There seems a kind +of contradiction in using such an expression as that one <em class="tei tei-emph"><span style="font-style: italic">thing</span></em> +is merely an attribute of another thing. And the announcement +of a Classification of Things would, I believe, prepare +most readers for an enumeration like those in natural history, +beginning with the great divisions of animal, vegetable, and +mineral, and subdividing them into classes and orders. If, +rejecting the word Thing, we endeavour to find another of a +more general import, or at least more exclusively confined +to that general import, a word denoting all that exists, and +connoting only simple existence; no word might be presumed +fitter for such a purpose than <span class="tei tei-hi"><span style="font-style: italic">being</span></span>: originally the +present participle of a verb which in one of its meanings is +exactly equivalent to the verb <span class="tei tei-hi"><span style="font-style: italic">exist</span></span>; and therefore suitable, +even by its grammatical formation, to be the concrete of the +abstract <em class="tei tei-emph"><span style="font-style: italic">existence</span></em>. But this word, strange as the fact may +<span class="tei tei-pb" id="page052">[pg 052]</span><a name="Pg052" id="Pg052" class="tei tei-anchor"></a> +appear, is still more completely spoiled for the purpose +which it seemed expressly made for, than the word Thing. +<span class="tei tei-hi"><span style="font-style: italic">Being</span></span> is, by custom, exactly synonymous with substance; +except that it is free from a slight taint of a second ambiguity; +being applied impartially to matter and to mind, +while substance, though originally and in strictness applicable +to both, is apt to suggest in preference the idea of +matter. Attributes are never called Beings; nor are Feelings. +A Being is that which excites feelings, and which +possesses attributes. The soul is called a Being; God and +angels are called Beings; but if we were to say, extension, +colour, wisdom, virtue are beings, we should perhaps be suspected +of thinking with some of the ancients, that the cardinal +virtues are animals; or, at the least, of holding with +the Platonic school the doctrine of self-existent Ideas, or +with the followers of Epicurus that of Sensible Forms, +which detach themselves in every direction from bodies, +and by coming in contact with our organs, cause our perceptions. +We should be supposed, in short, to believe +that Attributes are Substances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In consequence of this perversion of the word Being, +philosophers looking about for something to supply its +place, laid their hands upon the word Entity, a piece of +barbarous Latin, invented by the schoolmen to be used as +an abstract name, in which class its grammatical form would +seem to place it; but being seized by logicians in distress +to stop a leak in their terminology, it has ever since been +used as a concrete name. The kindred word <span class="tei tei-hi"><span style="font-style: italic">essence</span></span>, born +at the same time and of the same parents, scarcely underwent +a more complete transformation when, from being the +abstract of the verb <span class="tei tei-hi"><span style="font-style: italic">to be</span></span>, it came to denote something +sufficiently concrete to be enclosed in a glass bottle. The +word Entity, since it settled down into a concrete name, +has retained its universality of signification somewhat less +impaired than any of the names before mentioned. Yet +the same gradual decay to which, after a certain age, all the +language of psychology seems liable, has been at work even +here. If you call virtue an <span class="tei tei-hi"><span style="font-style: italic">entity</span></span>, you are indeed somewhat +<span class="tei tei-pb" id="page053">[pg 053]</span><a name="Pg053" id="Pg053" class="tei tei-anchor"></a> +less strongly suspected of believing it to be a substance than +if you called it a <span class="tei tei-hi"><span style="font-style: italic">being</span></span>; but you are by no means free from +the suspicion. Every word which was originally intended +to connote mere existence, seems, after a time, to enlarge its +connotation to <em class="tei tei-emph"><span style="font-style: italic">separate</span></em> existence, or existence freed from the +condition of belonging to a substance; which condition being +precisely what constitutes an attribute, attributes are gradually +shut out; and along with them feelings, which in ninety-nine +cases out of a hundred have no other name than that +of the attribute which is grounded on them. Strange that +when the greatest embarrassment felt by all who have any considerable +number of thoughts to express, is to find a sufficient +variety of precise words fitted to express them, there should +be no practice to which even scientific thinkers are more +addicted than that of taking valuable words to express ideas +which are sufficiently expressed by other words already appropriated +to them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When it is impossible to obtain good tools, the next best +thing is to understand thoroughly the defects of those we +have. I have therefore warned the reader of the ambiguity +of the very names which, for want of better, I am necessitated +to employ. It must now be the writer's endeavour so +to employ them as in no case to leave the meaning doubtful +or obscure. No one of the above terms being altogether +unambiguous, I shall not confine myself to any one, but +shall employ on each occasion the word which seems least +likely in the particular case to lead to misunderstanding; +nor do I pretend to use either these or any other words +with a rigorous adherence to one single sense. To do +so would often leave us without a word to express what +is signified by a known word in some one or other of its +senses: unless authors had an unlimited licence to coin new +words, together with (what it would be more difficult to +assume) unlimited power of making their readers adopt +them. Nor would it be wise in a writer, on a subject +involving so much of abstraction, to deny himself the advantage +derived from even an improper use of a term, when, +by means of it, some familiar association is called up +<span class="tei tei-pb" id="page054">[pg 054]</span><a name="Pg054" id="Pg054" class="tei tei-anchor"></a> +which brings the meaning home to the mind, as it were by +a flash. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The difficulty both to the writer and reader, of the +attempt which must be made to use vague words so as to +convey a precise meaning, is not wholly a matter of regret. +It is not unfitting that logical treatises should afford an +example of that, to facilitate which is among the most +important uses of logic. Philosophical language will for a +long time, and popular language still longer, retain so +much of vagueness and ambiguity, that logic would be of +little value if it did not, among its other advantages, exercise +the understanding in doing its work neatly and correctly +with these imperfect tools. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After this preamble it is time to proceed to our enumeration. +We shall commence with Feelings, the simplest class +of nameable things; the term Feeling being of course understood +in its most enlarged sense. +</p> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc15" id="toc15"></a> +<a name="pdf16" id="pdf16"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">I. Feelings, or States of Consciousness.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. A Feeling and a State of Consciousness are, in +the language of philosophy, equivalent expressions: everything +is a feeling of which the mind is conscious; everything +which it <em class="tei tei-emph"><span style="font-style: italic">feels</span></em>, or, in other words, which forms a part +of its own sentient existence. In popular language Feeling +is not always synonymous with State of Consciousness; +being often taken more peculiarly for those states which are +conceived as belonging to the sensitive, or to the emotional, +phasis of our nature, and sometimes, with a still narrower +restriction, to the emotional alone: as distinguished from +what are conceived as belonging to the percipient or to the +intellectual phasis. But this is an admitted departure from +correctness of language; just as, by a popular perversion +the exact converse of this, the word Mind is withdrawn from +its rightful generality of signification, and restricted to the +intellect. The still greater perversion by which Feeling is +sometimes confined not only to bodily sensations, but to the +<span class="tei tei-pb" id="page055">[pg 055]</span><a name="Pg055" id="Pg055" class="tei tei-anchor"></a> +sensations of a single sense, that of touch, needs not be more +particularly adverted to. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Feeling, in the proper sense of the term, is a genus, of +which Sensation, Emotion, and Thought, are subordinate +species. Under the word Thought is here to be included +whatever we are internally conscious of when we are said to +think; from the consciousness we have when we think of a +red colour without having it before our eyes, to the most +recondite thoughts of a philosopher or poet. Be it remembered, +however, that by a thought is to be understood what +passes in the mind itself, and not any object external to the +mind, which the person is commonly said to be thinking of. +He may be thinking of the sun, or of God, but the sun and +God are not thoughts; his mental image, however, of the +sun, and his idea of God, are thoughts; states of his mind, +not of the objects themselves: and so also is his belief of +the existence of the sun, or of God; or his disbelief, if the +case be so. Even imaginary objects, (which are said to +exist only in our ideas,) are to be distinguished from our +ideas of them. I may think of a hobgoblin, as I may think +of the loaf which was eaten yesterday, or of the flower which +will bloom to-morrow. But the hobgoblin which never +existed is not the same thing with my idea of a hobgoblin, +any more than the loaf which once existed is the same thing +with my idea of a loaf, or the flower which does not yet +exist, but which will exist, is the same with my idea of a +flower. They are all, not thoughts, but objects of thought; +though at the present time all the objects are alike non-existent. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In like manner, a Sensation is to be carefully distinguished +from the object which causes the sensation; our +sensation of white from a white object; nor is it less to be +distinguished from the attribute whiteness, which we ascribe +to the object in consequence of its exciting the sensation. +Unfortunately for clearness and due discrimination in considering +these subjects, our sensations seldom receive separate +names. We have a name for the objects which produce in +us a certain sensation; the word <span class="tei tei-hi"><span style="font-style: italic">white</span></span>. We have a name +<span class="tei tei-pb" id="page056">[pg 056]</span><a name="Pg056" id="Pg056" class="tei tei-anchor"></a> +for the quality in those objects, to which we ascribe the +sensation; the name <span class="tei tei-hi"><span style="font-style: italic">whiteness</span></span>. But when we speak of the +sensation itself, (as we have not occasion to do this often +except in our scientific speculations,) language, which adapts +itself for the most part only to the common uses of life, has +provided us with no single-worded or immediate designation; +we must employ a circumlocution, and say, The sensation +of white, or The sensation of whiteness; we must denominate +the sensation either from the object, or from the attribute, +by which it is excited. Yet the sensation, though it never +<em class="tei tei-emph"><span style="font-style: italic">does</span></em>, might very well be <em class="tei tei-emph"><span style="font-style: italic">conceived</span></em> to exist, without anything +whatever to excite it. We can conceive it as arising spontaneously +in the mind. But if it so arose, we should have +no name to denote it which would not be a misnomer. In +the case of our sensations of hearing we are better provided; +we have the word Sound, and a whole vocabulary of words +to denote the various kinds of sounds. For as we are often +conscious of these sensations in the absence of any <em class="tei tei-emph"><span style="font-style: italic">perceptible</span></em> +object, we can more easily conceive having them in +the absence of any object whatever. We need only shut +our eyes and listen to music, to have a conception of an +universe with nothing in it except sounds, and ourselves +hearing them: and what is easily conceived separately, easily +obtains a separate name. But in general our names of +sensations denote indiscriminately the sensation and the +attribute. Thus, <span class="tei tei-hi"><span style="font-style: italic">colour</span></span> stands for the sensations of white, +red, &c., but also for the quality in the coloured object. We +talk of the colours of things as among their <em class="tei tei-emph"><span style="font-style: italic">properties</span></em>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. In the case of sensations, another distinction has +also to be kept in view, which is often confounded, and +never without mischievous consequences. This is, the distinction +between the sensation itself, and the state of the +bodily organs which precedes the sensation, and which constitutes +the physical agency by which it is produced. One +of the sources of confusion on this subject is the division +commonly made of feelings into Bodily and Mental. Philosophically +speaking, there is no foundation at all for this +<span class="tei tei-pb" id="page057">[pg 057]</span><a name="Pg057" id="Pg057" class="tei tei-anchor"></a> +distinction: even sensations are states of the sentient mind, +not states of the body, as distinguished from it. What I am +conscious of when I see the colour blue, is a feeling of blue +colour, which is one thing; the picture on my retina, or the +phenomenon of hitherto mysterious nature which takes place +in my optic nerve or in my brain, is another thing, of which +I am not at all conscious, and which scientific investigation +alone could have apprised me of. These are states of my +body; but the sensation of blue, which is the consequence +of these states of body, is not a state of body: that which +perceives and is conscious is called Mind. When sensations +are called bodily feelings, it is only as being the class of +feelings which are immediately occasioned by bodily states; +whereas the other kinds of feelings, thoughts, for instance, +or emotions, are immediately excited not by anything acting +upon the bodily organs, but by sensations, or by previous +thoughts. This, however, is a distinction not in our feelings, +but in the agency which produces our feelings: all of them +when actually produced are states of mind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Besides the affection of our bodily organs from without, +and the sensation thereby produced in our minds, many +writers admit a third link in the chain of phenomena, which +they call a Perception, and which consists in the recognition +of an external object as the exciting cause of the sensation. +This perception, they say, is an <em class="tei tei-emph"><span style="font-style: italic">act</span></em> of the mind, proceeding +from its own spontaneous activity; while in sensation the +mind is passive, being merely acted upon by the outward +object. And according to some metaphysicians it is by an act +of the mind, similar to perception, except in not being +preceded by any sensation, that the existence of God, the +soul, and other hyperphysical objects is recognised. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These acts of what is termed perception, whatever be the +conclusion ultimately come to respecting their nature, must, +I conceive, take their place among the varieties of feelings +or states of mind. In so classing them, I have not the +smallest intention of declaring or insinuating any theory as +to the law of mind in which these mental processes may be +supposed to originate, or the conditions under which they +<span class="tei tei-pb" id="page058">[pg 058]</span><a name="Pg058" id="Pg058" class="tei tei-anchor"></a> +may be legitimate or the reverse. Far less do I mean (as +Dr. Whewell seems to suppose must be meant in an analogous +case<a id="noteref_12" name="noteref_12" href="#note_12"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">12</span></span></a>) to indicate that as they are <span class="tei tei-q">“<em class="tei tei-emph"><span style="font-style: italic">merely</span></em> states of +mind,”</span> it is superfluous to inquire into their distinguishing +peculiarities. I abstain from the inquiry as irrelevant to the +science of logic. In these so-called perceptions, or direct +recognitions by the mind, of objects, whether physical or +spiritual, which are external to itself, I can see only cases of +belief; but of belief which claims to be intuitive, or independent +of external evidence. When a stone lies before me, +I am conscious of certain sensations which I receive from it; +but when I say that these sensations come to me from an +external object which I <em class="tei tei-emph"><span style="font-style: italic">perceive</span></em>, the meaning of these words +is, that receiving the sensations, I intuitively <em class="tei tei-emph"><span style="font-style: italic">believe</span></em> that an +external cause of those sensations exists. The laws of intuitive +belief, and the conditions under which it is legitimate, +are a subject which, as we have already so often remarked, +belongs not to logic, but to the science of the ultimate laws +of the human mind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To the same region of speculation belongs all that can be +said respecting the distinction which the German metaphysicians +and their French and English followers so elaborately +draw between the <em class="tei tei-emph"><span style="font-style: italic">acts</span></em> of the mind and its merely passive +<em class="tei tei-emph"><span style="font-style: italic">states</span></em>; between what it receives from, and what it gives to, +the crude materials of its experience. I am aware that with +reference to the view which those writers take of the primary +elements of thought and knowledge, this distinction is fundamental. +But for the present purpose, which is to examine, +not the original groundwork of our knowledge, but how +we come by that portion of it which is not original; the +difference between active and passive states of mind is of +secondary importance. For us, they all are states of mind, +they all are feelings; by which, let it be said once more, I +mean to imply nothing of passivity, but simply that they are +psychological facts, facts which take place in the mind, and +are to be carefully distinguished from the external or physical +<span class="tei tei-pb" id="page059">[pg 059]</span><a name="Pg059" id="Pg059" class="tei tei-anchor"></a> +facts with which they may be connected, either as effects or +as causes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. Among active states of mind, there is however one +species which merits particular attention, because it forms a +principal part of the connotation of some important classes +of names. I mean <em class="tei tei-emph"><span style="font-style: italic">volitions</span></em>, or acts of the will. When we +speak of sentient beings by relative names, a large portion +of the connotation of the name usually consists of the <em class="tei tei-emph"><span style="font-style: italic">actions</span></em> +of those beings; actions past, present, and possible or probable +future. Take, for instance, the words Sovereign and +Subject. What meaning do these words convey, but that of +innumerable actions, done or to be done by the sovereign +and the subjects, to or in regard to one another reciprocally? +So with the words physician and patient, leader and +follower, tutor and pupil. In many cases the words also +connote actions which would be done under certain contingencies +by persons other than those denoted: as the words +mortgagor and mortgagee, obligor and obligee, and many +other words expressive of legal relation, which connote what +a court of justice would do to enforce the legal obligation if +not fulfilled. There are also words which connote actions +previously done by persons other than those denoted either +by the name itself or by its correlative; as the word brother. +From these instances, it may be seen how large a portion of +the connotation of names consists of actions. Now what is +an action? Not one thing, but a series of two things: the +state of mind called a volition, followed by an effect. The +volition or intention to produce the effect, is one thing; the +effect produced in consequence of the intention, is another +thing; the two together constitute the action. I form the +purpose of instantly moving my arm; that is a state of my +mind: my arm (not being tied or paralytic) moves in obedience +to my purpose; that is a physical fact, consequent on +a state of mind. The intention, followed by the fact, +or, (if we prefer the expression,) the fact when preceded +and caused by the intention, is called the action of moving +my arm. +</p> + +<span class="tei tei-pb" id="page060">[pg 060]</span><a name="Pg060" id="Pg060" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. Of the first leading division of nameable things, +viz. Feelings or States of Consciousness, we began by +recognising three sub-divisions; Sensations, Thoughts, and +Emotions. The first two of these we have illustrated at +considerable length; the third, Emotions, not being perplexed +by similar ambiguities, does not require similar +exemplification. And, finally, we have found it necessary +to add to these three a fourth species, commonly known by +the name Volitions. Without seeking to prejudge the metaphysical +question whether any mental state or phenomenon +can be found which is not included in one or other of these +four species, it appears to me that the amount of illustration +bestowed upon these may, so far as we are concerned, +suffice for the whole genus. We shall, therefore, proceed +to the two remaining classes of nameable things; all things +which are external to the mind being considered as belonging +either to the class of Substances or to that of Attributes. +</p> + +</div> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc17" id="toc17"></a> +<a name="pdf18" id="pdf18"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">II. Substances.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Logicians have endeavoured to define Substance and +Attribute; but their definitions are not so much attempts to +draw a distinction between the things themselves, as instructions +what difference it is customary to make in the grammatical +structure of the sentence, according as we are +speaking of substances or of attributes. Such definitions +are rather lessons of English, or of Greek, Latin, or German, +than of mental philosophy. An attribute, say the school +logicians, must be the attribute <em class="tei tei-emph"><span style="font-style: italic">of</span></em> something: colour, for +example, must be the colour <em class="tei tei-emph"><span style="font-style: italic">of</span></em> something; goodness must +be the goodness <em class="tei tei-emph"><span style="font-style: italic">of</span></em> something: and if this something should +cease to exist, or should cease to be connected with the +attribute, the existence of the attribute would be at an end. +A substance, on the contrary, is self-existent; in speaking +about it, we need not put <em class="tei tei-emph"><span style="font-style: italic">of</span></em> after its name. A stone is not +the stone <em class="tei tei-emph"><span style="font-style: italic">of</span></em> anything; the moon is not the moon <em class="tei tei-emph"><span style="font-style: italic">of</span></em> anything, +but simply the moon. Unless, indeed, the name which +we choose to give to the substance be a relative name; if so, +<span class="tei tei-pb" id="page061">[pg 061]</span><a name="Pg061" id="Pg061" class="tei tei-anchor"></a> +it must be followed either by <em class="tei tei-emph"><span style="font-style: italic">of</span></em> or by some other particle, +implying, as that preposition does, a reference to something +else: but then the other characteristic peculiarity of an +attribute would fail; the <em class="tei tei-emph"><span style="font-style: italic">something</span></em> might be destroyed, and +the substance might still subsist. Thus, a father must be the +father <em class="tei tei-emph"><span style="font-style: italic">of</span></em> something, and so far resembles an attribute, in +being referred to something besides himself: if there were +no child, there would be no father: but this, when we look +into the matter, only means that we should not call him +father. The man called father might still exist though there +were no child, as he existed before there was a child: and +there would be no contradiction in supposing him to exist, +although the whole universe except himself were destroyed. +But destroy all white substances, and where would be the +attribute whiteness? Whiteness, without any white thing, is +a contradiction in terms. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This is the nearest approach to a solution of the difficulty, +that will be found in the common treatises on logic. It will +scarcely be thought to be a satisfactory one. If an attribute +is distinguished from a substance by being the attribute <em class="tei tei-emph"><span style="font-style: italic">of</span></em> +something, it seems highly necessary to understand what is +meant by <em class="tei tei-emph"><span style="font-style: italic">of</span></em>: a particle which needs explanation too much +itself to be placed in front of the explanation of anything +else. And as for the self-existence of substances, it is very +true that a substance may be conceived to exist without any +other substance, but so also may an attribute without any +other attribute: and we can no more imagine a substance +without attributes than we can imagine attributes without a +substance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Metaphysicians, however, have probed the question +deeper, and given an account of Substance considerably +more satisfactory than this. Substances are usually distinguished +as Bodies or Minds. Of each of these, philosophers +have at length provided us with a definition which seems +unexceptionable. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. A Body, according to the received doctrine of +modern metaphysicians, may be defined the external cause +<span class="tei tei-pb" id="page062">[pg 062]</span><a name="Pg062" id="Pg062" class="tei tei-anchor"></a> +to which we ascribe our sensations. When I see and touch +a piece of gold, I am conscious of a sensation of yellow +colour, and sensations of hardness and weight; and by +varying the mode of handling, I may add to these sensations +many others completely distinct from them. The sensations +are all of which I am directly conscious; but I consider them +as produced by something not only existing independently +of my will, but external to my bodily organs and to my mind. +This external something I call a body. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It may be asked, how come we to ascribe our sensations +to any external cause? And is there sufficient ground for so +ascribing them? It is known, that there are metaphysicians +who have raised a controversy on the point; maintaining +that we are not warranted in referring our sensations to a +cause, such as we understand by the word Body, or to any +cause whatever, unless, indeed, a First Cause. Though +we have no concern here with this controversy, nor with the +metaphysical niceties on which it turns, one of the best ways +of showing what is meant by Substance is, to consider what +position it is necessary to take up, in order to maintain its +existence against opponents. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is certain, then, that a part of our notion of a body +consists of the notion of a number of sensations of our own, +or of other sentient beings, habitually occurring simultaneously. +My conception of the table at which I am writing +is compounded of its visible form and size, which are complex +sensations of sight; its tangible form and size, which +are complex sensations of our organs of touch and of our +muscles; its weight, which is also a sensation of touch and +of the muscles; its colour, which is a sensation of sight; +its hardness, which is a sensation of the muscles; its +composition, which is another word for all the varieties of +sensation which we receive under various circumstances from +the wood of which it is made; and so forth. All or most of +these various sensations frequently are, and, as we learn by +experience, always might be, experienced simultaneously, or +in many different orders of succession, at our own choice: +and hence the thought of any one of them makes us think +<span class="tei tei-pb" id="page063">[pg 063]</span><a name="Pg063" id="Pg063" class="tei tei-anchor"></a> +of the others, and the whole becomes mentally amalgamated +into one mixed state of consciousness, which, in the language +of the school of Locke and Hartley, is termed a Complex Idea. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, there are philosophers who have argued as follows. +If we take an orange, and conceive it to be divested of its +natural colour without acquiring any new one; to lose its +softness without becoming hard, its roundness without becoming +square or pentagonal, or of any other regular or +irregular figure whatever; to be deprived of size, of weight, +of taste, of smell; to lose all its mechanical and all its +chemical properties, and acquire no new ones; to become, +in short, invisible, intangible, imperceptible not only by all +our senses, but by the senses of all other sentient beings, real +or possible; nothing, say these thinkers, would remain. +For of what nature, they ask, could be the residuum? and +by what token could it manifest its presence? To the unreflecting +its existence seems to rest on the evidence of the +senses. But to the senses nothing is apparent except the +sensations. We know, indeed, that these sensations are +bound together by some law; they do not come together at +random, but according to a systematic order, which is part of +the order established in the universe. When we experience +one of these sensations, we usually experience the others +also, or know that we have it in our power to experience +them. But a fixed law of connexion, making the sensations +occur together, does not, say these philosophers, necessarily +require what is called a substratum to support them. The +conception of a substratum is but one of many possible forms +in which that connexion presents itself to our imagination; a +mode of, as it were, realizing the idea. If there be such a +substratum, suppose it this instant miraculously annihilated, +and let the sensations continue to occur in the same order, +and how would the substratum be missed? By what signs +should we be able to discover that its existence had terminated? +should we not have as much reason to believe that it +still existed as we now have? and if we should not then be +warranted in believing it, how can we be so now? A body, +therefore, according to these metaphysicians, is not anything +<span class="tei tei-pb" id="page064">[pg 064]</span><a name="Pg064" id="Pg064" class="tei tei-anchor"></a> +intrinsically different from the sensations which the body is +said to produce in us; it is, in short, a set of sensations +joined together according to a fixed law. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The controversies to which these speculations have given +rise, and the doctrines which have been developed in the +attempt to find a conclusive answer to them, have been +fruitful of important consequences to the Science of Mind. +The sensations (it was answered) which we are conscious of, +and which we receive not at random, but joined together in a +certain uniform manner, imply not only a law or laws of connexion, +but a cause external to our mind, which cause, by its +own laws, determines the laws according to which the sensations +are connected and experienced. The schoolmen used +to call this external cause by the name we have already employed, +a <span class="tei tei-hi"><span style="font-style: italic">substratum</span></span>; and its attributes (as they expressed +themselves) <em class="tei tei-emph"><span style="font-style: italic">inhered</span></em>, literally <em class="tei tei-emph"><span style="font-style: italic">stuck</span></em>, in it. To this substratum +the name Matter is usually given in philosophical discussions. +It was soon, however, acknowledged by all who reflected on +the subject, that the existence of matter could not be proved +by extrinsic evidence. The answer, therefore, now usually +made to Berkeley and his followers, is, that the belief is intuitive; +that mankind, in all ages, have felt themselves compelled, +by a necessity of their nature, to refer their sensations +to an external cause: that even those who deny it in theory, +yield to the necessity in practice, and both in speech, thought, +and feeling, do, equally with the vulgar, acknowledge their +sensations to be the effects of something external to them: +this knowledge, therefore, it is affirmed, is as evidently +intuitive as our knowledge of our sensations themselves is +intuitive. And here the question merges in the fundamental +problem of metaphysics properly so called; to which science +we leave it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But although the extreme doctrine of the Idealist metaphysicians, +that objects are nothing but our sensations and +the laws which connect them, has not been generally adopted +by subsequent thinkers; the point of most real importance +is one on which those metaphysicians are now very +generally considered to have made out their case: viz., that +<span class="tei tei-pb" id="page065">[pg 065]</span><a name="Pg065" id="Pg065" class="tei tei-anchor"></a> +<em class="tei tei-emph"><span style="font-style: italic">all we know</span></em> of objects is the sensations which they give us, +and the order of the occurrence of those sensations. Kant +himself, on this point, is as explicit as Berkeley or Locke. +However firmly convinced that there exists an universe of +<span class="tei tei-q">“Things in themselves,”</span> totally distinct from the universe of +phenomena, or of things as they appear to our senses; and +even when bringing into use a technical expression (<span class="tei tei-hi"><span style="font-style: italic">Noumenon</span></span>) +to denote what the thing is in itself, as contrasted with +the <em class="tei tei-emph"><span style="font-style: italic">representation</span></em> of it in our minds; he allows that this +representation (the matter of which, he says, consists of our +sensations, though the form is given by the laws of the mind +itself) is all we know of the object: and that the real nature +of the Thing is, and by the constitution of our faculties ever +must remain, at least in the present state of existence, an impenetrable +mystery to us.<a id="noteref_13" name="noteref_13" href="#note_13"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">13</span></span></a> There is not the slightest reason for +<span class="tei tei-pb" id="page066">[pg 066]</span><a name="Pg066" id="Pg066" class="tei tei-anchor"></a> +believing that what we call the sensible qualities of the object +are a type of anything inherent in itself, or bear any affinity +to its own nature. A cause does not, as such, resemble its +effects; an east wind is not like the feeling of cold, nor +heat like the steam of boiling water: why then should +matter resemble our sensations? why should the inmost +nature of fire or water resemble the impressions made by +these objects upon our senses?<a id="noteref_14" name="noteref_14" href="#note_14"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">14</span></span></a> And if not on the principle +of resemblance, on what other principle can the manner in +which objects affect us through our senses afford us any +insight into the inherent nature of those objects? It may +therefore safely be laid down as a truth both obvious in itself, +and admitted by all whom it is at present necessary to take +<span class="tei tei-pb" id="page067">[pg 067]</span><a name="Pg067" id="Pg067" class="tei tei-anchor"></a> +into consideration, that, of the outward world, we know and +can know absolutely nothing, except the sensations which +we experience from it. Those, however, who still look upon +Ontology as a possible science, and think, not only that +bodies have an essential constitution of their own, lying +deeper than our perceptions, but that this essence or nature +is accessible to human investigation, cannot expect to find +their refutation here. The question depends on the nature +and laws of Intuitive Knowledge, and is not within the province +of logic. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 8. Body having now been defined the external cause, +and (according to the more reasonable opinion) the +<em class="tei tei-emph"><span style="font-style: italic">hidden</span></em> external cause, to which we refer our sensations; it +remains to frame a definition of Mind. Nor, after the preceding +observations, will this be difficult. For, as our +conception of a body is that of an unknown exciting cause +of sensations, so our conception of a mind is that of an unknown +recipient, or percipient, of them; and not of them +alone, but of all our other feelings. As body is the mysterious +something which excites the mind to feel, so mind is +the mysterious something which feels, and thinks. It is +unnecessary to give in the case of mind, as we gave in the +case of matter, a particular statement of the sceptical system +by which its existence as a Thing in itself, distinct from the +series of what are denominated its states, is called in question. +But it is necessary to remark, that on the inmost +nature of the thinking principle, as well as on the inmost +nature of matter, we are, and with our faculties must always +remain, entirely in the dark. All which we are aware of, +even in our own minds, is (in the words of Mr. Mill) a certain +<span class="tei tei-q">“thread of consciousness;”</span> a series of feelings, that is, +of sensations, thoughts, emotions, and volitions, more or less +numerous and complicated. There is a something I call +Myself, or, by another form of expression, my mind, which I +consider as distinct from these sensations, thoughts, &c.; a +something which I conceive to be not the thoughts, but the +being that has the thoughts, and which I can conceive as +<span class="tei tei-pb" id="page068">[pg 068]</span><a name="Pg068" id="Pg068" class="tei tei-anchor"></a> +existing for ever in a state of quiescence, without any +thoughts at all. But what this being is, although it is myself, +I have no knowledge, other than the series of its states of +consciousness. As bodies manifest themselves to me only +through the sensations of which I regard them as the causes, +so the thinking principle, or mind, in my own nature, makes +itself known to me only by the feelings of which it is conscious. +I know nothing about myself, save my capacities of +feeling or being conscious (including, of course, thinking and +willing): and were I to learn anything new concerning my +own nature, I cannot with my present faculties conceive this +new information to be anything else, than that I have some +additional capacities, as yet unknown to me, of feeling, +thinking, or willing. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus, then, as body is the unsentient cause to which we +are naturally prompted to refer a certain portion of our feelings, +so mind may be described as the sentient <em class="tei tei-emph"><span style="font-style: italic">subject</span></em> (in the +German sense of the term) of all feelings; that which has or +feels them. But of the nature of either body or mind, further +than the feelings which the former excites, and which the +latter experiences, we do not, according to the best existing +doctrine, know anything; and if anything, logic has nothing +to do with it, or with the manner in which the knowledge is +acquired. With this result we may conclude this portion of +our subject, and pass to the third and only remaining class +or division of Nameable Things. +</p> + +</div> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc19" id="toc19"></a> +<a name="pdf20" id="pdf20"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">III. Attributes: and, first, Qualities.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 9. From what has already been said of Substance, +what is to be said of Attribute is easily deducible. For if +we know not, and cannot know, anything of bodies but the +sensations which they excite in us or others, those sensations +must be all that we can, at bottom, mean by their attributes; +and the distinction which we verbally make between the properties +of things and the sensations we receive from them, +must originate in the convenience of discourse rather than in +the nature of what is denoted by the terms. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Attributes are usually distributed under the three heads +<span class="tei tei-pb" id="page069">[pg 069]</span><a name="Pg069" id="Pg069" class="tei tei-anchor"></a> +of Quality, Quantity, and Relation. We shall come to the +two latter presently: in the first place we shall confine ourselves +to the former. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us take, then, as our example, one of what are termed +the sensible qualities of objects, and let that example be +whiteness. When we ascribe whiteness to any substance, +as, for instance, snow; when we say that snow has the quality +whiteness, what do we really assert? Simply, that when +snow is present to our organs, we have a particular sensation, +which we are accustomed to call the sensation of white. But +how do I know that snow is present? Obviously by the +sensations which I derive from it, and not otherwise. I infer +that the object is present, because it gives me a certain +assemblage or series of sensations. And when I ascribe to +it the attribute whiteness, my meaning is only, that, of the +sensations composing this group or series, that which I call +the sensation of white colour is one. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This is one view which may be taken of the subject. But +there is also another, and a different view. It may be said, +that it is true we <em class="tei tei-emph"><span style="font-style: italic">know</span></em> nothing of sensible objects, except the +sensations they excite in us; that the fact of our receiving +from snow the particular sensation which is called a sensation +of white, is the <em class="tei tei-emph"><span style="font-style: italic">ground</span></em> on which we ascribe to that substance +the quality whiteness; the sole proof of its possessing +that quality. But because one thing may be the sole evidence +of the existence of another thing, it does not follow +that the two are one and the same. The attribute whiteness +(it may be said) is not the fact of our receiving the +sensation, but something in the object itself; a <em class="tei tei-emph"><span style="font-style: italic">power</span></em> inherent +in it; something <em class="tei tei-emph"><span style="font-style: italic">in virtue</span></em> of which the object produces the +sensation. And when we affirm that snow possesses the +attribute whiteness, we do not merely assert that the presence +of snow produces in us that sensation, but that it does so +through, and by reason of, that power or quality. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For the purposes of logic it is not of material importance +which of these opinions we adopt. The full discussion of the +subject belongs to the other department of scientific inquiry, +so often alluded to under the name of metaphysics; but it +may be said here, that for the doctrine of the existence of a +<span class="tei tei-pb" id="page070">[pg 070]</span><a name="Pg070" id="Pg070" class="tei tei-anchor"></a> +peculiar species of entities called qualities, I can see no +foundation except in a tendency of the human mind which +is the cause of many delusions. I mean, the disposition, +wherever we meet with two names which are not precisely +synonymous, to suppose that they must be the names of two +different things; whereas in reality they may be names of +the same thing viewed in two different lights, which is as +much as to say under different suppositions as to surrounding +circumstances. Because <em class="tei tei-emph"><span style="font-style: italic">quality</span></em> and <em class="tei tei-emph"><span style="font-style: italic">sensation</span></em> cannot be +put indiscriminately one for the other, it is supposed that +they cannot both signify the same thing, namely, the impression +or feeling with which we are affected through our senses +by the presence of an object; although there is at least no +absurdity in supposing that this identical impression or feeling +may be called a sensation when considered merely in +itself, and a quality when regarded as emanating from any +one of the numerous objects, the presence of which to our +organs excites in our minds that among various other sensations +or feelings. And if this be admissible as a supposition, +it rests with those who contend for an entity <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> called a +quality, to show that their opinion is preferable, or is anything +in fact but a lingering remnant of the scholastic +doctrine of occult causes; the very absurdity which Molière +so happily ridiculed when he made one of his pedantic +physicians account for the fact that <span class="tei tei-q">“l'opium endormit,”</span> by +the maxim <span class="tei tei-q">“parcequ'il a une vertu soporifique.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is evident that when the physician stated that opium +had <span class="tei tei-q">“une vertu soporifique,”</span> he did not account for, but +merely asserted over again, the fact that it <span class="tei tei-hi"><span style="font-style: italic">endormit</span></span>. In like +manner, when we say that snow is white because it has +the quality of whiteness, we are only re-asserting in more +technical language the fact that it excites in us the sensation +of white. If it be said that the sensation must have some +cause, I answer, its cause is the presence of the assemblage +of phenomena which is termed the object. When we have +asserted that as often as the object is present, and our organs +in their normal state, the sensation takes place, we have +stated all that we know about the matter. There is no need, +<span class="tei tei-pb" id="page071">[pg 071]</span><a name="Pg071" id="Pg071" class="tei tei-anchor"></a> +after assigning a certain and intelligible cause, to suppose an +occult cause besides, for the purpose of enabling the real +cause to produce its effect. If I am asked, why does the +presence of the object cause this sensation in me, I cannot +tell: I can only say that such is my nature, and the nature +of the object; that the fact forms a part of the constitution +of things. And to this we must at last come, +even after interpolating the imaginary entity. Whatever +number of links the chain of causes and effects may consist +of, how any one link produces the one which is next to +it remains equally inexplicable to us. It is as easy to +comprehend that the object should produce the sensation +directly and at once, as that it should produce the same +sensation by the aid of something else called the <em class="tei tei-emph"><span style="font-style: italic">power</span></em> of +producing it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But as the difficulties which may be felt in adopting this +view of the subject cannot be removed without discussions +transcending the bounds of our science, I content myself +with a passing indication, and shall, for the purposes of logic, +adopt a language compatible with either view of the nature +of qualities. I shall say,—what at least admits of no dispute,—that +the quality of whiteness ascribed to the object +snow, is <em class="tei tei-emph"><span style="font-style: italic">grounded</span></em> on its exciting in us the sensation of white; +and adopting the language already used by the school logicians +in the case of the kind of attributes called Relations, I +shall term the sensation of white the <span class="tei tei-hi"><span style="font-style: italic">foundation</span></span> of the quality +whiteness. For logical purposes the sensation is the only +essential part of what is meant by the word; the only part +which we ever can be concerned in proving. When that is +proved, the quality is proved; if an object excites a sensation +it has, of course, the power of exciting it. +</p> + +</div> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc21" id="toc21"></a> +<a name="pdf22" id="pdf22"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">IV. Relations.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 10. The <em class="tei tei-emph"><span style="font-style: italic">qualities</span></em> of a body, we have said, are the +attributes grounded on the sensations which the presence of +that particular body to our organs excites in our minds. But +when we ascribe to any object the kind of attribute called a +<span class="tei tei-pb" id="page072">[pg 072]</span><a name="Pg072" id="Pg072" class="tei tei-anchor"></a> +Relation, the foundation of the attribute must be something +in which other objects are concerned besides itself and the +percipient. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As there may with propriety be said to be a relation +between any two things to which two correlative names are +or may be given; we may expect to discover what constitutes +a relation in general, if we enumerate the principal cases in +which mankind have imposed correlative names, and observe +what these cases have in common. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What, then, is the character which is possessed in common +by states of circumstances so heterogeneous and discordant +as these: one thing <em class="tei tei-emph"><span style="font-style: italic">like</span></em> another; one thing <em class="tei tei-emph"><span style="font-style: italic">unlike</span></em> +another; one thing <em class="tei tei-emph"><span style="font-style: italic">near</span></em> another; one thing <em class="tei tei-emph"><span style="font-style: italic">far from</span></em> another; +one thing <em class="tei tei-emph"><span style="font-style: italic">before</span></em>, <em class="tei tei-emph"><span style="font-style: italic">after</span></em>, <em class="tei tei-emph"><span style="font-style: italic">along with</span></em> another; one +thing <em class="tei tei-emph"><span style="font-style: italic">greater</span></em>, <em class="tei tei-emph"><span style="font-style: italic">equal</span></em>, <em class="tei tei-emph"><span style="font-style: italic">less</span></em>, than another; one +thing the <em class="tei tei-emph"><span style="font-style: italic">cause</span></em> of another, the <em class="tei tei-emph"><span style="font-style: italic">effect</span></em> of another; one person +the <em class="tei tei-emph"><span style="font-style: italic">master</span></em>, <em class="tei tei-emph"><span style="font-style: italic">servant</span></em>, <em class="tei tei-emph"><span style="font-style: italic">child</span></em>, <em class="tei tei-emph"><span style="font-style: italic">parent</span></em>, +<em class="tei tei-emph"><span style="font-style: italic">debtor</span></em>, <em class="tei tei-emph"><span style="font-style: italic">creditor</span></em>, <em class="tei tei-emph"><span style="font-style: italic">sovereign</span></em>, <em class="tei tei-emph"><span style="font-style: italic">subject</span></em>, +<em class="tei tei-emph"><span style="font-style: italic">attorney</span></em>, <em class="tei tei-emph"><span style="font-style: italic">client</span></em>, of another, +and so on? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Omitting, for the present, the case of Resemblance, (a +relation which requires to be considered separately,) there +seems to be one thing common to all these cases, and only +one; that in each of them there exists or occurs, or has +existed or occurred, or may be expected to exist or occur, +some <em class="tei tei-emph"><span style="font-style: italic">fact</span></em> or phenomenon, into which the two things which +are said to be related to each other, both enter as parties +concerned. This fact, or phenomenon, is what the Aristotelian +logicians called the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum +relationis</span></span>. Thus in the relation of greater and less between two magnitudes, +the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum relationis</span></span> +is the fact that one of the two +magnitudes could, under certain conditions, be included in, +without entirely filling, the space occupied by the other magnitude. +In the relation of master and servant, the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum relationis</span></span> +is the fact that the one has undertaken, or +is compelled, to perform certain services for the benefit, and +at the bidding of the other. Examples might be indefinitely +multiplied; but it is already obvious that whenever two things +are said to be related, there is some fact, or series of facts, +into which they both enter; and that whenever any two +<span class="tei tei-pb" id="page073">[pg 073]</span><a name="Pg073" id="Pg073" class="tei tei-anchor"></a> +things are involved in some one fact, or series of facts, we +may ascribe to those two things a mutual relation grounded +on the fact. Even if they have nothing in common but what +is common to all things, that they are members of the universe, +we call that a relation, and denominate them fellow-creatures, +fellow-beings, or fellow-denizens of the universe. +But in proportion as the fact into which the two objects enter +as parts is of a more special and peculiar, or of a more complicated +nature, so also is the relation grounded upon it. +And there are as many conceivable relations as there are +conceivable kinds of fact in which two things can be jointly +concerned. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the same manner, therefore, as a quality is an attribute +grounded on the fact that a certain sensation or sensations +are produced in us by the object, so an attribute grounded +on some fact into which the object enters jointly with another +object, is a relation between it and that other object. But +the fact in the latter case consists of the very same kind of +elements as the fact in the former: namely, states of consciousness. +In the case, for example, of any legal relation, +as debtor and creditor, principal and agent, guardian and +ward, the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum relationis</span></span> +consists entirely of thoughts, +feelings, and volitions (actual or contingent), either of the +persons themselves or of other persons concerned in the +same series of transactions; as, for instance, the intentions +which would be formed by a judge in case a complaint were +made to his tribunal of the infringement of any of the legal +obligations imposed by the relation; and the acts which the +judge would perform in consequence; acts being (as we +have already seen) another word for intentions followed +by an effect, and that effect being but another word for +sensations, or some other feelings, occasioned either to +oneself or to somebody else. There is no part of what the +names expressive of the relation imply, that is not resolvable +into states of consciousness; outward objects being, no doubt, +supposed throughout as the causes by which some of those +states of consciousness are excited, and minds as the subjects +by which all of them are experienced, but neither the +<span class="tei tei-pb" id="page074">[pg 074]</span><a name="Pg074" id="Pg074" class="tei tei-anchor"></a> +external objects nor the minds making their existence known +otherwise than by the states of consciousness. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Cases of relation are not always so complicated as those +to which we last alluded. The simplest of all cases of relation +are those expressed by the words antecedent and consequent, +and by the word simultaneous. If we say, for instance, that +dawn preceded sunrise, the fact in which the two things, dawn +and sunrise, were jointly concerned, consisted only of the two +things themselves; no third thing entered into the fact or +phenomenon at all; unless, indeed, we choose to call the succession +of the two objects a third thing; but their succession +is not something added to the things themselves; it is something +involved in them. Dawn and sunrise announce themselves +to our consciousness by two successive sensations; +our consciousness of the succession of these sensations is +not a third sensation or feeling added to them; we have not +first the two feelings, and then a feeling of their succession. +To have two feelings at all, implies having them either successively, +or else simultaneously. Sensations, or other feelings, +being given, succession and simultaneousness are the +two conditions, to the alternative of which they are subjected +by the nature of our faculties; and no one has been able, or +needs expect, to analyse the matter any farther. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 11. In a somewhat similar position are two other +sorts of relation, Likeness and Unlikeness. I have two +sensations; we will suppose them to be simple ones; two +sensations of white, or one sensation of white and another +of black. I call the first two sensations <span class="tei tei-hi"><span style="font-style: italic">like</span></span>; the last two +<span class="tei tei-hi"><span style="font-style: italic">unlike</span></span>. What is the fact or phenomenon constituting the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum</span></span> of this relation? +The two sensations first, and +then what we call a feeling of resemblance, or of want of +resemblance. Let us confine ourselves to the former case. +Resemblance is evidently a feeling; a state of the consciousness +of the observer. Whether the feeling of the resemblance +of the two colours be a third state of consciousness, +which I have <em class="tei tei-emph"><span style="font-style: italic">after</span></em> having the two sensations of colour, or +whether (like the feeling of their succession) it is involved +<span class="tei tei-pb" id="page075">[pg 075]</span><a name="Pg075" id="Pg075" class="tei tei-anchor"></a> +in the sensations themselves, may be a matter of discussion. +But in either case, these feelings of resemblance, and of its +opposite, dissimilarity, are parts of our nature; and parts +so far from being capable of analysis, that they are presupposed +in every attempt to analyse any of our other +feelings. Likeness and unlikeness, therefore, as well as +antecedence, sequence, and simultaneousness, must stand +apart among relations, as things <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">sui +generis</span></span>. They are +attributes grounded on facts, that is, on states of consciousness, +but on states which are peculiar, unresolvable, and +inexplicable. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But, although likeness or unlikeness cannot be resolved +into anything else, complex cases of likeness or unlikeness +can be resolved into simpler ones. When we say of two +things which consist of parts, that they are like one another, +the likeness of the wholes does admit of analysis; it is compounded +of likenesses between the various parts respectively. +Of how vast a variety of resemblances of parts must that +resemblance be composed, which induces us to say that a +portrait, or a landscape, is like its original. If one person +mimics another with any success, of how many simple likenesses +must the general or complex likeness be compounded: +likeness in a succession of bodily postures; likeness +in voice, or in the accents and intonations of the voice; +likeness in the choice of words, and in the thoughts or +sentiments expressed, whether by word, countenance, or +gesture. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All likeness and unlikeness of which we have any cognizance, +resolve themselves into likeness and unlikeness +between states of our own, or some other, mind. When we +say that one body is like another, (since we know nothing of +bodies but the sensations which they excite,) we mean really +that there is a resemblance between the sensations excited +by the two bodies, or between some portion at least of these +sensations. If we say that two attributes are like one +another, (since we know nothing of attributes except the +sensations or states of feeling on which they are grounded,) +we mean really that those sensations, or states of feeling, +<span class="tei tei-pb" id="page076">[pg 076]</span><a name="Pg076" id="Pg076" class="tei tei-anchor"></a> +resemble each other. We may also say that two relations +are alike. The fact of resemblance between relations is +sometimes called <span class="tei tei-hi"><span style="font-style: italic">analogy</span></span>, forming one of the numerous +meanings of that word. The relation in which Priam stood +to Hector, namely, that of father and son, resembles the +relation in which Philip stood to Alexander; resembles it so +closely that they are called the same relation. The relation +in which Cromwell stood to England resembles the relation +in which Napoleon stood to France, though not so closely as +to be called the same relation. The meaning in both these +instances must be, that a resemblance existed between the +facts which constituted the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum +relationis</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This resemblance may exist in all conceivable gradations, +from perfect undistinguishableness to something extremely +slight. When we say, that a thought suggested to +the mind of a person of genius is like a seed cast into the +ground, because the former produces a multitude of other +thoughts, and the latter a multitude of other seeds, this is +saying that between the relation of an inventive mind to a +thought contained in it, and the relation of a fertile soil to a +seed contained in it, there exists a resemblance: the real +resemblance being in the two <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamenta +relationis</span></span>, in each +of which there occurs a germ, producing by its development +a multitude of other things similar to itself. And as, whenever +two objects are jointly concerned in a phenomenon, this +constitutes a relation between those objects, so, if we suppose +a second pair of objects concerned in a second phenomenon, +the slightest resemblance between the two phenomena is +sufficient to admit of its being said that the two relations +resemble; provided, of course, the points of resemblance +are found in those portions of the two phenomena respectively +which are connoted by the relative names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +While speaking of resemblance, it is necessary to take +notice of an ambiguity of language, against which scarcely +any one is sufficiently on his guard. Resemblance, when it +exists in the highest degree of all, amounting to undistinguishableness, +is often called identity, and the two similar +things are said to be the same. I say often, not always; +<span class="tei tei-pb" id="page077">[pg 077]</span><a name="Pg077" id="Pg077" class="tei tei-anchor"></a> +for we do not say that two visible objects, two persons for +instance, are the same, because they are so much alike that +one might be mistaken for the other: but we constantly use +this mode of expression when speaking of feelings; as when +I say that the sight of any object gives me the <em class="tei tei-emph"><span style="font-style: italic">same</span></em> sensation +or emotion to-day that it did yesterday, or the <em class="tei tei-emph"><span style="font-style: italic">same</span></em> which it +gives to some other person. This is evidently an incorrect +application of the word <span class="tei tei-hi"><span style="font-style: italic">same</span></span>; for the feeling which I had +yesterday is gone, never to return; what I have to-day is +another feeling, exactly like the former perhaps, but distinct +from it; and it is evident that two different persons cannot +be experiencing the same feeling, in the sense in which we +say that they are both sitting at the same table. By a +similar ambiguity we say, that two persons are ill of the +<em class="tei tei-emph"><span style="font-style: italic">same</span></em> disease; that two persons hold the <em class="tei tei-emph"><span style="font-style: italic">same</span></em> office; not in +the sense in which we say that they are engaged in the same +adventure, or sailing in the same ship, but in the sense that +they fill offices exactly similar, though, perhaps, in distant +places. Great confusion of ideas is often produced, and +many fallacies engendered, in otherwise enlightened understandings, +by not being sufficiently alive to the fact (in itself +not always to be avoided,) that they use the same name to +express ideas so different as those of identity and undistinguishable +resemblance. Among modern writers, Archbishop +Whately stands almost alone in having drawn attention +to this distinction, and to the ambiguity connected +with it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Several relations, generally called by other names, are +really cases of resemblance. As, for example, equality; +which is but another word for the exact resemblance commonly +called identity, considered as subsisting between +things in respect of their <em class="tei tei-emph"><span style="font-style: italic">quantity</span></em>. And this example forms +a suitable transition to the third and last of the three heads, +under which, as already remarked, Attributes are commonly +arranged. +</p> + +</div> + +<span class="tei tei-pb" id="page078">[pg 078]</span><a name="Pg078" id="Pg078" class="tei tei-anchor"></a> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc23" id="toc23"></a> +<a name="pdf24" id="pdf24"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">V. Quantity.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 12. Let us imagine two things, between which there +is no difference (that is, no dissimilarity), except in quantity +alone: for instance, a gallon of water, and more than a +gallon of water. A gallon of water, like any other external +object, makes its presence known to us by a set of sensations +which it excites. Ten gallons of water are also an external +object, making its presence known to us in a similar manner; +and as we do not mistake ten gallons of water for a gallon +of water, it is plain that the set of sensations is more or less +different in the two cases. In like manner, a gallon of water, +and a gallon of wine, are two external objects, making their +presence known by two sets of sensations, which sensations +are different from each other. In the first case, however, we +say that the difference is in quantity; in the last there is a +difference in quality, while the quantity of the water and of +the wine is the same. What is the real distinction between +the two cases? It is not the province of Logic to analyse +it; nor to decide whether it is susceptible of analysis or not. +For us the following considerations are sufficient. It is +evident that the sensations I receive from the gallon of +water, and those I receive from the gallon of wine, are not +the same, that is, not precisely alike; neither are they altogether +unlike: they are partly similar, partly dissimilar; +and that in which they resemble is precisely that in which +alone the gallon of water and the ten gallons do not resemble. +That in which the gallon of water and the gallon of wine are +like each other, and in which the gallon and the ten gallons +of water are unlike each other, is called their quantity. This +likeness and unlikeness I do not pretend to explain, no more +than any other kind of likeness or unlikeness. But my object +is to show, that when we say of two things that they differ +in quantity, just as when we say that they differ in quality, +the assertion is always grounded on a difference in the sensations +which they excite. Nobody, I presume, will say, +that to see, or to lift, or to drink, ten gallons of water, does +not include in itself a different set of sensations from those +<span class="tei tei-pb" id="page079">[pg 079]</span><a name="Pg079" id="Pg079" class="tei tei-anchor"></a> +of seeing, lifting, or drinking one gallon; or that to see or +handle a foot rule, and to see or handle a yard-measure +made exactly like it, are the same sensations. I do not +undertake to say what the difference in the sensations is. +Everybody knows, and nobody can tell; no more than any +one could tell what white is, to a person who had never had +the sensation. But the difference, so far as cognizable by +our faculties, lies in the sensations. Whatever difference we +say there is in the things themselves, is, in this as in all other +cases, grounded, and grounded exclusively, on a difference +in the sensations excited by them. +</p> + +</div> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc25" id="toc25"></a> +<a name="pdf26" id="pdf26"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">VI. Attributes Concluded.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 13. Thus, then, all the attributes of bodies which are +classed under Quality or Quantity, are grounded on the +sensations which we receive from those bodies, and may be +defined, the powers which the bodies have of exciting those +sensations. And the same general explanation has been +found to apply to most of the attributes usually classed +under the head of Relation. They, too, are grounded on +some fact or phenomenon into which the related objects +enter as parts; that fact or phenomenon having no meaning +and no existence to us, except the series of sensations or +other states of consciousness by which it makes itself +known: and the relation being simply the power or capacity +which the object possesses, of taking part along with +the correlated object in the production of that series of +sensations or states of consciousness. We have been obliged, +indeed, to recognise a somewhat different character in certain +peculiar relations, those of succession and simultaneity, of +likeness and unlikeness. These, not being grounded on any +fact or phenomenon distinct from the related objects themselves, +do not admit of the same kind of analysis. But these +relations, though not, like other relations, grounded on states +of consciousness, are themselves states of consciousness: +resemblance is nothing but our feeling of resemblance; succession +is nothing but our feeling of succession. Or, if this +<span class="tei tei-pb" id="page080">[pg 080]</span><a name="Pg080" id="Pg080" class="tei tei-anchor"></a> +be disputed, (and we cannot, without transgressing the +bounds of our science, discuss it here,) at least our knowledge +of these relations, and even our possibility of knowledge, +is confined to those which subsist between sensations, +or other states of consciousness; for, though we ascribe +resemblance, or succession, or simultaneity, to objects +and to attributes, it is always in virtue of resemblance or +succession or simultaneity in the sensations or states of +consciousness which those objects excite, and on which those +attributes are grounded. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 14. In the preceding investigation we have, for the +sake of simplicity, considered bodies only, and omitted +minds. But what we have said, is applicable, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">mutatis mutandis</span></span>, +to the latter. The attributes of minds, as well as +those of bodies, are grounded on states of feeling or consciousness. +But in the case of a mind, we have to consider +its own states, as well as those which it produces in other +minds. Every attribute of a mind consists either in being +itself affected in a certain way, or affecting other minds in a +certain way. Considered in itself, we can predicate nothing +of it but the series of its own feelings. When we say of any +mind, that it is devout, or superstitious, or meditative, or +cheerful, we mean that the ideas, emotions, or volitions +implied in those words, form a frequently recurring part of +the series of feelings, or states of consciousness, which fill +up the sentient existence of that mind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In addition, however, to those attributes of a mind which +are grounded on its own states of feeling, attributes may also +be ascribed to it, in the same manner as to a body, grounded +on the feelings which it excites in other minds. A mind +does not, indeed, like a body, excite sensations, but it may +excite thoughts or emotions. The most important example +of attributes ascribed on this ground, is the employment of +terms expressive of approbation or blame. When, for example, +we say of any character, or (in other words) of any +mind, that it is admirable, we mean that the contemplation +<span class="tei tei-pb" id="page081">[pg 081]</span><a name="Pg081" id="Pg081" class="tei tei-anchor"></a> +of it excites the sentiment of admiration; and indeed somewhat +more, for the word implies that we not only feel +admiration, but approve that sentiment in ourselves. In +some cases, under the semblance of a single attribute, two +are really predicated: one of them, a state of the mind itself; +the other, a state with which other minds are affected by +thinking of it. As when we say of any one that he is +generous. The word generosity expresses a certain state of +mind, but being a term of praise, it also expresses that this +state of mind excites in us another mental state, called +approbation. The assertion made, therefore, is twofold, and +of the following purport: Certain feelings form habitually a +part of this person's sentient existence; and the idea of those +feelings of his, excites the sentiment of approbation in ourselves +or others. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As we thus ascribe attributes to minds on the ground of +ideas and emotions, so may we to bodies on similar grounds, +and not solely on the ground of sensations: as in speaking +of the beauty of a statue; since this attribute is grounded on +the peculiar feeling of pleasure which the statue produces in +our minds; which is not a sensation, but an emotion. +</p> + +</div> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<a name="toc27" id="toc27"></a> +<a name="pdf28" id="pdf28"></a> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">VII. General Results.</span></h3> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 15. Our survey of the varieties of Things which have +been, or which are capable of being, named—which have +been, or are capable of being, either predicated of other +Things, or made themselves the subject of predications—is +now concluded. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Our enumeration commenced with Feelings. These we +scrupulously distinguished from the objects which excite +them, and from the organs by which they are, or may be +supposed to be, conveyed. Feelings are of four sorts: +Sensations, Thoughts, Emotions, and Volitions. What are +called perceptions are merely a particular case of Belief, +and belief is a kind of thought. Actions are merely volitions +followed by an effect. If there be any other kind of mental +<span class="tei tei-pb" id="page082">[pg 082]</span><a name="Pg082" id="Pg082" class="tei tei-anchor"></a> +state not included under these subdivisions, we did not think +it necessary or proper in this place to discuss its existence, +or the rank which ought to be assigned to it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After Feelings we proceeded to Substances. These are +either Bodies or Minds. Without entering into the grounds +of the metaphysical doubts which have been raised concerning +the existence of Matter and Mind as objective realities, +we stated as sufficient for us the conclusion in which the +best thinkers are now very generally agreed, that all we can +know of Matter is the sensations which it gives us, and the +order of occurrence of those sensations; and that while the +substance Body is the unknown cause of our sensations, the +substance Mind is the unknown recipient. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The only remaining class of Nameable Things is Attributes; +and these are of three kinds, Quality, Relation, and +Quantity. Qualities, like substances, are known to us no +otherwise than by the sensations or other states of consciousness +which they excite: and while, in compliance with +common usage, we have continued to speak of them as a +distinct class of Things, we showed that in predicating them +no one means to predicate anything but those sensations or +states of consciousness, on which they may be said to be +grounded, and by which alone they can be defined or described. +Relations, except the simple cases of likeness and unlikeness, +succession and simultaneity, are similarly grounded on some +fact or phenomenon, that is, on some series of sensations or +states of consciousness, more or less complicated. The third +species of attribute, Quantity, is also manifestly grounded on +something in our sensations or states of feeling, since there +is an indubitable difference in the sensations excited by a +larger and a smaller bulk, or by a greater or a less degree +of intensity, in any object of sense or of consciousness. All +attributes, therefore, are to us nothing but either our sensations +and other states of feeling, or something inextricably +involved therein; and to this even the peculiar and simple +relations just adverted to are not exceptions. Those peculiar +relations, however, are so important, and, even if they +might in strictness be classed among states of consciousness, +<span class="tei tei-pb" id="page083">[pg 083]</span><a name="Pg083" id="Pg083" class="tei tei-anchor"></a> +are so fundamentally distinct from any other of those states, +that it would be a vain subtlety to confound them under that +common head, and it is necessary that they should be classed +apart. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As the result, therefore, of our analysis, we obtain the +following as an enumeration and classification of all Nameable +Things:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +1st. Feelings, or States of Consciousness. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +2nd. The Minds which experience those feelings. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +3rd. The Bodies, or external objects, which excite certain +of those feelings, together with the powers or properties +whereby they excite them; these being included rather +in compliance with common opinion, and because their existence +is taken for granted in the common language from +which I cannot prudently deviate, than because the recognition +of such powers or properties as real existences +appears to me warranted by a sound philosophy. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +4th, and last. The Successions and Co-existences, the +Likenesses and Unlikenesses, between feelings or states of +consciousness. Those relations, when considered as subsisting +between other things, exist in reality only between +the states of consciousness which those things, if bodies, excite, +if minds, either excite or experience. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, until a better can be suggested, may serve as +a substitute for the abortive Classification of Existences, +termed the Categories of Aristotle. The practical application +of it will appear when we commence the inquiry into +the Import of Propositions; in other words, when we inquire +what it is which the mind actually believes, when it gives +what is called its assent to a proposition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These four classes comprising, if the classification be +correct, all Nameable Things, these or some of them must +of course compose the signification of all names; and of +these, or some of them, is made up whatever we call a fact. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For distinction's sake, every fact which is solely composed +of feelings or states of consciousness considered as +such, is often called a Psychological or Subjective fact; +while every fact which is composed, either wholly or in part, +<span class="tei tei-pb" id="page084">[pg 084]</span><a name="Pg084" id="Pg084" class="tei tei-anchor"></a> +of something different from these, that is, of substances and +attributes, is called an Objective fact. We may say, then, +that every objective fact is grounded on a corresponding +subjective one; and has no meaning to us, (apart from the +subjective fact which corresponds to it,) except as a name +for the unknown and inscrutable process by which that subjective +or psychological fact is brought to pass. +</p> + +</div> + +</div> + +<span class="tei tei-pb" id="page085">[pg 085]</span><a name="Pg085" id="Pg085" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc29" id="toc29"></a> +<a name="pdf30" id="pdf30"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER IV. OF PROPOSITIONS.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In treating of Propositions, as already in treating of +Names, some considerations of a comparatively elementary +nature respecting their form and varieties must be premised, +before entering upon that analysis of the import conveyed +by them, which is the real subject and purpose of this preliminary +book. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A proposition, we have before said, is a portion of discourse +in which a predicate is affirmed or denied of a +subject. A predicate and a subject are all that is necessarily +required to make up a proposition: but as we cannot conclude +from merely seeing two names put together, that they +are a predicate and a subject, that is, that one of them is +intended to be affirmed or denied of the other, it is necessary +that there should be some mode or form of indicating that +such is the intention; some sign to distinguish a predication +from any other kind of discourse. This is sometimes done +by a slight alteration of one of the words, called an <span class="tei tei-hi"><span style="font-style: italic">inflection</span></span>; +as when we say, Fire burns; the change of the second word +from <span class="tei tei-hi"><span style="font-style: italic">burn</span></span> to <span class="tei tei-hi"><span style="font-style: italic">burns</span></span> showing that we mean to +affirm the predicate burn of the subject fire. But this function is more +commonly fulfilled by the word <span class="tei tei-hi"><span style="font-style: italic">is</span></span>, when an affirmation is +intended, <span class="tei tei-hi"><span style="font-style: italic">is not</span></span>, when a negation; or by some other part of +the verb <span class="tei tei-hi"><span style="font-style: italic">to be</span></span>. The word which thus serves the purpose of +a sign of predication is called, as we formerly observed, +the <span class="tei tei-hi"><span style="font-style: italic">copula</span></span>. It is important that there should be no +indistinctness in our conception of the nature and office +of the copula; for confused notions respecting it are among +the causes which have spread mysticism over the field of +logic, and perverted its speculations into logomachies. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is apt to be supposed that the copula is something more +<span class="tei tei-pb" id="page086">[pg 086]</span><a name="Pg086" id="Pg086" class="tei tei-anchor"></a> +than a mere sign of predication; that it also signifies +<em class="tei tei-emph"><span style="font-style: italic">existence</span></em>. In the proposition, Socrates is just, it may seem +to be implied not only that the quality <em class="tei tei-emph"><span style="font-style: italic">just</span></em> can be affirmed +of Socrates, but moreover that Socrates <em class="tei tei-emph"><span style="font-style: italic">is</span></em>, that is to say, +exists. This, however, only shows that there is an ambiguity +in the word <span class="tei tei-hi"><span style="font-style: italic">is</span></span>; a word which not only performs the function +of the copula in affirmations, but has also a meaning of its +own, in virtue of which it may itself be made the predicate +of a proposition. That the employment of it as a copula +does not necessarily include the affirmation of existence, +appears from such a proposition as this, A centaur is a fiction +of the poets; where it cannot possibly be implied that a +centaur exists, since the proposition itself expressly asserts +that the thing has no real existence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Many volumes might be filled with the frivolous speculations +concerning the nature of Being, (το ὄν, οὐσία, Ens, +Entitas, Essentia, and the like,) which have arisen from +overlooking this double meaning of the words <span class="tei tei-hi"><span style="font-style: italic">to be</span></span>; from +supposing that when it signifies <span class="tei tei-hi"><span style="font-style: italic">to exist</span></span>, and when it signifies +to <span class="tei tei-hi"><span style="font-style: italic">be</span></span> some specified thing, as to <em class="tei tei-emph"><span style="font-style: italic">be</span></em> a man, to +<em class="tei tei-emph"><span style="font-style: italic">be</span></em> Socrates, to <em class="tei tei-emph"><span style="font-style: italic">be</span></em> seen or spoken of, to <em class="tei tei-emph"><span style="font-style: italic">be</span></em> +a phantom, even to <em class="tei tei-emph"><span style="font-style: italic">be</span></em> a non-entity, +it must still, at bottom, answer to the same idea; and +that a meaning must be found for it which shall suit all these +cases. The fog which rose from this narrow spot diffused +itself at an early period over the whole surface of metaphysics. +Yet it becomes us not to triumph over the great +intellects of Plato and Aristotle because we are now able to +preserve ourselves from many errors into which they, perhaps +inevitably, fell. The fire-teazer of a modern steam-engine +produces by his exertions far greater effects than Milo of +Crotona could, but he is not therefore a stronger man. The +Greeks seldom knew any language but their own. This +rendered it far more difficult for them than it is for us, to +acquire a readiness in detecting ambiguities. One of the +advantages of having accurately studied a plurality of +languages, especially of those languages which eminent +thinkers have used as the vehicle of their thoughts, is the +practical lesson we learn respecting the ambiguities of words, +<span class="tei tei-pb" id="page087">[pg 087]</span><a name="Pg087" id="Pg087" class="tei tei-anchor"></a> +by finding that the same word in one language corresponds, +on different occasions, to different words in another. When +not thus exercised, even the strongest understandings find it +difficult to believe that things which have a common name, +have not in some respect or other a common nature; and +often expend much labour not only unprofitably but mischievously, +(as was frequently done by the two philosophers +just mentioned,) on vain attempts to discover in what this +common nature consists. But, the habit once formed, intellects +much inferior are capable of detecting even ambiguities +which are common to many languages: and it is surprising +that the one now under consideration, though it exists in +the modern languages as well as in the ancient, should have +been overlooked by almost all authors. The quantity of +futile speculation which had been caused by a misapprehension +of the nature of the copula, was hinted at by Hobbes; +but Mr. Mill<a id="noteref_15" name="noteref_15" href="#note_15"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">15</span></span></a> was, I believe, the first who distinctly characterized +the ambiguity, and pointed out how many errors in +the received systems of philosophy it has had to answer for. +It has indeed misled the moderns scarcely less than the +ancients, though their mistakes, because our understandings +are not yet so completely emancipated from their influence, +do not appear equally irrational. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We shall now briefly review the principal distinctions +which exist among propositions, and the technical terms +most commonly in use to express those distinctions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. A proposition being a portion of discourse in which +something is affirmed or denied of something, the first division +of propositions is into affirmative and negative. An +affirmative proposition is that in which the predicate is +<em class="tei tei-emph"><span style="font-style: italic">affirmed</span></em> of the subject; as, Cæsar is dead. A negative proposition +is that in which the predicate is <em class="tei tei-emph"><span style="font-style: italic">denied</span></em> of the subject; +as, Cæsar is not dead. The copula, in this last species of +proposition, consists of the words <span class="tei tei-hi"><span style="font-style: italic">is not</span></span>, which are the sign +of negation; <span class="tei tei-hi"><span style="font-style: italic">is</span></span> being the sign of affirmation. +</p> + +<span class="tei tei-pb" id="page088">[pg 088]</span><a name="Pg088" id="Pg088" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Some logicians, among whom may be mentioned Hobbes, +state this distinction differently; they recognise only one +form of copula, <span class="tei tei-hi"><span style="font-style: italic">is</span></span>, and attach the negative sign to the predicate. +<span class="tei tei-q">“Cæsar is dead,”</span> and <span class="tei tei-q">“Cæsar is not dead,”</span> according +to these writers, are propositions agreeing not in the subject +and predicate, but in the subject only. They do not consider +<span class="tei tei-q">“dead,”</span> but <span class="tei tei-q">“not dead,”</span> to be the predicate of the second +proposition, and they accordingly define a negative proposition +to be one in which the predicate is a negative name. +The point, though not of much practical moment, deserves +notice as an example (not unfrequent in logic) where by +means of an apparent simplification, but which is merely +verbal, matters are made more complex than before. The +notion of these writers was, that they could get rid of the distinction +between affirming and denying, by treating every +case of denying as the affirming of a negative name. But +what is meant by a negative name? A name expressive of +the <em class="tei tei-emph"><span style="font-style: italic">absence</span></em> of an attribute. So that when we affirm a negative +name, what we are really predicating is absence and not +presence; we are asserting not that anything <em class="tei tei-emph"><span style="font-style: italic">is</span></em>, but that +something is <em class="tei tei-emph"><span style="font-style: italic">not</span></em>; to express which operation no word seems +so proper as the word denying. The fundamental distinction +is between a fact and the non-existence of that fact; +between seeing something and not seeing it, between Cæsar's +being dead and his not being dead; and if this were a merely +verbal distinction, the generalization which brings both +within the same form of assertion would be a real simplification: +the distinction, however, being real, and in the facts, +it is the generalization confounding the distinction that is +merely verbal; and tends to obscure the subject, by treating +the difference between two kinds of truth as if it were only +a difference between two kinds of words. To put things +together, and to put them or keep them asunder, will +remain different operations, whatever tricks we may play +with language. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A remark of a similar nature may be applied to most of +those distinctions among propositions which are said to have +reference to their <em class="tei tei-emph"><span style="font-style: italic">modality</span></em>; as, difference of tense or time; +<span class="tei tei-pb" id="page089">[pg 089]</span><a name="Pg089" id="Pg089" class="tei tei-anchor"></a> +the sun <em class="tei tei-emph"><span style="font-style: italic">did</span></em> rise, the sun <em class="tei tei-emph"><span style="font-style: italic">is</span></em> rising, the sun <em class="tei tei-emph"><span style="font-style: italic">will</span></em> +rise. These differences, like that between affirmation and negation, might +be glossed over by considering the incident of time as a mere +modification of the predicate: thus, The sun is <em class="tei tei-emph"><span style="font-style: italic">an object +having risen</span></em>, The sun is <em class="tei tei-emph"><span style="font-style: italic">an object now rising</span></em>, The sun is +<em class="tei tei-emph"><span style="font-style: italic">an object to rise hereafter</span></em>. But the simplification would be merely +verbal. Past, present, and future, do not constitute so many +different kinds of rising; they are the designations belonging +to the event asserted, to the <em class="tei tei-emph"><span style="font-style: italic">sun's</span></em> rising to-day. They affect, +not the predicate, but the applicability of the predicate to the +particular subject. That which we affirm to be past, present, +or future, is not what the subject signifies, nor what the predicate +signifies, but specifically and expressly what the predication +signifies; what is expressed only by the proposition +as such, and not by either or both of the terms. Therefore +the circumstance of time is properly considered as attaching +to the copula, which is the sign of predication, and not to the +predicate. If the same cannot be said of such modifications +as these, Cæsar <em class="tei tei-emph"><span style="font-style: italic">may</span></em> be dead; Cæsar is <em class="tei tei-emph"><span style="font-style: italic">perhaps</span></em> dead; it is +<em class="tei tei-emph"><span style="font-style: italic">possible</span></em> that Cæsar is dead; it is only because these fall altogether +under another head, being properly assertions not of +anything relating to the fact itself, but of the state of our own +mind in regard to it; namely, our absence of disbelief of it. +Thus <span class="tei tei-q">“Cæsar may be dead”</span> means <span class="tei tei-q">“I am not sure that +Cæsar is alive.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The next division of propositions is into Simple +and Complex. A simple proposition is that in which one +predicate is affirmed or denied of one subject. A complex +proposition is that in which there is more than one predicate, +or more than one subject, or both. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +At first sight this division has the air of an absurdity; a +solemn distinction of things into one and more than one; as +if we were to divide horses into single horses and teams of +horses. And it is true that what is called a complex proposition +is often not a proposition at all, but several propositions, +held together by a conjunction. Such, for example, is +this: Cæsar is dead, and Brutus is alive: or even this, Cæsar +<span class="tei tei-pb" id="page090">[pg 090]</span><a name="Pg090" id="Pg090" class="tei tei-anchor"></a> +is dead, <em class="tei tei-emph"><span style="font-style: italic">but</span></em> Brutus is alive. There are here two distinct +assertions; and we might as well call a street a complex +house, as these two propositions a complex proposition. It +is true that the syncategorematic words <span class="tei tei-hi"><span style="font-style: italic">and</span></span> and +<span class="tei tei-hi"><span style="font-style: italic">but</span></span> have a meaning; but that meaning is so far from making the two +propositions one, that it adds a third proposition to them. +All particles are abbreviations, and generally abbreviations +of propositions; a kind of short-hand, whereby that which, +to be expressed fully, would have required a proposition or +a series of propositions, is suggested to the mind at once. +Thus the words, Cæsar is dead and Brutus is alive, are +equivalent to these: Cæsar is dead; Brutus is alive; it is +desired that the two preceding propositions should be thought +of together. If the words were, Cæsar is dead <em class="tei tei-emph"><span style="font-style: italic">but</span></em> Brutus is +alive, the sense would be equivalent to the same three propositions +together with a fourth; <span class="tei tei-q">“between the two preceding +propositions there exists a contrast:”</span> viz., either between the +two facts themselves, or between the feelings with which it is +desired that they should be regarded. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the instances cited, the two propositions are kept +visibly distinct, each subject having its separate predicate, +and each predicate its separate subject. For brevity, however, +and to avoid repetition, the propositions are often +blended together: as in this, <span class="tei tei-q">“Peter and James preached at +Jerusalem and in Galilee,”</span> which contains four propositions: +Peter preached at Jerusalem, Peter preached in Galilee, +James preached at Jerusalem, James preached in Galilee. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We have seen that when the two or more propositions +comprised in what is called a complex proposition, are stated +absolutely, and not under any condition or proviso, it is not +a proposition at all, but a plurality of propositions; since +what it expresses is not a single assertion, but several assertions, +which, if true when joined, are true also when separated. +But there is a kind of proposition which, though it contains +a plurality of subjects and of predicates, and may be said in +one sense of the word to consist of several propositions, contains +but one assertion; and its truth does not at all imply +that of the simple propositions which compose it. An +<span class="tei tei-pb" id="page091">[pg 091]</span><a name="Pg091" id="Pg091" class="tei tei-anchor"></a> +example of this is, when the simple propositions are connected +by the particle <span class="tei tei-hi"><span style="font-style: italic">or</span></span>; as, Either A is B <em class="tei tei-emph"><span style="font-style: italic">or</span></em> C is D; or +by the particle <span class="tei tei-hi"><span style="font-style: italic">if</span></span>; as, A is B <em class="tei tei-emph"><span style="font-style: italic">if</span></em> C is D. In the +former case, the proposition is called <span class="tei tei-hi"><span style="font-style: italic">disjunctive</span></span>, in the +latter <span class="tei tei-hi"><span style="font-style: italic">conditional</span></span>: the +name <span class="tei tei-hi"><span style="font-style: italic">hypothetical</span></span> was originally common to both. As has +been well remarked by Archbishop Whately and others, the +disjunctive form is resolvable into the conditional; every +disjunctive proposition being equivalent to two or more conditional +ones. <span class="tei tei-q">“Either A is B or C is D,”</span> means, <span class="tei tei-q">“if A is +not B, C is D; and if C is not D, A is B.”</span> All hypothetical +propositions, therefore, though disjunctive in form, are +conditional in meaning; and the words hypothetical and +conditional may be, as indeed they generally are, used +synonymously. Propositions in which the assertion is not +dependent on a condition, are said, in the language of logicians, +to be <span class="tei tei-hi"><span style="font-style: italic">categorical</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An hypothetical proposition is not, like the pretended +complex propositions which we previously considered, a +mere aggregation of simple propositions. The simple propositions +which form part of the words in which it is couched, +form no part of the assertion which it conveys. When we +say, If the Koran comes from God, Mahomet is the prophet +of God, we do not intend to affirm either that the Koran +does come from God, or that Mahomet is really his prophet. +Neither of these simple propositions may be true, and yet +the truth of the hypothetical proposition may be indisputable. +What is asserted is not the truth of either of the propositions, +but the inferribility of the one from the other. What, +then, is the subject, and what the predicate, of the hypothetical +proposition? <span class="tei tei-q">“The Koran”</span> is not the subject of it, nor +is <span class="tei tei-q">“Mahomet:”</span> for nothing is affirmed or denied either of +the Koran or of Mahomet. The real subject of the predication +is the entire proposition, <span class="tei tei-q">“Mahomet is the prophet of +God;”</span> and the affirmation is, that this is a legitimate inference +from the proposition, <span class="tei tei-q">“The Koran comes from God.”</span> +The subject and predicate, therefore, of an hypothetical proposition +are names of propositions. The subject is some one +proposition. The predicate is a general relative name applicable +<span class="tei tei-pb" id="page092">[pg 092]</span><a name="Pg092" id="Pg092" class="tei tei-anchor"></a> +to propositions; of this form—<span class="tei tei-q">“an inference from so +and so.”</span> A fresh instance is here afforded of the remark, +that all particles are abbreviations; since <span class="tei tei-q">“<em class="tei tei-emph"><span style="font-style: italic">If</span></em> A is B, C is +D,”</span> is found to be an abbreviation of the following: <span class="tei tei-q">“The +proposition C is D, is a legitimate inference from the proposition +A is B.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The distinction, therefore, between hypothetical and categorical +propositions, is not so great as it at first appears. In +the conditional, as well as in the categorical form, one predicate +is affirmed of one subject, and no more: but a conditional +proposition is a proposition concerning a proposition; the +subject of the assertion is itself an assertion. Nor is this a +property peculiar to hypothetical propositions. There are +other classes of assertions concerning propositions. Like +other things, a proposition has attributes which may be predicated +of it. The attribute predicated of it in an hypothetical +proposition, is that of being an inference from a certain other +proposition. But this is only one of many attributes that +might be predicated. We may say, That the whole is greater +than its part, is an axiom in mathematics: That the Holy +Ghost proceeds from the Father alone, is a tenet of the +Greek Church: The doctrine of the divine right of kings was +renounced by Parliament at the Revolution: The infallibility +of the Pope has no countenance from Scripture. In all +these cases the subject of the predication is an entire proposition. +That which these different predicates are affirmed +of, is <em class="tei tei-emph"><span style="font-style: italic">the proposition</span></em>, <span class="tei tei-q">“the whole is greater than its part;”</span> +<em class="tei tei-emph"><span style="font-style: italic">the proposition</span></em>, <span class="tei tei-q">“the Holy Ghost proceeds from the Father +alone;”</span> <em class="tei tei-emph"><span style="font-style: italic">the proposition</span></em>, <span class="tei tei-q">“kings have a divine right;”</span> <em class="tei tei-emph"><span style="font-style: italic">the +proposition</span></em>, <span class="tei tei-q">“the Pope is infallible.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Seeing, then, that there is much less difference between +hypothetical propositions and any others, than one might be +led to imagine from their form, we should be at a loss to +account for the conspicuous position which they have been +selected to fill in treatises on Logic, if we did not remember +that what they predicate of a proposition, namely, its being +an inference from something else, is precisely that one of its +attributes with which most of all a logician is concerned. +</p> + +<span class="tei tei-pb" id="page093">[pg 093]</span><a name="Pg093" id="Pg093" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. The next of the common divisions of Propositions +is into Universal, Particular, Indefinite, and Singular: a distinction +founded on the degree of generality in which the +name, which is the subject of the proposition, is to be understood. +The following are examples: +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="2"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell"><em class="tei tei-emph"><span style="font-style: italic">All men</span></em> are mortal—</td><td class="tei tei-cell">Universal.</td></tr><tr class="tei tei-row"><td class="tei tei-cell"><em class="tei tei-emph"><span style="font-style: italic">Some men</span></em> are mortal—</td><td class="tei tei-cell">Particular.</td></tr><tr class="tei tei-row"><td class="tei tei-cell"><em class="tei tei-emph"><span style="font-style: italic">Man</span></em> is mortal—</td><td class="tei tei-cell">Indefinite.</td></tr><tr class="tei tei-row"><td class="tei tei-cell"><em class="tei tei-emph"><span style="font-style: italic">Julius Cæsar</span></em> is mortal—</td><td class="tei tei-cell">Singular.</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The proposition is Singular, when the subject is an +individual name. The individual name needs not be a +proper name. <span class="tei tei-q">“The Founder of Christianity was crucified,”</span> +is as much a singular proposition as <span class="tei tei-q">“Christ was +crucified.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When the name which is the subject of the proposition +is a general name, we may intend to affirm or deny the predicate, +either of <em class="tei tei-emph"><span style="font-style: italic">all</span></em> the things that the subject denotes, or +only of some. When the predicate is affirmed or denied of +all and each of the things denoted by the subject, the proposition +is universal; when of some non-assignable portion of +them only, it is particular. Thus, All men are mortal; +Every man is mortal; are universal propositions. No man +is immortal, is also an universal proposition, since the predicate, +immortal, is denied of each and every individual +denoted by the term man; the negative proposition being +exactly equivalent to the following, Every man is not-immortal. +But <span class="tei tei-q">“some men are wise,”</span> <span class="tei tei-q">“some men are not wise,”</span> +are particular propositions; the predicate <em class="tei tei-emph"><span style="font-style: italic">wise</span></em> being in the +one case affirmed and in the other denied not of each and +every individual denoted by the term man, but only of each +and every one of some portion of those individuals, without +specifying what portion; for if this were specified, the proposition +would be changed either into a singular proposition, +or into an universal proposition with a different subject; as, +for instance, <span class="tei tei-q">“all <em class="tei tei-emph"><span style="font-style: italic">properly instructed</span></em> men are wise.”</span> There +are other forms of particular propositions: as, <span class="tei tei-q">“<em class="tei tei-emph"><span style="font-style: italic">Most</span></em> men +are imperfectly educated:”</span> it being immaterial how large +a portion of the subject the predicate is asserted of, as long +<span class="tei tei-pb" id="page094">[pg 094]</span><a name="Pg094" id="Pg094" class="tei tei-anchor"></a> +as it is left uncertain how that portion is to be distinguished +from the rest. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When the form of the expression does not clearly show +whether the general name which is the subject of the proposition +is meant to stand for all the individuals denoted by it, +or only for some of them, the proposition is commonly called +Indefinite; but this, as Archbishop Whately observes, is a +solecism, of the same nature as that committed by some grammarians +when in their list of genders they enumerate the +<em class="tei tei-emph"><span style="font-style: italic">doubtful</span></em> gender. The speaker must mean to assert the proposition +either as an universal or as a particular proposition, +though he has failed to declare which: and it often happens +that though the words do not show which of the two he intends, +the context, or the custom of speech, supplies the +deficiency. Thus, when it is affirmed that <span class="tei tei-q">“Man is mortal,”</span> +nobody doubts that the assertion is intended of all human +beings, and the word indicative of universality is commonly +omitted, only because the meaning is evident without it. In +the proposition, <span class="tei tei-q">“Wine is good,”</span> it is understood with equal +readiness, though for somewhat different reasons, that the +assertion is not intended to be universal, but particular. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When a general name stands for each and every individual +which it is a name of, or in other words, which it denotes, +it is said by logicians to be <span class="tei tei-hi"><span style="font-style: italic">distributed</span></span>, or taken +distributively. Thus, in the proposition, All men are mortal, the subject, +Man, is distributed, because mortality is affirmed of each +and every man. The predicate, Mortal, is not distributed, +because the only mortals who are spoken of in the proposition +are those who happen to be men; while the word may, +for aught that appears, (and in fact does,) comprehend within +it an indefinite number of objects besides men. In the proposition, +Some men are mortal, both the predicate and the subject +are undistributed. In the following, No men have wings, +both the predicate and the subject are distributed. Not only +is the attribute of having wings denied of the entire class +Man, but that class is severed and cast out from the whole +of the class Winged, and not merely from some part of that +class. +</p> + +<span class="tei tei-pb" id="page095">[pg 095]</span><a name="Pg095" id="Pg095" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This phraseology, which is of great service in stating and +demonstrating the rules of the syllogism, enables us to express +very concisely the definitions of an universal and a particular +proposition. An universal proposition is that of which the +subject is distributed; a particular proposition is that of +which the subject is undistributed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are many more distinctions among propositions +than those we have here stated, some of them of considerable +importance. But, for explaining and illustrating these, more +suitable opportunities will occur in the sequel. +</p> + +</div> + +<span class="tei tei-pb" id="page096">[pg 096]</span><a name="Pg096" id="Pg096" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc31" id="toc31"></a> +<a name="pdf32" id="pdf32"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER V. OF THE IMPORT OF PROPOSITIONS.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. An inquiry into the nature of propositions must +have one of two objects: to analyse the state of mind called +Belief, or to analyse what is believed. All language recognises +a difference between a doctrine or opinion, and the +act of entertaining the opinion; between assent, and what is +assented to. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Logic, according to the conception here formed of it, has +no concern with the nature of the act of judging or believing; +the consideration of that act, as a phenomenon of the mind, +belongs to another science. Philosophers, however, from +Descartes downwards, and especially from the era of Leibnitz +and Locke, have by no means observed this distinction; +and would have treated with great disrespect any attempt to +analyse the import of Propositions, unless founded on an +analysis of the act of Judgment. A proposition, they would +have said, is but the expression in words of a Judgment. +The thing expressed, not the mere verbal expression, is the +important matter. When the mind assents to a proposition, +it judges. Let us find out what the mind does when it +judges, and we shall know what propositions mean, and not +otherwise. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Conformably to these views, almost all the writers on +Logic in the last two centuries, whether English, German, or +French, have made their theory of Propositions, from one end +to the other, a theory of Judgments. They considered a +Proposition, or a Judgment, for they used the two words indiscriminately, +to consist in affirming or denying one <em class="tei tei-emph"><span style="font-style: italic">idea</span></em> of +another. To judge, was to put two ideas together, or to +bring one idea under another, or to compare two ideas, or to +perceive the agreement or disagreement between two ideas: +and the whole doctrine of Propositions, together with the +<span class="tei tei-pb" id="page097">[pg 097]</span><a name="Pg097" id="Pg097" class="tei tei-anchor"></a> +theory of Reasoning, (always necessarily founded on the +theory of Propositions,) was stated as if Ideas, or Conceptions, +or whatever other term the writer preferred as a name +for mental representations generally, constituted essentially +the subject matter and substance of those operations. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is, of course, true, that in any case of judgment, as +for instance when we judge that gold is yellow, a process +takes place in our minds, of which some one or other of +these theories is a partially correct account. We must have +the idea of gold and the idea of yellow, and these two ideas +must be brought together in our mind. But in the first +place, it is evident that this is only a part of what takes +place; for we may put two ideas together without any act +of belief; as when we merely imagine something, such as a +golden mountain; or when we actually disbelieve: for in +order even to disbelieve that Mahomet was an apostle of +God, we must put the idea of Mahomet and that of an apostle +of God together. To determine what it is that happens in +the case of assent or dissent besides putting two ideas +together, is one of the most intricate of metaphysical problems. +But whatever the solution may be, we may venture +to assert that it can have nothing whatever to do with the +import of propositions; for this reason, that propositions +(except where the mind itself is the subject treated of) are +not assertions respecting our ideas of things, but assertions +respecting the things themselves. In order to believe that +gold is yellow, I must, indeed, have the idea of gold, and the +idea of yellow, and something having reference to those ideas +must take place in my mind; but my belief has not reference +to the ideas, it has reference to the things. What I believe +is a fact relating to the outward thing, gold, and to the impression +made by that outward thing upon the human organs; +not a fact relating to my conception of gold, which would be +a fact in my mental history, not a fact of external nature. +It is true, that in order to believe this fact in external nature, +another fact must take place in my mind, a process must be +performed upon my ideas; but so it must in everything else +that I do. I cannot dig the ground unless I have the idea +<span class="tei tei-pb" id="page098">[pg 098]</span><a name="Pg098" id="Pg098" class="tei tei-anchor"></a> +of the ground, and of a spade, and of all the other things I +am operating upon, and unless I put those ideas together.<a id="noteref_16" name="noteref_16" href="#note_16"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">16</span></span></a> +But it would be a very ridiculous description of digging the +ground to say that it is putting one idea into another. Digging +is an operation which is performed upon the things +themselves, although it cannot be performed unless I have +in my mind the ideas of them. And so, in like manner, +believing is an act which has for its subject the facts themselves, +although a previous mental conception of the facts is +an indispensable condition. When I say that fire causes +heat, do I mean that my idea of fire causes my idea of heat? +No: I mean that the natural phenomenon, fire, causes the +natural phenomenon, heat. When I mean to assert anything +respecting the ideas, I give them their proper name, I +call them ideas: as when I say, that a child's idea of a +battle is unlike the reality, or that the ideas entertained of +the Deity have a great effect on the characters of mankind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The notion that what is of primary importance to the +logician in a proposition, is the relation between the two +<em class="tei tei-emph"><span style="font-style: italic">ideas</span></em> corresponding to the subject and predicate, (instead of +the relation between the two <em class="tei tei-emph"><span style="font-style: italic">phenomena</span></em> which they respectively +express,) seems to me one of the most fatal errors +ever introduced into the philosophy of Logic; and the principal +cause why the theory of the science has made such +inconsiderable progress during the last two centuries. The +treatises on Logic, and on the branches of Mental Philosophy +connected with Logic, which have been produced +since the intrusion of this cardinal error, though sometimes +written by men of extraordinary abilities and attainments, +almost always tacitly imply a theory that the investigation +of truth consists in contemplating and handling our ideas, +<span class="tei tei-pb" id="page099">[pg 099]</span><a name="Pg099" id="Pg099" class="tei tei-anchor"></a> +or conceptions of things, instead of the things themselves: a +doctrine tantamount to the assertion, that the only mode of +acquiring knowledge of nature is to study it at second hand, +as represented in our own minds. Meanwhile, inquiries into +every kind of natural phenomena were incessantly establishing +great and fruitful truths on the most important subjects, by +processes upon which these views of the nature of Judgment +and Reasoning threw no light, and in which they afforded no +assistance whatever. No wonder that those who knew by +practical experience how truths are come at, should deem a +science futile, which consisted chiefly of such speculations. +What has been done for the advancement of Logic since +these doctrines came into vogue, has been done not by professed +logicians, but by discoverers in the other sciences; in +whose methods of investigation many principles of logic, not +previously thought of, have successively come forth into +light, but who have generally committed the error of supposing +that nothing whatever was known of the art of philosophizing +by the old logicians, because their modern interpreters +have written to so little purpose respecting it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We have to inquire, then, on the present occasion, not +into Judgment, but judgments; not into the act of believing, +but into the thing believed. What is the immediate object +of belief in a Proposition? What is the matter of fact +signified by it? What is it to which, when I assert the +proposition, I give my assent, and call upon others to give +theirs? What is that which is expressed by the form of +discourse called a Proposition, and the conformity of which +to fact constitutes the truth of the proposition? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. One of the clearest and most consecutive thinkers +whom this country or the world has produced, I mean +Hobbes, has given the following answer to this question. +In every proposition (says he) what is signified is, the belief +of the speaker that the predicate is a name of the same +thing of which the subject is a name; and if it really is so, +the proposition is true. Thus the proposition, All men are +living beings (he would say) is true, because <em class="tei tei-emph"><span style="font-style: italic">living being</span></em> is +<span class="tei tei-pb" id="page100">[pg 100]</span><a name="Pg100" id="Pg100" class="tei tei-anchor"></a> +a name of everything of which <em class="tei tei-emph"><span style="font-style: italic">man</span></em> is a name. All men are +six feet high, is not true, because <em class="tei tei-emph"><span style="font-style: italic">six feet high</span></em> is not a name +of everything (though it is of some things) of which <em class="tei tei-emph"><span style="font-style: italic">man</span></em> is +a name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What is stated in this theory as the definition of a true +proposition, must be allowed to be a property which all true +propositions possess. The subject and predicate being both +of them names of things, if they were names of quite different +things the one name could not, consistently with its signification, +be predicated of the other. If it be true that some +men are copper-coloured, it must be true—and the proposition +does really assert—that among the individuals denoted +by the name man, there are some who are also among those +denoted by the name copper-coloured. If it be true that +all oxen ruminate, it must be true that all the individuals +denoted by the name ox are also among those denoted by +the name ruminating; and whoever asserts that all oxen +ruminate, undoubtedly does assert that this relation subsists +between the two names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The assertion, therefore, which, according to Hobbes, is +the only one made in any proposition, really is made in +every proposition: and his analysis has consequently one +of the requisites for being the true one. We may go a step +farther; it is the only analysis that is rigorously true of all +propositions without exception. What he gives as the meaning +of propositions, is part of the meaning of all propositions, +and the whole meaning of some. This, however, only shows +what an extremely minute fragment of meaning it is quite +possible to include within the logical formula of a proposition. +It does not show that no proposition means more. To +warrant us in putting together two words with a copula +between them, it is really enough that the thing or things +denoted by one of the names should be capable, without +violation of usage, of being called by the other name also. +If, then, this be all the meaning necessarily implied in the +form of discourse called a Proposition, why do I object to it +as the scientific definition of what a proposition means? +Because, though the mere collocation which makes the +<span class="tei tei-pb" id="page101">[pg 101]</span><a name="Pg101" id="Pg101" class="tei tei-anchor"></a> +proposition a proposition, conveys no more than this scanty +amount of meaning, that same collocation combined with +other circumstances, that <em class="tei tei-emph"><span style="font-style: italic">form</span></em> combined with other <em class="tei tei-emph"><span style="font-style: italic">matter</span></em>, +does convey more, and much more. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The only propositions of which Hobbes' principle is a +sufficient account, are that limited and unimportant class in +which both the predicate and the subject are proper names. +For, as has already been remarked, proper names have +strictly no meaning; they are mere marks for individual +objects: and when a proper name is predicated of another +proper name, all the signification conveyed is, that both the +names are marks for the same object. But this is precisely +what Hobbes produces as a theory of predication in general. +His doctrine is a full explanation of such predications as +these: Hyde was Clarendon, or, Tully is Cicero. It exhausts +the meaning of those propositions. But it is a sadly +inadequate theory of any others. That it should ever have +been thought of as such, can be accounted for only by the +fact, that Hobbes, in common with the other Nominalists, +bestowed little or no attention upon the <em class="tei tei-emph"><span style="font-style: italic">connotation</span></em> of words; +and sought for their meaning exclusively in what they <em class="tei tei-emph"><span style="font-style: italic">denote</span></em>: +as if all names had been (what none but proper names really +are) marks put upon individuals; and as if there were no +difference between a proper and a general name, except that +the first denotes only one individual, and the last a greater +number. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It has been seen, however, that the meaning of all names, +except proper names and that portion of the class of abstract +names which are not connotative, resides in the connotation. +When, therefore, we are analysing the meaning of any proposition +in which the predicate and the subject, or either of +them, are connotative names, it is to the connotation of those +terms that we must exclusively look, and not to what they +<em class="tei tei-emph"><span style="font-style: italic">denote</span></em>, or in the language of Hobbes, (language so far +correct,) are names of. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In asserting that the truth of a proposition depends on +the conformity of import between its terms, as, for instance, +that the proposition, Socrates is wise, is a true proposition, +<span class="tei tei-pb" id="page102">[pg 102]</span><a name="Pg102" id="Pg102" class="tei tei-anchor"></a> +because Socrates and wise are names applicable to, or, as +he expresses it, names of, the same person; it is very +remarkable that so powerful a thinker should not have asked +himself the question, But how came they to be names of the +same person? Surely not because such was the intention +of those who invented the words. When mankind fixed the +meaning of the word wise, they were not thinking of Socrates, +nor, when his parents gave him the name Socrates, were +they thinking of wisdom. The names <em class="tei tei-emph"><span style="font-style: italic">happen</span></em> to fit the same +person because of a certain <em class="tei tei-emph"><span style="font-style: italic">fact</span></em>, which fact was not known, +nor in being, when the names were invented. If we want to +know what the fact is, we shall find the clue to it in the +<em class="tei tei-emph"><span style="font-style: italic">connotation</span></em> of the names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A bird, or a stone, a man, or a wise man, means simply, +an object having such and such attributes. The real meaning +of the word man, is those attributes, and not John, Jane, +and the remainder of the individuals. The word <span class="tei tei-hi"><span style="font-style: italic">mortal</span></span>, in +like manner connotes a certain attribute or attributes; and +when we say, All men are mortal, the meaning of the +proposition is, that all beings which possess the one set of +attributes, possess also the other. If, in our experience, the +attributes connoted by <em class="tei tei-emph"><span style="font-style: italic">man</span></em> are always accompanied by the +attribute connoted by <em class="tei tei-emph"><span style="font-style: italic">mortal</span></em>, it will follow as a consequence, +that the class <em class="tei tei-emph"><span style="font-style: italic">man</span></em> will be wholly included in the class +<em class="tei tei-emph"><span style="font-style: italic">mortal</span></em>, and that <em class="tei tei-emph"><span style="font-style: italic">mortal</span></em> will be a name of all things of which +<em class="tei tei-emph"><span style="font-style: italic">man</span></em> is a name: but why? Those objects are brought under +the name, by possessing the attributes connoted by it: but +their possession of the attributes is the real condition on +which the truth of the proposition depends; not their being +called by the name. Connotative names do not precede, +but follow, the attributes which they connote. If one attribute +happens to be always found in conjunction with another +attribute, the concrete names which answer to those attributes +will of course be predicable of the same subjects, and may +be said, in Hobbes' language, (in the propriety of which on +this occasion I fully concur,) to be two names for the same +things. But the possibility of a concurrent application of the +two names, is a mere consequence of the conjunction between +<span class="tei tei-pb" id="page103">[pg 103]</span><a name="Pg103" id="Pg103" class="tei tei-anchor"></a> +the two attributes, and was, in most cases, never thought +of when the names were invented and their signification +fixed. That the diamond is combustible, was a proposition +certainly not dreamt of when the words Diamond and Combustible +first received their meaning; and could not have +been discovered by the most ingenious and refined analysis +of the signification of those words. It was found out by a +very different process, namely, by exerting the senses, and +learning from them, that the attribute of combustibility +existed in all those diamonds upon which the experiment was +tried; the number and character of the experiments being +such, that what was true of those individuals might be +concluded to be true of all substances <span class="tei tei-q">“called by the +name,”</span> that is, of all substances possessing the attributes +which the name connotes. The assertion, therefore, when +analysed, is, that wherever we find certain attributes, there +will be found a certain other attribute: which is not a question +of the signification of names, but of laws of nature; +the order existing among phenomena. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Although Hobbes' theory of Predication has not, +in the terms in which he stated it, met with a very favourable +reception from subsequent thinkers, a theory virtually +identical with it, and not by any means so perspicuously +expressed, may almost be said to have taken the rank of an +established opinion. The most generally received notion +of Predication decidedly is that it consists in referring something +to a <em class="tei tei-emph"><span style="font-style: italic">class</span></em>, <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span>, either placing an individual under +a class, or placing one class under another class. Thus, the proposition, +Man is mortal, asserts, according to this view of it, +that the class man is included in the class mortal. <span class="tei tei-q">“Plato +is a philosopher,”</span> asserts that the individual Plato is one of +those who compose the class philosopher. If the proposition +is negative, then instead of placing something in a class, it +is said to exclude something from a class. Thus, if the +following be the proposition, The elephant is not carnivorous; +what is asserted (according to this theory) is, that +the elephant is excluded from the class carnivorous, or is +<span class="tei tei-pb" id="page104">[pg 104]</span><a name="Pg104" id="Pg104" class="tei tei-anchor"></a> +not numbered among the things comprising that class. +There is no real difference, except in language, between +this theory of Predication and the theory of Hobbes. +For a class <em class="tei tei-emph"><span style="font-style: italic">is</span></em> absolutely nothing but an indefinite number of +individuals denoted by a general name. The name given to +them in common, is what makes them a class. To refer +anything to a class, therefore, is to look upon it as one of +the things which are to be called by that common name. +To exclude it from a class, is to say that the common name +is not applicable to it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +How widely these views of predication have prevailed, +is evident from this, that they are the basis of the celebrated +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni et nullo</span></span>. +When the syllogism is resolved, by +all who treat of it, into an inference that what is true of a +class is true of all things whatever that belong to the class; +and when this is laid down by almost all professed logicians +as the ultimate principle to which all reasoning owes its +validity; it is clear that in the general estimation of logicians, +the propositions of which reasonings are composed +can be the expression of nothing but the process of dividing +things into classes, and referring everything to its proper +class. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This theory appears to me a signal example of a logical +error very often committed in logic, that of ὕστερον προτέρον, +or explaining a thing by something which presupposes it. +When I say that snow is white, I may and ought to be +thinking of snow as a class, because I am asserting a proposition +as true of all snow: but I am certainly not thinking of +white objects as a class; I am thinking of no white object +whatever except snow, but only of that, and of the sensation +of white which it gives me. When, indeed, I have judged, +or assented to the propositions, that snow is white, and that +several other things also are white, I gradually begin to think +of white objects as a class, including snow and those other +things. But this is a conception which followed, not preceded, +those judgments, and therefore cannot be given as an +explanation of them. Instead of explaining the effect by +the cause, this doctrine explains the cause by the effect, and +<span class="tei tei-pb" id="page105">[pg 105]</span><a name="Pg105" id="Pg105" class="tei tei-anchor"></a> +is, I conceive, founded on a latent misconception of the +nature of classification. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is a sort of language very generally prevalent in +these discussions, which seems to suppose that classification +is an arrangement and grouping of definite and known individuals: +that when names were imposed, mankind took into +consideration all the individual objects in the universe, made +them up into parcels or lists, and gave to the objects of each +list a common name, repeating this operation <span class="tei tei-hi"><span style="font-style: italic">toties quoties</span></span> +until they had invented all the general names of which language +consists; which having been once done, if a question +subsequently arises whether a certain general name can be +truly predicated of a certain particular object, we have only +(as it were) to read the roll of the objects upon which that +name was conferred, and see whether the object about which +the question arises, is to be found among them. The framers +of language (it would seem to be supposed) have predetermined +all the objects that are to compose each class, and +we have only to refer to the record of an antecedent decision. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +So absurd a doctrine will be owned by nobody when thus +nakedly stated; but if the commonly received explanations +of classification and naming do not imply this theory, it requires +to be shown how they admit of being reconciled with +any other. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +General names are not marks put upon definite objects; +classes are not made by drawing a line round a given +number of assignable individuals. The objects which compose +any given class are perpetually fluctuating. We may +frame a class without knowing the individuals, or even any +of the individuals, of which it will be composed; we may do +so while believing that no such individuals exist. If by the +<em class="tei tei-emph"><span style="font-style: italic">meaning</span></em> of a general name are to be understood the things +which it is the name of, no general name, except by accident, +has a fixed meaning at all, or ever long retains the +same meaning. The only mode in which any general name +has a definite meaning, is by being a name of an indefinite +variety of things; namely, of all things, known or unknown, +<span class="tei tei-pb" id="page106">[pg 106]</span><a name="Pg106" id="Pg106" class="tei tei-anchor"></a> +past, present, or future, which possess certain definite attributes. +When, by studying not the meaning of words, but +the phenomena of nature, we discover that these attributes +are possessed by some object not previously known to possess +them, (as when chemists found that the diamond was +combustible,) we include this new object in the class; but +it did not already belong to the class. We place the individual +in the class because the proposition is true; the proposition +is not true because the object is placed in the +class. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It will appear hereafter in treating of reasoning, how +much the theory of that intellectual process has been vitiated +by the influence of these erroneous notions, and by the habit +which they exemplify of assimilating all the operations of +the human understanding which have truth for their object, +to processes of mere classification and naming. Unfortunately, +the minds which have been entangled in this net are +precisely those which have escaped the other cardinal error +commented upon in the beginning of the present chapter. +Since the revolution which dislodged Aristotle from the +schools, logicians may almost be divided into those who +have looked upon reasoning as essentially an affair of Ideas, +and those who have looked upon it as essentially an affair of +Names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although, however, Hobbes' theory of Predication, according +to the well-known remark of Leibnitz, and the +avowal of Hobbes himself,<a id="noteref_17" name="noteref_17" href="#note_17"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">17</span></span></a> +renders truth and falsity completely +arbitrary, with no standard but the will of men, it +must not be concluded that either Hobbes, or any of the +other thinkers who have in the main agreed with him, did +in fact consider the distinction between truth and error +as less real, or attached less importance to it, than +<span class="tei tei-pb" id="page107">[pg 107]</span><a name="Pg107" id="Pg107" class="tei tei-anchor"></a> +other people. To suppose that they did so would argue +total unacquaintance with their other speculations. But +this shows how little hold their doctrine possessed over +their own minds. No person at bottom ever imagined that +there was nothing more in truth than propriety of expression; +than using language in conformity to a previous convention. +When the inquiry was brought down from generals +to a particular case, it has always been acknowledged that +there is a distinction between verbal and real questions; +that some false propositions are uttered from ignorance of +the meaning of words, but that in others the source of the +error is a misapprehension of things; that a person who has +not the use of language at all may form propositions mentally, +and that they may be untrue, that is, he may believe +as matters of fact what are not really so. This last admission +cannot be made in stronger terms than it is by Hobbes +himself;<a id="noteref_18" name="noteref_18" href="#note_18"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">18</span></span></a> +though he will not allow such erroneous belief to +be called falsity, but only error. And he has himself laid +down, in other places, doctrines in which the true theory of +predication is by implication contained. He distinctly says +that general names are given to things on account of their +attributes, and that abstract names are the names of those +attributes. <span class="tei tei-q">“Abstract is that which in any subject denotes +the cause of the concrete name.... And these causes of +names are the same with the causes of our conceptions, +namely, some power of action, or affection, of the thing conceived, +which some call the manner by which anything works +<span class="tei tei-pb" id="page108">[pg 108]</span><a name="Pg108" id="Pg108" class="tei tei-anchor"></a> +upon our senses, but by most men they are called +<em class="tei tei-emph"><span style="font-style: italic">accidents</span></em>.”</span><a id="noteref_19" name="noteref_19" href="#note_19"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">19</span></span></a> +It is strange that having gone so far, he should not have +gone one step farther, and seen that what he calls the cause +of the concrete name, is in reality the meaning of it; and +that when we predicate of any subject a name which is given +<em class="tei tei-emph"><span style="font-style: italic">because</span></em> of an attribute, (or, as he calls it, an accident,) our +object is not to affirm the name, but, by means of the name, +to affirm the attribute. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. Let the predicate be, as we have said, a connotative +term; and to take the simplest case first, let the subject +be a proper name: <span class="tei tei-q">“The summit of Chimborazo is white.”</span> +The word white connotes an attribute which is possessed by +the individual object designated by the words, <span class="tei tei-q">“summit of +Chimborazo,”</span> which attribute consists in the physical fact, of +its exciting in human beings the sensation which we call a +sensation of white. It will be admitted that, by asserting the +proposition, we wish to communicate information of that +physical fact, and are not thinking of the names, except as +the necessary means of making that communication. The +meaning of the proposition, therefore, is, that the individual +thing denoted by the subject, has the attributes connoted by +the predicate. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If we now suppose the subject also to be a connotative +name, the meaning expressed by the proposition has advanced +a step farther in complication. Let us first suppose +the proposition to be universal, as well as affirmative: <span class="tei tei-q">“All +men are mortal.”</span> In this case, as in the last, what the proposition +asserts, (or expresses a belief of,) is, of course, that +the objects denoted by the subject (man) possess the attributes +connoted by the predicate (mortal). But the characteristic +of this case is, that the objects are no longer <em class="tei tei-emph"><span style="font-style: italic">individually</span></em> +designated. They are pointed out only by some of +their attributes: they are the objects called men, that is, +possessing the attributes connoted by the name man; and +the only thing known of them may be those attributes: +<span class="tei tei-pb" id="page109">[pg 109]</span><a name="Pg109" id="Pg109" class="tei tei-anchor"></a> +indeed, as the proposition is general, and the objects denoted +by the subject are therefore indefinite in number, most of +them are not known individually at all. The assertion, +therefore, is not, as before, that the attributes which the predicate +connotes are possessed by any given individual, or +by any number of individuals previously known as John, +Thomas, &c., but that those attributes are possessed by each +and every individual possessing certain other attributes; that +whatever has the attributes connoted by the subject, has also +those connoted by the predicate; that the latter set of attributes +<em class="tei tei-emph"><span style="font-style: italic">constantly accompany</span></em> the former set. Whatever has the +attributes of man has the attribute of mortality; mortality +constantly accompanies the attributes of man. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If it be remembered that every attribute is <em class="tei tei-emph"><span style="font-style: italic">grounded</span></em> on +some fact or phenomenon, either of outward sense or of +inward consciousness, and that to <em class="tei tei-emph"><span style="font-style: italic">possess</span></em> an attribute is another +phrase for being the cause of, or forming part of, the +fact or phenomenon upon which the attribute is grounded; +we may add one more step to complete the analysis. The +proposition which asserts that one attribute always accompanies +another attribute, really asserts thereby no other +thing than this, that one phenomenon always accompanies +another phenomenon; insomuch that where we find the one, +we have assurance of the existence of the other. Thus, in +the proposition, All men are mortal, the word man connotes +the attributes which we ascribe to a certain kind of living +creatures, on the ground of certain phenomena which they +exhibit, and which are partly physical phenomena, namely +the impressions made on our senses by their bodily form and +structure, and partly mental phenomena, namely the sentient +and intellectual life which they have of their own. All this +is understood when we utter the word man, by any one to +whom the meaning of the word is known. Now, when we +say, Man is mortal, we mean that wherever these various +physical and mental phenomena are all found, there we have +assurance that the other physical and mental phenomenon, +called death, will not fail to take place. The proposition +does not affirm <em class="tei tei-emph"><span style="font-style: italic">when</span></em>; for the connotation of the word <em class="tei tei-emph"><span style="font-style: italic">mortal</span></em> +<span class="tei tei-pb" id="page110">[pg 110]</span><a name="Pg110" id="Pg110" class="tei tei-anchor"></a> +goes no farther than to the occurrence of the phenomenon at +some time or other, leaving the precise time undecided. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. We have already proceeded far enough not only to +demonstrate the error of Hobbes, but to ascertain the real +import of by far the most numerous class of propositions. +The object of belief in a proposition, when it asserts anything +more than the meaning of words, is generally, as in the cases +which we have examined, either the coexistence or the +sequence of two phenomena. At the very commencement of +our inquiry, we found that every act of belief implied two +Things; we have now ascertained what, in the most frequent +case, these two things are, namely two Phenomena, in other +words, two states of consciousness; and what it is which the +proposition affirms (or denies) to subsist between them, +namely either succession, or coexistence. And this case +includes innumerable instances which no one, previous to +reflection, would think of referring to it. Take the following +example: A generous person is worthy of honour. Who +would expect to recognize here a case of coexistence between +phenomena? But so it is. The attribute which causes a +person to be termed generous, is ascribed to him on the +ground of states of his mind, and particulars of his conduct: +both are phenomena; the former are facts of internal consciousness, +the latter, so far as distinct from the former, are +physical facts, or perceptions of the senses. Worthy of +honour, admits of a similar analysis. Honour, as here used, +means a state of approving and admiring emotion, followed +on occasion by corresponding outward acts. <span class="tei tei-q">“Worthy of +honour”</span> connotes all this, together with our approval of the +act of showing honour. All these are phenomena; states of +internal consciousness, accompanied or followed by physical +facts. When we say, A generous person is worthy of honour, +we affirm coexistence between the two complicated phenomena +connoted by the two terms respectively. We affirm, +that wherever and whenever the inward feelings and outward +facts implied in the word generosity, have place, then and +there the existence and manifestation of an inward feeling, +<span class="tei tei-pb" id="page111">[pg 111]</span><a name="Pg111" id="Pg111" class="tei tei-anchor"></a> +honour, would be followed in our minds by another inward +feeling, approval. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After the analysis in a former chapter of the import of +names, many examples are not needed to illustrate the import +of propositions. When there is any obscurity or difficulty, it +does not lie in the meaning of the proposition, but in the +meaning of the names which compose it; in the very complicated +connotation of many words; the immense multitude +and prolonged series of facts which often constitute the +phenomenon connoted by a name. But where it is seen +what the phenomenon is, there is seldom any difficulty in +seeing that the assertion conveyed by the proposition is, the +coexistence of one such phenomenon with another; or the +succession of one such phenomenon to another: their <em class="tei tei-emph"><span style="font-style: italic">conjunction</span></em>, +in short, so that where the one is found, we may +calculate on finding both. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, however, though the most common, is not the only +meaning which propositions are ever intended to convey. +In the first place, sequences and coexistences are not only +asserted respecting Phenomena; we make propositions also +respecting those hidden causes of phenomena, which are +named substances and attributes. A substance, however, +being to us nothing but either that which causes, or that +which is conscious of, phenomena; and the same being true, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">mutatis mutandis</span></span>, +of attributes; no assertion can be made, at +least with a meaning, concerning these unknown and unknowable +entities, except in virtue of the Phenomena by +which alone they manifest themselves to our faculties. When +we say, Socrates was cotemporary with the Peloponnesian +war, the foundation of this assertion, as of all assertions +concerning substances, is an assertion concerning the phenomena +which they exhibit,—namely, that the series of facts +by which Socrates manifested himself to mankind, and the +series of mental states which constituted his sentient existence, +went on simultaneously with the series of facts known +by the name of the Peloponnesian war. Still, the proposition +does not assert that alone; it asserts that the Thing in +itself, the <span class="tei tei-hi"><span style="font-style: italic">noumenon</span></span> Socrates, was existing, and doing or +<span class="tei tei-pb" id="page112">[pg 112]</span><a name="Pg112" id="Pg112" class="tei tei-anchor"></a> +experiencing those various facts, during the same time. +Coexistence and sequence, therefore, may be affirmed or +denied not only between phenomena, but between noumena, +or between a noumenon and phenomena. And both of noumena +and of phenomena we may affirm simple existence. +But what is a noumenon? An unknown cause. In affirming, +therefore, the existence of a noumenon, we affirm causation. +Here, therefore, are two additional kinds of fact, capable of +being asserted in a proposition. Besides the propositions +which assert Sequence or Coexistence, there are some which +assert simple Existence; and others assert Causation, which, +subject to the explanations which will follow in the Third +Book, must be considered provisionally as a distinct and +peculiar kind of assertion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. To these four kinds of matter-of-fact or assertion, +must be added a fifth, Resemblance. This was a species of +attribute which we found it impossible to analyse; for which +no <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamentum</span></span>, +distinct from the objects themselves, could +be assigned. Besides propositions which assert a sequence +or coexistence between two phenomena, there are therefore +also propositions which assert resemblance between them: +as, This colour is like that colour;—The heat of to-day is +<em class="tei tei-emph"><span style="font-style: italic">equal</span></em> to the heat of yesterday. It is true that such an assertion +might with some plausibility be brought within the +description of an affirmation of sequence, by considering it +as an assertion that the simultaneous contemplation of the +two colours is <em class="tei tei-emph"><span style="font-style: italic">followed</span></em> by a specific feeling termed the feeling +of resemblance. But there would be nothing gained by +encumbering ourselves, especially in this place, with a +generalization which may be looked upon as strained. Logic +does not undertake to analyse mental facts into their ultimate +elements. Resemblance between two phenomena is more +intelligible in itself than any explanation could make it, and +under any classification must remain specifically distinct +from the ordinary cases of sequence and coexistence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is sometimes said that all propositions whatever, of +which the predicate is a general name, do, in point of fact, +<span class="tei tei-pb" id="page113">[pg 113]</span><a name="Pg113" id="Pg113" class="tei tei-anchor"></a> +affirm or deny resemblance. All such propositions affirm +that a thing belongs to a class; but things being classed +together according to their resemblance, everything is of +course classed with the things which it is supposed to +resemble most; and thence, it may be said, when we affirm +that Gold is a metal, or that Socrates is a man, the affirmation +intended is, that gold resembles other metals, and +Socrates other men, more nearly than they resemble the +objects contained in any other of the classes co-ordinate +with these. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is some slight degree of foundation for this remark, +but no more than a slight degree. The arrangement of +things into classes, such as the class <em class="tei tei-emph"><span style="font-style: italic">metal</span></em>, or the class <em class="tei tei-emph"><span style="font-style: italic">man</span></em>, +is grounded indeed on a resemblance among the things +which are placed in the same class, but not on a mere +general resemblance: the resemblance it is grounded on +consists in the possession by all those things, of certain +common peculiarities; and those peculiarities it is which the +terms connote, and which the propositions consequently +assert; not the resemblance: for though when I say, Gold +is a metal, I say by implication that if there be any other +metals it must resemble them, yet if there were no other +metals I might still assert the proposition with the same +meaning as at present, namely, that gold has the various +properties implied in the word metal; just as it might be +said, Christians are men, even if there were no men who +were not Christians. Propositions, therefore, in which objects +are referred to a class because they possess the attributes constituting +the class, are so far from asserting nothing but +resemblance, that they do not, properly speaking, assert +resemblance at all. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But we remarked some time ago, (and the reasons of the +remark will be more fully entered into in a subsequent +Book,<a id="noteref_20" name="noteref_20" href="#note_20"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">20</span></span></a>) +that there is sometimes a convenience in extending +<span class="tei tei-pb" id="page114">[pg 114]</span><a name="Pg114" id="Pg114" class="tei tei-anchor"></a> +the boundaries of a class so as to include things which possess +in a very inferior degree, if in any, some of the characteristic +properties of the class,—provided they resemble that +class more than any other, insomuch that the general propositions +which are true of the class will be nearer to being true +of those things than any other equally general propositions. +As, for instance, there are substances called metals which +have very few of the properties by which metals are commonly +recognised; and almost every great family of plants +or animals has a few anomalous genera or species on its +borders, which are admitted into it by a sort of courtesy, +and concerning which it has been matter of discussion to +what family they properly belonged. Now when the class-name +is predicated of any object of this description, we do, by +so predicating it, affirm resemblance and nothing more. And +in order to be scrupulously correct it ought to be said, that in +every case in which we predicate a general name, we affirm, not +absolutely that the object possesses the properties designated +by the name, but that it <em class="tei tei-emph"><span style="font-style: italic">either</span></em> possesses those properties, or +if it does not, at any rate resembles the things which do so, +more than it resembles any other things. In most cases, +however, it is unnecessary to suppose any such alternative, +the latter of the two grounds being very seldom that on +which the assertion is made: and when it is, there is generally +some slight difference in the form of the expression, as, +This species (or genus) is <em class="tei tei-emph"><span style="font-style: italic">considered</span></em>, or <em class="tei tei-emph"><span style="font-style: italic">may be ranked</span></em>, as +belonging to such and such a family: we should hardly say +positively that it does belong to it, unless it possessed unequivocally +the properties of which the class-name is scientifically +significant. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is still another exceptional case, in which, though +the predicate is a name of a class, yet in predicating it we +affirm nothing but resemblance, the class being founded not +on resemblance in any given particular, but on general unanalysable +resemblance. The classes in question are those +into which our simple sensations, or other simple feelings, +are divided. Sensations of white, for instance, are classed +together, not because we can take them to pieces, and say +<span class="tei tei-pb" id="page115">[pg 115]</span><a name="Pg115" id="Pg115" class="tei tei-anchor"></a> +they are alike in this, and not alike in that, but because we +feel them to be alike altogether, though in different degrees. +When, therefore, I say, The colour I saw yesterday was a +white colour, or, The sensation I feel is one of tightness, in +both cases the attribute I affirm of the colour or of the other +sensation is mere resemblance,—simple <em class="tei tei-emph"><span style="font-style: italic">likeness</span></em> to sensations +which I have had before, and which have had those names +bestowed upon them. The names of feelings, like other +concrete general names, are connotative; but they connote +a mere resemblance. When predicated of any individual +feeling, the information they convey is that of its likeness to +the other feelings which we have been accustomed to call by +the same name. Thus much may suffice in illustration of +the kind of Propositions in which the matter-of-fact asserted +(or denied) is simple Resemblance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Existence, Coexistence, Sequence, Causation, Resemblance: +one or other of these is asserted (or denied) in +every proposition without exception. This five-fold division +is an exhaustive classification of matters-of-fact; of all +things that can be believed or tendered for belief; of all +questions that can be propounded, and all answers that can +be returned to them. Instead of Coexistence and Sequence, +we shall sometimes say, for greater particularity, Order in +Place, and Order in Time: Order in Place being one of the +modes of coexistence, not necessary to be more particularly +analysed here; while the mere fact of coexistence, or +simultaneousness, may be classed, together with Sequence, +under the head of Order in Time. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. In the foregoing inquiry into the import of Propositions, +we have thought it necessary to analyse <em class="tei tei-emph"><span style="font-style: italic">directly</span></em> those +alone, in which the terms of the proposition (or the predicate +at least) are concrete terms. But, in doing so, we have indirectly +analysed those in which the terms are abstract. The +distinction between an abstract term and its corresponding +concrete, does not turn upon any difference in what they are +appointed to signify; for the real signification of a concrete +general name is, as we have so often said, its connotation; +<span class="tei tei-pb" id="page116">[pg 116]</span><a name="Pg116" id="Pg116" class="tei tei-anchor"></a> +and what the concrete term connotes, forms the entire +meaning of the abstract name. Since there is nothing in +the import of an abstract name which is not in the import of +the corresponding concrete, it is natural to suppose that +neither can there be anything in the import of a proposition +of which the terms are abstract, but what there is in some +proposition which can be framed of concrete terms. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And this presumption a closer examination will confirm. +An abstract name is the name of an attribute, or combination +of attributes. The corresponding concrete is a name given +to things, because of, and in order to express, their possessing +that attribute, or that combination of attributes. +When, therefore, we predicate of anything a concrete name, +the attribute is what we in reality predicate of it. But it +has now been shown that in all propositions of which the +predicate is a concrete name, what is really predicated is +one of five things: Existence, Coexistence, Causation, +Sequence, or Resemblance. An attribute, therefore, is necessarily +either an existence, a coexistence, a causation, a +sequence, or a resemblance. When a proposition consists +of a subject and predicate which are abstract terms, it consists +of terms which must necessarily signify one or other +of these things. When we predicate of anything an abstract +name, we affirm of the thing that it is one or other of these +five things; that it is a case of Existence, or of Coexistence, +or of Causation, or of Sequence, or of Resemblance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is impossible to imagine any proposition expressed in +abstract terms, which cannot be transformed into a precisely +equivalent proposition in which the terms are concrete, +namely, either the concrete names which connote the attributes +themselves, or the names of the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">fundamenta</span></span> of those +attributes, the facts or phenomena on which they are +grounded. To illustrate the latter case, let us take this +proposition, of which the subject only is an abstract name,—<span class="tei tei-q">“Thoughtlessness +is dangerous.”</span> Thoughtlessness is +an attribute grounded on the facts which we call thoughtless +actions; and the proposition is equivalent to this, +Thoughtless actions are dangerous. In the next example +<span class="tei tei-pb" id="page117">[pg 117]</span><a name="Pg117" id="Pg117" class="tei tei-anchor"></a> +the predicate as well as the subject are abstract names: +<span class="tei tei-q">“Whiteness is a colour;”</span> or <span class="tei tei-q">“The colour of snow is a +whiteness.”</span> These attributes being grounded on sensations, +the equivalent propositions in the concrete would be, The +sensation of white is one of the sensations called those of +colour,—The sensation of sight, caused by looking at snow, +is one of the sensations called sensations of white. In these +propositions, as we have before seen, the matter-of-fact +asserted is a Resemblance. In the following examples, the +concrete terms are those which directly correspond to the +abstract names; connoting the attribute which these denote. +<span class="tei tei-q">“Prudence is a virtue:”</span> this may be rendered, <span class="tei tei-q">“All prudent +persons, <em class="tei tei-emph"><span style="font-style: italic">in so far as</span></em> prudent, are virtuous:”</span> <span class="tei tei-q">“Courage is +deserving of honour,”</span> thus, <span class="tei tei-q">“All courageous persons are +deserving of honour <em class="tei tei-emph"><span style="font-style: italic">in so far</span></em> as they are courageous;”</span> +which is equivalent to this—<span class="tei tei-q">“All courageous persons deserve +an addition to the honour, or a diminution of the disgrace, +which would attach to them on other grounds.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In order to throw still further light upon the import of +propositions of which the terms are abstract, we will subject +one of the examples given above to a minuter analysis. +The proposition we shall select is the following:—<span class="tei tei-q">“Prudence +is a virtue.”</span> Let us substitute for the word virtue an equivalent +but more definite expression, such as <span class="tei tei-q">“a mental +quality beneficial to society,”</span> or <span class="tei tei-q">“a mental quality pleasing +to God,”</span> or whatever else we adopt as the definition of +virtue. What the proposition asserts is a sequence, accompanied +with causation, namely, that benefit to society, or +that the approval of God, is consequent on, and caused +by, prudence. Here is a sequence; but between what? +We understand the consequent of the sequence, but we have +yet to analyse the antecedent. Prudence is an attribute; +and, in connexion with it, two things besides itself are to be +considered; prudent persons, who are the <em class="tei tei-emph"><span style="font-style: italic">subjects</span></em> of the +attribute, and prudential conduct, which may be called the +<em class="tei tei-emph"><span style="font-style: italic">foundation</span></em> of it. Now is either of these the antecedent? +and, first, is it meant, that the approval of God, or benefit +to society, is attendant upon all prudent <em class="tei tei-emph"><span style="font-style: italic">persons</span></em>? No; except +<span class="tei tei-pb" id="page118">[pg 118]</span><a name="Pg118" id="Pg118" class="tei tei-anchor"></a> +<em class="tei tei-emph"><span style="font-style: italic">in so far</span></em> as they are prudent; for prudent persons who +are scoundrels can seldom on the whole be beneficial to +society, nor acceptable to any good being. Is it upon prudential +<em class="tei tei-emph"><span style="font-style: italic">conduct</span></em>, then, that divine approbation and benefit to +mankind are supposed to be invariably consequent? Neither +is this the assertion meant when it is said that prudence is a +virtue; except with the same reservation as before, and for the +same reason, namely, that prudential conduct, although in <em class="tei tei-emph"><span style="font-style: italic">so +far as</span></em> it is prudential it is beneficial to society, may yet, by +reason of some other of its qualities, be productive of an +injury outweighing the benefit, and deserve a displeasure +exceeding the approbation which would be due to the prudence. +Neither the substance, therefore, (viz., the person,) +nor the phenomenon, (the conduct,) is an antecedent on +which the other term of the sequence is universally consequent. +But the proposition, <span class="tei tei-q">“Prudence is a virtue,”</span> is an +universal proposition. What is it, then, upon which the +proposition affirms the effects in question to be universally +consequent? Upon that <em class="tei tei-emph"><span style="font-style: italic">in</span></em> the person, and in the conduct, +which causes them to be called prudent, and which is equally +in them when the action, though prudent, is wicked; namely, +a correct foresight of consequences, a just estimation of their +importance to the object in view, and repression of any unreflecting +impulse at variance with the deliberate purpose. +These, which are states of the person's mind, are the +real antecedent in the sequence, the real cause in the +causation, asserted by the proposition. But these are also +the real ground, or foundation, of the attribute Prudence; +since wherever these states of mind exist we may predicate +prudence, even before we know whether any conduct has +followed. And in this manner every assertion respecting +an attribute may be transformed into an assertion exactly +equivalent respecting the fact or phenomenon which is the +ground of the attribute. And no case can be assigned, +where that which is predicated of the fact or phenomenon, +does not belong to one or other of the five species formerly +enumerated: it is either simple Existence, or it is some +Sequence, Coexistence, Causation, or Resemblance. +</p> + +<span class="tei tei-pb" id="page119">[pg 119]</span><a name="Pg119" id="Pg119" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And as these five are the only things which can be +affirmed, so are they the only things which can be denied. +<span class="tei tei-q">“No horses are web-footed”</span> denies that the attributes of a +horse ever coexist with web-feet. It is scarcely necessary to +apply the same analysis to Particular affirmations and negations. +<span class="tei tei-q">“Some birds are web-footed,”</span> affirms that, with the +attributes connoted by <em class="tei tei-emph"><span style="font-style: italic">bird</span></em>, the phenomenon web-feet is +sometimes coexistent: <span class="tei tei-q">“Some birds are not web-footed,”</span> +asserts that there are other instances in which this coexistence +does not have place. Any further explanation of a thing +which, if the previous exposition has been assented to, is so +obvious, may here be spared. +</p> + +</div> + +<span class="tei tei-pb" id="page120">[pg 120]</span><a name="Pg120" id="Pg120" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc33" id="toc33"></a> +<a name="pdf34" id="pdf34"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VI. OF PROPOSITIONS MERELY VERBAL.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. As a preparation for the inquiry which is the proper +object of Logic, namely, in what manner propositions are to +be proved, we have found it necessary to inquire what they +contain which requires, or is susceptible of, proof; or (which +is the same thing) what they assert. In the course of this +preliminary investigation into the import of Propositions, we +examined the opinion of the Conceptualists, that a proposition +is the expression of a relation between two ideas; and +the doctrine of the Nominalists, that it is the expression of +an agreement or disagreement between the meanings of two +names. We decided that, as general theories, both of these +are erroneous; and that, although propositions may be made +both respecting names and respecting ideas, neither the one +nor the other are the subject-matter of Propositions considered +generally. We then examined the different kinds of +Propositions, and found that, with the exception of those +which are merely verbal, they assert five different kinds of +matters of fact, namely, Existence, Order in Place, Order in +Time, Causation, and Resemblance; that in every proposition +one of these five is either affirmed, or denied, of some +fact or phenomenon, or of some object the unknown source +of a fact or phenomenon. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In distinguishing, however, the different kinds of matters +of fact asserted in propositions, we reserved one class of propositions, +which do not relate to any matter of fact, in the +proper sense of the term, at all, but to the meaning of names. +Since names and their signification are entirely arbitrary, +such propositions are not, strictly speaking, susceptible of +truth or falsity, but only of conformity or disconformity to +usage or convention; and all the proof they are capable of, +<span class="tei tei-pb" id="page121">[pg 121]</span><a name="Pg121" id="Pg121" class="tei tei-anchor"></a> +is proof of usage; proof that the words have been employed +by others in the acceptation in which the speaker or writer +desires to use them. These propositions occupy, however, +a conspicuous place in philosophy; and their nature and +characteristics are of as much importance in logic, as those +of any of the other classes of propositions previously adverted +to. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If all propositions respecting the signification of words +were as simple and unimportant as those which served us for +examples when examining Hobbes' theory of predication, +viz. those of which the subject and predicate are proper +names, and which assert only that those names have, or that +they have not, been conventionally assigned to the same individual; +there would be little to attract to such propositions +the attention of philosophers. But the class of merely verbal +propositions embraces not only much more than these, but +much more than any propositions which at first sight present +themselves as verbal; comprehending a kind of assertions +which have been regarded not only as relating to things, but +as having actually a more intimate relation with them than +any other propositions whatever. The student in philosophy +will perceive that I allude to the distinction on which so +much stress was laid by the schoolmen, and which has been +retained either under the same or under other names by most +metaphysicians to the present day, viz. between what were +called <em class="tei tei-emph"><span style="font-style: italic">essential</span></em>, and what were called <em class="tei tei-emph"><span style="font-style: italic">accidental</span></em>, +propositions, and between essential and accidental properties or attributes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Almost all metaphysicians prior to Locke, as well +as many since his time, have made a great mystery of Essential +Predication, and of predicates which were said to be of +the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the subject. The essence of a thing, they said, +was that without which the thing could neither be, nor be +conceived to be. Thus, rationality was of the essence of man, +because without rationality, man could not be conceived to +exist. The different attributes which made up the essence +of the thing, were called its essential properties; and a proposition +<span class="tei tei-pb" id="page122">[pg 122]</span><a name="Pg122" id="Pg122" class="tei tei-anchor"></a> +in which any of these were predicated of it, was +called an Essential Proposition, and was considered to go +deeper into the nature of the thing, and to convey more important +information respecting it, than any other proposition +could do. All properties, not of the essence of the thing, were +called its accidents; were supposed to have nothing at all, +or nothing comparatively, to do with its inmost nature; and +the propositions in which any of these were predicated of it +were called Accidental Propositions. A connexion may be +traced between this distinction, which originated with the +schoolmen, and the well known dogmas of <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">substantiæ secundæ</span></span> +or general substances, and <em class="tei tei-emph"><span style="font-style: italic">substantial forms</span></em>, doctrines which +under varieties of language pervaded alike the Aristotelian and +the Platonic schools, and of which more of the spirit has come +down to modern times than might be conjectured from the +disuse of the phraseology. The false views of the nature of +classification and generalization which prevailed among the +schoolmen, and of which these dogmas were the technical +expression, afford the only explanation which can be given +of their having misunderstood the real nature of those +Essences which held so conspicuous a place in their philosophy. +They said, truly, that <em class="tei tei-emph"><span style="font-style: italic">man</span></em> cannot be conceived +without rationality. But though <em class="tei tei-emph"><span style="font-style: italic">man</span></em> cannot, a being may be +conceived exactly like a man in all points except that one +quality, and those others which are the conditions or consequences +of it. All therefore which is really true in the +assertion that man cannot be conceived without rationality, +is only, that if he had not rationality, he would not be reputed +a man. There is no impossibility in conceiving the +<em class="tei tei-emph"><span style="font-style: italic">thing</span></em>, nor, for aught we know, in its existing: the impossibility +is in the conventions of language, which will not allow +the thing, even if it exist, to be called by the name which is +reserved for rational beings. Rationality, in short, is involved +in the meaning of the word man; is one of the attributes +connoted by the name. The essence of man, simply +means the whole of the attributes connoted by the word; and +any one of those attributes taken singly, is an essential property +of man. +</p> + +<span class="tei tei-pb" id="page123">[pg 123]</span><a name="Pg123" id="Pg123" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The doctrines which prevented the real meaning of +Essences from being understood, not having assumed so +settled a shape in the time of Aristotle and his immediate +followers as was afterwards given to them by the Realists of +the middle ages, we find a nearer approach to a rational view +of the subject in the writings of the ancient Aristotelians than +in their more modern followers. Porphyry, in his <span class="tei tei-hi"><span style="font-style: italic">Isagoge</span></span>, +approached so near to the true conception of essences, that +only one step remained to be taken, but this step, so easy in +appearance, was reserved for the Nominalists of modern +times. By altering any property, not of the essence of the +thing, you merely, according to Porphyry, made a difference +in it; you made it ἀλλοῖον: but by altering any property which +was of its essence, you made it <em class="tei tei-emph"><span style="font-style: italic">another thing</span></em>, +ἄλλο.<a id="noteref_21" name="noteref_21" href="#note_21"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">21</span></span></a> To a +modern it is obvious that between the change which +only makes a thing different, and the change which makes it +<em class="tei tei-emph"><span style="font-style: italic">another thing</span></em>, the only distinction is that in the one case, +though changed, it is still called by the same name. Thus, +pound ice in a mortar, and being still called ice, it is only +made ἀλλοῖον: melt it, and it becomes ἄλλο, another thing, +namely, water. Now it is really the same thing, <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span> the same +particles of matter, in both cases; and you cannot so change +anything that it shall cease to be the same thing in this sense. +The identity which it can be deprived of is merely that of +the name: when the thing ceases to be called ice, it becomes +<em class="tei tei-emph"><span style="font-style: italic">another thing</span></em>; its essence, what constituted it ice, is gone; +while, as long as it continues to be so called, nothing is gone +except some of its accidents. But these reflections, so easy +to us, would have been difficult to persons who thought, as +most of the Aristotelians did, that objects were made what +they were called, that ice (for instance) was made ice, not by +the possession of certain properties to which mankind have +chosen to attach that name, but by participation in the nature +of a certain <em class="tei tei-emph"><span style="font-style: italic">general substance</span></em>, called <em class="tei tei-emph"><span style="font-style: italic">Ice in general</span></em>, +which substance, +<span class="tei tei-pb" id="page124">[pg 124]</span><a name="Pg124" id="Pg124" class="tei tei-anchor"></a> +together with all the properties that belonged to it, +<em class="tei tei-emph"><span style="font-style: italic">inhered</span></em> in every individual piece of ice. As they did not +consider these universal substances to be attached to all +general names, but only to some, they thought that an object +borrowed only a part of its properties from an universal substance, +and that the rest belonged to it individually: the +former they called its essence, and the latter its accidents. +The scholastic doctrine of essences long survived the theory +on which it rested, that of the existence of real entities corresponding +to general terms; and it was reserved for Locke, +at the end of the seventeenth century, to convince philosophers +that the supposed essences of classes were merely the +signification of their names; nor, among the signal services +which his writings rendered to philosophy, was there one +more needful or more valuable.<a id="noteref_22" name="noteref_22" href="#note_22"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">22</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, as the most familiar of the general names by which +an object is designated usually connotes not one only, but +several attributes of the object, each of which attributes separately +forms also the bond of union of some class, and the +<span class="tei tei-pb" id="page125">[pg 125]</span><a name="Pg125" id="Pg125" class="tei tei-anchor"></a> +meaning of some general name; we may predicate of a name +which connotes a variety of attributes, another name which +connotes only one of these attributes, or some smaller number +of them than all. In such cases, the universal affirmative +proposition will be true; since whatever possesses the whole +of any set of attributes, must possess any part of that same +set. A proposition of this sort, however, conveys no information +to any one who previously understood the whole +meaning of the terms. The propositions, Every man is a +corporeal being, Every man is a living creature, Every man +is rational, convey no knowledge to any one who was already +aware of the entire meaning of the word <span class="tei tei-hi"><span style="font-style: italic">man</span></span>, for the meaning +of the word includes all this: and, that every <em class="tei tei-emph"><span style="font-style: italic">man</span></em> has the +attributes connoted by all these predicates, is already +asserted when he is called a man. Now, of this nature are +all the propositions which have been called essential; they +are, in fact, identical propositions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is true that a proposition which predicates any attribute, +even though it be one implied in the name, is in most +cases understood to involve a tacit assertion that there <em class="tei tei-emph"><span style="font-style: italic">exists</span></em> +a thing corresponding to the name, and possessing the attributes +connoted by it; and this implied assertion may convey +information, even to those who understood the meaning of +the name. But all information of this sort, conveyed by all +the essential propositions of which man can be made the +subject, is included in the assertion, Men exist. And this +assumption of real existence is after all only the result of an +imperfection of language. It arises from the ambiguity of +the copula, which, in addition to its proper office of a mark +to show that an assertion is made, is also, as we have formerly +remarked, a concrete word connoting existence. The actual +existence of the subject of the proposition is therefore only +apparently, not really, implied in the predication, if an +essential one: we may say, A ghost is a disembodied spirit, +without believing in ghosts. But an accidental, or +non-essential, affirmation, does imply the real existence of the +subject, because in the case of a non-existent subject there is +nothing for the proposition to assert. Such a proposition as, +<span class="tei tei-pb" id="page126">[pg 126]</span><a name="Pg126" id="Pg126" class="tei tei-anchor"></a> +The ghost of a murdered person haunts the couch of the +murderer, can only have a meaning if understood as implying +a belief in ghosts; for since the signification of the word +ghost implies nothing of the kind, the speaker either means +nothing, or means to assert a thing which he wishes to be +believed to have really taken place. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It will be hereafter seen that when any important consequences +seem to follow, as in mathematics, from an essential +proposition, or, in other words, from a proposition involved +in the meaning of a name, what they really flow from is the +tacit assumption of the real existence of the object so named. +Apart from this assumption of real existence, the class of +propositions in which the predicate is of the essence of the +subject (that is, in which the predicate connotes the whole or +part of what the subject connotes, but nothing besides) +answer no purpose but that of unfolding the whole or some +part of the meaning of the name, to those who did not previously +know it. Accordingly, the most useful, and in strictness +the only useful kind of essential propositions, are +Definitions: which, to be complete, should unfold the whole +of what is involved in the meaning of the word defined; that +is, (when it is a connotative word,) the whole of what it connotes. +In defining a name, however, it is not usual to specify +its entire connotation, but so much only as is sufficient to +mark out the objects usually denoted by it from all other +known objects. And sometimes a merely accidental property, +not involved in the meaning of the name, answers this +purpose equally well. The various kinds of definition which +these distinctions give rise to, and the purposes to which they +are respectively subservient, will be minutely considered in +the proper place. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. According to the above view of essential propositions, +no proposition can be reckoned such which relates to +an individual by name, that is, in which the subject is a +proper name. Individuals have no essences. When the +schoolmen talked of the essence of an individual, they did +<span class="tei tei-pb" id="page127">[pg 127]</span><a name="Pg127" id="Pg127" class="tei tei-anchor"></a> +not mean the properties implied in its name, for the names +of individuals imply no properties. They regarded as of the +essence of an individual whatever was of the essence of the +species in which they were accustomed to place that individual; +<span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span> of the class to which it was most familiarly +referred, and to which, therefore, they conceived that it by +nature belonged. Thus, because the proposition, Man is a +rational being, was an essential proposition, they affirmed +the same thing of the proposition, Julius Cæsar is a rational +being. This followed very naturally if genera and species +were to be considered as entities, distinct from, but <em class="tei tei-emph"><span style="font-style: italic">inhering</span></em> +in, the individuals composing them. If <em class="tei tei-emph"><span style="font-style: italic">man</span></em> was a substance +inhering in each individual man, the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of man (whatever +that might mean) was naturally supposed to accompany it; to +inhere in John Thompson, and to form the <em class="tei tei-emph"><span style="font-style: italic">common essence</span></em> of +Thompson and Julius Cæsar. It might then be fairly said, that +rationality, being of the essence of Man, was of the essence +also of Thompson. But if Man altogether be only the individual +men and a name bestowed upon them in consequence +of certain common properties, what becomes of John +Thompson's essence? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A fundamental error is seldom expelled from philosophy +by a single victory. It retreats slowly, defends every inch of +ground, and often retains a footing in some remote fastness +after it has been driven from the open country. The essences +of individuals were an unmeaning figment arising from a +misapprehension of the essences of classes, yet even Locke, +when he extirpated the parent error, could not shake himself +free from that which was its fruit. He distinguished two sorts +of essences, Real and Nominal. His nominal essences were +the essences of classes, explained nearly as we have now +explained them. Nor is anything wanting to render the third +book of Locke's Essay a nearly unexceptionable treatise on +the connotation of names, except to free its language from the +assumption of what are called Abstract Ideas, which unfortunately +is involved in the phraseology, although not necessarily +connected with the thoughts, contained in that immortal +<span class="tei tei-pb" id="page128">[pg 128]</span><a name="Pg128" id="Pg128" class="tei tei-anchor"></a> +Third Book.<a id="noteref_23" name="noteref_23" href="#note_23"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">23</span></span></a> But, besides nominal essences, he admitted +real essences, or essences of individual objects, which he +supposed to be the causes of the sensible properties of those +objects. We know not (said he) what these are; (and this +acknowledgment rendered the fiction comparatively innocuous;) +but if we did, we could, from them alone, demonstrate +the sensible properties of the object, as the properties +of the triangle are demonstrated from the definition of the +triangle. I shall have occasion to revert to this theory in +treating of Demonstration, and of the conditions under which +one property of a thing admits of being demonstrated from +another property. It is enough here to remark that according +to this definition, the real essence of an object has, in +the progress of physics, come to be conceived as nearly equivalent, +in the case of bodies, to their corpuscular structure: +what it is now supposed to mean in the case of any other +entities, I would not take upon myself to define. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. An essential proposition, then, is one which is +purely verbal; which asserts of a thing under a particular +name, only what is asserted of it in the fact of calling it by +that name; and which therefore either gives no information, +or gives it respecting the name, not the thing. Non-essential, +or accidental propositions, on the contrary, may be called +Real Propositions, in opposition to Verbal. They predicate +of a thing, some fact not involved in the signification of the +name by which the proposition speaks of it; some attribute +<span class="tei tei-pb" id="page129">[pg 129]</span><a name="Pg129" id="Pg129" class="tei tei-anchor"></a> +not connoted by that name. Such are all propositions concerning +things individually designated, and all general or +particular propositions in which the predicate connotes any +attribute not connoted by the subject. All these, if true, +add to our knowledge: they convey information, not already +involved in the names employed. When I am told that all, +or even that some objects, which have certain qualities, or +which stand in certain relations, have also certain other +qualities, or stand in certain other relations, I learn from +this proposition a new fact; a fact not included in my knowledge +of the meaning of the words, nor even of the existence +of Things answering to the signification of those words. It +is this class of propositions only which are in themselves +instructive, or from which any instructive propositions can +be inferred. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Nothing has probably contributed more to the opinion so +commonly prevalent of the futility of the school logic, than +the circumstance that almost all the examples used in the +common school books to illustrate the doctrine of predication +and of the syllogism, consist of essential propositions. +They were usually taken either from the branches or from +the main trunk of the Predicamental Tree, which included +nothing but what was of the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the species: <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Omne corpus est substantia</span></span>, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Omne animal est corpus</span></span>, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Omnis homo est corpus</span></span>, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Omnis homo est animal</span></span>, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Omnis homo est rationalis</span></span>, and +so forth. It is far from wonderful that the syllogistic art +should have been thought to be of no use in assisting correct +reasoning, when almost the only propositions which, in the +hands of its professed teachers, it was employed to prove, +were such as every one assented to without proof the moment +he comprehended the meaning of the words; and stood +exactly on a level, in point of evidence, with the premisses +from which they were drawn. I have, therefore, throughout +this work, avoided the employment of essential propositions +as examples, except where the nature of the principle to +be illustrated specifically required them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. With respect to propositions which do convey information—which +<span class="tei tei-pb" id="page130">[pg 130]</span><a name="Pg130" id="Pg130" class="tei tei-anchor"></a> +assert something of a Thing, under a name +that does not already presuppose what is about to be asserted; +there are two different aspects in which these, or rather such +of them as are general propositions, may be considered: we +may either look at them as portions of speculative truth, or +as memoranda for practical use. According as we consider +propositions in one or the other of these lights, their import +may be conveniently expressed in one or in the other of two +formulas. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +According to the formula which we have hitherto employed, +and which is best adapted to express the import of +the proposition as a portion of our theoretical knowledge, +All men are mortal, means that the attributes of man are +always accompanied by the attribute mortality: No men are +gods, means that the attributes of man are never accompanied +by the attributes, or at least never by all the attributes, +signified by the word god. But when the proposition is considered +as a memorandum for practical use, we shall find a +different mode of expressing the same meaning better adapted +to indicate the office which the proposition performs. The +practical use of a proposition is, to apprise or remind us +what we have to expect, in any individual case which comes +within the assertion contained in the proposition. In reference +to this purpose, the proposition, All men are mortal, +means that the attributes of man are <em class="tei tei-emph"><span style="font-style: italic">evidence of</span></em>, are a <em class="tei tei-emph"><span style="font-style: italic">mark</span></em> +of, mortality; an indication by which the presence of that +attribute is made manifest. No men are gods, means that the +attributes of man are a mark or evidence that some or all of +the attributes supposed to belong to a god are not there; that +where the former are, we need not expect to find the latter. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These two forms of expression are at bottom equivalent; +but the one points the attention more directly to what a +proposition means, the latter to the manner in which it is +to be used. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now it is to be observed that Reasoning (the subject to +which we are next to proceed) is a process into which propositions +enter not as ultimate results, but as means to +the establishment of other propositions. We may expect, +<span class="tei tei-pb" id="page131">[pg 131]</span><a name="Pg131" id="Pg131" class="tei tei-anchor"></a> +therefore, that the mode of exhibiting the import of a general +proposition which shows it in its application to practical use, +will best express the function which propositions perform in +Reasoning. And accordingly, in the theory of Reasoning, +the mode of viewing the subject which considers a Proposition +as asserting that one fact or phenomenon is a <em class="tei tei-emph"><span style="font-style: italic">mark</span></em> or +<em class="tei tei-emph"><span style="font-style: italic">evidence</span></em> of another fact or phenomenon, will be found almost +indispensable. For the purposes of that Theory, the best +mode of defining the import of a proposition is not the +mode which shows most clearly what it is in itself, but that +which most distinctly suggests the manner in which it may +be made available for advancing from it to other propositions. +</p> + +</div> + +<span class="tei tei-pb" id="page132">[pg 132]</span><a name="Pg132" id="Pg132" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc35" id="toc35"></a> +<a name="pdf36" id="pdf36"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VII. OF THE NATURE OF CLASSIFICATION, AND THE FIVE +PREDICABLES.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In examining into the nature of general propositions, +we have adverted much less than is usual with +Logicians, to the ideas of a Class, and Classification; ideas +which, since the Realist doctrine of General Substances went +out of vogue, have formed the basis of almost every attempt +at a philosophical theory of general terms and general propositions. +We have considered general names as having a +meaning, quite independently of their being the names of +classes. That circumstance is in truth accidental, it being +wholly immaterial to the signification of the name whether +there are many objects or only one to which it happens to +be applicable, or whether there be any at all. God is as +much a general term to the Christian or the Jew as to the +Polytheist; and dragon, hippogriff, chimera, mermaid, ghost, +are as much so as if real objects existed, corresponding to +those names. Every name the signification of which is constituted +by attributes, is potentially a name of an indefinite +number of objects; but it needs not be actually the name of +any; and if of any, it may be the name of only one. As +soon as we employ a name to connote attributes, the things, +be they more or fewer, which happen to possess those attributes, +are constituted, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">ipso facto</span></span>, +a class. But in predicating +the name we predicate only the attributes; and the fact of +belonging to a class does not, in ordinary cases, come into +view at all. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although, however, Predication does not presuppose +Classification, and although the theory of Names and of +Propositions is not cleared up, but only encumbered, by +intruding the idea of classification into it, there is nevertheless +a close connexion between Classification and the employment +<span class="tei tei-pb" id="page133">[pg 133]</span><a name="Pg133" id="Pg133" class="tei tei-anchor"></a> +of General Names. By every general name which +we introduce, we create a class, if there be any things, real +or imaginary, to compose it; that is, any Things corresponding +to the signification of the name. Classes, therefore, +mostly owe their existence to general language. But general +language, also, though that is not the most common case, +sometimes owes its existence to classes. A general, which +is as much as to say a significant, name, is indeed mostly +introduced because we have a signification to express by it; +because we need a word by means of which to predicate the +attributes which it connotes. But it is also true that a name +is sometimes introduced because we have found it convenient +to create a class; because we have thought it useful for the +regulation of our mental operations, that a certain group of +objects should be thought of together. A naturalist, for +purposes connected with his particular science, sees reason +to distribute the animal or vegetable creation into certain +groups rather than into any others, and he requires a name +to bind, as it were, each of his groups together. It must +not however be supposed that such names, when introduced, +differ in any respect, as to their mode of signification, from +other connotative names. The classes which they denote are, +as much as any other classes, constituted by certain common +attributes, and their names are significant of those attributes, +and of nothing else. The names of Cuvier's classes and +orders, <span class="tei tei-hi"><span style="font-style: italic">Plantigrades</span></span>, <span class="tei tei-hi"><span style="font-style: italic">Digitigrades</span></span>, +&c., are as much the expression +of attributes as if those names had preceded, instead +of growing out of, his classification of animals. The only +peculiarity of the case is, that the convenience of classification +was here the primary motive for introducing the names; +while in other cases the name is introduced as a means of +predication, and the formation of a class denoted by it is +only an indirect consequence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The principles which ought to regulate Classification as +a logical process subservient to the investigation of truth, +cannot be discussed to any purpose until a much later stage +of our inquiry. But, of classification as resulting from, and +implied in, the fact of employing general language, we cannot +<span class="tei tei-pb" id="page134">[pg 134]</span><a name="Pg134" id="Pg134" class="tei tei-anchor"></a> +forbear to treat here, without leaving the theory of +general names, and of their employment in predication, +mutilated and formless. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. This portion of the theory of general language is +the subject of what is termed the doctrine of the Predicables; +a set of distinctions handed down from Aristotle, and his +follower Porphyry, many of which have taken a firm root in +scientific, and some of them even in popular, phraseology. +The predicables are a five-fold division of General Names, +not grounded as usual on a difference in their meaning, that +is, in the attribute which they connote, but on a difference in +the kind of class which they denote. We may predicate of +a thing five different varieties of class-name:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">genus</span></span> of the thing (γένος).<br /> +A <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">species</span></span> (εἴδος).<br /> +A <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">differentia</span></span> (διαφορὰ).<br /> +A <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">proprium</span></span> (ἰδιόν).<br /> +An <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">accidens</span></span> (συμβεβηκός). +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is to be remarked of these distinctions, that they express, +not what the predicate is in its own meaning, but what +relation it bears to the subject of which it happens on the +particular occasion to be predicated. There are not some +names which are exclusively genera, and others which are +exclusively species, or differentiæ; but the same name is referred +to one or another Predicable, according to the subject +of which it is predicated on the particular occasion. <em class="tei tei-emph"><span style="font-style: italic">Animal</span></em>, +for instance, is a genus with respect to man, or John; a +species with respect to Substance, or Being. <em class="tei tei-emph"><span style="font-style: italic">Rectangular</span></em> is +one of the Differentiæ of a geometrical square; it is merely +one of the Accidentia of the table at which I am writing. +The words genus, species, &c., are therefore relative terms; +they are names applied to certain predicates, to express the +relation between them and some given subject: a relation +grounded, as we shall see, not on what the predicate connotes, +but on the class which it <em class="tei tei-emph"><span style="font-style: italic">de</span></em>notes, and on the place +which, in some given classification, that class occupies relatively +to the particular subject. +</p> + +<span class="tei tei-pb" id="page135">[pg 135]</span><a name="Pg135" id="Pg135" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Of these five names, two, Genus and Species, are +not only used by naturalists in a technical acceptation not +precisely agreeing with their philosophical meaning, but have +also acquired a popular acceptation, much more general than +either. In this popular sense any two classes, one of which +includes the whole of the other and more, may be called a +Genus and a Species. Such, for instance, are Animal and +Man; Man and Mathematician. Animal is a genus; Man +and Brute are its two species; or we may divide it into a +greater number of species, as man, horse, dog, &c. <em class="tei tei-emph"><span style="font-style: italic">Biped</span></em>, +or <em class="tei tei-emph"><span style="font-style: italic">two-footed animal</span></em>, may also be considered a genus, of +which man and bird are two species. <em class="tei tei-emph"><span style="font-style: italic">Taste</span></em> is a genus, of +which sweet taste, sour taste, salt taste, &c. are species. +<em class="tei tei-emph"><span style="font-style: italic">Virtue</span></em> is a genus; justice, prudence, courage, fortitude, generosity, +&c. are its species. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The same class which is a genus with reference to the +sub-classes or species included in it, may be itself a species +with reference to a more comprehensive, or, as it is often +called, a superior, genus. Man is a species with reference +to animal, but a genus with reference to the species mathematician. +Animal is a genus, divided into two species, man +and brute; but animal is also a species, which, with another +species, vegetable, makes up the genus, organized being. +Biped is a genus with reference to man and bird, but a +species with respect to the superior genus, animal. Taste is +a genus divided into species, but also a species of the genus +sensation. Virtue, a genus with reference to justice, temperance, +&c., is one of the species of the genus, mental +quality. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In this popular sense the words Genus and Species have +passed into common discourse. And it should be observed +that, in ordinary parlance, not the name of the class, but the +class itself, is said to be the genus or species; not, of course, +the class in the sense of each individual of that class, but the +individuals collectively, considered as an aggregate whole; +the name by which the class is designated being then called +not the genus or species, but the generic or specific name. +<span class="tei tei-pb" id="page136">[pg 136]</span><a name="Pg136" id="Pg136" class="tei tei-anchor"></a> +And this is an admissible form of expression; nor is it of +any importance which of the two modes of speaking we +adopt, provided the rest of our language is consistent with it; +but if we call the class itself the genus, we must not talk of +predicating the genus. We predicate of man the <em class="tei tei-emph"><span style="font-style: italic">name</span></em> +mortal; and by predicating the name, we may be said, in an +intelligible sense, to predicate what the name expresses, the +<em class="tei tei-emph"><span style="font-style: italic">attribute</span></em> mortality; but in no allowable sense of the word +predication do we predicate of man the <em class="tei tei-emph"><span style="font-style: italic">class</span></em> mortal. We +predicate of him the fact of <em class="tei tei-emph"><span style="font-style: italic">belonging</span></em> to the class. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +By the Aristotelian logicians, the terms genus and species +were used in a more restricted sense. They did not admit +every class which could be divided into other classes to be a +genus, or every class which could be included in a larger +class to be a species. Animal was by them considered a +genus; and man and brute co-ordinate species under that +genus: <em class="tei tei-emph"><span style="font-style: italic">biped</span></em> would not have been admitted to be a genus with reference to +man, but a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">proprium</span></span> or +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">accidens</span></span> only. It +was requisite, according to their theory, that genus and +species should be of the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the subject. <em class="tei tei-emph"><span style="font-style: italic">Animal</span></em> was +of the essence of man; <em class="tei tei-emph"><span style="font-style: italic">biped</span></em> was not. And in every classification +they considered some one class as the lowest or <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">infima</span></span> +species. Man, for instance, was a lowest species. Any +further divisions into which the class might be capable of +being broken down, as man into white, black, and red man, +or into priest and layman, they did not admit to be species. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It has been seen, however, in the preceding chapter, that +the distinction between the essence of a class, and the attributes +or properties which are not of its essence—a distinction +which has given occasion to so much abstruse speculation, +and to which so mysterious a character was formerly, and by +many writers is still, attached,—amounts to nothing more +than the difference between those attributes of the class which +are, and those which are not, involved in the signification of +the class-name. As applied to individuals, the word Essence, +we found, has no meaning, except in connexion with the exploded +tenets of the Realists; and what the schoolmen +chose to call the essence of an individual, was simply the +<span class="tei tei-pb" id="page137">[pg 137]</span><a name="Pg137" id="Pg137" class="tei tei-anchor"></a> +essence of the class to which that individual was most familiarly +referred. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Is there no difference, then, save this merely verbal one, +between the classes which the schoolmen admitted to be +genera or species, and those to which they refused the title? +Is it an error to regard some of the differences which exist +among objects as differences <em class="tei tei-emph"><span style="font-style: italic">in kind</span></em> +(<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">genere</span></span> or +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">specie</span></span>), and +others only as differences in the accidents? Were the schoolmen +right or wrong in giving to some of the classes into +which things may be divided, the name of <em class="tei tei-emph"><span style="font-style: italic">kinds</span></em>, and considering +others as secondary divisions, grounded on differences +of a comparatively superficial nature? Examination will +show that the Aristotelians did mean something by this distinction, +and something important; but which, being but +indistinctly conceived, was inadequately expressed by the +phraseology of essences, and by the various other modes of +speech to which they had recourse. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. It is a fundamental principle in logic, that the +power of framing classes is unlimited, as long as there is +any (even the smallest) difference to found a distinction +upon. Take any attribute whatever, and if some things have +it, and others have not, we may ground on the attribute a +division of all things into two classes; and we actually do so, +the moment we create a name which connotes the attribute. +The number of possible classes, therefore, is boundless; and +there are as many actual classes (either of real or of imaginary +things) as there are of general names, positive and +negative together. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But if we contemplate any one of the classes so formed, +such as the class animal or plant, or the class sulphur or +phosphorus, or the class white or red, and consider in what +particulars the individuals included in the class differ from +those which do not come within it, we find a very remarkable +diversity in this respect between some classes and others. +There are some classes, the things contained in which differ +from other things only in certain particulars which may be +numbered; while others differ in more than can be numbered, +<span class="tei tei-pb" id="page138">[pg 138]</span><a name="Pg138" id="Pg138" class="tei tei-anchor"></a> +more even than we need ever expect to know. Some +classes have little or nothing in common to characterise them +by, except precisely what is connoted by the name: white +things, for example, are not distinguished by any common +properties, except whiteness; or if they are, it is only by +such as are in some way dependent on, or connected with, +whiteness. But a hundred generations have not exhausted +the common properties of animals or of plants, of sulphur or +of phosphorus; nor do we suppose them to be exhaustible, +but proceed to new observations and experiments, in the full +confidence of discovering new properties which were by no +means implied in those we previously knew. While, if any +one were to propose for investigation the common properties +of all things which are of the same colour, the same shape, +or the same specific gravity, the absurdity would be palpable. +We have no ground to believe that any such common properties +exist, except such as may be shown to be involved in +the supposition itself, or to be derivable from it by some law +of causation. It appears, therefore, that the properties, on +which we ground our classes, sometimes exhaust all that the +class has in common, or contain it all by some mode of +implication; but in other instances we make a selection of a +few properties from among not only a greater number, but a +number inexhaustible by us, and to which as we know no +bounds, they may, so far as we are concerned, be regarded +as infinite. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is no impropriety in saying that of these two +classifications, the one answers to a much more radical distinction +in the things themselves, than the other does. And +if any one even chooses to say that the one classification is +made by nature, the other by us for our convenience, he will +be right; provided he means no more than this: Where a +certain apparent difference between things (although perhaps +in itself of little moment) answers to we know not what +number of other differences, pervading not only their known +properties but properties yet undiscovered, it is not optional +but imperative to recognise this difference as the foundation +of a specific distinction: while, on the contrary, differences +<span class="tei tei-pb" id="page139">[pg 139]</span><a name="Pg139" id="Pg139" class="tei tei-anchor"></a> +that are merely finite and determinate, like those designated +by the words white, black, or red, may be disregarded if the +purpose for which the classification is made does not require +attention to those particular properties. The differences, +however, are made by nature, in both cases; while the recognition +of those differences as grounds of classification and of +naming, is, equally in both cases, the act of man: only in +the one case, the ends of language and of classification would +be subverted if no notice were taken of the difference, while +in the other case, the necessity of taking notice of it depends +on the importance or unimportance of the particular qualities +in which the difference happens to consist. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, these classes, distinguished by unknown multitudes +of properties, and not solely by a few determinate ones, are +the only classes which, by the Aristotelian logicians, were +considered as genera or species. Differences which extended +only to a certain property or properties, and there terminated, +they considered as differences only in the <em class="tei tei-emph"><span style="font-style: italic">accidents</span></em> +of things; but where any class differed from other things by +an infinite series of differences, known and unknown, they +considered the distinction as one of <em class="tei tei-emph"><span style="font-style: italic">kind</span></em>, and spoke of it as +being an <em class="tei tei-emph"><span style="font-style: italic">essential</span></em> difference, which is also one of the usual +meanings of that vague expression at the present day. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Conceiving the schoolmen to have been justified in drawing +a broad line of separation between these two kinds of +classes and of class-distinctions, I shall not only retain the +division itself, but continue to express it in their language. +According to that language, the proximate (or lowest) Kind +to which any individual is referrible, is called its species. +Conformably to this, Sir Isaac Newton would be said to be +of the species man. There are indeed numerous sub-classes +included in the class man, to which Newton also belongs; +as, for example, Christian, and Englishman, and Mathematician. +But these, though distinct classes, are not, in our +sense of the term, distinct Kinds of men. A Christian, for +example, differs from other human beings; but he differs +only in the attribute which the word expresses, namely, +belief in Christianity, and whatever else that implies, either +<span class="tei tei-pb" id="page140">[pg 140]</span><a name="Pg140" id="Pg140" class="tei tei-anchor"></a> +as involved in the fact itself, or connected with it through +some law of cause and effect. We should never think of +inquiring what properties, unconnected with Christianity +either as cause or effect, are common to all Christians and +peculiar to them; while in regard to all Men, physiologists +are perpetually carrying on such an inquiry; nor is +the answer ever likely to be completed. Man, therefore, +we may call a species; Christian, or Mathematician, +we cannot. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Note here, that it is by no means intended to imply that +there may not be different Kinds, or logical species, of man. +The various races and temperaments, the two sexes, and +even the various ages, maybe differences of kind, within our +meaning of the term. I do not say that they are so. For +in the progress of physiology it may almost be said to be +made out, that the differences which really exist between +different races, sexes, &c., follow as consequences, under +laws of nature, from a small number of primary differences +which can be precisely determined, and which, as the phrase +is, <em class="tei tei-emph"><span style="font-style: italic">account for</span></em> all the rest. If this be so, these are not distinctions +in kind; no more than Christian, Jew, Mussulman, +and Pagan, a difference which also carries many consequences +along with it. And in this way classes are often +mistaken for real kinds, which are afterwards proved not to +be so. But if it turned out, that the differences were not +capable of being thus accounted for, then Caucasian, Mongolian, +Negro, &c., would be really different Kinds of human +beings, and entitled to be ranked as species by the logician; +though not by the naturalist. For (as already noticed) the +word species is used in a very different signification in logic +and in natural history. By the naturalist, organized beings +are never said to be of different species, if it is supposed +that they could possibly have descended from the same +stock. That, however, is a sense artificially given to the +word, for the technical purposes of a particular science. To +the logician, if a negro and a white man differ in the same +manner (however less in degree) as a horse and a camel do, +that is, if their differences are inexhaustible, and not referrible +<span class="tei tei-pb" id="page141">[pg 141]</span><a name="Pg141" id="Pg141" class="tei tei-anchor"></a> +to any common cause, they are different species, whether +they are descended from common ancestors or not. But if +their differences can all be traced to climate and habits, or +to some one special difference in structure, they are not, in +the logician's view, specifically distinct. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">infima species</span></span>, +or proximate Kind, to which +an individual belongs, has been ascertained, the properties +common to that Kind include necessarily the whole of the +common properties of every other real Kind to which the +individual can be referrible. Let the individual, for example, +be Socrates, and the proximate Kind, man. Animal, or +living creature, is also a real Kind, and includes Socrates; +but since it likewise includes man, or in other words, since +all men are animals, the properties common to animals form +a portion of the common properties of the sub-class, man: +and if there be any class which includes Socrates without +including man, that class is not a real Kind. Let the class, +for example, be <span class="tei tei-hi"><span style="font-style: italic">flat-nosed</span></span>; that being a class which includes +Socrates, without including all men. To determine whether +it is a real Kind, we must ask ourselves this question: Have +all flat-nosed animals, in addition to whatever is implied in +their flat noses, any common properties, other than those +which are common to all animals whatever? If they had; +if a flat nose were a mark or index to an indefinite number +of other peculiarities, not deducible from the former by any +ascertainable law; then out of the class man we might cut +another class, flat-nosed man, which, according to our definition, +would be a Kind. But if we could do this, man +would not be, as it was assumed to be, the proximate Kind. +Therefore, the properties of the proximate Kind do comprehend +those (whether known or unknown) of all other Kinds +to which the individual belongs; which was the point we +undertook to prove. And hence, every other Kind which is +predicable of the individual, will be to the proximate Kind +in the relation of a genus, according to even the popular +acceptation of the terms genus and species; that is, it will +be a larger class, including it and more. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We are now able to fix the logical meaning of these +<span class="tei tei-pb" id="page142">[pg 142]</span><a name="Pg142" id="Pg142" class="tei tei-anchor"></a> +terms. Every class which is a real Kind, that is, which is +distinguished from all other classes by an indeterminate multitude +of properties not derivable from one another, is either +a genus or a species. A Kind which is not divisible into +other Kinds, cannot be a genus, because it has no species +under it; but it is itself a species, both with reference to the +individuals below and to the genera above, (Species Prædicabilis +and Species Subjicibilis.) But every Kind which +admits of division into real Kinds (as animal into quadruped, +bird, &c., or quadruped into various species of quadrupeds) is a +genus to all below it, a species to all genera in which it is +itself included. And here we may close this part of the +discussion, and pass to the three remaining predicables, +Differentia, Proprium, and Accidens. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. To begin with Differentia. This word is correlative +with the words genus and species, and as all admit, it signifies +the attribute which distinguishes a given species from +every other species of the same genus. This is so far clear: +but we may still ask, which of the distinguishing attributes +it signifies. For we have seen that every Kind (and a species +must be a Kind) is distinguished from other Kinds not by +any one attribute, but by an indefinite number. Man, for +instance, is a species of the genus animal; Rational (or +rationality, for it is of no consequence whether we use the concrete +or the abstract form) is generally assigned by logicians +as the Differentia; and doubtless this attribute serves the +purpose of distinction: but it has also been remarked of +man, that he is a cooking animal; the only animal that +dresses its food. This, therefore, is another of the attributes +by which the species man is distinguished from other species +of the same genus: would this attribute serve equally well +for a differentia? The Aristotelians say No; having laid it +down that the differentia must, like the genus and species, +be of the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the subject. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And here we lose even that vestige of a meaning grounded +in the nature of the things themselves, which may be supposed +to be attached to the word essence when it is said that +<span class="tei tei-pb" id="page143">[pg 143]</span><a name="Pg143" id="Pg143" class="tei tei-anchor"></a> +genus and species must be of the essence of the thing. There +can be no doubt that when the schoolmen talked of the essences +of things as opposed to their accidents, they had confusedly +in view the distinction between differences of kind, +and the differences which are not of kind; they meant to +intimate that genera and species must be Kinds. Their +notion of the essence of a thing was a vague notion of a +something which makes it what it is, <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span>, which makes it +the Kind of thing that it is—which causes it to have all that +variety of properties which distinguish its Kind. But when +the matter came to be looked at more closely, nobody could +discover what caused the thing to have all those properties, +nor even that there was anything which caused it to have +them. Logicians, however, not liking to admit this, and +being unable to detect what made the thing to be what it +was, satisfied themselves with what made it to be what it was +called. Of the innumerable properties, known and unknown, +that are common to the class man, a portion only, and of +course a very small portion, are connoted by its name; these +few, however, will naturally have been thus distinguished +from the rest either for their greater obviousness, or for +greater supposed importance. These properties, then, which +were connoted by the name, logicians seized upon, and called +them the essence of the species; and not stopping there, +they affirmed them, in the case of the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">infima species</span></span>, to be the +essence of the individual too; for it was their maxim, that +the species contained the <span class="tei tei-q">“whole essence”</span> of the thing. +Metaphysics, that fertile field of delusion propagated by +language, does not afford a more signal instance of such +delusion. On this account it was that rationality, being +connoted by the name man, was allowed to be a differentia +of the class; but the peculiarity of cooking their food, not +being connoted, was relegated to the class of accidental +properties. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The distinction, therefore, between Differentia, Proprium, +and Accidens, is not founded in the nature of things, but in +the connotation of names; and we must seek it there, if we +wish to find what it is. +</p> + +<span class="tei tei-pb" id="page144">[pg 144]</span><a name="Pg144" id="Pg144" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From the fact that the genus includes the species, in +other words <em class="tei tei-emph"><span style="font-style: italic">de</span></em>notes more than the species, or is predicable +of a greater number of individuals, it follows that the species +must connote more than the genus. It must connote all the +attributes which the genus connotes, or there would be +nothing to prevent it from denoting individuals not included +in the genus. And it must connote something besides, +otherwise it would include the whole genus. Animal denotes +all the individuals denoted by man, and many more. +Man, therefore, must connote all that animal connotes, +otherwise there might be men who are not animals; and it +must connote something more than animal connotes, otherwise +all animals would be men. This surplus of connotation—this +which the species connotes over and above the +connotation of the genus—is the Differentia, or specific difference; +or, to state the same proposition in other words, +the Differentia is that which must be added to the connotation +of the genus, to complete the connotation of the +species. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The word man, for instance, exclusively of what it connotes +in common with animal, also connotes rationality, and +at least some approximation to that external form, which we +all know, but which, as we have no name for it considered +in itself, we are content to call the human. The differentia, +or specific difference, therefore, of man, as referred to the +genus animal, is that outward form and the possession of +reason. The Aristotelians said, the possession of reason, +without the outward form. But if they adhered to this, they +would have been obliged to call the Houyhnhms men. The +question never arose, and they were never called upon to +decide how such a case would have affected their notion of +essentiality. However this may be, they were satisfied with +taking such a portion of the differentia as sufficed to distinguish +the species from all other <em class="tei tei-emph"><span style="font-style: italic">existing</span></em> things, although +by so doing they might not exhaust the connotation of the +name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. And here, to prevent the notion of differentia from +being restricted within too narrow limits, it is necessary +<span class="tei tei-pb" id="page145">[pg 145]</span><a name="Pg145" id="Pg145" class="tei tei-anchor"></a> +to remark, that a species, even as referred to the same +genus, will not always have the same differentia, but a +different one, according to the principle and purpose which +preside over the particular classification. For example, +a naturalist surveys the various kinds of animals, and looks +out for the classification of them most in accordance with +the order in which, for zoological purposes, he thinks it +desirable that our ideas should arrange themselves. With +this view he finds it advisable that one of his fundamental +divisions should be into warm-blooded and cold-blooded +animals; or into animals which breathe with lungs and those +which breathe with gills; or into carnivorous, and frugivorous +or graminivorous; or into those which walk on the flat part +and those which walk on the extremity of the foot, a distinction +on which some of Cuvier's families are founded. +In doing this, the naturalist creates so many new classes, +which are by no means those to which the individual animal +is familiarly and spontaneously referred; nor should we ever +think of assigning to them so prominent a position in our +arrangement of the animal kingdom, unless for a preconceived +purpose of scientific convenience. And to the liberty +of doing this there is no limit. In the examples we have +given, most of the classes are real Kinds, since each of the +peculiarities is an index to a multitude of properties, belonging +to the class which it characterizes: but even if the case +were otherwise—if the other properties of those classes could +all be derived, by any process known to us, from the one +peculiarity on which the class is founded—even then, if +those derivative properties were of primary importance for the +purposes of the naturalist, he would be warranted in founding +his primary divisions on them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If, however, practical convenience is a sufficient warrant +for making the main demarcations in our arrangement of +objects run in lines not coinciding with any distinction of +Kind, and so creating genera and species in the popular +sense which are not genera or species in the rigorous sense +at all; <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à fortiori</span></span> +must we be warranted, when our genera +and species <em class="tei tei-emph"><span style="font-style: italic">are</span></em> real genera and species, in marking the distinction +<span class="tei tei-pb" id="page146">[pg 146]</span><a name="Pg146" id="Pg146" class="tei tei-anchor"></a> +between them by those of their properties which +considerations of practical convenience most strongly recommend. +If we cut a species out of a given genus—the species +man, for instance, out of the genus animal—with an intention +on our part that the peculiarity by which we are to be +guided in the application of the name man should be +rationality, then rationality is the differentia of the species +man. Suppose, however, that, being naturalists, we, for the +purposes of our particular study, cut out of the genus animal +the same species man, but with an intention that the distinction +between man and all other species of animal should +be, not rationality, but the possession of <span class="tei tei-q">“four incisors in +each jaw, tusks solitary, and erect posture.”</span> It is evident +that the word man, when used by us as naturalists, no longer +connotes rationality, but connotes the three other properties +specified; for that which we have expressly in view when +we impose a name, assuredly forms part of the meaning of +that name. We may, therefore, lay it down as a maxim, +that wherever there is a Genus, and a Species marked out +from that genus by an assignable differentia, the name of +the species must be connotative, and must connote the +differentia; but the connotation may be special—not involved +in the signification of the term as ordinarily used, but +given to it when employed as a term of art or science. The +word Man, in common use, connotes rationality and a certain +form, but does not connote the number or character of +the teeth: in the Linnæan system it connotes the number of +incisor and canine teeth, but does not connote rationality +nor any particular form. The word <em class="tei tei-emph"><span style="font-style: italic">man</span></em> has, therefore, two +different meanings; although not commonly considered as +ambiguous, because it happens in both cases to <em class="tei tei-emph"><span style="font-style: italic">de</span></em>note the +same individual objects. But a case is conceivable in which +the ambiguity would become evident: we have only to +imagine that some new kind of animal were discovered, +having Linnæus's three characteristics of humanity, but not +rational, or not of the human form. In ordinary parlance +these animals would not be called men; but in natural history +they must still be called so by those, if any there be, +<span class="tei tei-pb" id="page147">[pg 147]</span><a name="Pg147" id="Pg147" class="tei tei-anchor"></a> +who adhere to the Linnæan classification; and the question +would arise, whether the word should continue to be used in +two senses, or the classification be given up, and the technical +sense of the term be abandoned along with it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Words not otherwise connotative may, in the mode just +adverted to, acquire a special or technical connotation. Thus +the word whiteness, as we have so often remarked, connotes +nothing; it merely denotes the attribute corresponding to a +certain sensation: but if we are making a classification of +colours, and desire to justify, or even merely to point out, +the particular place assigned to whiteness in our arrangement, +we may define it <span class="tei tei-q">“the colour produced by the mixture +of all the simple rays;”</span> and this fact, though by no means +implied in the meaning of the word whiteness as ordinarily +used, but only known by subsequent scientific investigation, +is part of its meaning in the particular essay or treatise, and +becomes the differentia of the species.<a id="noteref_24" name="noteref_24" href="#note_24"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">24</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The differentia, therefore, of a species, may be defined +to be, that part of the connotation of the specific name, +whether ordinary, or special and technical, which distinguishes +the species in question from all other species of the +genus to which on the particular occasion we are referring +it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. Having disposed of Genus, Species, and Differentia, +we shall not find much difficulty in attaining a clear +conception of the distinction between the other two predicables, +as well as between them and the first three. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the Aristotelian phraseology, Genus and Differentia +are of the <em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the subject; by which, as we have seen, +is really meant that the properties signified by the genus +and those signified by the differentia, form part of the connotation +of the name denoting the species. Proprium and +<span class="tei tei-pb" id="page148">[pg 148]</span><a name="Pg148" id="Pg148" class="tei tei-anchor"></a> +Accidens, on the other hand, form no part of the essence, +but are predicated of the species only <em class="tei tei-emph"><span style="font-style: italic">accidentally</span></em>. Both +are Accidents, in the wider sense in which the accidents of +a thing are opposed to its essence; though, in the doctrine +of the Predicables, Accidens is used for one sort of accident +only, Proprium being another sort. Proprium, continue the +schoolmen, is predicated <em class="tei tei-emph"><span style="font-style: italic">accidentally</span></em>, indeed, but <em class="tei tei-emph"><span style="font-style: italic">necessarily</span></em>; +or, as they further explain it, signifies an attribute which is +not indeed part of the essence, but which flows from, or is a +consequence of, the essence, and is, therefore, inseparably +attached to the species; <span class="tei tei-hi"><span style="font-style: italic">e.g.</span></span> the various properties of a +triangle, which, though no part of its definition, must necessarily +be possessed by whatever comes under that definition. +Accidens, on the contrary, has no connexion whatever with +the essence, but may come and go, and the species still +remain what it was before. If a species could exist without its +Propria, it must be capable of existing without that on which +its Propria are necessarily consequent, and therefore without +its essence, without that which constitutes it a species. But +an Accidens, whether separable or inseparable from the +species in actual experience, may be supposed separated, +without the necessity of supposing any other alteration; or +at least, without supposing any of the essential properties of +the species to be altered, since with them an Accidens has +no connexion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A Proprium, therefore, of the species, may be defined, +any attribute which belongs to all the individuals included +in the species, and which, although not connoted by the +specific name, (either ordinarily if the classification we are +considering be for ordinary purposes, or specially if it be for +a special purpose,) yet follows from some attribute which the +name either ordinarily or specially connotes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +One attribute may follow from another in two ways; and +there are consequently two kinds of Proprium. It may +follow as a conclusion follows premisses, or it may follow as +an effect follows a cause. Thus, the attribute of having the +opposite sides equal, which is not one of those connoted by +the word Parallelogram, nevertheless follows from those connoted +<span class="tei tei-pb" id="page149">[pg 149]</span><a name="Pg149" id="Pg149" class="tei tei-anchor"></a> +by it, namely, from having the opposite sides straight +lines and parallel, and the number of sides four. The attribute, +therefore, of having the opposite sides equal, is a Proprium +of the class parallelogram; and a Proprium of the +first kind, which follows from the connoted attributes by way +of <em class="tei tei-emph"><span style="font-style: italic">demonstration</span></em>. The attribute of being capable of understanding +language, is a Proprium of the species man, since, +without being connoted by the word, it follows from an +attribute which the word does connote, viz. from the attribute +of rationality. But this is a Proprium of the second kind, +which follows by way of <em class="tei tei-emph"><span style="font-style: italic">causation</span></em>. How it is that one property +of a thing follows, or can be inferred, from another; +under what conditions this is possible, and what is the exact +meaning of the phrase; are among the questions which will +occupy us in the two succeeding Books. At present it needs +only be said, that whether a Proprium follows by demonstration +or by causation, it follows <em class="tei tei-emph"><span style="font-style: italic">necessarily</span></em>; that is to say, it +<em class="tei tei-emph"><span style="font-style: italic">cannot but</span></em> follow, consistently with some law which we regard +as a part of the constitution either of our thinking faculty or +of the universe. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 8. Under the remaining predicable, Accidens, are included +all attributes of a thing which are neither involved in +the signification of the name, (whether ordinarily or as a +term of art,) nor have, so far as we know, any necessary +connexion with attributes which are so involved. They are +commonly divided into Separable and Inseparable Accidents. +Inseparable accidents are those which—although we know of +no connexion between them and the attributes constitutive of +the species, and although, therefore, so far as we are aware, +they might be absent without making the name inapplicable +and the species a different species—are yet never in fact +known to be absent. A concise mode of expressing the +same meaning is, that inseparable accidents are properties +which are universal to the species, but not necessary to it. +Thus, blackness is an attribute of a crow, and, as far as we +know, a universal one. But if we were to discover a race of +white birds, in other respects resembling crows, we should +<span class="tei tei-pb" id="page150">[pg 150]</span><a name="Pg150" id="Pg150" class="tei tei-anchor"></a> +not say, These are not crows; we should say, These are +white crows. Crow, therefore, does not connote blackness; +nor, from any of the attributes which it does connote, whether +as a word in popular use or as a term of art, could blackness +be inferred. Not only, therefore, can we conceive a white +crow, but we know of no reason why such an animal should +not exist. Since, however, none but black crows are known +to exist, blackness, in the present state of our knowledge, +ranks as an accident, but an inseparable accident, of the +species crow. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Separable Accidents are those which are found, in point +of fact, to be sometimes absent from the species; which are +not only not necessary, but not even universal. They are +such as do not belong to every individual of the species, but +only to some individuals; or if to all, not at all times. Thus +the colour of an European is one of the separable accidents +of the species man, because it is not an attribute of all +human creatures. Being born, is also (speaking in the +logical sense) a separable accident of the species man, because, +although an attribute of all human beings, it is so only +at one particular time. <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">A fortiori</span></span> +those attributes which +are not constant even in the same individual, as, to be in one +or in another place, to be hot or cold, sitting or walking, +must be ranked as separable accidents. +</p> + +</div> + +<span class="tei tei-pb" id="page151">[pg 151]</span><a name="Pg151" id="Pg151" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc37" id="toc37"></a> +<a name="pdf38" id="pdf38"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VIII. OF DEFINITION.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. One necessary part of the theory of Names and of +Propositions remains to be treated of in this place: the theory +of Definitions. As being the most important of the class of +propositions which we have characterized as purely verbal, they +have already received some notice in the chapter preceding +the last. But their fuller treatment was at that time postponed, +because definition is so closely connected with classification, +that, until the nature of the latter process is in some +measure understood, the former cannot be discussed to much +purpose. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The simplest and most correct notion of a Definition is, +a proposition declaratory of the meaning of a word; namely, +either the meaning which it bears in common acceptation, or +that which the speaker or writer, for the particular purposes +of his discourse, intends to annex to it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The definition of a word being the proposition which +enunciates its meaning, words which have no meaning are +unsusceptible of definition. Proper names, therefore, cannot +be defined. A proper name being a mere mark put upon an +individual, and of which it is the characteristic property to be +destitute of meaning, its meaning cannot of course be declared; +though we may indicate by language, as we might +indicate still more conveniently by pointing with the finger, +upon what individual that particular mark has been, or is +intended to be, put. It is no definition of <span class="tei tei-q">“John Thomson”</span> +to say he is <span class="tei tei-q">“the son of General Thomson;”</span> for the name +John Thomson does not express this. Neither is it any +definition of <span class="tei tei-q">“John Thomson”</span> to say he is <span class="tei tei-q">“the man now +crossing the street.”</span> These propositions may serve to make +known who is the particular man to whom the name belongs; +<span class="tei tei-pb" id="page152">[pg 152]</span><a name="Pg152" id="Pg152" class="tei tei-anchor"></a> +but that may be done still more unambiguously by pointing +to him, which, however, has not usually been esteemed one +of the modes of definition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the case of connotative names, the meaning, as has +been so often observed, is the connotation; and the definition +of a connotative name, is the proposition which declares +its connotation. This may be done either directly or indirectly. +The direct mode would be by a proposition in this +form: <span class="tei tei-q">“Man”</span> (or whatsover the word may be) <span class="tei tei-q">“is a name +connoting such and such attributes,”</span> or <span class="tei tei-q">“is a name which, +when predicated of anything, signifies the possession of such +and such attributes by that thing.”</span> Or thus: Man is everything +which possesses such and such attributes: Man is +everything which possesses corporeity, organization, life, +rationality, and certain peculiarities of external form. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This form of definition is the most precise and least +equivocal of any; but it is not brief enough, and is besides +too technical and pedantic for common discourse. The +more usual mode of declaring the connotation of a name, is +to predicate of it another name or names of known signification, +which connote the same aggregation of attributes. +This may be done either by predicating of the name intended +to be defined, another connotative name exactly +synonymous, as, <span class="tei tei-q">“Man is a human being,”</span> which is not +commonly accounted a definition at all; or by predicating +two or more connotative names, which make up among them +the whole connotation of the name to be defined. In this +last case, again, we may either compose our definition of as +many connotative names as there are attributes, each attribute +being connoted by one; as, Man is a corporeal, organized, +animated, rational being, shaped so and so; or we may +employ names which connote several of the attributes at +once, as, Man is a rational <em class="tei tei-emph"><span style="font-style: italic">animal</span></em>, shaped so and so. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The definition of a name, according to this view of it, is +the sum total of all the <em class="tei tei-emph"><span style="font-style: italic">essential</span></em> propositions which can be +framed with that name for their subject. All propositions +the truth of which is implied in the name, all those which +we are made aware of by merely hearing the name, are included +<span class="tei tei-pb" id="page153">[pg 153]</span><a name="Pg153" id="Pg153" class="tei tei-anchor"></a> +in the definition, if complete, and may be evolved +from it without the aid of any other premisses; whether the +definition expresses them in two or three words, or in a +larger number. It is, therefore, not without reason that +Condillac and other writers have affirmed a definition to be +an <em class="tei tei-emph"><span style="font-style: italic">analysis</span></em>. To resolve any complex whole into the +elements of which it is compounded, is the meaning of +analysis; and this we do when we replace one word which +connotes a set of attributes collectively, by two or more +which connote the same attributes singly, or in smaller +groups. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. From this, however, the question naturally arises, +in what manner are we to define a name which connotes +only a single attribute? for instance, <span class="tei tei-q">“white,”</span> which connotes +nothing but whiteness; <span class="tei tei-q">“rational,”</span> which connotes +nothing but the possession of reason. It might seem that +the meaning of such names could only be declared in two +ways; by a synonymous term, if any such can be found; +or in the direct way already alluded to: <span class="tei tei-q">“White is a name +connoting the attribute whiteness.”</span> Let us see, however, +whether the analysis of the meaning of the name, that is, +the breaking down of that meaning into several parts, admits +of being carried farther. Without at present deciding this +question as to the word <em class="tei tei-emph"><span style="font-style: italic">white</span></em>, it is obvious that in the case +of <em class="tei tei-emph"><span style="font-style: italic">rational</span></em> some further explanation may be given of its +meaning than is contained in the proposition, <span class="tei tei-q">“Rational is +that which possesses the attribute of reason;”</span> since the +attribute reason itself admits of being defined. And here +we must turn our attention to the definitions of attributes, +or rather of the names of attributes, that is, of abstract +names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In regard to such names of attributes as are connotative, +and express attributes of those attributes, there is no difficulty: +like other connotative names, they are defined by +declaring their connotation. Thus, the word <span class="tei tei-hi"><span style="font-style: italic">fault</span></span> may be +defined, <span class="tei tei-q">“a quality productive of evil or inconvenience.”</span> +Sometimes, again, the attribute to be defined is not one +<span class="tei tei-pb" id="page154">[pg 154]</span><a name="Pg154" id="Pg154" class="tei tei-anchor"></a> +attribute, but an union of several: we have only, therefore, +to put together the names of all the attributes taken separately, +and we obtain the definition of the name which +belongs to them all taken together; a definition which will +correspond exactly to that of the corresponding concrete +name. For, as we define a concrete name by enumerating +the attributes which it connotes, and as the attributes connoted +by a concrete name form the entire signification of the +corresponding abstract one, the same enumeration will serve +for the definition of both. Thus, if the definition of <em class="tei tei-emph"><span style="font-style: italic">a human +being</span></em> be this, <span class="tei tei-q">“a being, corporeal, animated, rational, and +shaped so and so,”</span> the definition of <em class="tei tei-emph"><span style="font-style: italic">humanity</span></em> will be, corporeity +and animal life, combined with rationality, and with +such and such a shape. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, on the other hand, the abstract name does not +express a complication of attributes, but a single attribute, +we must remember that every attribute is grounded on some +fact or phenomenon, from which, and which alone, it derives +its meaning. To that fact or phenomenon, called in a former +chapter the foundation of the attribute, we must, therefore, +have recourse for its definition. Now, the foundation of the +attribute may be a phenomenon of any degree of complexity, +consisting of many different parts, either coexistent or in +succession. To obtain a definition of the attribute, we must +analyse the phenomenon into these parts. Eloquence, for +example, is the name of one attribute only; but this attribute +is grounded on external effects of a complicated nature, +flowing from acts of the person to whom we ascribe the +attribute; and by resolving this phenomenon of causation +into its two parts, the cause and the effect, we obtain a +definition of eloquence, viz., the power of influencing the +feelings by speech or writing. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A name, therefore, whether concrete or abstract, admits +of definition, provided we are able to analyse, that is, to +distinguish into parts, the attribute or set of attributes which +constitute the meaning both of the concrete name and of the +corresponding abstract: if a set of attributes, by enumerating +them; if a single attribute, by dissecting the fact or phenomenon +<span class="tei tei-pb" id="page155">[pg 155]</span><a name="Pg155" id="Pg155" class="tei tei-anchor"></a> +(whether of perception or of internal consciousness) +which is the foundation of the attribute. But, further, even +when the fact is one of our simple feelings or states of +consciousness, and therefore unsusceptible of analysis, the +names both of the object and of the attribute still admit of +definition; or, rather, would do so if all our simple feelings +had names. Whiteness may be defined, the property or +power of exciting the sensation of white. A white object +may be defined an object which excites the sensation of +white. The only names which are unsusceptible of definition, +because their meaning is unsusceptible of analysis, +are the names of the simple feelings themselves. These are +in the same condition as proper names. They are not +indeed, like proper names, unmeaning; for the words <em class="tei tei-emph"><span style="font-style: italic">sensation +of white</span></em> signify, that the sensation which I so denominate +resembles other sensations which I remember to +have had before, and to have called by that name. But as +we have no words by which to recall those former sensations, +except the very word which we seek to define, or some other +which, being exactly synonymous with it, requires definition +as much, words cannot unfold the signification of this class +of names; and we are obliged to make a direct appeal to the +personal experience of the individual whom we address. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Having stated what seems to be the true idea of a +Definition, we proceed to examine some opinions of philosophers, +and some popular conceptions on the subject, which +conflict more or less with that idea. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The only adequate definition of a name is, as already +remarked, one which declares the facts, and the whole of the +facts, which the name involves in its signification. But with +most persons the object of a definition does not embrace so +much; they look for nothing more, in a definition, than a +guide to the correct use of the term—a protection against +applying it in a manner inconsistent with custom and convention. +Anything, therefore, is to them a sufficient definition +of a term, which will serve as a correct index to what +the term <em class="tei tei-emph"><span style="font-style: italic">de</span></em>notes; although not embracing the whole, and +<span class="tei tei-pb" id="page156">[pg 156]</span><a name="Pg156" id="Pg156" class="tei tei-anchor"></a> +sometimes, perhaps, not even any part, of what it connotes. +This gives rise to two sorts of imperfect, or unscientific definition; +namely, Essential but incomplete Definitions, and +Accidental Definitions, or Descriptions. In the former, a +connotative name is defined by a part only of its connotation; +in the latter, by something which forms no part of the connotation +at all. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An example of the first kind of imperfect definitions is +the following:—Man is a rational animal. It is impossible +to consider this as a complete definition of the word Man, +since (as before remarked) if we adhered to it we should be +obliged to call the Houyhnhms men; but as there happen +to be no Houyhnhms, this imperfect definition is sufficient to +mark out and distinguish from all other things, the objects at +present denoted by <span class="tei tei-q">“man;”</span> all the beings actually known to +exist, of whom the name is predicable. Though the word is +defined by some only among the attributes which it connotes, +not by all, it happens that all known objects which +possess the enumerated attributes, possess also those which +are omitted; so that the field of predication which the word +covers, and the employment of it which is conformable to +usage, are as well indicated by the inadequate definition as +by an adequate one. Such definitions, however, are always +liable to be overthrown by the discovery of new objects in +nature. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Definitions of this kind are what logicians have had in +view, when they laid down the rule, that the definition of a +species should be <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per genus et +differentiam</span></span>. Differentia being seldom taken to mean the whole +of the peculiarities constitutive of the species, but some one of those +peculiarities only, a complete definition would be +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per genus et differentias</span></span>, +rather than <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">differentiam</span></span>. +It would include, with the name of the superior genus, not merely <em class="tei tei-emph"><span style="font-style: italic">some</span></em> +attribute which distinguishes the species intended to be defined from all other +species of the same genus, but <em class="tei tei-emph"><span style="font-style: italic">all</span></em> the attributes implied in +the name of the species, which the name of the superior genus +has not already implied. The assertion, however, that a +definition must of necessity consist of a genus and differentiæ, +<span class="tei tei-pb" id="page157">[pg 157]</span><a name="Pg157" id="Pg157" class="tei tei-anchor"></a> +is not tenable. It was early remarked by logicians, +that the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">summum genus</span></span> +in any classification, having no genus +superior to itself, could not be defined in this manner. Yet +we have seen that all names, except those of our elementary +feelings, are susceptible of definition in the strictest sense; +by setting forth in words the constituent parts of the fact or +phenomenon, of which the connotation of every word is +ultimately composed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. Although the first kind of imperfect definition, +(which defines a connotative term by a part only of what it +connotes, but a part sufficient to mark out correctly the +boundaries of its denotation,) has been considered by the +ancients, and by logicians in general, as a complete definition; +it has always been deemed necessary that the attributes +employed should really form part of the connotation; +for the rule was that the definition must be drawn from the +<em class="tei tei-emph"><span style="font-style: italic">essence</span></em> of the class; and this would not have been the case +if it had been in any degree made up of attributes not connoted +by the name. The second kind of imperfect definition, +therefore, in which the name of a class is defined by any of +its accidents,—that is, by attributes which are not included +in its connotation,—has been rejected from the rank of +genuine Definition by all logicians, and has been termed +Description. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This kind of imperfect definition, however, takes its rise +from the same cause as the other, namely, the willingness to +accept as a definition anything which, whether it expounds +the meaning of the name or not, enables us to discriminate +the things denoted by the name from all other things, and +consequently to employ the term in predication without +deviating from established usage. This purpose is duly +answered by stating any (no matter what) of the attributes +which are common to the whole of the class, and peculiar to +it; or any combination of attributes which may happen to +be peculiar to it, though separately each of those attributes +may be common to it with some other things. It is only +necessary that the definition (or description) thus formed, +<span class="tei tei-pb" id="page158">[pg 158]</span><a name="Pg158" id="Pg158" class="tei tei-anchor"></a> +should be <em class="tei tei-emph"><span style="font-style: italic">convertible</span></em> with the name which it professes to +define; that is, should be exactly co-extensive with it, being +predicable of everything of which it is predicable, and of +nothing of which it is not predicable; although the attributes +specified may have no connexion with those which mankind +had in view when they formed or recognised the class, and +gave it a name. The following are correct definitions of +Man, according to this test: Man is a mammiferous animal, +having (by nature) two hands (for the human species answers +to this description, and no other animal does): Man is an +animal who cooks his food: Man is a featherless biped. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What would otherwise be a mere description, may be +raised to the rank of a real definition by the peculiar purpose +which the speaker or writer has in view. As was seen +in the preceding chapter, it may, for the ends of a particular +art or science, or for the more convenient statement of an +author's particular doctrines, be advisable to give to some +general name, without altering its denotation, a special connotation, +different from its ordinary one. When this is done, +a definition of the name by means of the attributes which +make up the special connotation, though in general a mere +accidental definition or description, becomes on the particular +occasion and for the particular purpose a complete +and genuine definition. This actually occurs with respect +to one of the preceding examples, <span class="tei tei-q">“Man is a mammiferous +animal having two hands,”</span> which is the scientific definition +of man considered as one of the species in Cuvier's distribution +of the animal kingdom. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In cases of this sort, although the definition is still a +declaration of the meaning which in the particular instance +the name is appointed to convey, it cannot be said that to +state the meaning of the word is the purpose of the definition. +The purpose is not to expound a name, but to help to expound +a classification. The special meaning which Cuvier +assigned to the word Man, (quite foreign to its ordinary +meaning, though involving no change in the denotation of +the word,) was incidental to a plan of arranging animals into +classes on a certain principle, that is, according to a certain +<span class="tei tei-pb" id="page159">[pg 159]</span><a name="Pg159" id="Pg159" class="tei tei-anchor"></a> +set of distinctions. And since the definition of Man according +to the ordinary connotation of the word, though it would +have answered every other purpose of a definition, would +not have pointed out the place which the species ought to +occupy in that particular classification; he gave the word a +special connotation, that he might be able to define it by the +kind of attributes on which, for reasons of scientific convenience, +he had resolved to found his division of animated +nature. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Scientific definitions, whether they are definitions of +scientific terms or of common terms used in a scientific sense, +are almost always of the kind last spoken of: their main +purpose is to serve as the landmarks of scientific classification. +And since the classifications in any science are continually +modified as scientific knowledge advances, the +definitions in the sciences are also constantly varying. A +striking instance is afforded by the words Acid and Alkali, +especially the former. As experimental discovery advanced, +the substances classed with acids have been constantly multiplying, +and by a natural consequence the attributes connoted +by the word have receded and become fewer. At first +it connoted the attributes, of combining with an alkali to +form a neutral substance (called a salt); being compounded +of a base and oxygen; causticity to the taste and touch; +fluidity, &c. The true analysis of muriatic acid, into chlorine +and hydrogen, caused the second property, composition from +a base and oxygen, to be excluded from the connotation. +The same discovery fixed the attention of chemists upon +hydrogen as an important element in acids; and more recent +discoveries having led to the recognition of its presence in +sulphuric, nitric, and many other acids, where its existence +was not previously suspected, there is now a tendency to +include the presence of this element in the connotation of the +word. But carbonic acid, silica, sulphurous acid, have no +hydrogen in their composition; that property cannot therefore +be connoted by the term, unless those substances are no +longer to be considered acids. Causticity, and fluidity, have +long since been excluded from the characteristics of the +<span class="tei tei-pb" id="page160">[pg 160]</span><a name="Pg160" id="Pg160" class="tei tei-anchor"></a> +class, by the inclusion of silica and many other substances in +it; and the formation of neutral bodies by combination with +alkalis, together with such electro-chemical peculiarities as +this is supposed to imply, are now the only <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">differentiæ</span></span> which +form the fixed connotation of the word Acid, as a term of +chemical science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Scientific men are still seeking, and may be long ere they +find, a suitable definition of one of the earliest words in the +vocabulary of the human race, and one of those of which the +popular sense is plainest and best understood. The word I +mean is Heat; and the source of the difficulty is the imperfect +state of our scientific knowledge, which has shown to us multitudes +of phenomena certainly connected with the same +power which causes what our senses recognise as heat, but +has not yet taught us the laws of those phenomena with +sufficient accuracy to admit of our determining under what +characteristics the whole of those phenomena shall ultimately +be embodied as a class: which characteristics would of +course be so many differentiæ for the definition of the power +itself. We have advanced far enough to know that one of +the attributes connoted must be that of operating as a repulsive +force; but this is certainly not all which must ultimately +be included in the scientific definition of heat. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What is true of the definition of any term of science, is +of course true of the definition of a science itself: and accordingly, +(as observed in the Introductory Chapter of this +work,) the definition of a science must necessarily be progressive +and provisional. Any extension of knowledge or +alteration in the current opinions respecting the subject +matter, may lead to a change more or less extensive in the +particulars included in the science; and its composition +being thus altered, it may easily happen that a different +set of characteristics will be found better adapted as differentiæ +for defining its name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the same manner in which a special or technical +definition has for its object to expound the artificial classification +out of which it grows; the Aristotelian logicians +seem to have imagined that it was also the business of +<span class="tei tei-pb" id="page161">[pg 161]</span><a name="Pg161" id="Pg161" class="tei tei-anchor"></a> +ordinary definition to expound the ordinary, and what they +deemed the natural, classification of things, namely, the +division of them into Kinds; and to show the place which +each Kind occupies, as superior, collateral, or subordinate +among other Kinds. This notion would account for the rule +that all definition must necessarily be +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per genus et differentiam</span></span>, +and would also explain why any one differentia was deemed +sufficient. But to expound, or express in words, a distinction +of Kind, has already been shown to be an impossibility: +the very meaning of a Kind is, that the properties which distinguish +it do not grow out of one another, and cannot therefore +be set forth in words, even by implication, otherwise +than by enumerating them all: and all are not known, nor +ever will be so. It is idle, therefore, to look to this as one +of the purposes of a definition: while, if it be only required +that the definition of a Kind should indicate what Kinds include +it or are included by it, any definitions which expound +the connotation of the names will do this: for the name of +each class must necessarily connote enough of its properties +to fix the boundaries of the class. If the definition, therefore, +be a full statement of the connotation, it is all that a +definition can be required to be. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. Of the two incomplete or unscientific modes of +definition, and in what they differ from the complete or +scientific mode, enough has now been said. We shall next +examine an ancient doctrine, once generally prevalent and +still by no means exploded, which I regard as the source of +a great part of the obscurity hanging over some of the most +important processes of the understanding in the pursuit of +truth. According to this, the definitions of which we have +now treated are only one of two sorts into which definitions +may be divided, viz. definitions of names, and definitions of +things. The former are intended to explain the meaning of +a term; the latter, the nature of a thing; the last being incomparably +the most important. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This opinion was held by the ancient philosophers, and +by their followers, with the exception of the Nominalists; +<span class="tei tei-pb" id="page162">[pg 162]</span><a name="Pg162" id="Pg162" class="tei tei-anchor"></a> +but as the spirit of modern metaphysics, until a recent period, +has been on the whole a Nominalist spirit, the notion of definitions +of things has been to a certain extent in abeyance, +still continuing, however, to breed confusion in logic, by its +consequences indeed rather than by itself. Yet the doctrine +in its own proper form now and then breaks out, and has +appeared (among other places) where it was scarcely to be +expected, in a deservedly popular work, Archbishop Whately's +<span class="tei tei-hi"><span style="font-style: italic">Logic</span></span>.<a id="noteref_25" name="noteref_25" href="#note_25"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">25</span></span></a> +In a review of that work published by me in the +<span class="tei tei-hi"><span style="font-style: italic">Westminster Review</span></span> for January 1828, and containing some +opinions which I no longer entertain, I find the following +observations on the question now before us; observations +with which my present view of that question is still sufficiently +in accordance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“The distinction between nominal and real definitions, +<span class="tei tei-pb" id="page163">[pg 163]</span><a name="Pg163" id="Pg163" class="tei tei-anchor"></a> +between definitions of words and what are called definitions +of things, though conformable to the ideas of most of the Aristotelian +logicians, cannot, as it appears to us, be maintained. +We apprehend that no definition is ever intended to <span class="tei tei-q">‘explain +and unfold the nature of the thing.’</span> It is some confirmation +of our opinion, that none of those writers who have thought +that there were definitions of things, have ever succeeded in +discovering any criterion by which the definition of a thing +can be distinguished from any other proposition relating to +the thing. The definition, they say, unfolds the nature of +the thing: but no definition can unfold its whole nature; +and every proposition in which any quality whatever is predicated +of the thing, unfolds some part of its nature. The +true state of the case we take to be this. All definitions are +of names, and of names only; but, in some definitions, it is +clearly apparent, that nothing is intended except to explain +the meaning of the word; while in others, besides explaining +the meaning of the word, it is intended to be implied that +there exists a thing, corresponding to the word. Whether +this be or be not implied in any given case, cannot be collected +from the mere form of the expression. <span class="tei tei-q">‘A centaur is +an animal with the upper parts of a man and the lower parts +of a horse,’</span> and <span class="tei tei-q">‘A triangle is a rectilineal figure with three +sides,’</span> are, in form, expressions precisely similar; although +in the former it is not implied that any <em class="tei tei-emph"><span style="font-style: italic">thing</span></em>, conformable to +the term, really exists, while in the latter it is; as may be +seen by substituting, in both definitions, the word <em class="tei tei-emph"><span style="font-style: italic">means</span></em> for +<em class="tei tei-emph"><span style="font-style: italic">is</span></em>. In the first expression, <span class="tei tei-q">‘A centaur means an animal,’</span> +&c., the sense would remain unchanged: in the second <span class="tei tei-q">‘A +triangle means,’</span> &c., the meaning would be altered, since it +would be obviously impossible to deduce any of the truths +of geometry from a proposition expressive only of the manner +in which we intend to employ a particular sign.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“There are, therefore, expressions, commonly passing for +definitions, which include in themselves more than the mere +explanation of the meaning of a term. But it is not correct +to call an expression of this sort a peculiar kind of definition. +Its difference from the other kind consists in this, that it is +<span class="tei tei-pb" id="page164">[pg 164]</span><a name="Pg164" id="Pg164" class="tei tei-anchor"></a> +not a definition, but a definition and something more. The +definition above given of a triangle, obviously comprises +not one, but two propositions, perfectly distinguishable. The +one is, <span class="tei tei-q">‘There may exist a figure, bounded by three straight +lines:’</span> the other, <span class="tei tei-q">‘And this figure may be termed a triangle.’</span> +The former of these propositions is not a definition at all: the +latter is a mere nominal definition, or explanation of the use +and application of a term. The first is susceptible of truth +or falsehood, and may therefore be made the foundation of a +train of reasoning. The latter can neither be true nor false; +the only character it is susceptible of is that of conformity or +disconformity to the ordinary usage of language.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is a real distinction, then, between definitions of +names, and what are erroneously called definitions of things; +but it is, that the latter, along with the meaning of a name, +covertly asserts a matter of fact. This covert assertion is not +a definition, but a postulate. The definition is a mere identical +proposition, which gives information only about the use +of language, and from which no conclusions affecting matters +of fact can possibly be drawn. The accompanying postulate, +on the other hand, affirms a fact, which may lead to consequences +of every degree of importance. It affirms the real +existence of Things possessing the combination of attributes +set forth in the definition; and this, if true, may be +foundation sufficient on which to build a whole fabric of +scientific truth. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We have already made, and shall often have to repeat, +the remark, that the philosophers who overthrew Realism +by no means got rid of the consequences of Realism, but +retained long afterwards, in their own philosophy, numerous +propositions which could only have a rational meaning as +part of a Realistic system. It had been handed down from +Aristotle, and probably from earlier times, as an obvious +truth, that the science of Geometry is deduced from definitions. +This, so long as a definition was considered to be a +proposition <span class="tei tei-q">“unfolding the nature of the thing,”</span> did well +enough. But Hobbes followed, and rejected utterly the +notion that a definition declares the nature of the thing, or +does anything but state the meaning of a name; yet he continued +<span class="tei tei-pb" id="page165">[pg 165]</span><a name="Pg165" id="Pg165" class="tei tei-anchor"></a> +to affirm as broadly as any of his predecessors, that +the ἀρχαὶ, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">principia</span></span>, +or original premisses of mathematics, +and even of all science, are definitions; producing the singular +paradox, that systems of scientific truth, nay, all truths +whatever at which we arrive by reasoning, are deduced from +the arbitrary conventions of mankind concerning the signification +of words. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To save the credit of the doctrine that definitions are the +premisses of scientific knowledge, the proviso is sometimes +added, that they are so only under a certain condition, +namely, that they be framed conformably to the phenomena +of nature; that is, that they ascribe such meanings to terms +as shall suit objects actually existing. But this is only an +instance of the attempt so often made, to escape from the +necessity of abandoning old language after the ideas which it +expresses have been exchanged for contrary ones. From +the meaning of a name (we are told) it is possible to infer +physical facts, provided the name has corresponding to it +an existing thing. But if this proviso be necessary, from +which of the two is the inference really drawn? from the +existence of a thing having the properties? or from the +existence of a name meaning them? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Take, for instance, any of the definitions laid down as +premisses in Euclid's Elements; the definition, let us say, of +a circle. This, being analysed, consists of two propositions; +the one an assumption with respect to a matter of fact, the +other a genuine definition. <span class="tei tei-q">“A figure may exist, having all +the points in the line which bounds it equally distant from a +single point within it:”</span> <span class="tei tei-q">“Any figure possessing this property +is called a circle.”</span> Let us look at one of the demonstrations +which are said to depend on this definition, and observe to +which of the two propositions contained in it the demonstration +really appeals. <span class="tei tei-q">“About the centre A, describe the +circle BCD.”</span> Here is an assumption, that a figure, such +as the definition expresses, <em class="tei tei-emph"><span style="font-style: italic">may</span></em> be described; which is no +other than the postulate, or covert assumption, involved in the +so-called definition. But whether that figure be called a +circle or not is quite immaterial. The purpose would be as +well answered, in all respects except brevity, were we to say, +<span class="tei tei-pb" id="page166">[pg 166]</span><a name="Pg166" id="Pg166" class="tei tei-anchor"></a> +<span class="tei tei-q">“Through the point B, draw a line returning into itself, of +which every point shall be at an equal distance from the +point A.”</span> By this the definition of a circle would be got +rid of, and rendered needless; but not the postulate implied +in it; without that the demonstration could not stand. The +circle being now described, let us proceed to the consequence. +<span class="tei tei-q">“Since B C D is a circle, the radius B A is equal to the +radius C A.”</span> B A is equal to C A, not because B C D is a +circle, but because B C D is a figure with the radii equal. +Our warrant for assuming that such a figure about the centre +A, with the radius B A, may be made to exist, is the postulate. +Whether the admissibility of these postulates rests +on intuition, or on proof, may be a matter of dispute; but in +either case they are the premisses on which the theorems +depend; and while these are retained it would make no +difference in the certainty of geometrical truths, though +every definition in Euclid, and every technical term therein +defined, were laid aside. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is, perhaps, superfluous to dwell at so much length +on what is so nearly self-evident; but when a distinction, +obvious as it may appear, has been confounded, and by +powerful intellects, it is better to say too much than too +little for the purpose of rendering such mistakes impossible +in future. I will, therefore, detain the reader while I point +out one of the absurd consequences flowing from the supposition +that definitions, as such, are the premisses in any +of our reasonings, except such as relate to words only. If +this supposition were true, we might argue correctly from +true premisses, and arrive at a false conclusion. We should +only have to assume as a premiss the definition of a nonentity; +or rather of a name which has no entity corresponding +to it. Let this, for instance, be our definition: +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">A dragon is a serpent breathing flame.</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This proposition, considered only as a definition, is +indisputably correct. A dragon <em class="tei tei-emph"><span style="font-style: italic">is</span></em> a serpent breathing +flame: the word <em class="tei tei-emph"><span style="font-style: italic">means</span></em> that. The tacit assumption, indeed, +(if there were any such understood assertion,) of the +existence of an object with properties corresponding to +<span class="tei tei-pb" id="page167">[pg 167]</span><a name="Pg167" id="Pg167" class="tei tei-anchor"></a> +the definition, would, in the present instance, be false. +Out of this definition we may carve the premisses of the +following syllogism: +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">A dragon is a thing which breathes flame:</div> +<div class="tei tei-l" style="text-align: left">A dragon is a serpent:</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From which the conclusion is, +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">Therefore some serpent or serpents breathe flame:—</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +an unexceptionable syllogism in the first mode of the third +figure, in which both premisses are true and yet the conclusion +false; which every logician knows to be an absurdity. +The conclusion being false and the syllogism correct, the +premisses cannot be true. But the premisses, considered as +parts of a definition, are true. Therefore, the premisses +considered as parts of a definition cannot be the real ones. +The real premisses must be— +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">A dragon is a <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">really existing</span></em> thing which breathes flame:</div> +<div class="tei tei-l" style="text-align: left">A dragon is a <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">really existing</span></em> serpent:</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +which implied premisses being false, the falsity of the conclusion +presents no absurdity. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If we would determine what conclusion follows from the +same ostensible premisses when the tacit assumption of real +existence is left out, let us, according to the recommendation +in the Westminster Review, substitute <em class="tei tei-emph"><span style="font-style: italic">means</span></em> for <em class="tei tei-emph"><span style="font-style: italic">is</span></em>. We +then have— +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">Dragon is <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">a word meaning</span></em> a thing which breathes flame:</div> +<div class="tei tei-l" style="text-align: left">Dragon is <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">a word meaning</span></em> a serpent:</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From which the conclusion is, +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">Some <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">word or words which mean</span></em> a serpent, also mean a thing which +breathes flame:</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +where the conclusion (as well as the premisses) is true, and +is the only kind of conclusion which can ever follow from a +definition, namely, a proposition relating to the meaning of +words. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is still another shape into which we may transform +this syllogism. We may suppose the middle term to be the +designation neither of a thing nor of a name, but of an idea. +We then have— +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">The <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">idea of</span></em> a dragon is <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">an idea of</span></em> a thing which +breathes flame:</div> +<span class="tei tei-pb" id="page168">[pg 168]</span><a name="Pg168" id="Pg168" class="tei tei-anchor"></a> +<div class="tei tei-l" style="text-align: left">The <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">idea of</span></em> a dragon is <em class="tei tei-emph" style="text-align: left"><span style="font-style: italic">an idea of</span></em> a serpent:</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Therefore, there is <em class="tei tei-emph"><span style="font-style: italic">an idea of</span></em> a serpent, which is <em class="tei tei-emph"><span style="font-style: italic">an +idea of</span></em> a thing breathing flame. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Here the conclusion is true, and also the premisses; but +the premisses are not definitions. They are propositions +affirming that an idea existing in the mind, includes certain +ideal elements. The truth of the conclusion follows from +the existence of the psychological phenomenon called the +idea of a dragon; and therefore still from the tacit assumption +of a matter of fact.<a id="noteref_26" name="noteref_26" href="#note_26"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">26</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, as in this last syllogism, the conclusion is a +proposition respecting an idea, the assumption on which it +depends may be merely that of the existence of an idea. +<span class="tei tei-pb" id="page169">[pg 169]</span><a name="Pg169" id="Pg169" class="tei tei-anchor"></a> +But when the conclusion is a proposition concerning a Thing, +the postulate involved in the definition which stands as the +apparent premiss, is the existence of a Thing conformable to +the definition, and not merely of an idea conformable to it. +This assumption of real existence we always convey the +impression that we intend to make, when we profess to define +any name which is already known to be a name of really +existing objects. On this account it is, that the assumption +was not necessarily implied in the definition of a dragon, +while there was no doubt of its being included in the definition +of a circle. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. One of the circumstances which have contributed to +keep up the notion, that demonstrative truths follow from +definitions rather than from the postulates implied in those +definitions, is, that the postulates, even in those sciences +which are considered to surpass all others in demonstrative +certainty, are not always exactly true. It is not true that a +circle exists, or can be described, which has all its radii <em class="tei tei-emph"><span style="font-style: italic">exactly</span></em> +equal. Such accuracy is ideal only; it is not found in +nature, still less can it be realised by art. People had a difficulty, +therefore, in conceiving that the most certain of all +conclusions could rest on premisses which, instead of being +certainly true, are certainly not true to the full extent asserted. +This apparent paradox will be examined when we come to +treat of Demonstration; where we shall be able to show that +as much of the postulate is true, as is required to support as +much as is true of the conclusion. Philosophers however to +whom this view had not occurred, or whom it did not satisfy, +have thought it indispensable that there should be found in +definitions something <em class="tei tei-emph"><span style="font-style: italic">more</span></em> certain, or at least more accurately +true, than the implied postulate of the real existence +of a corresponding object. And this something they flattered +themselves they had found, when they laid it down that a +definition is a statement and analysis not of the mere meaning +of a word, nor yet of the nature of a thing, but of an idea. +Thus, the proposition, <span class="tei tei-q">“A circle is a plane figure bounded +by a line all the points of which are at an equal distance from +<span class="tei tei-pb" id="page170">[pg 170]</span><a name="Pg170" id="Pg170" class="tei tei-anchor"></a> +a given point within it,”</span> was considered by them, not as an +assertion that any real circle has that property, (which would +not be exactly true,) but that we <em class="tei tei-emph"><span style="font-style: italic">conceive</span></em> a circle as having +it; that our abstract idea of a circle is an idea of a figure +with its radii exactly equal. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Conformably to this it is said, that the subject matter of +mathematics, and of every other demonstrative science, is +not things as they really exist, but abstractions of the mind. +A geometrical line is a line without breadth; but no such +line exists in nature; it is a notion made up by the mind, +out of the materials in nature. The definition (it is said) +is a definition of this mental line, not of any actual line: +and it is only of the mental line, not of any line existing in +nature, that the theorems of geometry are accurately true. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Allowing this doctrine respecting the nature of demonstrative +truth to be correct, (which, in a subsequent place, I +shall endeavour to prove that it is not;) even on that supposition, +the conclusions which seem to follow from a definition, +do not follow from the definition as such, but from an +implied postulate. Even if it be true that there is no object +in nature answering to the definition of a line, and that the +geometrical properties of lines are not true of any lines in +nature, but only of the idea of a line; the definition, at all +events, postulates the real existence of such an idea: it +assumes that the mind can frame, or rather has framed, the +notion of length without breadth, and without any other +sensible property whatever. To me, indeed, it appears +that the mind cannot form any such notion; it cannot +conceive length without breadth; it can only, in contemplating +objects, <em class="tei tei-emph"><span style="font-style: italic">attend</span></em> to their length, exclusively of +their other sensible qualities, and so determine what properties +may be predicated of them in virtue of their length +alone. If this be true, the postulate involved in the geometrical +definition of a line, is the real existence, not of length +without breadth, but merely of length, that is, of long objects. +This is quite enough to support all the truths of geometry, +since every property of a geometrical line is really a property +of all physical objects possessing length. But even what I +<span class="tei tei-pb" id="page171">[pg 171]</span><a name="Pg171" id="Pg171" class="tei tei-anchor"></a> +hold to be the false doctrine on the subject, leaves the conclusion +that our reasonings are grounded on the matters of +fact postulated in definitions, and not on the definitions +themselves, entirely unaffected; and accordingly this conclusion +is one which I have in common with Dr. Whewell, +in his <span class="tei tei-hi"><span style="font-style: italic">Philosophy of the Inductive Sciences</span></span>: although, on the +nature of demonstrative truth, Dr. Whewell's opinions are +greatly at variance with mine. And here, as in many other +instances, I gladly acknowledge that his writings are eminently +serviceable in clearing from confusion the initial steps +in the analysis of the mental processes, even where his views +respecting the ultimate analysis are such as (though with +unfeigned respect) I cannot but regard as fundamentally +erroneous. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. Although, according to the opinion here presented, +Definitions are properly of names only, and not of things, it +does not follow from this that definitions are arbitrary. How +to define a name, may not only be an inquiry of considerable +difficulty and intricacy, but may involve considerations +going deep into the nature of the things which are denoted +by the name. Such, for instance, are the inquiries which +form the subjects of the most important of Plato's Dialogues; +as, <span class="tei tei-q">“What is rhetoric?”</span> the topic of the Gorgias, or <span class="tei tei-q">“What +is justice?”</span> that of the Republic. Such, also, is the question +scornfully asked by Pilate, <span class="tei tei-q">“What is truth?”</span> and the fundamental +question with speculative moralists in all ages, +<span class="tei tei-q">“What is virtue?”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It would be a mistake to represent these difficult and +noble inquiries as having nothing in view beyond ascertaining +the conventional meaning of a name. They are +inquiries not so much to determine what is, as what should +be, the meaning of a name; which, like other practical +questions of terminology, requires for its solution that we +should enter, and sometimes enter very deeply, into the +properties not merely of names but of the things named. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although the meaning of every concrete general name +resides in the attributes which it connotes, the objects were +<span class="tei tei-pb" id="page172">[pg 172]</span><a name="Pg172" id="Pg172" class="tei tei-anchor"></a> +named before the attributes; as appears from the fact that +in all languages, abstract names are mostly compounds or +other derivatives of the concrete names which correspond to +them. Connotative names, therefore, were, after proper +names, the first which were used: and in the simpler cases, +no doubt, a distinct connotation was present to the minds of +those who first used the name, and was distinctly intended +by them to be conveyed by it. The first person who used +the word <span class="tei tei-hi"><span style="font-style: italic">white</span></span>, as applied to snow or to any other object, +knew, no doubt, very well what quality he intended to predicate, +and had a perfectly distinct conception in his mind +of the attribute signified by the name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But where the resemblances and differences on which +our classifications are founded are not of this palpable and +easily determinable kind; especially where they consist not +in any one quality but in a number of qualities, the effects +of which being blended together are not very easily discriminated, +and referred each to its true source; it often +happens that names are applied to nameable objects, with +no distinct connotation present to the minds of those who +apply them. They are only influenced by a general resemblance +between the new object and all or some of the old +familiar objects which they have been accustomed to call by +that name. This, as we have seen, is the law which even +the mind of the philosopher must follow, in giving names to +the simple elementary feelings of our nature: but, where the +things to be named are complex wholes, a philosopher is not +content with noticing a general resemblance; he examines +what the resemblance consists in: and he only gives the +same name to things which resemble one another in the +same definite particulars. The philosopher, therefore, habitually +employs his general names with a definite connotation. +But language was not made, and can only in some small +degree be mended, by philosophers. In the minds of the +real arbiters of language, general names, especially where +the classes they denote cannot be brought before the tribunal +of the outward senses to be identified and discriminated, +connote little more than a vague gross resemblance +<span class="tei tei-pb" id="page173">[pg 173]</span><a name="Pg173" id="Pg173" class="tei tei-anchor"></a> +to the things which they were earliest, or have been most, +accustomed to call by those names. When, for instance, +ordinary persons predicate the words <span class="tei tei-hi"><span style="font-style: italic">just</span></span> or +<span class="tei tei-hi"><span style="font-style: italic">unjust</span></span> of any action, <span class="tei tei-hi"><span style="font-style: italic">noble</span></span> or +<span class="tei tei-hi"><span style="font-style: italic">mean</span></span> of any sentiment, expression, or demeanour, +<span class="tei tei-hi"><span style="font-style: italic">statesman</span></span> or <span class="tei tei-hi"><span style="font-style: italic">charlatan</span></span> of any personage +figuring in politics, do they mean to affirm of those various subjects +any determinate attributes, of whatever kind? No: they +merely recognise, as they think, some likeness, more or less +vague and loose, between these and some other things which +they have been accustomed to denominate or to hear denominated +by those appellations. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Language, as Sir James Mackintosh used to say of +governments, <span class="tei tei-q">“is not made, but grows.”</span> A name is not +imposed at once and by previous purpose upon a <em class="tei tei-emph"><span style="font-style: italic">class</span></em> of +objects, but is first applied to one thing, and then extended +by a series of transitions to another and another. By this +process (as has been remarked by several writers, and illustrated +with great force and clearness by Dugald Stewart, in +his Philosophical Essays,) a name not unfrequently passes +by successive links of resemblance from one object to +another, until it becomes applied to things having nothing +in common with the first things to which the name was +given; which, however, do not, for that reason, drop the +name; so that it at last denotes a confused huddle of objects, +having nothing whatever in common; and connotes nothing, +not even a vague and general resemblance. When a name +has fallen into this state, in which by predicating it of any +object we assert literally nothing about the object, it has +become unfit for the purposes either of thought or of the +communication of thought; and can only be made serviceable +by stripping it of some part of its multifarious denotation, +and confining it to objects possessed of some attributes +in common, which it may be made to connote. Such are +the inconveniences of a language which <span class="tei tei-q">“is not made, but +grows.”</span> Like the governments which are in a similar case, +it may be compared to a road which is not made but has +made itself: it requires continual mending in order to be +passable. +</p> + +<span class="tei tei-pb" id="page174">[pg 174]</span><a name="Pg174" id="Pg174" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From this it is already evident, why the question respecting +the definition of an abstract name is often one of so +much difficulty. The question, What is justice? is, in other +words, What is the attribute which mankind mean to predicate +when they call an action just? To which the first +answer is, that having come to no precise agreement on the +point, they do not mean to predicate distinctly any attribute +at all. Nevertheless, all believe that there is some common +attribute belonging to all the actions which they are in the +habit of calling just. The question then must be, whether +there is any such common attribute? and, in the first place, +whether mankind agree sufficiently with one another as to +the particular actions which they do or do not call just, to +render the inquiry, what quality those actions have in +common, a possible one: if so, whether the actions really +have any quality in common; and if they have, what it is. +Of these three, the first alone is an inquiry into usage and +convention; the other two are inquiries into matters of fact. +And if the second question (whether the actions form a class +at all) has been answered negatively, there remains a fourth, +often more arduous than all the rest, namely, how best to +form a class artificially, which the name may denote. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And here it is fitting to remark, that the study of the +spontaneous growth of languages is of the utmost importance +to those who would logically remodel them. The classifications +rudely made by established language, when retouched, +as they almost always require to be, by the hands of the +logician, are often in themselves excellently suited to +his purposes. When compared with the classifications of +a philosopher, they are like the customary law of a country, +which has grown up as it were spontaneously, compared +with laws methodized and digested into a code: the former +are a far less perfect instrument than the latter; but being +the result of a long, though unscientific, course of experience, +they contain a mass of materials which may be made very +usefully available in the formation of the systematic body of +written law. In like manner, the established grouping of +objects under a common name, though it may be founded +<span class="tei tei-pb" id="page175">[pg 175]</span><a name="Pg175" id="Pg175" class="tei tei-anchor"></a> +only on a gross and general resemblance, is evidence, in the +first place, that the resemblance is obvious, and therefore +considerable; and, in the next place, that it is a resemblance +which has struck great numbers of persons during a series +of years and ages. Even when a name, by successive extensions, +has come to be applied to things among which +there does not exist this gross resemblance common to them +all, still at every step in its progress we shall find such a +resemblance. And these transitions of the meaning of words +are often an index to real connexions between the things +denoted by them, which might otherwise escape the notice +of thinkers; of those at least who, from using a different +language, or from any difference in their habitual associations, +have fixed their attention in preference on some +other aspect of the things. The history of philosophy +abounds in examples of such oversights, committed for +want of perceiving the hidden link that connected together +the seemingly disparate meanings of some ambiguous word.<a id="noteref_27" name="noteref_27" href="#note_27"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">27</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Whenever the inquiry into the definition of the name of +any real object consists of anything else than a mere comparison +of authorities, we tacitly assume that a meaning +must be found for the name, compatible with its continuing +to denote, if possible all, but at any rate the greater or the +more important part, of the things of which it is commonly +predicated. The inquiry, therefore, into the definition, is an +<span class="tei tei-pb" id="page176">[pg 176]</span><a name="Pg176" id="Pg176" class="tei tei-anchor"></a> +inquiry into the resemblances and differences among those +things: whether there be any resemblance running through +them all; if not, through what portion of them such a general +resemblance can be traced: and finally, what are the common +attributes, the possession of which gives to them all, or to +that portion of them, the character of resemblance which has +led to their being classed together. When these common +attributes have been ascertained and specified, the name +which belongs in common to the resembling objects acquires +a distinct instead of a vague connotation; and by possessing +this distinct connotation, becomes susceptible of definition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In giving a distinct connotation to the general name, the +philosopher will endeavour to fix upon such attributes as, +while they are common to all the things usually denoted by +the name, are also of greatest importance in themselves; +either directly, or from the number, the conspicuousness, or +the interesting character, of the consequences to which they +lead. He will select, as far as possible, such <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">differentiæ</span></span> as lead to the greatest number +of interesting <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">propria</span></span>. For +these, rather than the more obscure and recondite qualities +on which they often depend, give that general character and +aspect to a set of objects, which determine the groups into +which they naturally fall. But to penetrate to the more +hidden agreement on which these obvious and superficial +agreements depend, is often one of the most difficult of +scientific problems. As it is among the most difficult, so it +seldom fails to be among the most important. And since +upon the result of this inquiry respecting the causes of the +properties of a class of things, there incidentally depends the +question what shall be the meaning of a word; some of the +most profound and most valuable investigations which philosophy +presents to us, have been introduced by, and have +offered themselves under the guise of, inquiries into the +definition of a name. +</p> + +</div> + +</div> + +<span class="tei tei-pb" id="page177">[pg 177]</span><a name="Pg177" id="Pg177" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc39" id="toc39"></a> +<a name="pdf40" id="pdf40"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">BOOK II. OF REASONING.</span></h1> + +<span class="tei tei-pb" id="page178">[pg 178]</span><a name="Pg178" id="Pg178" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Διωρισμένων δε τούτων, λέγωμεν ἤδη, διὰ τίνων, καὶ πότε, καὶ +πῶς γίνεται πᾶς συλλογισμός; ὕστερον δὲ λεκτέον περὶ ἀποδείξεως. +Πρότερον γὰρ περὶ συλλογισμοῦ λεκτέον, ἣ περὶ ἀποδείξεως, διὰ τὸ +καθόλου μᾶλλον εἰναὶ τὸν συλλογισμόν. Ἡ μὲν γὰρ ἀπόδειξις, συλλογισμός +τις; ὁ συλλογισμός δὲ οὐ πᾶς, ἀπόδειξις. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Arist.</span></span> <span class="tei tei-hi"><span style="font-style: italic">Analyt. Prior.</span></span> 1. i. cap. 4. +</p> + +<span class="tei tei-pb" id="page179">[pg 179]</span><a name="Pg179" id="Pg179" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc41" id="toc41"></a> +<a name="pdf42" id="pdf42"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER I. OF INFERENCE, OR REASONING, IN GENERAL.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In the preceding Book, we have been occupied not +with the nature of Proof, but with the nature of Assertion: +the import conveyed by a Proposition, whether that Proposition +be true or false; not the means by which to discriminate +true from false Propositions. The proper subject, +however, of Logic is Proof. Before we could understand +what Proof is, it was necessary to understand what that is +to which proof is applicable; what that is which can be a +subject of belief or disbelief, of affirmation or denial; what, +in short, the different kinds of Propositions assert. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This preliminary inquiry we have prosecuted to a definite +result. Assertion, in the first place, relates either to the +meaning of words, or to some property of the things which +words signify. Assertions respecting the meaning of words, +among which definitions are the most important, hold a place, +and an indispensable one, in philosophy; but as the meaning +of words is essentially arbitrary, this class of assertions +are not susceptible of truth or falsity, nor therefore of proof +or disproof. Assertions respecting Things, or what may be +called Real Propositions in contradistinction to verbal ones, +are of various sorts. We have analysed the import of each +sort, and have ascertained the nature of the things they relate +to, and the nature of what they severally assert respecting +those things. We found that whatever be the form of the +proposition, and whatever its nominal subject or predicate, +the real subject of every proposition is some one or more +facts or phenomena of consciousness, or some one or more +of the hidden causes or powers to which we ascribe those +facts; and that what is predicated or asserted, either in the +affirmative or negative, of those phenomena or those powers, +<span class="tei tei-pb" id="page180">[pg 180]</span><a name="Pg180" id="Pg180" class="tei tei-anchor"></a> +is always either Existence, Order in Place, Order in Time, +Causation, or Resemblance. This, then, is the theory of the +Import of Propositions, reduced to its ultimate elements: +but there is another and a less abstruse expression for it, +which, though stopping short in an earlier stage of the analysis, +is sufficiently scientific for many of the purposes for +which such a general expression is required. This expression +recognises the commonly received distinction between +Subject and Attribute, and gives the following as the analysis +of the meaning of propositions:—Every Proposition +asserts, that some given subject does or does not possess +some attribute; or that some attribute is or is not (either in +all or in some portion of the subjects in which it is met with) +conjoined with some other attribute. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We shall now for the present take our leave of this portion +of our inquiry, and proceed to the peculiar problem of the +Science of Logic, namely, how the assertions, of which we +have analysed the import, are proved, or disproved: such of +them, at least, as, not being amenable to direct consciousness +or intuition, are appropriate subjects of proof. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We say of a fact or statement, that it is proved, when we +believe its truth by reason of some other fact or statement +from which it is said to <em class="tei tei-emph"><span style="font-style: italic">follow</span></em>. Most of the propositions, +whether affirmative or negative, universal, particular, or +singular, which we believe, are not believed on their own +evidence, but on the ground of something previously assented +to, and from which they are said to be <em class="tei tei-emph"><span style="font-style: italic">inferred</span></em>. To infer a +proposition from a previous proposition or propositions; to +give credence to it, or claim credence for it, as a conclusion +from something else; is to <em class="tei tei-emph"><span style="font-style: italic">reason</span></em>, in the most extensive sense +of the term. There is a narrower sense, in which the name +reasoning is confined to the form of inference which is termed +ratiocination, and of which the syllogism is the general type. +The reasons for not conforming to this restricted use of the +term were stated in an early stage of our inquiry, and additional +motives will be suggested by the considerations on +which we are now about to enter. +</p> + +<span class="tei tei-pb" id="page181">[pg 181]</span><a name="Pg181" id="Pg181" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. In proceeding to take into consideration the cases +in which inferences can legitimately be drawn, we shall first +mention some cases in which the inference is apparent, not +real; and which require notice chiefly that they may not be +confounded with cases of inference properly so called. This +occurs when the proposition ostensibly inferred from another, +appears on analysis to be merely a repetition of the same, or +part of the same, assertion, which was contained in the first. +All the cases mentioned in books of Logic as examples of +æquipollency or equivalence of propositions, are of this +nature. Thus, if we were to argue, No man is incapable of +reason, for every man is rational; or, All men are mortal, +for no man is exempt from death; it would be plain that we +were not proving the proposition, but only appealing to +another mode of wording it, which may or may not be more +readily comprehensible by the hearer, or better adapted to +suggest the real proof, but which contains in itself no shadow +of proof. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Another case is where, from an universal proposition, we +affect to infer another which differs from it only in being +particular: as, All A is B, therefore Some A is B: No A +is B, therefore Some A is not B. This, too, is not +to conclude one proposition from another, but to repeat a +second time something which had been asserted at first; +with the difference, that we do not here repeat the whole of +the previous assertion, but only an indefinite part of it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A third case is where, the antecedent having affirmed a +predicate of a given subject, the consequent affirms of the +same subject something already connoted by the former +predicate: as, Socrates is a man, therefore Socrates is a +living creature; where all that is connoted by living creature +was affirmed of Socrates when he was asserted to be a man. +If the propositions are negative, we must invert their order, +thus: Socrates is not a living creature, therefore he is not a +man; for if we deny the less, the greater, which includes it, +is already denied by implication. These, therefore, are not +really cases of inference; and yet the trivial examples by +which, in manuals of Logic, the rules of the syllogism are +<span class="tei tei-pb" id="page182">[pg 182]</span><a name="Pg182" id="Pg182" class="tei tei-anchor"></a> +illustrated, are often of this ill-chosen kind; demonstrations +in form, of conclusions to which whoever understands the +terms used in the statement of the data, has already, and +consciously, assented. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The most complex case of this sort of apparent inference +is what is called the Conversion of Propositions; which +consists in turning the predicate into a subject, and the +subject into a predicate, and framing out of the same terms +thus reversed, another proposition, which must be true if +the former is true. Thus, from the particular affirmative +proposition, Some A is B, we may infer that Some B is A. +From the universal negative, No A is B, we may conclude +that No B is A. From the universal affirmative proposition, +All A is B, it cannot be inferred that All B is A; though +all water is liquid, it is not implied that all liquid is water; +but it is implied that some liquid is so; and hence the proposition, +All A is B, is legitimately convertible into Some +B is A. This process, which converts an universal proposition +into a particular, is termed conversion <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per accidens</span></span>. +From the proposition, Some A is not B, we cannot even +infer that some B is not A; though some men are not +Englishmen, it does not follow that some Englishmen are +not men. The only legitimate conversion, if such it can be +called, of a particular negative proposition, is in the form, +Some A is not B, therefore, something which is not B is A; +and this is termed conversion by contraposition. In this +case, however, the predicate and subject are not merely +reversed, but one of them is altered. Instead of [A] and +[B], the terms of the new proposition are [a thing which is +not B], and [A]. The original proposition, Some A <em class="tei tei-emph"><span style="font-style: italic">is not</span></em> +B, is first changed into a proposition æquipollent with it, +Some A <em class="tei tei-emph"><span style="font-style: italic">is</span></em> <span class="tei tei-q">“a thing which is not B”</span>; and the proposition, +being now no longer a particular negative, but a particular +affirmative, admits of conversion in the first mode, or, as it is +called, <em class="tei tei-emph"><span style="font-style: italic">simple</span></em> conversion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In all these cases there is not really any inference; +there is in the conclusion no new truth, nothing but what +was already asserted in the premisses, and obvious to whoever +<span class="tei tei-pb" id="page183">[pg 183]</span><a name="Pg183" id="Pg183" class="tei tei-anchor"></a> +apprehends them. The fact asserted in the conclusion +is either the very same fact, or part of the fact, asserted in +the original proposition. This follows from our previous +analysis of the Import of Propositions. When we say, for +example, that some lawful sovereigns are tyrants, what is +the meaning of the assertion? That the attributes connoted +by the term <span class="tei tei-q">“lawful sovereign,”</span> and the attributes connoted +by the term <span class="tei tei-q">“tyrant,”</span> sometimes coexist in the same individual. +Now this is also precisely what we mean, when we +say that some tyrants are lawful sovereigns; which, therefore, +is not a second proposition inferred from the first, any +more than the English translation of Euclid's Elements is a +collection of theorems different from, and consequences of, +those contained in the Greek original. Again, if we assert that +no great general is a rash man, we mean that the attributes +connoted by <span class="tei tei-q">“great general,”</span> and those connoted by <span class="tei tei-q">“rash,”</span> +never coexist in the same subject; which is also the exact +meaning which would be expressed by saying, that no rash +man is a great general. When we say, that all quadrupeds +are warm-blooded, we assert, not only that the attributes connoted +by <span class="tei tei-q">“quadruped”</span> and those connoted by <span class="tei tei-q">“warm-blooded”</span> +sometimes coexist, but that the former never exist +without the latter: now the proposition, Some warm-blooded +creatures are quadrupeds, expresses the first half of this +meaning, dropping the latter half; and, therefore, has been +already affirmed in the antecedent proposition, All quadrupeds +are warm-blooded. But that <em class="tei tei-emph"><span style="font-style: italic">all</span></em> warm-blooded creatures +are quadrupeds, or, in other words, that the attributes +connoted by <span class="tei tei-q">“warm-blooded”</span> never exist without those connoted +by <span class="tei tei-q">“quadruped,”</span> has not been asserted, and cannot +be inferred. In order to reassert, in an inverted form, the +whole of what was affirmed in the proposition, All quadrupeds +are warm-blooded, we must convert it by contraposition, +thus, Nothing which is not warm-blooded is a +quadruped. This proposition, and the one from which it +is derived, are exactly equivalent, and either of them may +be substituted for the other; for, to say that when the attributes +of a quadruped are present, those of a warm-blooded +<span class="tei tei-pb" id="page184">[pg 184]</span><a name="Pg184" id="Pg184" class="tei tei-anchor"></a> +creature are present, is to say that when the latter are +absent the former are absent. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In a manual for young students, it would be proper to +dwell at greater length on the conversion and æquipollency +of propositions. For, although that cannot be called reasoning +or inference which is a mere reassertion in different +words of what had been asserted before, there is no more +important intellectual habit, nor any the cultivation of which +falls more strictly within the province of the art of logic, than +that of discerning rapidly and surely the identity of an assertion +when disguised under diversity of language. That important +chapter in logical treatises which relates to the +Opposition of Propositions, and the excellent technical +language which logic provides for distinguishing the different +kinds or modes of opposition, are of use chiefly +for this purpose. Such considerations as these, that contrary +propositions may both be false, but cannot both +be true; that sub-contrary propositions may both be true, +but cannot both be false; that of two contradictory propositions +one must be true and the other false; that of two +subalternate propositions the truth of the universal proves +the truth of the particular, and the falsity of the particular +proves the falsity of the universal, but not <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">vice versâ</span></span><a id="noteref_28" name="noteref_28" href="#note_28"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">28</span></span></a>; are +apt to appear, at first sight, very technical and mysterious, +but when explained, seem almost too obvious to require so +formal a statement, since the same amount of explanation +which is necessary to make the principles intelligible, would +enable the truths which they convey to be apprehended in +<span class="tei tei-pb" id="page185">[pg 185]</span><a name="Pg185" id="Pg185" class="tei tei-anchor"></a> +any particular case which can occur. In this respect, however, +these axioms of logic are on a level with those of mathematics. +That things which are equal to the same thing are +equal to one another, is as obvious in any particular case as +it is in the general statement: and if no such general maxim +had ever been laid down, the demonstrations in Euclid would +never have halted for any difficulty in stepping across the +gap which this axiom at present serves to bridge over. Yet +no one has ever censured writers on geometry, for placing a +list of these elementary generalizations at the head of their +treatises, as a first exercise to the learner of the faculty which +will be required in him at every step, that of apprehending a +<em class="tei tei-emph"><span style="font-style: italic">general</span></em> truth. And the student of logic, in the discussion +even of such truths as we have cited above, acquires habits +of circumspect interpretation of words, and of exactly measuring +the length and breadth of his assertions, which are +among the most indispensable conditions of any considerable +mental attainment, and which it is one of the primary +objects of logical discipline to cultivate. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Having noticed, in order to exclude from the province +of Reasoning or Inference properly so called, the +cases in which the progression from one truth to another is +only apparent, the logical consequent being a mere repetition +of the logical antecedent; we now pass to those which are +cases of inference in the proper acceptation of the term, +those in which we set out from known truths, to arrive at +others really distinct from them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Reasoning, in the extended sense in which I use the +term, and in which it is synonymous with Inference, is popularly +said to be of two kinds: reasoning from particulars +to generals, and reasoning from generals to particulars; the +former being called Induction, the latter Ratiocination or +Syllogism. It will presently be shown that there is a third +species of reasoning, which falls under neither of these +descriptions, and which, nevertheless, is not only valid, but +is the foundation of both the others. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is necessary to observe, that the expressions, reasoning +<span class="tei tei-pb" id="page186">[pg 186]</span><a name="Pg186" id="Pg186" class="tei tei-anchor"></a> +from particulars to generals, and reasoning from generals +to particulars, are recommended by brevity rather than by +precision, and do not adequately mark, without the aid of a +commentary, the distinction between Induction (in the sense +now adverted to) and Ratiocination. The meaning intended +by these expressions is, that Induction is inferring a +proposition from propositions <em class="tei tei-emph"><span style="font-style: italic">less general</span></em> than itself, and +Ratiocination is inferring a proposition from propositions +<em class="tei tei-emph"><span style="font-style: italic">equally</span></em> or <em class="tei tei-emph"><span style="font-style: italic">more</span></em> general. When, from the observation of a +number of individual instances, we ascend to a general +proposition, or when, by combining a number of general propositions, +we conclude from them another proposition still +more general, the process, which is substantially the same +in both instances, is called Induction. When from a general +proposition, not alone (for from a single proposition nothing +can be concluded which is not involved in the terms,) but by +combining it with other propositions, we infer a proposition +of the same degree of generality with itself, or a less general +proposition, or a proposition merely individual, the process +is Ratiocination. When, in short, the conclusion is more +general than the largest of the premisses, the argument is +commonly called Induction; when less general, or equally +general, it is Ratiocination. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As all experience begins with individual cases, and proceeds +from them to generals, it might seem most conformable +to the natural order of thought that Induction should be +treated of before we touch upon Ratiocination. It will, however, +be advantageous, in a science which aims at tracing our +acquired knowledge to its sources, that the inquirer should +commence with the latter rather than with the earlier stages +of the process of constructing our knowledge; and should +trace derivative truths backward to the truths from which they +are deduced, and on which they depend for their evidence, +before attempting to point out the original spring from which +both ultimately take their rise. The advantages of this order +of proceeding in the present instance will manifest themselves +as we advance, in a manner superseding the necessity +of any further justification or explanation. +</p> + +<span class="tei tei-pb" id="page187">[pg 187]</span><a name="Pg187" id="Pg187" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of Induction, therefore, we shall say no more at present, +than that it at least is, without doubt, a process of real inference. +The conclusion in an induction embraces more +than is contained in the premisses. The principle or law +collected from particular instances, the general proposition +in which we embody the result of our experience, covers a +much larger extent of ground than the individual experiments +which are said to form its basis. A principle ascertained +by experience, is more than a mere summing up of +what has been specifically observed in the individual cases +which have been examined; it is a generalization grounded +on those cases, and expressive of our belief, that what we +there found true is true in an indefinite number of cases +which we have not examined, and are never likely to +examine. The nature and grounds of this inference, and the +conditions necessary to make it legitimate, will be the subject +of discussion in the Third Book: but that such inference +really takes place is not susceptible of question. In every +induction we proceed from truths which we knew, to truths +which we did not know; from facts certified by observation, +to facts which we have not observed, and even to facts not +capable of being now observed; future facts, for example; +but which we do not hesitate to believe on the sole evidence +of the induction itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Induction, then, is a real process of Reasoning or Inference. +Whether, and in what sense, so much can be said +of the Syllogism, remains to be determined by the examination +into which we are about to enter. +</p> + +</div> + +<span class="tei tei-pb" id="page188">[pg 188]</span><a name="Pg188" id="Pg188" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc43" id="toc43"></a> +<a name="pdf44" id="pdf44"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER II. OF RATIOCINATION, OR SYLLOGISM.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The analysis of the Syllogism has been so accurately +and fully performed in the common manuals of Logic, +that in the present work, which is not designed as a manual, +it is sufficient to recapitulate, +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">memoriæ causâ</span></span>, the leading +results of that analysis, as a foundation for the remarks to be +afterwards made on the functions of the syllogism, and the +place which it holds in science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To a legitimate syllogism it is essential that there should +be three, and no more than three, propositions, namely, the +conclusion, or proposition to be proved, and two other propositions +which together prove it, and which are called the +premisses. It is essential that there should be three, and no +more than three, terms, namely, the subject and predicate of +the conclusion, and another called the middleterm, which +must be found in both premisses, since it is by means of it +that the other two terms are to be connected together. The +predicate of the conclusion is called the major term of the +syllogism; the subject of the conclusion is called the minor +term. As there can be but three terms, the major and minor +terms must each be found in one, and only one, of the premisses, +together with the middleterm which is in them both. +The premiss which contains the middleterm and the major +term is called the major premiss; that which contains the +middle term and the minor term is called the minor premiss. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Syllogisms are divided by some logicians into three +<em class="tei tei-emph"><span style="font-style: italic">figures</span></em>, by others into four, according to the position of the +middleterm, which may either be the subject in both premisses, +the predicate in both, or the subject in one and the +predicate in the other. The most common case is that in +which the middleterm is the subject of the major premiss +and the predicate of the minor. This is reckoned as the +<span class="tei tei-pb" id="page189">[pg 189]</span><a name="Pg189" id="Pg189" class="tei tei-anchor"></a> +first figure. When the middleterm is the predicate in both +premisses, the syllogism belongs to the second figure; when +it is the subject in both, to the third. In the fourth figure +the middleterm is the subject of the minor premiss and the +predicate of the major. Those writers who reckon no more +than three figures, include this case in the first. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Each figure is divided into <em class="tei tei-emph"><span style="font-style: italic">modes</span></em>, according to what are +called the <em class="tei tei-emph"><span style="font-style: italic">quantity</span></em> and <em class="tei tei-emph"><span style="font-style: italic">quality</span></em> of the propositions, that is, +according as they are universal or particular, affirmative or +negative. The following are examples of all the legitimate +modes, that is, all those in which the conclusion correctly +follows from the premisses. A is the minor term, C the +major, B the middleterm. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">First Figure.</span></span> +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="4"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">All B is C</td><td class="tei tei-cell">No B is C</td> +<td class="tei tei-cell">All B is C</td><td class="tei tei-cell">No B is C</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All A is B</td><td class="tei tei-cell">All A is B</td> +<td class="tei tei-cell">Some A is B</td><td class="tei tei-cell">Some A is B</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td> +<td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All A is C</td><td class="tei tei-cell">No A is C</td> +<td class="tei tei-cell">Some A is C</td><td class="tei tei-cell">Some A is not C</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Second Figure.</span></span> +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="4"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">No C is B</td><td class="tei tei-cell">All C is B</td> +<td class="tei tei-cell">No C is B</td><td class="tei tei-cell">All C is B</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All A is B</td><td class="tei tei-cell">No A is B</td> +<td class="tei tei-cell">Some A is B</td><td class="tei tei-cell">Some A is not B</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td> +<td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">No A is C</td><td class="tei tei-cell">No A is C</td> +<td class="tei tei-cell">Some A is not C</td><td class="tei tei-cell">Some A is not C</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Third Figure.</span></span> +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="6"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">All B is C</td><td class="tei tei-cell">No B is C</td><td class="tei tei-cell">Some B is C</td> +<td class="tei tei-cell">All B is C</td><td class="tei tei-cell">Some B is not C</td><td class="tei tei-cell">No B is C</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All B is A</td><td class="tei tei-cell">All B is A</td><td class="tei tei-cell">All B is A</td> +<td class="tei tei-cell">Some B is A</td><td class="tei tei-cell">All B is A</td><td class="tei tei-cell">Some B is A</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td> +<td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">Some A is C</td><td class="tei tei-cell">Some A is not C</td><td class="tei tei-cell">Some A is C</td> +<td class="tei tei-cell">Some A is C</td><td class="tei tei-cell">Some A is not C</td><td class="tei tei-cell">Some A is not C</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Fourth Figure.</span></span> +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="5"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">All C is B</td><td class="tei tei-cell">All C is B</td><td class="tei tei-cell">Some C is B</td> +<td class="tei tei-cell">No C is B</td><td class="tei tei-cell">No C is B</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All B is A</td><td class="tei tei-cell">No B is A</td><td class="tei tei-cell">All B is A</td> +<td class="tei tei-cell">All B is A</td><td class="tei tei-cell">Some B is A</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td> +<td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">Some A is C</td><td class="tei tei-cell">Some A is not C</td><td class="tei tei-cell">Some A is C</td> +<td class="tei tei-cell">Some A is not C</td><td class="tei tei-cell">Some A is not C</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In these exemplars, or blank forms of making syllogisms, +no place is assigned to <em class="tei tei-emph"><span style="font-style: italic">singular</span></em> propositions; not, of course, +because such propositions are not used in ratiocination, but +because, their predicate being affirmed or denied of the +whole of the subject, they are ranked, for the purposes of +the syllogism, with universal propositions. Thus, these two +syllogisms— +</p> + +<span class="tei tei-pb" id="page190">[pg 190]</span><a name="Pg190" id="Pg190" class="tei tei-anchor"></a> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="2"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">All men are mortal,</td><td class="tei tei-cell">All men are mortal,</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All kings are men,</td><td class="tei tei-cell">Socrates is a man,</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All kings are mortal,</td><td class="tei tei-cell">Socrates is mortal,</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +are arguments precisely similar, and are both ranked in the +first mode of the first figure. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The reasons why syllogisms in any of the above forms +are legitimate, that is, why, if the premisses be true, the +conclusion must necessarily be so, and why this is not the +case in any other possible <em class="tei tei-emph"><span style="font-style: italic">mode</span></em>, (that is, in any other combination +of universal and particular, affirmative and negative +propositions,) any person taking interest in these inquiries +may be presumed to have either learnt from the common +school books of the syllogistic logic, or to be capable of +divining for himself. The reader may, however, be referred, +for every needful explanation, to Archbishop Whately's +<span class="tei tei-hi"><span style="font-style: italic">Elements of Logic</span></span>, where he will find stated with philosophical +precision, and explained with remarkable perspicuity, +the whole of the common doctrine of the syllogism. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All valid ratiocination; all reasoning by which, from +general propositions previously admitted, other propositions +equally or less general are inferred; may be exhibited in +some of the above forms. The whole of Euclid, for example, +might be thrown without difficulty into a series of syllogisms, +regular in mode and figure. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although a syllogism framed according to any of these +formulæ is a valid argument, all correct ratiocination admits +of being stated in syllogisms of the first figure alone. The +rules for throwing an argument in any of the other figures +into the first figure, are called rules for the <em class="tei tei-emph"><span style="font-style: italic">reduction</span></em> of syllogisms. +It is done by the <em class="tei tei-emph"><span style="font-style: italic">conversion</span></em> of one or other, or both, +of the premisses. Thus an argument in the first mode of the +second figure, as— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +No C is B<br /> +All A is B<br /> +therefore<br /> +No A is C, +</p> + +<span class="tei tei-pb" id="page191">[pg 191]</span><a name="Pg191" id="Pg191" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +may be reduced as follows. The proposition, No C is B, +being an universal negative, admits of simple conversion, +and may be changed into No B is C, which, as we showed, is +the very same assertion in other words—the same fact differently +expressed. This transformation having been effected, +the argument assumes the following form:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +No B is C<br /> +All A is B<br /> +therefore<br /> +No A is C, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +which is a good syllogism in the second mode of the first +figure. Again, an argument in the first mode of the third +figure must resemble the following:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All B is C<br /> +All B is A<br /> +therefore<br /> +Some A is C, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +where the minor premiss, All B is A, conformably to what +was laid down in the last chapter respecting universal affirmatives, +does not admit of simple conversion, but may be +converted <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per accidens</span></span>, +thus, Some A is B; which, though it +does not express the whole of what is asserted in the proposition +All B is A, expresses, as was formerly shown, part +of it, and must therefore be true if the whole is true. We +have, then, as the result of the reduction, the following syllogism +in the third mode of the first figure:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All B is C<br /> +Some A is B,<br /> +from which it obviously follows, that<br /> +Some A is C. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the same manner, or in a manner on which after these +examples it is not necessary to enlarge, every mode of the +second, third, and fourth figures may be reduced to some one +of the four modes of the first. In other words, every conclusion +which can be proved in any of the last three figures, +may be proved in the first figure from the same premisses, +<span class="tei tei-pb" id="page192">[pg 192]</span><a name="Pg192" id="Pg192" class="tei tei-anchor"></a> +with a slight alteration in the mere manner of expressing +them. Every valid ratiocination, therefore, may be stated in +the first figure, that is, in one of the following forms:— +</p> + +<table summary="This is a table" cellspacing="0" class="tei tei-table" style="margin-bottom: 1.00em"><colgroup span="2"></colgroup><tbody><tr class="tei tei-row"><td class="tei tei-cell">Every B is C</td><td class="tei tei-cell">No B is C</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All A is B,</td><td class="tei tei-cell">All A is B,</td></tr><tr class="tei tei-row"><td class="tei tei-cell">Some A is B,</td><td class="tei tei-cell">Some A is B,</td></tr><tr class="tei tei-row"><td class="tei tei-cell">therefore</td><td class="tei tei-cell">therefore</td></tr><tr class="tei tei-row"><td class="tei tei-cell">All A is C.</td><td class="tei tei-cell">No A is C.</td></tr><tr class="tei tei-row"><td class="tei tei-cell">Some A is C.</td><td class="tei tei-cell">Some A is not C.</td></tr></tbody></table> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Or if more significant symbols are preferred:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To prove an affirmative, the argument must admit of +being stated in this form:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All animals are mortal;<br /> +All men/Some men/Socrates are animals;<br /> +therefore<br /> +All men/Some men/Socrates are mortal. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To prove a negative, the argument must be capable of +being expressed in this form:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +No one who is capable of self-control is necessarily vicious;<br /> +All negroes/Some negroes/Mr. A's negro are capable of self-control;<br /> +therefore<br /> +No negroes are/Some negroes are not/Mr. A's negro is not necessarily vicious. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although all ratiocination admits of being thrown into one +or the other of these forms, and sometimes gains considerably +by the transformation, both in clearness and in the +obviousness of its consequence; there are, no doubt, cases +in which the argument falls more naturally into one of the +other three figures, and in which its conclusiveness is more +<span class="tei tei-pb" id="page193">[pg 193]</span><a name="Pg193" id="Pg193" class="tei tei-anchor"></a> +apparent at the first glance in those figures, than when +reduced to the first. Thus, if the proposition were that +pagans may be virtuous, and the evidence to prove it were +the example of Aristides; a syllogism in the third figure, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Aristides was virtuous,<br /> +Aristides was a pagan,<br /> +therefore<br /> +Some pagan was virtuous, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +would be a more natural mode of stating the argument, and +would carry conviction more instantly home, than the same +ratiocination strained into the first figure, thus— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Aristides was virtuous,<br /> +Some pagan was Aristides,<br /> +therefore<br /> +Some pagan was virtuous. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A German philosopher, Lambert, whose <span class="tei tei-hi"><span style="font-style: italic">Neues Organon</span></span> +(published in the year 1764) contains among other things +one of the most elaborate and complete expositions ever yet +made of the syllogistic doctrine, has expressly examined +what sorts of arguments fall most naturally and suitably +into each of the four figures; and his solution is characterized +by great ingenuity and clearness of thought.<a id="noteref_29" name="noteref_29" href="#note_29"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">29</span></span></a> The +<span class="tei tei-pb" id="page194">[pg 194]</span><a name="Pg194" id="Pg194" class="tei tei-anchor"></a> +argument, however, is one and the same, in whichever figure +it is expressed; since, as we have already seen, the premisses +of a syllogism in the second, third, or fourth figure, +and those of the syllogism in the first figure to which it may +be reduced, are the same premisses in everything except +language, or, at least, as much of them as contributes to the +proof of the conclusion is the same. We are therefore at +liberty, in conformity with the general opinion of logicians, +to consider the two elementary forms of the first figure as +the universal types of all correct ratiocination; the one, when +the conclusion to be proved is affirmative, the other, when +it is negative; even though certain arguments may have a +tendency to clothe themselves in the forms of the second, +third, and fourth figures; which, however, cannot possibly +happen with the only class of arguments which are of first-rate +<span class="tei tei-pb" id="page195">[pg 195]</span><a name="Pg195" id="Pg195" class="tei tei-anchor"></a> +scientific importance, those in which the conclusion is +an universal affirmative, such conclusions being susceptible +of proof in the first figure alone. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. On examining, then, these two general formulæ, +we find that in both of them, one premiss, the major, is an +universal proposition; and according as this is affirmative +or negative, the conclusion is so too. All ratiocination, +therefore, starts from a <em class="tei tei-emph"><span style="font-style: italic">general</span></em> proposition, principle, or +assumption: a proposition in which a predicate is affirmed +or denied of an entire class; that is, in which some attribute, +or the negation of some attribute, is asserted of an indefinite +number of objects distinguished by a common characteristic, +and designated, in consequence, by a common name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The other premiss is always affirmative, and asserts that +something (which may be either an individual, a class, or +<span class="tei tei-pb" id="page196">[pg 196]</span><a name="Pg196" id="Pg196" class="tei tei-anchor"></a> +part of a class) belongs to, or is included in, the class +respecting which something was affirmed or denied in the +major premiss. It follows that the attribute affirmed or +denied of the entire class may (if there was truth in that +affirmation or denial) be affirmed or denied of the object or +objects alleged to be included in the class: and this is precisely +the assertion made in the conclusion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Whether or not the foregoing is an adequate account of +the constituent parts of the syllogism, will be presently considered; +but as far as it goes it is a true account. It has +accordingly been generalized, and erected into a logical +maxim, on which all ratiocination is said to be founded, insomuch +that to reason, and to apply the maxim, are supposed +to be one and the same thing. The maxim is, That whatever +can be affirmed (or denied) of a class, may be affirmed +(or denied) of everything included in the class. This axiom, +supposed to be the basis of the syllogistic theory, is termed +by logicians the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni et +nullo</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This maxim, however, when considered as a principle of +reasoning, appears suited to a system of metaphysics once +indeed generally received, but which for the last two centuries +has been considered as finally abandoned, though there have +not been wanting, in our own day, attempts at its revival. +So long as what were termed Universals were regarded as a +peculiar kind of substances, having an objective existence +distinct from the individual objects classed under them, the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni</span></span> +conveyed an important meaning; because it +expressed the intercommunity of nature, which it was necessary +on that theory that we should suppose to exist +between those general substances and the particular substances +which were subordinated to them. That everything +predicable of the universal was predicable of the +various individuals contained under it, was then no identical +proposition, but a statement of what was conceived as a +fundamental law of the universe. The assertion that the +entire nature and properties of the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">substantia secunda</span></span> formed +part of the properties of each of the individual substances +called by the same name; that the properties of Man, for +<span class="tei tei-pb" id="page197">[pg 197]</span><a name="Pg197" id="Pg197" class="tei tei-anchor"></a> +example, were properties of all men; was a proposition of +real significance when man did not <em class="tei tei-emph"><span style="font-style: italic">mean</span></em> all men, but something +inherent in men, and vastly superior to them in dignity. +Now, however, when it is known that a class, an universal, a +genus or species, is not an entity <span class="tei tei-hi"><span style="font-style: italic">per se</span></span>, but neither more +nor less than the individual substances themselves which +are placed in the class, and that there is nothing real in the +matter except those objects, a common name given to them, +and common attributes indicated by the name; what, I +should be glad to know, do we learn by being told, that +whatever can be affirmed of a class, may be affirmed of every +object contained in the class? The class <em class="tei tei-emph"><span style="font-style: italic">is</span></em> nothing but the +objects contained in it: and the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de +omni</span></span> merely +amounts to the identical proposition, that whatever is true of +certain objects, is true of each of those objects. If all ratiocination +were no more than the application of this maxim to +particular cases, the syllogism would indeed be, what it has +so often been declared to be, solemn trifling. The <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de +omni</span></span> is on a par with another truth, which in its time was +also reckoned of great importance, <span class="tei tei-q">“Whatever is, is;”</span> and +not to be compared in point of significance to the cognate +aphorism, <span class="tei tei-q">“It is impossible for the same thing to be and not +to be;”</span> since this is, at the lowest, equivalent to the logical +axiom that contradictory propositions cannot both be true. +To give any real meaning to the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni</span></span>, we must +consider it not as an axiom, but as a definition; we must +look upon it as intended to explain, in a circuitous and +paraphrastic manner, the meaning of the word <span class="tei tei-hi"><span style="font-style: italic">class</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An error which seemed finally refuted and dislodged +from thought, often needs only put on a new suit of phrases, +to be welcomed back to its old quarters, and allowed to +repose unquestioned for another cycle of ages. Modern +philosophers have not been sparing in their contempt for +the scholastic dogma that genera and species are a peculiar +kind of substances, which general substances being the only +permanent things, while the individual substances comprehended +under them are in a perpetual flux, knowledge, +which necessarily imports stability, can only have relation +<span class="tei tei-pb" id="page198">[pg 198]</span><a name="Pg198" id="Pg198" class="tei tei-anchor"></a> +to those general substances or universals, and not to the +facts or particulars included under them. Yet, though +nominally rejected, this very doctrine, whether disguised +under the Abstract Ideas of Locke (whose speculations, +however, it has less vitiated than those of perhaps any other +writer who has been infected with it), under the ultra-nominalism +of Hobbes and Condillac, or the ontology of the +later Kantians, has never ceased to poison philosophy. +Once accustomed to consider scientific investigation as essentially +consisting in the study of universals, men did not drop +this habit of thought when they ceased to regard universals +as possessing an independent existence: and even those +who went the length of considering them as mere names, +could not free themselves from the notion that the investigation +of truth consisted entirely or partly in some kind of +conjuration or juggle with those names. When a philosopher +adopted fully the Nominalist view of the signification +of general language, retaining along with it the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni</span></span> +as the foundation of all reasoning, two such premisses fairly +put together were likely, if he was a consistent thinker, to +land him in rather startling conclusions. Accordingly it +has been seriously held, by writers of deserved celebrity, +that the process of arriving at new truths by reasoning consists +in the mere substitution of one set of arbitrary signs +for another; a doctrine which they supposed to derive irresistible +confirmation from the example of algebra. If +there were any process in sorcery or necromancy more preternatural +than this, I should be much surprised. The +culminating point of this philosophy is the noted aphorism +of Condillac, that a science is nothing, or scarcely anything, +but <span lang="fr" class="tei tei-foreign" xml:lang="fr"><span style="font-style: italic">une langue bien faite</span></span>: +in other words, that the one +sufficient rule for discovering the nature and properties of +objects is to name them properly: as if the reverse were not +the truth, that it is impossible to name them properly +except in proportion as we are already acquainted with their +nature and properties. Can it be necessary to say, that +none, not even the most trivial knowledge with respect to +Things, ever was or could be originally got at by any conceivable +<span class="tei tei-pb" id="page199">[pg 199]</span><a name="Pg199" id="Pg199" class="tei tei-anchor"></a> +manipulation of mere names, as such; and that +what can be learnt from names, is only what somebody who +used the names, knew before? Philosophical analysis +confirms the indication of common sense, that the function +of names is but that of enabling us to <em class="tei tei-emph"><span style="font-style: italic">remember</span></em> and +to <em class="tei tei-emph"><span style="font-style: italic">communicate</span></em> our thoughts. That they also strengthen, +even to an incalculable extent, the power of thought itself, +is most true: but they do this by no intrinsic and peculiar +virtue; they do it by the power inherent in an artificial +memory, an instrument of which few have adequately considered +the immense potency. As an artificial memory, +language truly is, what it has so often been called, an +instrument of thought: but it is one thing to be the instrument, +and another to be the exclusive subject upon which +the instrument is exercised. We think, indeed, to a considerable +extent, by means of names, but what we think of, +are the things called by those names; and there cannot be +a greater error than to imagine that thought can be carried +on with nothing in our mind but names, or that we can +make the names think for us. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Those who considered the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni</span></span> as the +foundation of the syllogism, looked upon arguments in a +manner corresponding to the erroneous view which Hobbes +took of propositions. Because there are some propositions +which are merely verbal, Hobbes, in order apparently +that his definition might be rigorously universal, +defined a proposition as if no propositions declared +anything except the meaning of words. If Hobbes was +right; if no further account than this could be given of +the import of propositions; no theory could be given but +the commonly received one, of the combination of propositions +in a syllogism. If the minor premiss asserted +nothing more than that something belongs to a class, and +if the major premiss asserted nothing of that class except +that it is included in another class, the conclusion would +only be, that what was included in the lower class is +included in the higher, and the result, therefore, nothing +<span class="tei tei-pb" id="page200">[pg 200]</span><a name="Pg200" id="Pg200" class="tei tei-anchor"></a> +except that the classification is consistent with itself. But +we have seen that it is no sufficient account of the meaning +of a proposition, to say that it refers something to, or excludes +something from, a class. Every proposition which +conveys real information asserts a matter of fact, dependent +on the laws of nature, and not on artificial classification. It +asserts that a given object does or does not possess a given +attribute; or it asserts that two attributes, or sets of attributes, +do or do not (constantly or occasionally) coexist. +Since such is the purport of all propositions which convey +any real knowledge, and since ratiocination is a mode of +acquiring real knowledge, any theory of ratiocination which +does not recognise this import of propositions, cannot, we +may be sure, be the true one. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Applying this view of propositions to the two premisses +of a syllogism, we obtain the following results. The major +premiss, which, as already remarked, is always universal, +asserts, that all things which have a certain attribute (or +attributes) have or have not along with it, a certain other +attribute (or attributes). The minor premiss asserts that +the thing or set of things which are the subject of that +premiss, have the first-mentioned attribute; and the conclusion +is, that they have (or that they have not) the second. +Thus in our former example, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All men are mortal,<br /> +Socrates is a man,<br /> +therefore<br /> +Socrates is mortal, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +the subject and predicate of the major premiss are connotative +terms, denoting objects and connoting attributes. The +assertion in the major premiss is, that along with one of +the two sets of attributes, we always find the other: that +the attributes connoted by <span class="tei tei-q">“man”</span> never exist unless conjoined +with the attribute called mortality. The assertion in +the minor premiss is that the individual named Socrates +possesses the former attributes; and it is concluded that he +possesses also the attribute mortality. Or if both the premisses +are general propositions, as +</p> + +<span class="tei tei-pb" id="page201">[pg 201]</span><a name="Pg201" id="Pg201" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All men are mortal,<br /> +All kings are men,<br /> +therefore<br /> +All kings are mortal, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +the minor premiss asserts that the attributes denoted by +kingship only exist in conjunction with those signified by +the word man. The major asserts as before, that the last +mentioned attributes are never found without the attribute +of mortality. The conclusion is, that wherever the attributes +of kingship are found, that of mortality is found +also. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If the major premiss were negative, as, No men are +omnipotent, it would assert, not that the attributes connoted +by <span class="tei tei-q">“man”</span> never exist without, but that they never exist +with, those connoted by <span class="tei tei-q">“omnipotent:”</span> from which, together +with the minor premiss, it is concluded, that the same incompatibility +exists between the attribute omnipotence and +those constituting a king. In a similar manner we might +analyse any other example of the syllogism. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If we generalize this process, and look out for the +principle or law involved in every such inference, and +presupposed in every syllogism the propositions of which +are anything more than merely verbal; we find, not the +unmeaning <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum +de omni et nullo</span></span>, but a fundamental principle, +or rather two principles, strikingly resembling the +axioms of mathematics. The first, which is the principle of +affirmative syllogisms, is, that things which coexist with the +same thing, coexist with one another. The second is the +principle of negative syllogisms, and is to this effect: that a +thing which coexists with another thing, with which other a +third thing does not coexist, is not coexistent with that third +thing. These axioms manifestly relate to facts, and not to +conventions; and one or other of them is the ground of the +legitimacy of every argument in which facts and not conventions +are the matter treated of. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. It remains to translate this exposition of the +syllogism from the one into the other of the two languages +<span class="tei tei-pb" id="page202">[pg 202]</span><a name="Pg202" id="Pg202" class="tei tei-anchor"></a> +in which we formerly remarked<a id="noteref_30" name="noteref_30" href="#note_30"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">30</span></span></a> that all propositions, and +of course therefore all combinations of propositions, might +be expressed. We observed that a proposition might be considered +in two different lights; as a portion of our knowledge +of nature, or as a memorandum for our guidance. Under the +former, or speculative aspect, an affirmative general proposition +is an assertion of a speculative truth, viz. that whatever +has a certain attribute has a certain other attribute. Under +the other aspect, it is to be regarded not as a part of our +knowledge, but as an aid for our practical exigencies, by +enabling us, when we see or learn that an object possesses +one of the two attributes, to infer that it possesses the other; +thus employing the first attribute as a mark or evidence of +the second. Thus regarded, every syllogism comes within +the following general formula:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Attribute A is a mark of attribute B,<br /> +A given object has the mark A,<br /> +therefore<br /> +The given object has the attribute B. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Referred to this type, the arguments which we have lately +cited as specimens of the syllogism, will express themselves +in the following manner:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The attributes of man are a mark of the attribute mortality,<br /> +Socrates has the attributes of man,<br /> +therefore<br /> +Socrates has the attribute mortality. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And again, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The attributes of man are a mark of the attribute mortality,<br /> +The attributes of a king are a mark of the attributes of man,<br /> +therefore<br /> +The attributes of a king are a mark of the attribute mortality. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And lastly, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The attributes of man are a mark of the <em class="tei tei-emph"><span style="font-style: italic">absence</span></em> of the attribute +omnipotence,<br /> +<span class="tei tei-pb" id="page203">[pg 203]</span><a name="Pg203" id="Pg203" class="tei tei-anchor"></a> +The attributes of a king are a mark of the attributes of man,<br /> +therefore<br /> +The attributes of a king are a mark of the absence of the attribute signified +by the word omnipotent, +(or, are <em class="tei tei-emph"><span style="font-style: italic">evidence</span></em> of the absence of that attribute.) +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To correspond with this alteration in the form of the +syllogisms, the axioms on which the syllogistic process is +founded must undergo a corresponding transformation. In +this altered phraseology, both those axioms may be brought +under one general expression; namely, that whatever possesses +any mark, possesses that which it is a mark of. Or, +when the minor premiss as well as the major is universal, +we may state it thus: Whatever is a mark of any mark, is a +mark of that which this last is a mark of. To trace the +identity of these axioms with those previously laid down, +may be left to the intelligent reader. We shall find, as we +proceed, the great convenience of the phraseology into which +we have last thrown them, and which is better adapted than +any I am acquainted with, to express with precision and +force what is aimed at, and actually accomplished, in every +case of the ascertainment of a truth by ratiocination. +</p> + +</div> + +<span class="tei tei-pb" id="page204">[pg 204]</span><a name="Pg204" id="Pg204" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc45" id="toc45"></a> +<a name="pdf46" id="pdf46"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER III. OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE +SYLLOGISM.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. We have shown what is the real nature of the +truths with which the Syllogism is conversant, in contradistinction +to the more superficial manner in which their import +is conceived in the common theory; and what are the fundamental +axioms on which its probative force or conclusiveness +depends. We have now to inquire, whether the syllogistic +process, that of reasoning from generals to particulars, is, or +is not, a process of inference; a progress from the known to +the unknown; a means of coming to a knowledge of something +which we did not know before. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Logicians have been remarkably unanimous in their mode +of answering this question. It is universally allowed that a +syllogism is vicious if there be anything more in the conclusion +than was assumed in the premisses. But this is, in +fact, to say, that nothing ever was, or can be, proved by syllogism, +which was not known, or assumed to be known, +before. Is ratiocination, then, not a process of inference? +And is the syllogism, to which the word reasoning has so +often been represented to be exclusively appropriate, not +really entitled to be called reasoning at all? This seems +an inevitable consequence of the doctrine, admitted by all +writers on the subject, that a syllogism can prove no more +than is involved in the premisses. Yet the acknowledgment +so explicitly made, has not prevented one set of writers from +continuing to represent the syllogism as the correct analysis +of what the mind actually performs in discovering and proving +the larger half of the truths, whether of science or of daily +life, which we believe; while those who have avoided this +inconsistency, and followed out the general theorem respecting +the logical value of the syllogism to its legitimate corollary, +<span class="tei tei-pb" id="page205">[pg 205]</span><a name="Pg205" id="Pg205" class="tei tei-anchor"></a> +have been led to impute uselessness and frivolity to the +syllogistic theory itself, on the ground of the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">petitio principii</span></span> +which they allege to be inherent in every syllogism. As I +believe both these opinions to be fundamentally erroneous, +I must request the attention of the reader to certain considerations, +without which any just appreciation of the true +character of the syllogism, and the functions it performs in +philosophy, appears to me impossible; but which seem to +have been either overlooked, or insufficiently adverted to, +both by the defenders of the syllogistic theory and by its +assailants. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. It must be granted that in every syllogism, considered +as an argument to prove the conclusion, there is a +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">petitio principii</span></span>. When we say, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All men are mortal<br /> +Socrates is a man<br /> +therefore<br /> +Socrates is mortal; +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +it is unanswerably urged by the adversaries of the syllogistic +theory, that the proposition, Socrates is mortal, is presupposed +in the more general assumption, All men are mortal: +that we cannot be assured of the mortality of all men, unless +we are already certain of the mortality of every individual +man: that if it be still doubtful whether Socrates, or any +other individual you choose to name, be mortal or not, the +same degree of uncertainty must hang over the assertion, +All men are mortal: that the general principle, instead of +being given as evidence of the particular case, cannot itself +be taken for true without exception, until every shadow of +doubt which could affect any case comprised with it, is dispelled +by evidence <span class="tei tei-hi"><span style="font-style: italic">aliundè</span></span>; and then what remains for the +syllogism to prove? That, in short, no reasoning from +generals to particulars can, as such, prove anything: since +from a general principle you cannot infer any particulars, +but those which the principle itself assumes as known. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This doctrine appears to me irrefragable; and if logicians, +<span class="tei tei-pb" id="page206">[pg 206]</span><a name="Pg206" id="Pg206" class="tei tei-anchor"></a> +though unable to dispute it, have usually exhibited a strong +disposition to explain it away, this was not because they could +discover any flaw in the argument itself, but because the +contrary opinion seemed to rest on arguments equally indisputable. +In the syllogism last referred to, for example, +or in any of those which we previously constructed, is it not +evident that the conclusion may, to the person to whom the +syllogism is presented, be actually and <span class="tei tei-hi"><span style="font-style: italic">bonâ fide</span></span> a new +truth? Is it not matter of daily experience that truths +previously undreamt of, facts which have not been, and +cannot be, directly observed, are arrived at by way of +general reasoning? We believe that the Duke of Wellington +is mortal. We do not know this by direct observation, +since he is not dead. If we were asked how, this being the +case, we know the duke to be mortal, we should probably +answer, Because all men are so. Here, therefore, we arrive +at the knowledge of a truth not (as yet) susceptible of observation, +by a reasoning which admits of being exhibited in +the following syllogism:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All men are mortal<br /> +The Duke of Wellington is a man<br /> +therefore<br /> +The Duke of Wellington is mortal. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And since a large portion of our knowledge is thus acquired, +logicians have persisted in representing the syllogism as a +process of inference or proof; although none of them has +cleared up the difficulty which arises from the inconsistency +between that assertion, and the principle, that if there be +anything in the conclusion which was not already asserted +in the premisses, the argument is vicious. For it is impossible +to attach any serious scientific value to such a mere +salvo, as the distinction drawn between being involved <em class="tei tei-emph"><span style="font-style: italic">by +implication</span></em> in the premisses, and being directly asserted in +them. When Archbishop Whately, for example, says,<a id="noteref_31" name="noteref_31" href="#note_31"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">31</span></span></a> +that the object of reasoning is <span class="tei tei-q">“merely to expand and unfold +<span class="tei tei-pb" id="page207">[pg 207]</span><a name="Pg207" id="Pg207" class="tei tei-anchor"></a> +the assertions wrapt up, as it were, and implied in those +with which we set out, and to bring a person to perceive and +acknowledge the full force of that which he has admitted,”</span> +he does not, I think, meet the real difficulty requiring to be +explained, namely, how it happens that a science, like +geometry, <em class="tei tei-emph"><span style="font-style: italic">can</span></em> be all <span class="tei tei-q">“wrapt up”</span> in a few definitions and +axioms. Nor does this defence of the syllogism differ much +from what its assailants urge against it as an accusation, +when they charge it with being of no use except to those +who seek to press the consequences of an admission into which +a person has been entrapped without having considered and +understood its full force. When you admitted the major +premiss, you asserted the conclusion; but, says Archbishop +Whately, you asserted it by implication merely: this, however, +can here only mean that you asserted it unconsciously; +that you did not know you were asserting it; but, if so, +the difficulty revives in this shape—Ought you not to have +known? Were you warranted in asserting the general proposition +without having satisfied yourself of the truth of +everything which it fairly includes? And if not, what then +is the syllogistic art but a contrivance for catching you in a +trap, and holding you fast in it?<a id="noteref_32" name="noteref_32" href="#note_32"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">32</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. From this difficulty there appears to be but one +issue. The proposition that the Duke of Wellington is +<span class="tei tei-pb" id="page208">[pg 208]</span><a name="Pg208" id="Pg208" class="tei tei-anchor"></a> +mortal, is evidently an inference; it is got at as a conclusion +from something else; but do we, in reality, conclude it from +the proposition, All men are mortal? I answer, no. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The error committed is, I conceive, that of overlooking +the distinction between the two parts of the process of +philosophizing, the inferring part, and the registering part; +and ascribing to the latter the functions of the former. The +mistake is that of referring a person to his own notes for +the origin of his knowledge. If a person is asked a question, +and is at the moment unable to answer it, he may refresh +his memory by turning to a memorandum which he carries +about with him. But if he were asked, how the fact came +to his knowledge, he would scarcely answer, because it was +set down in his note-book: unless the book was written, +like the Koran, with a quill from the wing of the angel +Gabriel. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Assuming that the proposition, The Duke of Wellington +is mortal, is immediately an inference from the proposition, +All men are mortal; whence do we derive our knowledge of +that general truth? Of course from observation. Now, all +which man can observe are individual cases. From these all +general truths must be drawn, and into these they may be +again resolved: for a general truth is but an aggregate of +particular truths; a comprehensive expression, by which an +indefinite number of individual facts are affirmed or denied +at once. But a general proposition is not merely a compendious +form for recording and preserving in the memory +a number of particular facts, all of which have been observed. +Generalization is not a process of mere naming, it is also a +process of inference. From instances which we have observed, +we feel warranted in concluding, that what we found +true in those instances, holds in all similar ones, past, +present, and future, however numerous they may be. We +then, by that valuable contrivance of language which enables +us to speak of many as if they were one, record all that we +have observed, together with all that we infer from our +observations, in one concise expression; and have thus +only one proposition, instead of an endless number, to +<span class="tei tei-pb" id="page209">[pg 209]</span><a name="Pg209" id="Pg209" class="tei tei-anchor"></a> +remember or to communicate. The results of many observations +and inferences, and instructions for making innumerable +inferences in unforeseen cases, are compressed +into one short sentence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, therefore, we conclude from the death of John and +Thomas, and every other person we ever heard of in whose +case the experiment had been fairly tried, that the Duke of +Wellington is mortal like the rest; we may, indeed, pass +through the generalization, All men are mortal, as an intermediate +stage; but it is not in the latter half of the process, +the descent from all men to the Duke of Wellington, that +the <em class="tei tei-emph"><span style="font-style: italic">inference</span></em> resides. The inference is finished when we +have asserted that all men are mortal. What remains to +be performed afterwards is merely decyphering our own +notes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Archbishop Whately has contended that syllogising, or +reasoning from generals to particulars, is not, agreeably to +the vulgar idea, a peculiar <em class="tei tei-emph"><span style="font-style: italic">mode</span></em> of reasoning, but the philosophical +analysis of <em class="tei tei-emph"><span style="font-style: italic">the</span></em> mode in which all men reason, and +must do so if they reason at all. With the deference due +to so high an authority, I cannot help thinking that the +vulgar notion is, in this case, the more correct. If, from our +experience of John, Thomas, &c., who once were living, but +are now dead, we are entitled to conclude that all human +beings are mortal, we might surely without any logical inconsequence +have concluded at once from those instances, +that the Duke of Wellington is mortal. The mortality of +John, Thomas, and company is, after all, the whole evidence +we have for the mortality of the Duke of Wellington. Not +one iota is added to the proof by interpolating a general +proposition. Since the individual cases are all the evidence +we can possess, evidence which no logical form into which +we choose to throw it can make greater than it is; and since +that evidence is either sufficient in itself, or, if insufficient +for the one purpose, cannot be sufficient for the other; I am +unable to see why we should be forbidden to take the shortest +cut from these sufficient premisses to the conclusion, and +constrained to travel the <span class="tei tei-q">“high priori road,”</span> by the arbitrary +<span class="tei tei-pb" id="page210">[pg 210]</span><a name="Pg210" id="Pg210" class="tei tei-anchor"></a> +fiat of logicians. I cannot perceive why it should be impossible +to journey from one place to another unless we <span class="tei tei-q">“march +up a hill, and then march down again.”</span> It may be the safest +road, and there may be a resting place at the top of the hill, +affording a commanding view of the surrounding country; +but for the mere purpose of arriving at our journey's end, our +taking that road is perfectly optional; it is a question of time, +trouble, and danger. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Not only <em class="tei tei-emph"><span style="font-style: italic">may</span></em> we reason from particulars to particulars +without passing through generals, but we perpetually do so +reason. All our earliest inferences are of this nature. From +the first dawn of intelligence we draw inferences, but years +elapse before we learn the use of general language. The +child, who, having burnt his fingers, avoids to thrust them +again into the fire, has reasoned or inferred, though he has +never thought of the general maxim, Fire burns. He knows +from memory that he has been burnt, and on this evidence +believes, when he sees a candle, that if he puts his finger +into the flame of it, he will be burnt again. He believes this +in every case which happens to arise; but without looking, +in each instance, beyond the present case. He is not generalizing; +he is inferring a particular from particulars. In the +same way, also, brutes reason. There is no ground for +attributing to any of the lower animals the use of signs, of +such a nature as to render general propositions possible. +But those animals profit by experience, and avoid what +they have found to cause them pain, in the same manner, +though not always with the same skill, as a human creature. +Not only the burnt child, but the burnt dog, dreads the fire. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I believe that, in point of fact, when drawing inferences +from our personal experience, and not from maxims handed +down to us by books or tradition, we much oftener conclude +from particulars to particulars directly, than through the +intermediate agency of any general proposition. We are +constantly reasoning from ourselves to other people, or from +one person to another, without giving ourselves the trouble +to erect our observations into general maxims of human or +external nature. When we conclude that some person will, +<span class="tei tei-pb" id="page211">[pg 211]</span><a name="Pg211" id="Pg211" class="tei tei-anchor"></a> +on some given occasion, feel or act so and so, we sometimes +judge from an enlarged consideration of the manner in which +human beings in general, or persons of some particular +character, are accustomed to feel and act; but much oftener +from having known the feelings and conduct of the same +person in some previous instance, or from considering how +we should feel or act ourselves. It is not only the village +matron who, when called to a consultation upon the case of +a neighbour's child, pronounces on the evil and its remedy +simply on the recollection and authority of what she accounts +the similar case of her Lucy. We all, where we have no +definite maxims to steer by, guide ourselves in the same +way; and if we have an extensive experience, and retain its +impressions strongly, we may acquire in this manner a very +considerable power of accurate judgment, which we may be +utterly incapable of justifying or of communicating to others. +Among the higher order of practical intellects, there have +been many of whom it was remarked how admirably they +suited their means to their ends, without being able to give +any sufficient reasons for what they did; and applied, or +seemed to apply, recondite principles which they were +wholly unable to state. This is a natural consequence of +having a mind stored with appropriate particulars, and +having been long accustomed to reason at once from these +to fresh particulars, without practising the habit of stating +to oneself or to others the corresponding general propositions. +An old warrior, on a rapid glance at the outlines of the +ground, is able at once to give the necessary orders for a +skilful arrangement of his troops; though if he has received +little theoretical instruction, and has seldom been called +upon to answer to other people for his conduct, he may +never have had in his mind a single general theorem +respecting the relation between ground and array. But his +experience of encampments, in circumstances more or less +similar, has left a number of vivid, unexpressed, ungeneralized +analogies in his mind, the most appropriate of which, +instantly suggesting itself, determines him to a judicious +arrangement. +</p> + +<span class="tei tei-pb" id="page212">[pg 212]</span><a name="Pg212" id="Pg212" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The skill of an uneducated person in the use of weapons, +or of tools, is of a precisely similar nature. The savage who +executes unerringly the exact throw which brings down his +game, or his enemy, in the manner most suited to his purpose, +under the operation of all the conditions necessarily involved, +the weight and form of the weapon, the direction and distance +of the object, the action of the wind, &c., owes this power +to a long series of previous experiments, the results of which +he certainly never framed into any verbal theorems or rules. +The same thing may generally be said of any other extraordinary +manual dexterity. Not long ago a Scotch manufacturer +procured from England, at a high rate of wages, a working +dyer, famous for producing very fine colours, with the view +of teaching to his other workmen the same skill. The workman +came; but his mode of proportioning the ingredients, +in which lay the secret of the effects he produced, was by +taking them up in handfuls, while the common method was to +weigh them. The manufacturer sought to make him turn his +handling system into an equivalent weighing system, that the +general principle of his peculiar mode of proceeding might +be ascertained. This, however, the man found himself quite +unable to do, and therefore could impart his skill to nobody. +He had, from the individual cases of his own experience, +established a connexion in his mind between fine effects of +colour, and tactual perceptions in handling his dyeing +materials; and from these perceptions he could, in any particular +case, infer the means to be employed, and the effects +which would be produced, but could not put others in possession +of the grounds on which he proceeded, from having +never generalized them in his own mind, or expressed them +in language. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Almost every one knows Lord Mansfield's advice to a +man of practical good sense, who, being appointed governor +of a colony, had to preside in its court of justice, without +previous judicial practice or legal education. The advice +was to give his decision boldly, for it would probably be +right; but never to venture on assigning reasons, for they +would almost infallibly be wrong. In cases like this, which +<span class="tei tei-pb" id="page213">[pg 213]</span><a name="Pg213" id="Pg213" class="tei tei-anchor"></a> +are of no uncommon occurrence, it would be absurd to suppose +that the bad reason was the source of the good decision. +Lord Mansfield knew that if any reason were assigned it +would be necessarily an afterthought, the judge being <em class="tei tei-emph"><span style="font-style: italic">in fact</span></em> +guided by impressions from past experience, without the +circuitous process of framing general principles from them, +and that if he attempted to frame any such he would +assuredly fail. Lord Mansfield, however, would not have +doubted that a man of equal experience, who had also a +mind stored with general propositions derived by legitimate +induction from that experience, would have been greatly preferable +as a judge, to one, however sagacious, who could not +be trusted with the explanation and justification of his own +judgments. The cases of men of talent performing wonderful +things they know not how, are examples of the rudest and +most spontaneous form of the operations of superior minds; +it is a defect in them, and often a source of errors, not to +have generalized as they went on; but generalization, though +a help, the most important indeed of all helps, is not an +essential. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Even the scientifically instructed, who possess, in the +form of general propositions, a systematic record of the results +of the experience of mankind, need not always revert to +those general propositions in order to apply that experience +to a new case. It is justly remarked by Dugald Stewart, +that though our reasonings in mathematics depend entirely +on the axioms, it is by no means necessary to our seeing +the conclusiveness of the proof, that the axioms should be +expressly adverted to. When it is inferred that A B is equal +to C D because each of them is equal to E F, the most uncultivated +understanding, as soon as the propositions were +understood, would assent to the inference, without having +ever heard of the general truth that <span class="tei tei-q">“things which are equal +to the same thing are equal to one another.”</span> This remark +of Stewart, consistently followed out, goes to the root, as I +conceive, of the philosophy of ratiocination; and it is to be +regretted that he himself stopt short at a much more limited +application of it. He saw that the general propositions on +<span class="tei tei-pb" id="page214">[pg 214]</span><a name="Pg214" id="Pg214" class="tei tei-anchor"></a> +which a reasoning is said to depend, may, in certain cases, +be altogether omitted, without impairing its probative force. +But he imagined this to be a peculiarity belonging to axioms; +and argued from it, that axioms are not the foundations or +first principles of geometry, from which all the other truths of +the science are synthetically deduced (as the laws of motion +and of the composition of forces in dynamics, the equal +mobility of fluids in hydrostatics, the laws of reflection and +refraction in optics, are the first principles of those sciences); +but are merely necessary assumptions, self-evident indeed, +and the denial of which would annihilate all demonstration, +but from which, as premisses, nothing can be demonstrated. +In the present, as in many other instances, this thoughtful +and elegant writer has perceived an important truth, but only +by halves. Finding, in the case of geometrical axioms, that +general names have not any talismanic virtue for conjuring +new truths out of the pit of darkness, and not seeing that +this is equally true in every other case of generalization, he +contended that axioms are in their nature barren of consequences, +and that the really fruitful truths, the real first principles +of geometry, are the definitions; that the definition, for +example, of the circle is to the properties of the circle, what +the laws of equilibrium and of the pressure of the atmosphere +are to the rise of the mercury in the Torricellian tube. Yet +all that he had asserted respecting the function to which the +axioms are confined in the demonstrations of geometry, +holds equally true of the definitions. Every demonstration +in Euclid might be carried on without them. This is apparent +from the ordinary process of proving a proposition of +geometry by means of a diagram. What assumption, in fact, +do we set out from, to demonstrate by a diagram any of the +properties of the circle? Not that in all circles the radii are +equal, but only that they are so in the circle ABC. As our +warrant for assuming this, we appeal, it is true, to the definition +of a circle in general; but it is only necessary that the +assumption be granted in the case of the particular circle +supposed. From this, which is not a general but a singular +proposition, combined with other propositions of a similar +<span class="tei tei-pb" id="page215">[pg 215]</span><a name="Pg215" id="Pg215" class="tei tei-anchor"></a> +kind, some of which <em class="tei tei-emph"><span style="font-style: italic">when generalized</span></em> are called definitions, +and others axioms, we prove that a certain conclusion is true, +not of all circles, but of the particular circle ABC; or at +least would be so, if the facts precisely accorded with our +assumptions. The enunciation, as it is called, that is, the +general theorem which stands at the head of the demonstration, +is not the proposition actually demonstrated. One +instance only is demonstrated: but the process by which +this is done, is a process which, when we consider its nature, +we perceive might be exactly copied in an indefinite number +of other instances; in every instance which conforms to certain +conditions. The contrivance of general language furnishing +us with terms which connote these conditions, we are +able to assert this indefinite multitude of truths in a single +expression, and this expression is the general theorem. By +dropping the use of diagrams, and substituting, in the demonstrations, +general phrases for the letters of the alphabet, +we might prove the general theorem directly, that is, we +might demonstrate all the cases at once; and to do this we +must, of course, employ as our premisses, the axioms and +definitions in their general form. But this only means, that +if we can prove an individual conclusion by assuming an +individual fact, then in whatever case we are warranted in +making an exactly similar assumption, we may draw an +exactly similar conclusion. The definition is a sort of notice +to ourselves and others, what assumptions we think ourselves +entitled to make. And so in all cases, the general propositions, +whether called definitions, axioms, or laws of nature, +which we lay down at the beginning of our reasonings, are +merely abridged statements, in a kind of short-hand, of the +particular facts, which, as occasion arises, we either think we +may proceed on as proved, or intend to assume. In any one +demonstration it is enough if we assume for a particular case +suitably selected, what by the statement of the definition or +principle we announce that we intend to assume in all cases +which may arise. The definition of the circle, therefore, is +to one of Euclid's demonstrations, exactly what, according to +Stewart, the axioms are; that is, the demonstration does not +<span class="tei tei-pb" id="page216">[pg 216]</span><a name="Pg216" id="Pg216" class="tei tei-anchor"></a> +depend on it, but yet if we deny it the demonstration fails. +The proof does not rest on the general assumption, but on +a similar assumption confined to the particular case: that +case, however, being chosen as a specimen or paradigm of +the whole class of cases included in the theorem, there can +be no ground for making the assumption in that case which +does not exist in every other; and if you deny the assumption +as a general truth, you deny the right to make it in the +particular instance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are, undoubtedly, the most ample reasons for +stating both the principles and the theorems in their general +form, and these will be explained presently, so far as explanation +is requisite. But, that unpractised learners, even +in making use of one theorem to demonstrate another, reason +rather from particular to particular than from the general +proposition, is manifest from the difficulty they find in applying +a theorem to a case in which the configuration of the +diagram is extremely unlike that of the diagram by which +the original theorem was demonstrated. A difficulty which, +except in cases of unusual mental power, long practice can +alone remove, and removes chiefly by rendering us familiar +with all the configurations consistent with the general conditions +of the theorem. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. From the considerations now adduced, the following +conclusions seem to be established. All inference is +from particulars to particulars: General propositions are +merely registers of such inferences already made, and short +formulæ for making more: The major premiss of a syllogism, +consequently, is a formula of this description: and the conclusion +is not an inference drawn <em class="tei tei-emph"><span style="font-style: italic">from</span></em> the formula, but an +inference drawn <em class="tei tei-emph"><span style="font-style: italic">according</span></em> to the formula: the real logical +antecedent, or premisses, being the particular facts from +which the general proposition was collected by induction. +Those facts, and the individual instances which supplied +them, may have been forgotten; but a record remains, not +indeed descriptive of the facts themselves, but showing how +those cases may be distinguished respecting which the facts, +<span class="tei tei-pb" id="page217">[pg 217]</span><a name="Pg217" id="Pg217" class="tei tei-anchor"></a> +when known, were considered to warrant a given inference. +According to the indications of this record we draw our conclusion; +which is, to all intents and purposes, a conclusion +from the forgotten facts. For this it is essential that we +should read the record correctly: and the rules of the +syllogism are a set of precautions to ensure our doing so. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This view of the functions of the syllogism is confirmed +by the consideration of precisely those cases which might be +expected to be least favourable to it, namely, those in which +ratiocination is independent of any previous induction. We +have already observed that the syllogism, in the ordinary +course of our reasoning, is only the latter half of the process +of travelling from premisses to a conclusion. There are, +however, some peculiar cases in which it is the whole process. +Particulars alone are capable of being subjected to observation; +and all knowledge which is derived from observation, +begins, therefore, of necessity, in particulars; but our knowledge +may, in cases of a certain description, be conceived +as coming to us from other sources than observation. It +may present itself as coming from testimony, which, on the +occasion and for the purpose in hand, is accepted as of an +authoritative character: and the information thus communicated, +may be conceived to comprise not only particular facts +but general propositions, as when a scientific doctrine is +accepted without examination on the authority of writers. +Or the generalization may not be, in the ordinary sense, an +assertion at all, but a command; a law, not in the philosophical, +but in the moral and political sense of the term: +an expression of the desire of a superior, that we, or any +number of other persons, shall conform our conduct to certain +general instructions. So far as this asserts a fact, namely, a +volition of the legislator, that fact is an individual fact, and +the proposition, therefore, is not a general proposition. But +the description therein contained of the conduct which it is +the will of the legislator that his subjects should observe, is +general. The proposition asserts, not that all men <em class="tei tei-emph"><span style="font-style: italic">are</span></em> anything, +but that all men <em class="tei tei-emph"><span style="font-style: italic">shall</span></em> do something. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In both these cases the generalities are the original data, +<span class="tei tei-pb" id="page218">[pg 218]</span><a name="Pg218" id="Pg218" class="tei tei-anchor"></a> +and the particulars are elicited from them by a process which +correctly resolves itself into a series of syllogisms. The real +nature, however, of the supposed deductive process, is evident +enough. The only point to be determined is, whether the +authority which declared the general proposition, intended +to include this case in it; and whether the legislator intended +his command to apply to the present case among others, or +not. This is ascertained by examining whether the case +possesses the marks by which, as those authorities have +signified, the cases which they meant to certify or to influence +may be known. The object of the inquiry is to make +out the witness's or the legislator's intention, through the +indication given by their words. This is a question, as the +Germans express it, of hermeneutics. The operation is not +a process of inference, but a process of interpretation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In this last phrase we have obtained an expression which +appears to me to characterize, more aptly than any other, the +functions of the syllogism in all cases. When the premisses +are given by authority, the function of Reasoning is to ascertain +the testimony of a witness, or the will of a legislator, by +interpreting the signs in which the one has intimated his +assertion and the other his command. In like manner, +when the premisses are derived from observation, the function +of Reasoning is to ascertain what we (or our predecessors) +formerly thought might be inferred from the observed +facts, and to do this by interpreting a memorandum of ours, +or of theirs. The memorandum reminds us, that from evidence, +more or less carefully weighed, it formerly appeared +that a certain attribute might be inferred wherever we perceive +a certain mark. The proposition, All men are mortal, +(for instance) shows that we have had experience from which +we thought it followed that the attributes connoted by the +term man, are a mark of mortality. But when we conclude +that the Duke of Wellington is mortal, we do not infer this +from the memorandum, but from the former experience. All +that we infer from the memorandum, is our own previous +belief, (or that of those who transmitted to us the proposition,) +<span class="tei tei-pb" id="page219">[pg 219]</span><a name="Pg219" id="Pg219" class="tei tei-anchor"></a> +concerning the inferences which that former experience +would warrant. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This view of the nature of the syllogism renders consistent +and intelligible what otherwise remains obscure and +confused in the theory of Archbishop Whately and other +enlightened defenders of the syllogistic doctrine, respecting +the limits to which its functions are confined. They affirm +in as explicit terms as can be used, that the sole office +of general reasoning is to prevent inconsistency in our +opinions; to prevent us from assenting to anything, the +truth of which would contradict something to which we had +previously on good grounds given our assent. And they +tell us, that the sole ground which a syllogism affords for +assenting to the conclusion, is that the supposition of its +being false, combined with the supposition that the premisses +are true, would lead to a contradiction in terms. Now +this would be but a lame account of the real grounds which +we have for believing the facts which we learn from reasoning, +in contradistinction to observation. The true reason +why we believe that the Duke of Wellington will die, is that +his fathers, and our fathers, and all other persons who were +cotemporary with them, have died. Those facts are the +real premisses of the reasoning. But we are not led to +infer the conclusion from those premisses, by the necessity +of avoiding any verbal inconsistency. There is no contradiction +in supposing that all those persons have died, and +that the Duke of Wellington may, notwithstanding, live for +ever. But there would be a contradiction if we first, on the +ground of those same premisses, made a general assertion +including and covering the case of the Duke of Wellington, +and then refused to stand to it in the individual case. There +is an inconsistency to be avoided between the memorandum +we make of the inferences which may be justly drawn in +future cases, and the inferences we actually draw in those +cases when they arise. With this view we interpret our own +formula, precisely as a judge interprets a law: in order that +we may avoid drawing any inferences not conformable to +<span class="tei tei-pb" id="page220">[pg 220]</span><a name="Pg220" id="Pg220" class="tei tei-anchor"></a> +our former intention, as a judge avoids giving any decision +not conformable to the legislator's intention. The rules for +this interpretation are the rules of the syllogism: and its +sole purpose is to maintain consistency between the conclusions +we draw in every particular case, and the previous +general directions for drawing them; whether those general +directions were framed by ourselves as the result of induction, +or were received by us from an authority competent to +give them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. In the above observations it has, I think, been +clearly shown, that, although there is always a process of +reasoning or inference where a syllogism is used, the syllogism +is not a correct analysis of that process of reasoning or +inference; which is, on the contrary, (when not a mere inference +from testimony,) an inference from particulars to +particulars; authorized by a previous inference from particulars +to generals, and substantially the same with it; of +the nature, therefore, of Induction. But, while these conclusions +appear to me undeniable, I must yet enter a +protest, as strong as that of Archbishop Whately himself; +against the doctrine that the syllogistic art is useless for +the purposes of reasoning. The reasoning lies in the act +of generalization, not in interpreting the record of that act; +but the syllogistic form is an indispensable collateral security +for the correctness of the generalization itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It has already been seen, that if we have a collection of +particulars sufficient for grounding an induction, we need +not frame a general proposition; we may reason at once +from those particulars to other particulars. But it is to be +remarked withal, that whenever, from a set of particular +cases, we can legitimately draw any inference, we may legitimately +make our inference a general one. If, from observation +and experiment, we can conclude to one new case, so +may we to an indefinite number. If that which has held +true in our past experience will therefore hold in time to +come, it will hold not merely in some individual case, but +in all cases of a given description. Every induction, therefore, +<span class="tei tei-pb" id="page221">[pg 221]</span><a name="Pg221" id="Pg221" class="tei tei-anchor"></a> +which suffices to prove one fact, proves an indefinite +multitude of facts: the experience which justifies a single +prediction must be such as will suffice to bear out a general +theorem. This theorem it is extremely important to ascertain +and declare, in its broadest form of generality; and +thus to place before our minds, in its full extent, the whole +of what our evidence must prove if it proves anything. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This throwing of the whole body of possible inferences +from a given set of particulars, into one general expression, +operates as a security for their being just inferences, in more +ways than one. First, the general principle presents a +larger object to the imagination than any of the singular +propositions which it contains. A process of thought which +leads to a comprehensive generality, is felt as of greater +importance than one which terminates in an insulated fact; +and the mind is, even unconsciously, led to bestow greater +attention upon the process, and to weigh more carefully the +sufficiency of the experience appealed to, for supporting the +inference grounded upon it. There is another, and a more +important, advantage. In reasoning from a course of individual +observations to some new and unobserved case, which +we are but imperfectly acquainted with (or we should not be +inquiring into it), and in which, since we are inquiring into +it, we probably feel a peculiar interest; there is very little +to prevent us from giving way to negligence, or to any bias +which may affect our wishes or our imagination, and, under +that influence, accepting insufficient evidence as sufficient. +But if, instead of concluding straight to the particular case, +we place before ourselves an entire class of facts—the whole +contents of a general proposition, every tittle of which is +legitimately inferrible from our premisses, if that one particular +conclusion is so; there is then a considerable likelihood +that if the premisses are insufficient, and the general +inference, therefore, groundless, it will comprise within it +some fact or facts the reverse of which we already know to +be true; and we shall thus discover the error in our generalization +by what the schoolmen termed a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio ad +impossibile</span></span>. +</p> + +<span class="tei tei-pb" id="page222">[pg 222]</span><a name="Pg222" id="Pg222" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus if, during the reign of Marcus Aurelius, a subject +of the Roman empire, under the bias naturally given to the +imagination and expectations by the lives and characters of +the Antonines, had been disposed to conclude that Commodus +would be a just ruler; supposing him to stop there, +he might only have been undeceived by sad experience. But +if he reflected that this conclusion could not be justifiable +unless from the same evidence he was also warranted in concluding +some general proposition, as, for instance, that all +Roman emperors are just rulers; he would immediately +have thought of Nero, Domitian, and other instances, which, +showing the falsity of the general conclusion, and therefore +the insufficiency of the premisses, would have warned him +that those premisses could not prove in the instance of +Commodus, what they were inadequate to prove in any +collection of cases in which his was included. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The advantage, in judging whether any controverted +inference is legitimate, of referring to a parallel case, is +universally acknowledged. But by ascending to the general +proposition, we bring under our view not one parallel case +only, but all possible parallel cases at once; all cases to which +the same set of evidentiary considerations are applicable. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, therefore, we argue from a number of known +cases to another case supposed to be analogous, it is always +possible, and generally advantageous, to divert our argument +into the circuitous channel of an induction from those known +cases to a general proposition, and a subsequent application +of that general proposition to the unknown case. This second +part of the operation, which, as before observed, is essentially +a process of interpretation, will be resolvable into a syllogism +or a series of syllogisms, the majors of which will be general +propositions embracing whole classes of cases; every one of +which propositions must be true in all its extent, if the argument +is maintainable. If, therefore, any fact fairly coming +within the range of one of these general propositions, and +consequently asserted by it, is known or suspected to be +other than the proposition asserts it to be, this mode of +stating the argument causes us to know or to suspect that +<span class="tei tei-pb" id="page223">[pg 223]</span><a name="Pg223" id="Pg223" class="tei tei-anchor"></a> +the original observations, which are the real grounds of our +conclusion, are not sufficient to support it. And in proportion +to the greater chance of our detecting the inconclusiveness +of our evidence, will be the increased reliance we are +entitled to place in it if no such evidence of defect shall +appear. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The value, therefore, of the syllogistic form, and of the +rules for using it correctly, does not consist in their being +the form and the rules according to which our reasonings +are necessarily, or even usually, made; but in their furnishing +us with a mode in which those reasonings may always be +represented, and which is admirably calculated, if they are +inconclusive, to bring their inconclusiveness to light. An +induction from particulars to generals, followed by a syllogistic +process from those generals to other particulars, is a +form in which we may always state our reasonings if we +please. It is not a form in which we <em class="tei tei-emph"><span style="font-style: italic">must</span></em> reason, but it is +a form in which we <em class="tei tei-emph"><span style="font-style: italic">may</span></em> reason, and into which it is indispensable +to throw our reasoning, when there is any doubt of +its validity: though when the case is familiar and little complicated, +and there is no suspicion of error, we may, and do, +reason at once from the known particular cases to unknown +ones. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These are the uses of syllogism, as a mode of verifying +any given argument. Its ulterior uses, as respects the general +course of our intellectual operations, hardly require illustration, +being in fact the acknowledged uses of general language. +They amount substantially to this, that the inductions may +be made once for all: a single careful interrogation of experience +may suffice, and the result may be registered in the +form of a general proposition, which is committed to memory +or to writing, and from which afterwards we have only to +syllogize. The particulars of our experiments may then be +dismissed from the memory, in which it would be impossible +to retain so great a multitude of details; while the knowledge +which those details afforded for future use, and which would +otherwise be lost as soon as the observations were forgotten, +or as their record became too bulky for reference, is retained +<span class="tei tei-pb" id="page224">[pg 224]</span><a name="Pg224" id="Pg224" class="tei tei-anchor"></a> +in a commodious and immediately available shape by means +of general language. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Against this advantage is to be set the countervailing +inconvenience, that inferences originally made on insufficient +evidence, become consecrated, and, as it were, hardened into +general maxims; and the mind cleaves to them from habit, +after it has outgrown any liability to be misled by similar +fallacious appearances if they were now for the first time +presented; but having forgotten the particulars, it does +not think of revising its own former decision. An inevitable +drawback, which, however considerable in itself, forms evidently +but a small deduction from the immense advantages +of general language. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The use of the syllogism is in truth no other than the use +of general propositions in reasoning. We <em class="tei tei-emph"><span style="font-style: italic">can</span></em> reason without +them; in simple and obvious cases we habitually do so; +minds of great sagacity can do it in cases not simple and +obvious, provided their experience supplies them with instances +essentially similar to every combination of circumstances +likely to arise. But other minds, or the same minds +without the same pre-eminent advantages of personal experience, +are quite helpless without the aid of general propositions, +wherever the case presents the smallest complication; +and if we made no general propositions, few persons would +get much beyond those simple inferences which are drawn +by the more intelligent of the brutes. Though not necessary +to reasoning, general propositions are necessary to any +considerable progress in reasoning. It is, therefore, natural +and indispensable to separate the process of investigation +into two parts; and obtain general formulæ for determining +what inferences may be drawn, before the occasion arises for +drawing the inferences. The work of drawing them is then +that of applying the formulæ; and the rules of syllogism +are a system of securities for the correctness of the application. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. To complete the series of considerations connected +with the philosophical character of the syllogism, it is requisite +<span class="tei tei-pb" id="page225">[pg 225]</span><a name="Pg225" id="Pg225" class="tei tei-anchor"></a> +to consider, since the syllogism is not the universal type +of the reasoning process, what is the real type. This resolves +itself into the question, what is the nature of the minor +premiss, and in what manner it contributes to establish +the conclusion: for as to the major, we now fully understand, +that the place which it nominally occupies in our +reasonings, properly belongs to the individual facts or +observations of which it expresses the general result; the +major itself being no real part of the argument, but an intermediate +halting place for the mind, interposed by an artifice +of language between the real premisses and the conclusion, +by way of a security, which it is in a most material degree, +for the correctness of the process. The minor, however, +being an indispensable part of the syllogistic expression of +an argument, without doubt either is, or corresponds to, an +equally indispensable part of the argument itself, and we +have only to inquire what part. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is perhaps worth while to notice here a speculation +of one of the philosophers to whom mental science is +most indebted, but who, though a very penetrating, was a +very hasty thinker, and whose want of due circumspection +rendered him fully as remarkable for what he did not see, +as for what he saw. I allude to Dr. Thomas Brown, whose +theory of ratiocination is peculiar. He saw the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">petitio principii</span></span> +which is inherent in every syllogism, if we consider the +major to be itself the evidence by which the conclusion is +proved, instead of being, what in fact it is, an assertion of +the existence of evidence sufficient to prove any conclusion +of a given description. Seeing this, Dr. Brown not only +failed to see the immense advantage, in point of security for +correctness, which is gained by interposing this step between +the real evidence and the conclusion; but he thought it +incumbent on him to strike out the major altogether from +the reasoning process, without substituting anything else, +and maintained that our reasonings consist only of the minor +premiss and the conclusion, Socrates is a man, therefore +Socrates is mortal: thus actually suppressing, as an unnecessary +step in the argument, the appeal to former experience. +<span class="tei tei-pb" id="page226">[pg 226]</span><a name="Pg226" id="Pg226" class="tei tei-anchor"></a> +The absurdity of this was disguised from him by the opinion +he adopted, that reasoning is merely analysing our own +general notions, or abstract ideas; and that the proposition, +Socrates is mortal, is evolved from the proposition, Socrates +is a man, simply by recognising the notion of mortality as +already contained in the notion we form of a man. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After the explanations so fully entered into on the subject +of propositions, much further discussion cannot be necessary +to make the radical error of this view of ratiocination apparent. +If the word man connoted mortality; if the meaning +of <span class="tei tei-q">“mortal”</span> were involved in the meaning of <span class="tei tei-q">“man;”</span> we +might, undoubtedly, evolve the conclusion from the minor +alone, because the minor would have distinctly asserted it. +But if, as is in fact the case, the word man does not connote +mortality, how does it appear that in the mind of every +person who admits Socrates to be a man, the idea of man +must include the idea of mortality? Dr. Brown could not +help seeing this difficulty, and in order to avoid it, was led, +contrary to his intention, to re-establish, under another +name, that step in the argument which corresponds to the +major, by affirming the necessity of <em class="tei tei-emph"><span style="font-style: italic">previously perceiving</span></em> the +relation between the idea of man and the idea of mortal. If +the reasoner has not previously perceived this relation, he +will not, says Dr. Brown, infer because Socrates is a man, +that Socrates is mortal. But even this admission, though +amounting to a surrender of the doctrine that an argument +consists of the minor and the conclusion alone, will not save +the remainder of Dr. Brown's theory. The failure of assent +to the argument does not take place merely because the +reasoner, for want of due analysis, does not perceive that his +idea of man includes the idea of mortality; it takes place, +much more commonly, because in his mind that relation +between the two ideas has never existed. And in truth it +never does exist, except as the result of experience. Consenting, +for the sake of the argument, to discuss the question +on a supposition of which we have recognised the radical +incorrectness, namely, that the meaning of a proposition +relates to the ideas of the things spoken of, and not to the +<span class="tei tei-pb" id="page227">[pg 227]</span><a name="Pg227" id="Pg227" class="tei tei-anchor"></a> +things themselves; I must yet observe, that the idea of man, +as an universal idea, the common property of all rational +creatures, cannot involve anything but what is strictly implied +in the name. If any one includes in his own private idea of +man, as no doubt is almost always the case, some other +attributes, such for instance as mortality, he does so only as +the consequence of experience, after having satisfied himself +that all men possess that attribute: so that whatever the +idea contains, in any person's mind, beyond what is included +in the conventional signification of the word, has been added +to it as the result of assent to a proposition; while Dr. +Brown's theory requires us to suppose, on the contrary, that +assent to the proposition is produced by evolving, through +an analytic process, this very element out of the idea. This +theory, therefore, may be considered as sufficiently refuted; +and the minor premiss must be regarded as totally insufficient +to prove the conclusion, except with the assistance +of the major, or of that which the major represents, namely, +the various singular propositions expressive of the series of +observations, of which the generalization called the major +premiss is the result. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the argument, then, which proves that Socrates is +mortal, one indispensable part of the premisses will be as +follows: <span class="tei tei-q">“My father, and my father's father, A, B, C, and +an indefinite number of other persons, were mortal;”</span> which +is only an expression in different words of the observed fact +that they have died. This is the major premiss, divested of +the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">petitio principii</span></span>, +and cut down to as much as is really +known by direct evidence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In order to connect this proposition with the conclusion, +Socrates is mortal, the additional link necessary is such a +proposition as the following: <span class="tei tei-q">“Socrates resembles my father, +and my father's father, and the other individuals specified.”</span> +This proposition we assert when we say that Socrates is a +man. By saying so we likewise assert in what respect he +resembles them, namely, in the attributes connoted by the +word man. And from this we conclude that he further +resembles them in the attribute mortality. +</p> + +<span class="tei tei-pb" id="page228">[pg 228]</span><a name="Pg228" id="Pg228" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. We have thus obtained what we were seeking, an +universal type of the reasoning process. We find it resolvable +in all cases into the following elements: Certain individuals +have a given attribute; an individual or individuals +resemble the former in certain other attributes; therefore +they resemble them also in the given attribute. This type +of ratiocination does not claim, like the syllogism, to be conclusive +from the mere form of the expression; nor can it +possibly be so. That one proposition does or does not +assert the very fact which was already asserted in another, +may appear from the form of the expression, that is, from a +comparison of the language; but when the two propositions +assert facts which are <span class="tei tei-hi"><span style="font-style: italic">bonâ fide</span></span> different, whether the one +fact proves the other or not can never appear from the language, +but must depend on other considerations. Whether, +from the attributes in which Socrates resembles those men +who have heretofore died, it is allowable to infer that he +resembles them also in being mortal, is a question of Induction; +and is to be decided by the principles or canons which +we shall hereafter recognise as tests of the correct performance +of that great mental operation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Meanwhile, however, it is certain, as before remarked, +that if this inference can be drawn as to Socrates, it can be +drawn as to all others who resemble the observed individuals +in the same attributes in which he resembles them; that is +(to express the thing concisely), of all mankind. If, therefore, +the argument be conclusive in the case of Socrates, we +are at liberty, once for all, to treat the possession of the +attributes of man as a mark, or satisfactory evidence, of the +attribute of mortality. This we do by laying down the universal +proposition, All men are mortal, and interpreting this, +as occasion arises, in its application to Socrates and others. +By this means we establish a very convenient division of the +entire logical operation into two steps; first, that of ascertaining +what attributes are marks of mortality; and, secondly, +whether any given individuals possess those marks. And +it will generally be advisable, in our speculations on the +reasoning process, to consider this double operation as in +<span class="tei tei-pb" id="page229">[pg 229]</span><a name="Pg229" id="Pg229" class="tei tei-anchor"></a> +fact taking place, and all reasoning as carried on in the form +into which it must necessarily be thrown to enable us to +apply to it any test of its correct performance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although, therefore, all processes of thought in which the +ultimate premisses are particulars, whether we conclude from +particulars to a general formula, or from particulars to other +particulars according to that formula, are equally Induction; +we shall yet, conformably to usage, consider the name Induction +as more peculiarly belonging to the process of establishing +the general proposition, and the remaining operation, +which is substantially that of interpreting the general proposition, +we shall call by its usual name, Deduction. And we +shall consider every process by which anything is inferred +respecting an unobserved case, as consisting of an Induction +followed by a Deduction; because, although the process +needs not necessarily be carried on in this form, it is always +susceptible of the form, and must be thrown into it when +assurance of scientific accuracy is needed and desired. +</p> + +<div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"> +<h3 class="tei tei-head" style="text-align: left; margin-bottom: 2.40em; margin-top: 2.40em"><span style="font-size: 120%">NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER.</span></h3> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +This theory of the syllogism, (which has received the important adhesion +of Dr. Whewell,</span><a id="noteref_33" name="noteref_33" href="#note_33"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">33</span></span></a><span style="font-size: 90%">) +has been controverted by a writer in the </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">British +Quarterly Review.</span><span style="font-size: 90%">”</span></span><a id="noteref_34" name="noteref_34" href="#note_34"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">34</span></span></a><span style="font-size: 90%"> +The doctrine being new, discussion respecting it is extremely +desirable, to ensure that nothing essential to the question escapes observation; +and I shall, therefore, reply to this writer's objections with somewhat +more minuteness than their strength may seem to require. +</span></div> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +The reviewer denies that there is a +</span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">petitio principii</span></span><span style="font-size: 90%"> +in the syllogism, or that +the proposition, All men are mortal, asserts or assumes that Socrates is mortal. +In support of this denial, he argues that we may, and in fact do, admit the +general proposition that all men are mortal, without having particularly examined +the case of Socrates, and even without knowing whether the individual +so named is a man or not. But this of course was never denied. That we can +and do draw conclusions concerning cases specifically unknown to us, is the +datum from which all who discuss this subject must set out. The question is, +in what terms the evidence, or ground, on which we draw these conclusions, may +best be designated—whether it is most correct to say, that the unknown case is +proved by known cases, or that it is proved by a general proposition, including +both sets of cases, the unknown and the known? I contend for the former +</span><span class="tei tei-pb" id="page230">[pg 230]</span><a name="Pg230" id="Pg230" class="tei tei-anchor"></a><span style="font-size: 90%"> +mode of expression. I hold it an abuse of language to say, that the proof that +Socrates is mortal, is that all men are mortal. Turn it in what way we will, this +seems to me to be asserting that a thing is the proof of itself. Whoever pronounces +the words, All men are mortal, has affirmed that Socrates is mortal, +though he may never have heard of Socrates; for since Socrates, whether +known to be so or not, really is a man, he is included in the words, All men, +and in every assertion of which they are the subject. If the reviewer does not +see that there is a difficulty here, I can only advise him to reconsider the subject +until he does: after which he will be a more competent judge of the success +or failure of an attempt to remove the difficulty.</span><a id="noteref_35" name="noteref_35" href="#note_35"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">35</span></span></a><span style="font-size: 90%"> That he had reflected very +little on the point when he wrote his remarks, is shown by his oversight +respecting the </span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">dictum de omni et +nullo</span></span><span style="font-size: 90%">. He acknowledges that this maxim as commonly +expressed,—</span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">Whatever is true of a class, is true of everything included +in the class,</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> is a mere identical proposition, since the class </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">is</span></em><span style="font-size: 90%"> +nothing but the things included in it. But he thinks this defect would be cured by +wording the maxim thus,—</span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">Whatever is true of a class, is true of everything +which </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">can be shown</span></em><span style="font-size: 90%"> to be a member of the class:</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> as if a thing could +</span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">be shown</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> to be a member of the class without being one. If a class means the sum +of all the things included in the class, the things which </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">can be shown</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> to be +included in it are a part of these; it is the sum of them too, and the +</span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">dictum</span></span><span style="font-size: 90%"> is as much an +identical proposition with respect to them as to the rest. One would almost +imagine that, in the reviewer's opinion, things are not members of a class until +they are called up publicly to take their place in it—that so long, in fact, as +Socrates is not known to be a man, he </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">is not</span></em><span style="font-size: 90%"> a man, and any assertion which +can be made concerning men does not at all regard him, nor is affected as to +its truth or falsity by anything in which he is concerned. +</span></div> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +The reviewer says that if the major premiss included the conclusion, </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">we +should be able to affirm the conclusion without the intervention of the minor +premiss; but every one sees that that is impossible.</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> It does not follow, because +the major premiss contains the conclusion, that the words themselves must +show all the conclusions which it contains, and which, or evidence of which, it +presupposes. The minor is equally required on both theories. It is respecting +the functions of the major premiss that the theories differ; whether that premiss +merely affirms the existence of proof, or is itself part of the proof—whether +the conclusion follows from the minor and major, or from the minor and the +</span><span class="tei tei-pb" id="page231">[pg 231]</span><a name="Pg231" id="Pg231" class="tei tei-anchor"></a><span style="font-size: 90%"> +particular instances which are the foundation of the major. On either supposition, +it is necessary that the new case should be perceived to be one coming +within the description of those to which the previous experience is applicable; +which is the purport of the minor premiss. When we say that all men are +mortal, we make an assertion reaching beyond the sphere of our knowledge of +individual cases; and when a new individual, Socrates, is brought within the +field of our knowledge by means of the minor premiss, we learn that we have +already made an assertion respecting Socrates without knowing it: our own +general formula is, to that extent, for the first time </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">interpreted</span></em><span style="font-size: 90%"> to us. +But according to the reviewer's theory, it is our having </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">made</span></em><span style="font-size: 90%"> the assertion +which proves the assertion: while I contend that the proof is not the assertion, but +the grounds (of experience) on which the assertion was made, and by which it +must be justified. +</span></div> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +The reviewer comes much nearer to the gist of the question, when he objects +that the formula in which the major is left out—</span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">A, B, C, &c., were mortal, +therefore the Duke of Wellington is mortal,</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> does not express all the steps of +the mental process, but omits one of the most essential, that which consists in +recognising the cases A, B, C, as </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">sufficient evidence</span></em><span style="font-size: 90%"> of what is true of +the Duke of Wellington. This recognition of the sufficiency of the induction he calls an +</span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">inference,</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> and says, that its result must be interpolated between the cases +A, B, C, and the case of the Duke of Wellington; and that </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">our final conclusion +is from what is thus interpolated, and not directly from the individual facts +that A, B, C, &c. were mortal.</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> On this it may first be observed, that the +formula does express all that takes place in ordinary unscientific reasoning. +Mankind in general conclude at once from experience of death in past cases, +to the expectation of it in future, without testing the experience by any principles +of induction, or passing through any general proposition. This is not +safe reasoning, but it is reasoning; and the syllogism, therefore, is not the +universal type of reasoning, but only a form in which it is </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">desirable</span></em><span style="font-size: 90%"> that +we should reason. But, in the second place, suppose that the enquirer does logically +satisfy himself that the conditions of legitimate induction are realized in +the cases A, B, C. It is still obvious, that if he knows the Duke of Wellington +to be a man, he is as much justified in concluding at once that the Duke of +Wellington is mortal, as in concluding that all men are mortal. The general +conclusion is not legitimate, unless the particular one would be so too; and +in no sense, intelligible to me, can the particular conclusion be said to be +drawn </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">from</span></em><span style="font-size: 90%"> the general one.</span><a id="noteref_36" name="noteref_36" href="#note_36"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">36</span></span></a><span style="font-size: 90%"> That the process of testing the sufficiency of +an inductive inference is an operation of a general character, I readily concede +to the reviewer; I had myself said as much, by laying down as a fundamental +law, that whenever there is ground for drawing any conclusion at all from particular +</span><span class="tei tei-pb" id="page232">[pg 232]</span><a name="Pg232" id="Pg232" class="tei tei-anchor"></a><span style="font-size: 90%"> +instances, there is ground for a </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">general</span></em><span style="font-size: 90%"> conclusion. But that this general +conclusion should be actually drawn, however useful, cannot be an indispensable +condition of the validity of the inference in the particular case. A man gives +away sixpence by the same power by which he disposes of his whole fortune; +but it is not necessary to the lawfulness of his doing the one, that he should formally +assert, even to himself, his right to do the other. +</span></div> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +The reviewer has recourse for an example, to syllogisms in the second +figure (though all are, by a mere verbal transformation, reducible to the first), +and asks, where is the </span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">petitio +principii</span></span><span style="font-size: 90%"> in this syllogism, </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">Every poet is a man of +genius, A B is not a man of genius, therefore A B is not a poet.</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> It is true +that in a syllogism of this particular type, the +</span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">petitio principii</span></span><span style="font-size: 90%"> is disguised. +A B is not included in the terms, every poet. But the proposition, </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">every poet +is a man of genius</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> (a very questionable proposition, by the way), cannot have +been inductively proved, unless the negative branch of the enquiry has been +attended to as well as the positive; unless it has been fully considered whether +among persons who are not </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">men of genius,</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> there are not some who ought to +be termed poets, and unless this has been determined in the negative. Therefore, +the case of A B has been decided by implication, as much as the case of +Socrates in the first example. The proposition, Every poet is a man of genius, +is confessedly æquipollent with </span><span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">No one who is not a man of genius is a poet,</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%"> +and in this the </span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">petitio principii</span></span><span style="font-size: 90%">, +as regards A B, is no longer implied, but express, +as in an ordinary syllogism of the first figure. +</span></div> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%"> +Another critic has endeavoured to get rid of the </span><span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-size: 90%; font-style: italic">petitio principii</span></span><span style="font-size: 90%"> in the syllogism +by substituting for the common form of expression, the following form—All +</span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">known</span></em><span style="font-size: 90%"> men were mortal, Socrates is a man, therefore Socrates is mortal. To +this, however, there is the fatal objection, that the syllogism, thus transformed, +does not prove the conclusion; it wants not the form only, but the substance of +proof. It is not merely because a thing is true in all </span><em class="tei tei-emph"><span style="font-size: 90%; font-style: italic">known</span></em><span style="font-size: 90%"> instances that +it can be inferred to be true in any new instance: many things may be true of all +known men which would not be true of all men; while, on the other hand, a thing +may be superabundantly proved true of all men, without having been ascertained +by actual experience to be true of all known men, or even of the hundredth +part of them. +</span></div> + +</div> + +</div> + +<span class="tei tei-pb" id="page233">[pg 233]</span><a name="Pg233" id="Pg233" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc47" id="toc47"></a> +<a name="pdf48" id="pdf48"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In our analysis of the syllogism it appeared that +the minor premiss always affirms a resemblance between a +new case, and some cases previously known; while the major +premiss asserts something which, having been found true of +those known cases, we consider ourselves warranted in +holding true of any other case resembling the former in +certain given particulars. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If all ratiocinations resembled, as to the minor premiss, +the examples which were exclusively employed in the preceding +chapter; if the resemblance, which that premiss asserts, +were obvious to the senses, as in the proposition <span class="tei tei-q">“Socrates +is a man,”</span> or were at once ascertainable by direct observation; +there would be no necessity for trains of reasoning, +and Deductive or Ratiocinative Sciences would not exist. +Trains of reasoning exist only for the sake of extending an +induction, founded, as all inductions must be, on observed +cases, to other cases in which we not only cannot directly +observe what is to be proved, but cannot directly observe +even the mark which is to prove it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Suppose the syllogism to be, All cows ruminate, +the animal which is before me is a cow, therefore it ruminates. +The minor, if true at all, is obviously so: the only premiss +the establishment of which requires any anterior process of +inquiry, is the major; and provided the induction of which +that premiss is the expression was correctly performed, the +conclusion respecting the animal now present will be instantly +drawn; because, as soon as she is compared with the +formula, she will be identified as being included in it. But +suppose the syllogism to be the following:—All arsenic is +poisonous, the substance which is before me is arsenic, +<span class="tei tei-pb" id="page234">[pg 234]</span><a name="Pg234" id="Pg234" class="tei tei-anchor"></a> +therefore it is poisonous. The truth of the minor may not +here be obvious at first sight; it may not be intuitively evident, +but may itself be known only by inference. It may be +the conclusion of another argument, which, thrown into the +syllogistic form, would stand thus:—Whatever forms a compound +with hydrogen, which yields a black precipitate with +nitrate of silver, is arsenic; the substance before me conforms +to this condition; therefore it is arsenic. To establish, +therefore, the ultimate conclusion, The substance before me +is poisonous, requires a process, which, in order to be syllogistically +expressed, stands in need of two syllogisms; and +we have a Train of Reasoning. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, however, we thus add syllogism to syllogism, we +are really adding induction to induction. Two separate +inductions must have taken place to render this chain of +inference possible; inductions founded, probably, on different +sets of individual instances, but which converge in their +results, so that the instance which is the subject of inquiry +comes within the range of them both. The record of these +inductions is contained in the majors of the two syllogisms. +First, we, or others for us, have examined various objects +which yielded under the given circumstances the given precipitate, +and found that they possessed the properties connoted +by the word arsenic; they were metallic, volatile, their +vapour had a smell of garlic, and so forth. Next, we, or +others for us, have examined various specimens which possessed +this metallic and volatile character, whose vapour had +this smell, &c., and have invariably found that they were +poisonous. The first observation we judge that we may +extend to all substances whatever which yield the precipitate: +the second, to all metallic and volatile substances resembling +those we examined; and consequently, not to those only +which are seen to be such, but to those which are concluded +to be such by the prior induction. The substance before us +is only seen to come within one of these inductions; but by +means of this one, it is brought within the other. We are +still, as before, concluding from particulars to particulars; +but we are now concluding from particulars observed, to +<span class="tei tei-pb" id="page235">[pg 235]</span><a name="Pg235" id="Pg235" class="tei tei-anchor"></a> +other particulars which are not, as in the simple case, <em class="tei tei-emph"><span style="font-style: italic">seen</span></em> +to resemble them in the material points, but <em class="tei tei-emph"><span style="font-style: italic">inferred</span></em> to do so, +because resembling them in something else, which we have +been led by quite a different set of instances to consider as +a mark of the former resemblance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This first example of a train of reasoning is still extremely +simple, the series consisting of only two syllogisms. The +following is somewhat more complicated:—No government, +which earnestly seeks the good of its subjects, is likely to +be overthrown; some particular government earnestly seeks +the good of its subjects, therefore it is not likely to be overthrown. +The major premiss in this argument we shall suppose +not to be derived from considerations <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, but to be a +generalization from history, which, whether correct or erroneous, +must have been founded on observation of governments +concerning whose desire of the good of their subjects there +was no doubt. It has been found, or thought to be found, +that these were not likely to be overthrown, and it has been +deemed that those instances warranted an extension of the +same predicate to any and every government which resembles +them in the attribute of desiring earnestly the good of its +subjects. But <em class="tei tei-emph"><span style="font-style: italic">does</span></em> the government in question thus resemble +them? This may be debated <span class="tei tei-hi"><span style="font-style: italic">pro</span></span> +and <span class="tei tei-hi"><span style="font-style: italic">con</span></span> by many arguments, +and must, in any case, be proved by another induction; +for we cannot directly observe the sentiments and +desires of the persons who carry on the government. To +prove the minor, therefore, we require an argument in this +form: Every government which acts in a certain manner, +desires the good of its subjects; the supposed government +acts in that particular manner, therefore it desires the good +of its subjects. But is it true that the government acts in +the manner supposed? This minor also may require proof; +still another induction, as thus:—What is asserted by intelligent +and disinterested witnesses, may be believed to be +true; that the government acts in this manner, is asserted by +such witnesses, therefore it may be believed to be true. The +argument hence consists of three steps. Having the evidence +of our senses that the case of the government under consideration +<span class="tei tei-pb" id="page236">[pg 236]</span><a name="Pg236" id="Pg236" class="tei tei-anchor"></a> +resembles a number of former cases, in the circumstance +of having something asserted respecting it by intelligent +and disinterested witnesses, we infer, first, that, as in those +former instances, so in this instance, the assertion is true. +Secondly, what was asserted of the government being that it +acts in a particular manner, and other governments or persons +having been observed to act in the same manner, the +government in question is brought into known resemblance +with those other governments or persons; and since they +were known to desire the good of the people, it is thereupon, +by a second induction, inferred that the particular government +spoken of, desires the good of the people. This brings that +government into known resemblance with the other governments +which were thought likely to escape revolution, and +thence, by a third induction, it is predicted that this particular +government is also likely to escape. This is still reasoning +from particulars to particulars, but we now reason to the new +instance from three distinct sets of former instances: to one +only of those sets of instances do we directly perceive the +new one to be similar; but from that similarity we inductively +infer that it has the attribute by which it is assimilated +to the next set, and brought within the corresponding +induction; after which by a repetition of the same operation +we infer it to be similar to the third set, and hence a third +induction conducts us to the ultimate conclusion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Notwithstanding the superior complication of +these examples, compared with those by which in the preceding +chapter we illustrated the general theory of reasoning, +every doctrine which we then laid down holds equally true in +these more intricate cases. The successive general propositions +are not steps in the reasoning, are not intermediate +links in the chain of inference, between the particulars +observed and those to which we apply the observation. If +we had sufficiently capacious memories, and a sufficient +power of maintaining order among a huge mass of details, +the reasoning could go on without any general propositions; +they are mere formulæ for inferring particulars from particulars. +<span class="tei tei-pb" id="page237">[pg 237]</span><a name="Pg237" id="Pg237" class="tei tei-anchor"></a> +The principle of general reasoning is, (as before explained,) +that if from observation of certain known particulars, +what was seen to be true of them can be inferred to be true +of any others, it may be inferred of all others which are of a +certain description. And in order that we may never fail to +draw this conclusion in a new case when it can be drawn +correctly, and may avoid drawing it when it cannot, we determine +once for all what are the distinguishing marks by which +such cases may be recognised. The subsequent process is +merely that of identifying an object, and ascertaining it to +have those marks; whether we identify it by the very marks +themselves, or by others which we have ascertained (through +another and a similar process) to be marks of those marks. +The real inference is always from particulars to particulars, +from the observed instances to an unobserved one: but in +drawing this inference, we conform to a formula which we +have adopted for our guidance in such operations, and which +is a record of the criteria by which we thought we had ascertained +that we might distinguish when the inference could, +and when it could not, be drawn. The real premisses are +the individual observations, even though they may have been +forgotten, or, being the observations of others and not of +ourselves, may, to us, never have been known: but we have +before us proof that we or others once thought them sufficient +for an induction, and we have marks to show whether any +new case is one of those to which, if then known, the induction +would have been deemed to extend. These marks we +either recognise at once, or by the aid of other marks, which +by another previous induction we collected to be marks of +<em class="tei tei-emph"><span style="font-style: italic">them</span></em>. Even these marks of marks may only be recognised +through a third set of marks; and we may have a train of +reasoning, of any length, to bring a new case within the scope +of an induction grounded on particulars its similarity to which +is only ascertained in this indirect manner. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus, in the preceding example, the ultimate inductive +inference was, that a certain government was not likely to be +overthrown: this inference was drawn according to a formula +in which desire of the public good was set down as a mark +<span class="tei tei-pb" id="page238">[pg 238]</span><a name="Pg238" id="Pg238" class="tei tei-anchor"></a> +of not being likely to be overthrown; a mark of this mark was, +acting in a particular manner; and a mark of acting in that +manner was, being asserted to do so by intelligent and disinterested +witnesses: this mark, the government under discussion +was recognised by the senses as possessing. Hence +that government fell within the last induction, and by it was +brought within all the others. The perceived resemblance of +the case to one set of observed particular cases, brought it into +known resemblance with another set, and that with a third. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the more complex branches of knowledge, the deductions +seldom consist, as in the examples hitherto exhibited, +of a single chain, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> a mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">b</span></span> of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, <span class="tei tei-hi"><span style="font-style: italic">c</span></span> +of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, therefore <span class="tei tei-hi"><span style="font-style: italic">a</span></span> a +mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>. They consist (to carry on the same metaphor) of +several chains united at the extremity, as thus: <span class="tei tei-hi"><span style="font-style: italic">a</span></span> a mark of +<span class="tei tei-hi"><span style="font-style: italic">d</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span> of <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> of <span class="tei tei-hi"><span style="font-style: italic">f</span></span>, <span class="tei tei-hi"><span style="font-style: italic">d e f</span></span> +of <span class="tei tei-hi"><span style="font-style: italic">n</span></span>, therefore <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span> a mark of +<span class="tei tei-hi"><span style="font-style: italic">n</span></span>. Suppose, +for example, the following combination of circumstances: +1st, rays of light impinging on a reflecting surface; +2nd, that surface parabolic; 3rd, those rays parallel to each +other and to the axis of the surface. It is to be proved that +the concourse of these three circumstances is a mark that +the reflected rays will pass through the focus of the parabolic +surface. Now, each of the three circumstances is singly a +mark of something material to the case. Rays of light impinging +on a reflecting surface, are a mark that those rays +will be reflected at an angle equal to the angle of incidence. +The parabolic form of the surface is a mark that, from any +point of it, a line drawn to the focus and a line parallel to +the axis will make equal angles with the surface. And finally, +the parallelism of the rays to the axis is a mark that their +angle of incidence coincides with one of these equal angles. +The three marks taken together are therefore a mark of all +these three things united. But the three united are evidently a +mark that the angle of reflexion must coincide with the other +of the two equal angles, that formed by a line drawn to the +focus; and this again, by the fundamental axiom concerning +straight lines, is a mark that the reflected rays pass +through the focus. Most chains of physical deduction are of +this more complicated type; and even in mathematics such +<span class="tei tei-pb" id="page239">[pg 239]</span><a name="Pg239" id="Pg239" class="tei tei-anchor"></a> +are abundant, as in all propositions where the hypothesis +includes numerous conditions: <span class="tei tei-q">“<em class="tei tei-emph"><span style="font-style: italic">If</span></em> a circle be taken, and +<em class="tei tei-emph"><span style="font-style: italic">if</span></em> within that circle a point be taken, not the centre, and +<em class="tei tei-emph"><span style="font-style: italic">if</span></em> straight lines be drawn from that point to the circumference, +then,”</span> &c. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. The considerations now stated remove a serious +difficulty from the view we have taken of reasoning; which +view might otherwise have seemed not easily reconcilable +with the fact that there are Deductive or Ratiocinative +Sciences. It might seem to follow, if all reasoning be induction, +that the difficulties of philosophical investigation must +lie in the inductions exclusively, and that when these were +easy, and susceptible of no doubt or hesitation, there could +be no science, or, at least, no difficulties in science. The +existence, for example, of an extensive Science of Mathematics, +requiring the highest scientific genius in those who +contributed to its creation, and calling for a most continued +and vigorous exertion of intellect in order to appropriate it +when created, may seem hard to be accounted for on the +foregoing theory. But the considerations more recently +adduced remove the mystery, by showing, that even when +the inductions themselves are obvious, there may be much +difficulty in finding whether the particular case which is the +subject of inquiry comes within them; and ample room for +scientific ingenuity in so combining various inductions, as, +by means of one within which the case evidently falls, to +bring it within others in which it cannot be directly seen to +be included. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When the more obvious of the inductions which can be +made in any science from direct observations, have been +made, and general formulas have been framed, determining +the limits within which these inductions are applicable; as +often as a new case can be at once seen to come within one +of the formulas, the induction is applied to the new case, and +the business is ended. But new cases are continually arising, +which do not obviously come within any formula whereby +the question we want solved in respect of them could be +<span class="tei tei-pb" id="page240">[pg 240]</span><a name="Pg240" id="Pg240" class="tei tei-anchor"></a> +answered. Let us take an instance from geometry; and as +it is taken only for illustration, let the reader concede to us +for the present, what we shall endeavour to prove in the +next chapter, that the first principles of geometry are +results of induction. Our example shall be the fifth proposition +of the first book of Euclid. The inquiry is, +Are the angles at the base of an isosceles triangle +equal or unequal? The first thing to be considered is, +what inductions we have, from which we can infer equality +or inequality. For inferring equality we have the following +formulæ:—Things which being applied to each other coincide, +are equals. Things which are equal to the same thing +are equals. A whole and the sum of its parts are equals. +The sums of equal things are equals. The differences +of equal things are equals. There are no other formulæ +to prove equality. For inferring inequality we have +the following:—A whole and its parts are unequals. +The sums of equal things and unequal things are unequals. +The differences of equal things and unequal +things are unequals. In all, eight formulæ. The angles at +the base of an isosceles triangle do not obviously come within +any of these. The formulæ specify certain marks of equality +and of inequality, but the angles cannot be perceived intuitively +to have any of those marks. We can, however, examine +whether they have properties which, in any other formulæ, +are set down as marks of those marks. On examination it +appears that they have; and we ultimately succeed in bringing +them within this formula, <span class="tei tei-q">“The differences of equal +things are equal.”</span> Whence comes the difficulty in recognising +these angles as the differences of equal things? Because +each of them is the difference not of one pair only, but of +innumerable pairs of angles; and out of these we had to +imagine and select two, which could either be intuitively perceived +to be equals, or possessed some of the marks of +equality set down in the various formulæ. By an exercise +of ingenuity, which, on the part of the first inventor, deserves +to be regarded as considerable, two pairs of angles were hit +upon, which united these requisites. First, it could be perceived +<span class="tei tei-pb" id="page241">[pg 241]</span><a name="Pg241" id="Pg241" class="tei tei-anchor"></a> +intuitively that their differences were the angles at +the base; and, secondly; they possessed one of the marks of +equality, namely, coincidence when applied to one another. +This coincidence, however, was not perceived intuitively, but +inferred, in conformity to another formula. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For greater clearness, I subjoin an analysis of the +demonstration. Euclid, it will be remembered, demonstrates +his fifth proposition by means of the fourth. This it +is not allowable for us to do, because we are undertaking to +trace deductive truths not to prior deductions, but to their +original inductive foundation. We must therefore use the premisses +of the fourth proposition +instead of its conclusion, and +prove the fifth directly from first +principles. To do so requires +six formulas. (We presuppose an equilateral triangle, whose vertices are +A, D, E, with point B on the side AD, and point C on the side AE, such that +BC is parallel to DE. +We must begin +as in Euclid, by prolonging the +equal sides AB, AC, to equal distances, +and joining the extremities +BE, DC.) +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">First Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">The sums of equals are +equal.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A D and A E are sums of equals by the supposition. +Having that mark of equality, they are concluded by this +formula to be equal. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Second Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">Equal straight lines being +applied to one another coincide</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A C, A B, are within this formula by supposition; A D, +A E, have been brought within it by the preceding step. +Both these pairs of straight lines have the property of +equality; which, according to the second formula, is a mark +that, if applied to each other, they will coincide. Coinciding +altogether means coinciding in every part, and of course at +their extremities, D, E, and B, C. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Third Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">Straight lines, having +their extremities coincident, coincide</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +B E and C D have been brought within this formula by +the preceding induction; they will, therefore, coincide. +</p> + +<span class="tei tei-pb" id="page242">[pg 242]</span><a name="Pg242" id="Pg242" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Fourth Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">Angles, having their sides +coincident, coincide</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The third induction having shown that B E and C D +coincide, and the second that A B, A C, coincide, the angles +A B E and A C D are thereby brought within the fourth +formula, and accordingly coincide. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Fifth Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">Things which coincide are +equal</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The angles A B E and A C D are brought within this +formula by the induction immediately preceding. This +train of reasoning being also applicable, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">mutatis mutandis</span></span>, +to the angles E B C, D C B, these also are brought within +the fifth formula. And, finally, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Sixth Formula</span></span>. <span class="tei tei-hi"><span style="font-style: italic">The differences of equals are +equal</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The angle A B C being the difference of A B E, C B E, +and the angle A C B being the difference of A C D, D C B; +which have been proved to be equals; A B C and A C B +are brought within the last formula by the whole of the +previous process. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The difficulty here encountered is chiefly that of figuring +to ourselves the two angles at the base of the triangle A B C, +as remainders made by cutting one pair of angles out of +another, while each pair shall be corresponding angles of +triangles which have two sides and the intervening angle +equal. It is by this happy contrivance that so many +different inductions are brought to bear upon the same particular +case. And this not being at all an obvious idea, it +may be seen from an example so near the threshold of +mathematics, how much scope there may well be for scientific +dexterity in the higher branches of that and other +sciences, in order so to combine a few simple inductions, +as to bring within each of them innumerable cases which +are not obviously included in it; and how long, and numerous, +and complicated may be the processes necessary for +bringing the inductions together, even when each induction +may itself be very easy and simple. All the inductions +<span class="tei tei-pb" id="page243">[pg 243]</span><a name="Pg243" id="Pg243" class="tei tei-anchor"></a> +involved in all geometry are comprised in those simple ones, +the formulæ of which are the Axioms, and a few of the +so-called Definitions. The remainder of the science is +made up of the processes employed for bringing unforeseen +cases within these inductions; or (in syllogistic language) +for proving the minors necessary to complete the syllogisms; +the majors being the definitions and axioms. In those definitions +and axioms are laid down the whole of the marks, +by an artful combination of which it has been found possible +to discover and prove all that is proved in geometry. The +marks being so few, and the inductions which furnish them +being so obvious and familiar; the connecting of several of +them together, which constitutes Deductions, or Trains of +Reasoning, forms the whole difficulty of the science, and, +with a trifling exception, its whole bulk; and hence Geometry +is a Deductive Science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. It will be seen hereafter that there are weighty +scientific reasons for giving to every science as much of the +character of a Deductive Science as possible; for endeavouring +to construct the science from the fewest and the +simplest possible inductions, and to make these, by any +combinations however complicated, suffice for proving even +such truths, relating to complex cases, as could be proved, +if we chose, by inductions from specific experience. Every +branch of natural philosophy was originally experimental; +each generalization rested on a special induction, and was +derived from its own distinct set of observations and experiments. +From being sciences of pure experiment, as the +phrase is, or, to speak more correctly, sciences in which the +reasonings mostly consist of no more than one step, and are +expressed by single syllogisms, all these sciences have become +to some extent, and some of them in nearly the whole +of their extent, sciences of pure reasoning; whereby multitudes +of truths, already known by induction from as many +different sets of experiments, have come to be exhibited as +deductions or corollaries from inductive propositions of a +simpler and more universal character. Thus mechanics, +<span class="tei tei-pb" id="page244">[pg 244]</span><a name="Pg244" id="Pg244" class="tei tei-anchor"></a> +hydrostatics, optics, acoustics, and thermology, have successively +been rendered mathematical; and astronomy was +brought by Newton within the laws of general mechanics. +Why it is that the substitution of this circuitous mode of +proceeding for a process apparently much easier and more +natural, is held, and justly, to be the greatest triumph of the +investigation of nature, we are not, in this stage of our inquiry, +prepared to examine. But it is necessary to remark, +that although, by this progressive transformation, all sciences +tend to become more and more Deductive, they are not +therefore the less Inductive; every step in the Deduction is +still an Induction. The opposition is not between the terms +Deductive and Inductive, but between Deductive and Experimental. +A science is experimental, in proportion as every +new case, which presents any peculiar features, stands in +need of a new set of observations and experiments, a fresh +induction. It is Deductive, in proportion as it can draw +conclusions, respecting cases of a new kind, by processes +which bring those cases under old inductions; by ascertaining +that cases which cannot be observed to have the +requisite marks, have, however, marks of those marks. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We can now, therefore, perceive what is the generic distinction +between sciences which can be made Deductive, and +those which must as yet remain Experimental. The difference +consists in our having been able, or not yet able, to +discover marks of marks. If by our various inductions we +have been able to proceed no further than to such propositions +as these, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> a mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +or <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and <span class="tei tei-hi"><span style="font-style: italic">b</span></span> marks of one another, +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> a mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +or <span class="tei tei-hi"><span style="font-style: italic">c</span></span> and <span class="tei tei-hi"><span style="font-style: italic">d</span></span> marks of one another, without +anything to connect <span class="tei tei-hi"><span style="font-style: italic">a</span></span> or <span class="tei tei-hi"><span style="font-style: italic">b</span></span> with +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> or <span class="tei tei-hi"><span style="font-style: italic">d</span></span>; we have a science +of detached and mutually independent generalizations, such +as these, that acids redden vegetable blues, and that alkalies +colour them green; from neither of which propositions could +we, directly or indirectly, infer the other: and a science, so +far as it is composed of such propositions, is purely experimental. +Chemistry, in the present state of our knowledge, +has not yet thrown off this character. There are other +sciences, however, of which the propositions are of this +<span class="tei tei-pb" id="page245">[pg 245]</span><a name="Pg245" id="Pg245" class="tei tei-anchor"></a> +kind: <span class="tei tei-hi"><span style="font-style: italic">a</span></span> a mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">b</span></span> a mark of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">d</span></span> of <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, &c. In +these sciences we can mount the ladder from <span class="tei tei-hi"><span style="font-style: italic">a</span></span> to +<span class="tei tei-hi"><span style="font-style: italic">e</span></span> by a +process of ratiocination; we can conclude that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is a mark +of <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, and that every object which has the mark +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> has the property <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, +although, perhaps, we never were able to observe <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +and <span class="tei tei-hi"><span style="font-style: italic">e</span></span> together, and although even <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +our only direct mark of <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, may be not perceptible in +those objects, but only inferrible. Or varying the first metaphor, we may be said to get +from <span class="tei tei-hi"><span style="font-style: italic">a</span></span> to <span class="tei tei-hi"><span style="font-style: italic">e</span></span> underground: +the marks <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">d</span></span>, which indicate +the route, must all be possessed somewhere by the objects +concerning which we are inquiring; but they are below the +surface: <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is the only mark that is visible, and by it we are +able to trace in succession all the rest. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. We can now understand how an experimental may +transform itself into a deductive science by the mere progress +of experiment. In an experimental science, the inductions, +as we have said, lie detached, as, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +a mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">c</span></span> a mark of +<span class="tei tei-hi"><span style="font-style: italic">d</span></span>, <span class="tei tei-hi"><span style="font-style: italic">e</span></span> a mark of +<span class="tei tei-hi"><span style="font-style: italic">f</span></span>, and so on: now, a new set of instances, and +a consequent new induction, may at any time bridge over +the interval between two of these unconnected arches; <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, for +example, may be ascertained to be a mark of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, which enables +us thenceforth to prove deductively that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +is a mark of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>. +Or, as sometimes happens, some comprehensive induction +may raise an arch high in the air, which bridges over hosts +of them at once: <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">f</span></span>, and all the rest, turning out to be +marks of some one thing, or of things between which a connexion +has already been traced. As when Newton discovered +that the motions, whether regular or apparently anomalous, +of all the bodies of the solar system, (each of which motions +had been inferred by a separate logical operation, from +separate marks,) were all marks of moving round a common +centre, with a centripetal force varying directly as the mass, +and inversely as the square of the distance from that centre. +This is the greatest example which has yet occurred of the +transformation, at one stroke, of a science which was still +to a great degree merely experimental, into a deductive +science. +</p> + +<span class="tei tei-pb" id="page246">[pg 246]</span><a name="Pg246" id="Pg246" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Transformations of the same nature, but on a smaller +scale, continually take place in the less advanced branches +of physical knowledge, without enabling them to throw off +the character of experimental sciences. Thus with regard +to the two unconnected propositions before cited, namely, +Acids redden vegetable blues, Alkalies make them green; +it is remarked by Liebig, that all blue colouring matters +which are reddened by acids (as well as, reciprocally, +all red colouring matters which are rendered blue by alkalies) +contain nitrogen: and it is quite possible that this +circumstance may one day furnish a bond of connexion between +the two propositions in question, by showing that the +antagonist action of acids and alkalies in producing or destroying +the colour blue, is the result of some one, more +general, law. Although this connecting of detached generalizations +is so much gain, it tends but little to give a deductive +character to any science as a whole; because the new +courses of observation and experiment, which thus enable +us to connect together a few general truths, usually make +known to us a still greater number of unconnected new ones. +Hence chemistry, though similar extensions and simplifications +of its generalizations are continually taking place, is +still in the main an experimental science; and is likely so to +continue, unless some comprehensive induction should be +hereafter arrived at, which, like Newton's, shall connect a +vast number of the smaller known inductions together, and +change the whole method of the science at once. Chemistry +has already one great generalization, which, though relating +to one of the subordinate aspects of chemical phenomena, +possesses within its limited sphere this comprehensive character; +the principle of Dalton, called the atomic theory, or +the doctrine of chemical equivalents: which by enabling us +to a certain extent to foresee the proportions in which two +substances will combine, before the experiment has been +tried, constitutes undoubtedly a source of new chemical +truths obtainable by deduction, as well as a connecting principle +for all truths of the same description previously obtained +by experiment. +</p> + +<span class="tei tei-pb" id="page247">[pg 247]</span><a name="Pg247" id="Pg247" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. The discoveries which change the method of a +science from experimental to deductive, mostly consist in +establishing, either by deduction or by direct experiment, +that the varieties of a particular phenomenon uniformly +accompany the varieties of some other phenomenon better +known. Thus the science of sound, which previously stood +in the lowest rank of merely experimental science, became +deductive when it was proved by experiment that every +variety of sound was consequent on, and therefore a mark +of, a distinct and definable variety of oscillatory motion +among the particles of the transmitting medium. When this +was ascertained, it followed that every relation of succession +or coexistence which obtained between phenomena of the +more known class, obtained also between the phenomena +which corresponded to them in the other class. Every +sound, being a mark of a particular oscillatory motion, became +a mark of everything which, by the laws of dynamics, +was known to be inferrible from that motion; and everything +which by those same laws was a mark of any oscillatory +motion among the particles of an elastic medium, became a +mark of the corresponding sound. And thus many truths, +not before suspected, concerning sound, become deducible +from the known laws of the propagation of motion through +an elastic medium; while facts already empirically known +respecting sound, become an indication of corresponding +properties of vibrating bodies, previously undiscovered. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But the grand agent for transforming experimental into +deductive sciences, is the science of number. The properties +of numbers, alone among all known phenomena, are, +in the most rigorous sense, properties of all things whatever. +All things are not coloured, or ponderable, or even extended; +but all things are numerable. And if we consider this science +in its whole extent, from common arithmetic up to the +calculus of variations, the truths already ascertained seem +all but infinite, and admit of indefinite extension. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These truths, though affirmable of all things whatever, +of course apply to them only in respect of their quantity. +But if it comes to be discovered that variations of quality in +<span class="tei tei-pb" id="page248">[pg 248]</span><a name="Pg248" id="Pg248" class="tei tei-anchor"></a> +any class of phenomena, correspond regularly to variations +of quantity either in those same or in some other phenomena; +every formula of mathematics applicable to quantities which +vary in that particular manner, becomes a mark of a corresponding +general truth respecting the variations in quality +which accompany them: and the science of quantity being +(as far as any science can be) altogether deductive, the +theory of that particular kind of qualities becomes, to this +extent, deductive likewise. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The most striking instance in point which history affords +(though not an example of an experimental science rendered +deductive, but of an unparalleled extension given to the +deductive process in a science which was deductive already,) +is the revolution in geometry which originated with Descartes, +and was completed by Clairaut. These great mathematicians +pointed out the importance of the fact, that to +every variety of position in points, direction in lines, or form +in curves or surfaces, (all of which are Qualities,) there +corresponds a peculiar relation of quantity between either +two or three rectilineal co-ordinates; insomuch that if the +law were known according to which those co-ordinates vary +relatively to one another, every other geometrical property +of the line or surface in question, whether relating to quantity +or quality, would be capable of being inferred. Hence it +followed that every geometrical question could be solved, if +the corresponding algebraical one could; and geometry received +an accession (actual or potential) of new truths, corresponding +to every property of numbers which the progress +of the calculus had brought, or might in future bring, to +light. In the same general manner, mechanics, astronomy, +and in a less degree, every branch of natural philosophy +commonly so called, have been made algebraical. The +varieties of physical phenomena with which those sciences +are conversant, have been found to answer to determinable +varieties in the quantity of some circumstance or other; or +at least to varieties of form or position, for which corresponding +equations of quantity had already been, or were +susceptible of being, discovered by geometers. +</p> + +<span class="tei tei-pb" id="page249">[pg 249]</span><a name="Pg249" id="Pg249" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In these various transformations, the propositions of the +science of number do but fulfil the function proper to all +propositions forming a train of reasoning, viz. that of +enabling us to arrive in an indirect method, by marks of +marks, at such of the properties of objects as we cannot +directly ascertain (or not so conveniently) by experiment. We +travel from a given visible or tangible fact, through the truths +of numbers, to the fact sought. The given fact is a mark +that a certain relation subsists between the quantities of +some of the elements concerned; while the fact sought presupposes +a certain relation between the quantities of some +other elements: now, if these last quantities are dependent +in some known manner upon the former, or <span class="tei tei-hi"><span style="font-style: italic">vice versa</span></span>, we +can argue from the numerical relation between the one set +of quantities, to determine that which subsists between the +other set; the theorems of the calculus affording the intermediate +links. And thus one of the two physical facts +becomes a mark of the other, by being a mark of a mark of +a mark of it. +</p> + +</div> + +<span class="tei tei-pb" id="page250">[pg 250]</span><a name="Pg250" id="Pg250" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc49" id="toc49"></a> +<a name="pdf50" id="pdf50"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER V. OF DEMONSTRATION, AND NECESSARY TRUTHS.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. If, as laid down in the two preceding chapters, the +foundation of all sciences, even deductive or demonstrative +sciences, is Induction; if every step in the ratiocinations +even of geometry is an act of induction; and if a train of +reasoning is but bringing many inductions to bear upon the +same subject of inquiry, and drawing a case within one +induction by means of another; wherein lies the peculiar +certainty always ascribed to the sciences which are entirely, +or almost entirely, deductive? Why are they called the +Exact Sciences? Why are mathematical certainty, and the +evidence of demonstration, common phrases to express the +very highest degree of assurance attainable by reason? Why +are mathematics by almost all philosophers, and (by many) +even those branches of natural philosophy which, through +the medium of mathematics, have been converted into deductive +sciences, considered to be independent of the evidence +of experience and observation, and characterized as systems +of Necessary Truth? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The answer I conceive to be, that this character of necessity, +ascribed to the truths of mathematics, and even (with +some reservations to be hereafter made) the peculiar certainty +attributed to them, is an illusion; in order to sustain +which, it is necessary to suppose that those truths relate to, +and express the properties of, purely imaginary objects. It +is acknowledged that the conclusions of geometry are deduced, +partly at least, from the so-called Definitions, and +that those definitions are assumed to be correct descriptions, +as far as they go, of the objects with which geometry is conversant. +Now we have pointed out that, from a definition +as such, no proposition, unless it be one concerning the +<span class="tei tei-pb" id="page251">[pg 251]</span><a name="Pg251" id="Pg251" class="tei tei-anchor"></a> +meaning of a word, can ever follow; and that what apparently +follows from a definition, follows in reality from an +implied assumption that there exists a real thing conformable +thereto. This assumption, in the case of the definitions +of geometry, is false: there exist no real things exactly +conformable to the definitions. There exist no points without +magnitude; no lines without breadth, nor perfectly +straight; no circles with all their radii exactly equal, nor +squares with all their angles perfectly right. It will perhaps +be said that the assumption does not extend to the actual, +but only to the possible, existence of such things. I answer +that, according to any test we have of possibility, they are +not even possible. Their existence, so far as we can form +any judgment, would seem to be inconsistent with the +physical constitution of our planet at least, if not of the +universe. To get rid of this difficulty, and at the same time +to save the credit of the supposed system of necessary truth, +it is customary to say that the points, lines, circles, and +squares which are the subject of geometry, exist in our conceptions +merely, and are part of our minds; which minds, +by working on their own materials, construct an +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +science, the evidence of which is purely mental, and has +nothing whatever to do with outward experience. By howsoever +high authorities this doctrine may have been sanctioned, +it appears to me psychologically incorrect. The +points, lines, circles, and squares, which any one has in his +mind, are (I apprehend) simply copies of the points, lines, +circles, and squares which he has known in his experience. +Our idea of a point, I apprehend to be simply our idea of +the <em class="tei tei-emph"><span style="font-style: italic">minimum visibile</span></em>, the smallest portion of surface which +we can see. A line, as defined by geometers, is wholly inconceivable. +We can reason about a line as if it had no +breadth; because we have a power, which is the foundation +of all the control we can exercise over the operations of +our minds; the power, when a perception is present to our +senses, or a conception to our intellects, of <em class="tei tei-emph"><span style="font-style: italic">attending</span></em> to a +part only of that perception or conception, instead of the +whole. But we cannot <em class="tei tei-emph"><span style="font-style: italic">conceive</span></em> a line without breadth; we +<span class="tei tei-pb" id="page252">[pg 252]</span><a name="Pg252" id="Pg252" class="tei tei-anchor"></a> +can form no mental picture of such a line: all the lines +which we have in our minds are lines possessing breadth. +If any one doubts this, we may refer him to his own experience. +I much question if any one who fancies that he +can conceive what is called a mathematical line, thinks so +from the evidence of his consciousness: I suspect it is rather +because he supposes that unless such a conception were +possible, mathematics could not exist as a science: a supposition +which there will be no difficulty in showing to be +entirely groundless. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Since, then, neither in nature, nor in the human mind, do +there exist any objects exactly corresponding to the definitions +of geometry, while yet that science cannot be supposed +to be conversant about non-entities; nothing remains but to +consider geometry as conversant with such lines, angles, and +figures, as really exist; and the definitions, as they are +called, must be regarded as some of our first and most +obvious generalizations concerning those natural objects. +The correctness of those generalizations, <em class="tei tei-emph"><span style="font-style: italic">as</span></em> generalizations, +is without a flaw: the equality of all the radii of a circle is +true of all circles, so far as it is true of any one: but it is not +exactly true of any circle: it is only nearly true; so nearly +that no error of any importance in practice will be incurred +by feigning it to be exactly true. When we have occasion +to extend these inductions, or their consequences, to cases +in which the error would be appreciable—to lines of perceptible +breadth or thickness, parallels which deviate sensibly +from equidistance, and the like—we correct our conclusions, +by combining with them a fresh set of propositions relating +to the aberration; just as we also take in propositions relating +to the physical or chemical properties of the material, if those +properties happen to introduce any modification into the +result; which they easily may, even with respect to figure +and magnitude, as in the case, for instance, of expansion by +heat. So long, however, as there exists no practical necessity +for attending to any of the properties of the object +except its geometrical properties, or to any of the natural +irregularities in those, it is convenient to neglect the consideration +<span class="tei tei-pb" id="page253">[pg 253]</span><a name="Pg253" id="Pg253" class="tei tei-anchor"></a> +of the other properties and of the irregularities, and +to reason as if these did not exist: accordingly, we formally +announce, in the definitions, that we intend to proceed on +this plan. But it is an error to suppose, because we resolve +to confine our attention to a certain number of the properties +of an object, that we therefore conceive, or have an idea of +the object, denuded of its other properties. We are thinking, +all the time, of precisely such objects as we have seen and +touched, and with all the properties which naturally belong +to them; but for scientific convenience, we feign them to be +divested of all properties, except those which are material to +our purpose, and in regard to which we design to consider +them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The peculiar accuracy, supposed to be characteristic of +the first principles of geometry, thus appears to be fictitious. +The assertions on which the reasonings of the science are +founded, do not, any more than in other sciences, exactly +correspond with the fact; but we <em class="tei tei-emph"><span style="font-style: italic">suppose</span></em> that they do so, for +the sake of tracing the consequences which follow from the +supposition. The opinion of Dugald Stewart respecting the +foundations of geometry, is, I conceive, substantially correct; +that it is built on hypotheses; that it owes to this alone +the peculiar certainty supposed to distinguish it; and that in +any science whatever, by reasoning from a set of hypotheses, +we may obtain a body of conclusions as certain as those of +geometry, that is, as strictly in accordance with the hypotheses, +and as irresistibly compelling assent, <em class="tei tei-emph"><span style="font-style: italic">on condition</span></em> that +those hypotheses are true. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When, therefore, it is affirmed that the conclusions of +geometry are necessary truths, the necessity consists in +reality only in this, that they necessarily follow from the +suppositions from which they are deduced. Those suppositions +are so far from being necessary, that they are not even +true; they purposely depart, more or less widely, from the +truth. The only sense in which necessity can be ascribed +to the conclusions of any scientific investigation, is that of +necessarily following from some assumption, which, by the +conditions of the inquiry, is not to be questioned. In this +<span class="tei tei-pb" id="page254">[pg 254]</span><a name="Pg254" id="Pg254" class="tei tei-anchor"></a> +relation, of course, the derivative truths of every deductive +science must stand to the inductions, or assumptions, on +which the science is founded, and which, whether true or +untrue, certain or doubtful in themselves, are always supposed +certain for the purposes of the particular science. +And therefore the conclusions of all deductive sciences were +said by the ancients to be necessary propositions. We +have observed already that to be predicated necessarily +was characteristic of the predicable Proprium, and that a +proprium was any property of a thing which could be deduced +from its essence, that is, from the properties included +in its definition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. The important doctrine of Dugald Stewart, +which I have endeavoured to enforce, has been contested +by Dr. Whewell, both in the dissertation appended to +his excellent <span class="tei tei-hi"><span style="font-style: italic">Mechanical Euclid</span></span>, and in his more recent +elaborate work on the <span class="tei tei-hi"><span style="font-style: italic">Philosophy of the Inductive Sciences</span></span>; +in which last he also replies to an article in the <span class="tei tei-hi"><span style="font-style: italic">Edinburgh +Review</span></span>, (ascribed to a writer of great scientific eminence,) +in which Stewart's opinion was defended against his former +strictures. The supposed refutation of Stewart consists in +proving against him (as has also been done in this work) +that the premisses of geometry are not definitions, but assumptions +of the real existence of things corresponding to those +definitions. This, however, is doing little for Dr. Whewell's +purpose; for it is these very assumptions which are asserted +to be hypotheses, and which he, if he denies that +geometry is founded on hypotheses, must show to be absolute +truths. All he does, however, is to observe, that they at any +rate are not <em class="tei tei-emph"><span style="font-style: italic">arbitrary</span></em> hypotheses; that we should not be at +liberty to substitute other hypotheses for them; that not +only <span class="tei tei-q">“a definition, to be admissible, must necessarily refer +to and agree with some conception which we can distinctly +frame in our thoughts,”</span> but that the straight lines, for instance, +which we define, must be <span class="tei tei-q">“those by which angles are +contained, those by which triangles are bounded, those of +<span class="tei tei-pb" id="page255">[pg 255]</span><a name="Pg255" id="Pg255" class="tei tei-anchor"></a> +which parallelism may be predicated, and the +like.”</span><a id="noteref_37" name="noteref_37" href="#note_37"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">37</span></span></a> And +this is true; but this has never been contradicted. Those +who say that the premisses of geometry are hypotheses, are +not bound to maintain them to be hypotheses which have no +relation whatever to fact. Since an hypothesis framed for +the purpose of scientific inquiry must relate to something +which has real existence, (for there can be no science respecting +non-entities,) it follows that any hypothesis we +make respecting an object, to facilitate our study of it, must +not involve anything which is distinctly false, and repugnant +to its real nature: we must not ascribe to the thing any property +which it has not; our liberty extends only to suppressing +some of those which it has, under the indispensable +obligation of restoring them whenever, and in as far as, their +presence or absence would make any material difference in +the truth of our conclusions. Of this nature, accordingly, +are the first principles involved in the definitions of geometry. +In their positive part they are observed facts; it is only in +their negative part that they are hypothetical. That the +hypotheses should be of this particular character, is however +no further necessary, than inasmuch as no others could +enable us to deduce conclusions which, with due corrections, +would be true of real objects: and in fact, when our aim is +only to illustrate truths, and not to investigate them, we are +not under any such restriction. We might suppose an imaginary +animal, and work out by deduction, from the known +laws of physiology, its natural history; or an imaginary +commonwealth, and from the elements composing it, might +argue what would be its fate. And the conclusions which +we might thus draw from purely arbitrary hypotheses, might +form a highly useful intellectual exercise: but as they could +only teach us what <em class="tei tei-emph"><span style="font-style: italic">would</span></em> be the properties of objects which +do not really exist, they would not constitute any addition +to our knowledge of nature: while on the contrary, if the +hypothesis merely divests a real object of some portion of its +properties, without clothing it in false ones, the conclusions +<span class="tei tei-pb" id="page256">[pg 256]</span><a name="Pg256" id="Pg256" class="tei tei-anchor"></a> +will always express, under known liability to correction, actual +truth. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. But although Dr. Whewell has not shaken Stewart's +doctrine as to the hypothetical character of that portion of +the first principles of geometry which are involved in the +so-called definitions, he has, I conceive, greatly the advantage +of Stewart on another important point in the theory of +geometrical reasoning; the necessity of admitting, among +those first principles, axioms as well as definitions. Some +of the axioms of Euclid might, no doubt, be exhibited in +the form of definitions, or might be deduced, by reasoning, +from propositions similar to what are so called. Thus, if +instead of the axiom, Magnitudes which can be made to +coincide are equal, we introduce a definition, <span class="tei tei-q">“Equal magnitudes +are those which may be so applied to one another +as to coincide;”</span> the three axioms which follow, (Magnitudes +which are equal to the same are equal to one another—If +equals are added to equals the sums are equal—If equals +are taken from equals the remainders are equal,) may be +proved by an imaginary superposition, resembling that by +which the fourth proposition of the first book of Euclid is +demonstrated. But although these and several others may +be struck out of the list of first principles, because, though +not requiring demonstration, they are susceptible of it; there +will be found in the list of axioms two or three fundamental +truths, not capable of being demonstrated: among which +must be reckoned the proposition that two straight lines +cannot inclose a space, (or its equivalent, Straight lines +which coincide in two points coincide altogether,) and some +property of parallel lines, other than that which constitutes +their definition: the most suitable, perhaps, being that +selected by Professor Playfair: <span class="tei tei-q">“Two straight lines which +intersect each other cannot both of them be parallel to a +third straight line.”</span><a id="noteref_38" name="noteref_38" href="#note_38"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">38</span></span></a> +</p> + +<span class="tei tei-pb" id="page257">[pg 257]</span><a name="Pg257" id="Pg257" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The axioms, as well those which are indemonstrable +as those which admit of being demonstrated, differ from that +other class of fundamental principles which are involved in +the definitions, in this, that they are true without any mixture +of hypothesis. That things which are equal to the same +thing are equal to one another, is as true of the lines and +figures in nature, as it would be of the imaginary ones +assumed in the definitions. In this respect, however, mathematics +are only on a par with most other sciences. In almost +all sciences there are some general propositions which are +exactly true, while the greater part are only more or less +distant approximations to the truth. Thus in mechanics, the +first law of motion (the continuance of a movement once +impressed, until stopped or slackened by some resisting +force) is true without qualification or error. The rotation +of the earth in twenty-four hours, of the same length as in +our time, has gone on since the first accurate observations, +without the increase or diminution of one second in all that +period. These are inductions which require no fiction to +make them be received as accurately true: but along with +them there are others, as for instance the propositions respecting +the figure of the earth, which are but approximations +to the truth; and in order to use them for the further +advancement of our knowledge, we must feign that they are +exactly true, though they really want something of being +so. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. It remains to inquire, what is the ground of our +belief in axioms—what is the evidence on which they rest? +I answer, they are experimental truths; generalizations from +<span class="tei tei-pb" id="page258">[pg 258]</span><a name="Pg258" id="Pg258" class="tei tei-anchor"></a> +observation. The proposition, Two straight lines cannot +inclose a space—or in other words, Two straight lines which +have once met, do not meet again, but continue to diverge—is +an induction from the evidence of our senses. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This opinion runs counter to a scientific prejudice of +long standing and great strength, and there is probably no +one proposition enunciated in this work for which a more +unfavourable reception is to be expected. It is, however, no +new opinion; and even if it were so, would be entitled to be +judged, not by its novelty, but by the strength of the arguments +by which it can be supported. I consider it very +fortunate that so eminent a champion of the contrary opinion +as Dr. Whewell, has recently found occasion for a most +elaborate treatment of the whole theory of axioms, in +attempting to construct the philosophy of the mathematical +and physical sciences on the basis of the doctrine against +which I now contend. Whoever is anxious that a discussion +should go to the bottom of the subject, must rejoice to see +the opposite side of the question worthily represented. If +what is said by Dr. Whewell, in support of an opinion which +he has made the foundation of a systematic work, can be +shown not to be conclusive, enough will have been done +without going further to seek stronger arguments and a more +powerful adversary. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is not necessary to show that the truths which we call +axioms are originally <em class="tei tei-emph"><span style="font-style: italic">suggested</span></em> by observation, and that we +should never have known that two straight lines cannot +inclose a space if we had never seen a straight line: thus +much being admitted by Dr. Whewell, and by all, in recent +times, who have taken his view of the subject. But they +contend, that it is not experience which <em class="tei tei-emph"><span style="font-style: italic">proves</span></em> the axiom; +but that its truth is perceived <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, by the constitution of +the mind itself, from the first moment when the meaning of +the proposition is apprehended; and without any necessity +for verifying it by repeated trials, as is requisite in the case +of truths really ascertained by observation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +They cannot, however, but allow that the truth of the +axiom, Two straight lines cannot inclose a space, even if +<span class="tei tei-pb" id="page259">[pg 259]</span><a name="Pg259" id="Pg259" class="tei tei-anchor"></a> +evident independently of experience, is also evident from +experience. Whether the axiom <em class="tei tei-emph"><span style="font-style: italic">needs</span></em> confirmation or not, +it <em class="tei tei-emph"><span style="font-style: italic">receives</span></em> confirmation in almost every instant of our lives; +since we cannot look at any two straight lines which intersect +one another, without seeing that from that point +they continue to diverge more and more. Experimental +proof crowds in upon us in such endless profusion, and +without one instance in which there can be even a suspicion +of an exception to the rule, that we should soon have a +stronger ground for believing the axiom, even as an experimental +truth, than we have for almost any of the general +truths which we confessedly learn from the evidence of our +senses. Independently of <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> evidence, we should certainly +believe it with an intensity of conviction far greater +than we accord to any ordinary physical truth: and this too +at a time of life much earlier than that from which we date +almost any part of our acquired knowledge, and much too +early to admit of our retaining any recollection of the history +of our intellectual operations at that period. Where then is +the necessity for assuming that our recognition of these truths +has a different origin from the rest of our knowledge, when +its existence is perfectly accounted for by supposing its origin +to be the same? when the causes which produce belief in all +other instances, exist in this instance, and in a degree of +strength as much superior to what exists in other cases, as +the intensity of the belief itself is superior? The burden of +proof lies on the advocates of the contrary opinion: it is for +them to point out some fact, inconsistent with the supposition +that this part of our knowledge of nature is derived from +the same sources as every other part. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, for instance, they would be able to do, if they could +prove chronologically that we had the conviction (at least +practically) so early in infancy as to be anterior to those +impressions on the senses, upon which, on the other theory, +the conviction is founded. This, however, cannot be proved: +the point being too far back to be within the reach of memory, +and too obscure for external observation. The advocates +of the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +theory are obliged to have recourse to other +<span class="tei tei-pb" id="page260">[pg 260]</span><a name="Pg260" id="Pg260" class="tei tei-anchor"></a> +arguments. These are reducible to two, which I shall endeavour +to state as clearly and as forcibly as possible. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. In the first place it is said, that if our assent to the +proposition that two straight lines cannot inclose a space, +were derived from the senses, we could only be convinced of +its truth by actual trial, that is, by seeing or feeling the +straight lines; whereas in fact it is seen to be true by merely +thinking of them. That a stone thrown into water goes to +the bottom, may be perceived by our senses, but mere thinking +of a stone thrown into the water would never have led +us to that conclusion: not so, however, with the axioms +relating to straight lines: if I could be made to conceive +what a straight line is, without having seen one, I should at +once recognise that two such lines cannot inclose a space. +Intuition is <span class="tei tei-q">“imaginary looking;”</span><a id="noteref_39" name="noteref_39" href="#note_39"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">39</span></span></a> +but experience must be +real looking: if we see a property of straight lines to be true +by merely fancying ourselves to be looking at them, the +ground of our belief cannot be the senses, or experience; it +must be something mental. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To this argument it might be added in the case of this +particular axiom, (for the assertion would not be true of all +axioms,) that the evidence of it from actual ocular inspection, +is not only unnecessary, but unattainable. What says +the axiom? That two straight lines <em class="tei tei-emph"><span style="font-style: italic">cannot</span></em> inclose a space; +that after having once intersected, if they are prolonged to +infinity they do not meet, but continue to diverge from one +another. How can this, in any single case, be proved by +actual observation? We may follow the lines to any distance +we please; but we cannot follow them to infinity: for aught +our senses can testify, they may, immediately beyond the +farthest point to which we have traced them, begin to +approach, and at last meet. Unless, therefore, we had +some other proof of the impossibility than observation +affords us, we should have no ground for believing the axiom +at all. +</p> + +<span class="tei tei-pb" id="page261">[pg 261]</span><a name="Pg261" id="Pg261" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To these arguments, which I trust I cannot be accused +of understating, a satisfactory answer will, I conceive, be +found, if we advert to one of the characteristic properties of +geometrical forms—their capacity of being painted in the +imagination with a distinctness equal to reality: in other +words, the exact resemblance of our ideas of form to the +sensations which suggest them. This, in the first place, +enables us to make (at least with a little practice) mental +pictures of all possible combinations of lines and angles, +which resemble the realities quite as well as any which we +could make on paper; and in the next place, makes those +pictures just as fit subjects of geometrical experimentation +as the realities themselves; inasmuch as pictures, if sufficiently +accurate, exhibit of course all the properties which +would be manifested by the realities at one given instant, +and on simple inspection: and in geometry we are concerned +only with such properties, and not with that which +pictures could not exhibit, the mutual action of bodies one +upon another. The foundations of geometry would therefore +be laid in direct experience, even if the experiments +(which in this case consist merely in attentive contemplation) +were practised solely upon what we call our ideas, that +is, upon the diagrams in our minds, and not upon outward +objects. For in all systems of experimentation we take some +objects to serve as representatives of all which resemble +them; and in the present case the conditions which qualify +a real object to be the representative of its class, are completely +fulfilled by an object existing only in our fancy. +Without denying, therefore, the possibility of satisfying ourselves +that two straight lines cannot inclose a space, by +merely thinking of straight lines without actually looking at +them; I contend, that we do not believe this truth on the +ground of the imaginary intuition simply, but because we +know that the imaginary lines exactly resemble real ones, +and that we may conclude from them to real ones with quite +as much certainty as we could conclude from one real line +to another. The conclusion, therefore, is still an induction +from observation. And we should not be authorized to substitute +<span class="tei tei-pb" id="page262">[pg 262]</span><a name="Pg262" id="Pg262" class="tei tei-anchor"></a> +observation of the image in our mind, for observation +of the reality, if we had not learnt by long-continued experience +that the properties of the reality are faithfully +represented in the image; just as we should be scientifically +warranted in describing an animal which we had never seen, +from a picture made of it with a daguerreotype; but not +until we had learnt by ample experience, that observation of +such a picture is precisely equivalent to observation of the +original. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These considerations also remove the objection arising +from the impossibility of ocularly following the lines in their +prolongation to infinity, for though, in order actually to +see that two given lines never meet, it would be necessary +to follow them to infinity; yet without doing so we may +know that if they ever do meet, or if, after diverging from +one another, they begin again to approach, this must take +place not at an infinite, but at a finite distance. Supposing, +therefore, such to be the case, we can transport ourselves +thither in imagination, and can frame a mental image of the +appearance which one or both of the lines must present at +that point, which we may rely on as being precisely similar +to the reality. Now, whether we fix our contemplation upon +this imaginary picture, or call to mind the generalizations +we have had occasion to make from former ocular observation, +we learn by the evidence of experience, that a line +which, after diverging from another straight line, begins to +approach to it, produces the impression on our senses which +we describe by the expression, <span class="tei tei-q">“a bent line,”</span> not by the +expression, <span class="tei tei-q">“a straight line.”</span><a id="noteref_40" name="noteref_40" href="#note_40"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">40</span></span></a> +</p> + +<span class="tei tei-pb" id="page263">[pg 263]</span><a name="Pg263" id="Pg263" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. The first of the two arguments in support of the +theory that axioms are <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à +priori</span></span> truths, having, I think, been +sufficiently answered; I proceed to the second, which is +usually the most relied on. Axioms (it is asserted) are +conceived by us not only as true, but as universally and +necessarily true. Now, experience cannot possibly give to +any proposition this character. I may have seen snow a +hundred times, and may have seen that it was white, but +this cannot give me entire assurance even that all snow is +white; much less that snow <em class="tei tei-emph"><span style="font-style: italic">must</span></em> be white. <span class="tei tei-q">“However +many instances we may have observed of the truth of a proposition, +there is nothing to assure us that the next case +shall not be an exception to the rule. If it be strictly true +that every ruminant animal yet known has cloven hoofs, we +still cannot be sure that some creature will not hereafter be +discovered which has the first of these attributes, without +<span class="tei tei-pb" id="page264">[pg 264]</span><a name="Pg264" id="Pg264" class="tei tei-anchor"></a> +having the other.... Experience must always consist of a +limited number of observations; and, however numerous +these may be, they can show nothing with regard to the infinite +number of cases in which the experiment has not been +made.”</span> Besides, axioms are not only universal, they are +also necessary. Now <span class="tei tei-q">“experience cannot offer the smallest +ground for the necessity of a proposition. She can observe +and record what has happened; but she cannot find, in any +case, or in any accumulation of cases, any reason for what +<em class="tei tei-emph"><span style="font-style: italic">must</span></em> happen. She may see objects side by side; but she +cannot see a reason why they must ever be side by side. She +finds certain events to occur in succession; but the succession +supplies, in its occurrence, no reason for its recurrence. +She contemplates external objects; but she cannot detect +any internal bond, which indissolubly connects the future +with the past, the possible with the real. To learn a proposition +by experience, and to see it to be necessarily true, +are two altogether different processes of +thought.”</span><a id="noteref_41" name="noteref_41" href="#note_41"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">41</span></span></a> And +Dr. Whewell adds, <span class="tei tei-q">“If any one does not clearly comprehend +this distinction of necessary and contingent truths, he will +not be able to go along with us in our researches into the +foundations of human knowledge; nor, indeed, to pursue +with success any speculation on the subject.”</span><a id="noteref_42" name="noteref_42" href="#note_42"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">42</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the following passage, we are told what the distinction +is, the non-recognition of which incurs this denunciation. +<span class="tei tei-q">“Necessary truths are those in which we not only learn that +the proposition <em class="tei tei-emph"><span style="font-style: italic">is</span></em> true, but see that it <em class="tei tei-emph"><span style="font-style: italic">must be</span></em> true; in which +the negation of the truth is not only false, but impossible; +in which we cannot, even by an effort of imagination, or in +a supposition, conceive the reverse of that which is asserted. +That there are such truths cannot be doubted. We may +take, for example, all relations of number. Three and Two, +added together, make Five. We cannot conceive it to be +otherwise. We cannot, by any freak of thought, imagine +Three and Two to make Seven.”</span><a id="noteref_43" name="noteref_43" href="#note_43"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">43</span></span></a> +</p> + +<span class="tei tei-pb" id="page265">[pg 265]</span><a name="Pg265" id="Pg265" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although Dr. Whewell has naturally and properly employed +a variety of phrases to bring his meaning more +forcibly home, he will, I presume, allow that they are all +equivalent; and that what he means by a necessary truth, +would be sufficiently defined, a proposition the negation of +which is not only false but inconceivable. I am unable to +find in any of his expressions, turn them what way you will, +a meaning beyond this, and I do not believe he would contend +that they mean anything more. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, therefore, is the principle asserted: that propositions, +the negation of which is inconceivable, or in other +words, which we cannot figure to ourselves as being false, +must rest on evidence of a higher and more cogent description +than any which experience can afford. And we have next +to consider whether there is any ground for this assertion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now I cannot but wonder that so much stress should be +laid on the circumstance of inconceivableness, when there +is such ample experience to show, that our capacity or incapacity +of conceiving a thing has very little to do with the +possibility of the thing in itself; but is in truth very much an +affair of accident, and depends on the past history and habits +of our own minds. There is no more generally acknowledged +fact in human nature, than the extreme difficulty at +first felt in conceiving anything as possible, which is in contradiction +to long established and familiar experience; or +even to old familiar habits of thought. And this difficulty +is a necessary result of the fundamental laws of the +human mind. When we have often seen and thought of two +things together, and have never in any one instance either +seen or thought of them separately, there is by the primary +law of association an increasing difficulty, which may in the +end become insuperable, of conceiving the two things apart. +This is most of all conspicuous in uneducated persons, who +are in general utterly unable to separate any two ideas +which have once become firmly associated in their minds; +and if persons of cultivated intellect have any advantage on +the point, it is only because, having seen and heard and read +more, and being more accustomed to exercise their imagination, +<span class="tei tei-pb" id="page266">[pg 266]</span><a name="Pg266" id="Pg266" class="tei tei-anchor"></a> +they have experienced their sensations and thoughts in +more varied combinations, and have been prevented from +forming many of these inseparable associations. But this +advantage has necessarily its limits. The most practised +intellect is not exempt from the universal laws of our conceptive +faculty. If daily habit presents to any one for a long +period two facts in combination, and if he is not led during +that period either by accident or by his voluntary mental +operations to think of them apart, he will probably in time +become incapable of doing so even by the strongest effort; and +the supposition that the two facts can be separated in nature, +will at last present itself to his mind with all the characters +of an inconceivable phenomenon.<a id="noteref_44" name="noteref_44" href="#note_44"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">44</span></span></a> +There are remarkable +instances of this in the history of science: instances in which +the most instructed men rejected as impossible, because inconceivable, +things which their posterity, by earlier practice +and longer perseverance in the attempt, found it quite easy +to conceive, and which everybody now knows to be true. +There was a time when men of the most cultivated intellects, +and the most emancipated from the dominion of early prejudice, +could not credit the existence of antipodes; were +unable to conceive, in opposition to old association, the force +of gravity acting upwards instead of downwards. The Cartesians +long rejected the Newtonian doctrine of the gravitation +of all bodies towards one another, on the faith of a +general proposition, the reverse of which seemed to them to +be inconceivable—the proposition that a body cannot act +where it is not. All the cumbrous machinery of imaginary +vortices, assumed without the smallest particle of evidence, +appeared to these philosophers a more rational mode of explaining +the heavenly motions, than one which involved what +<span class="tei tei-pb" id="page267">[pg 267]</span><a name="Pg267" id="Pg267" class="tei tei-anchor"></a> +seemed to them so great an absurdity.<a id="noteref_45" name="noteref_45" href="#note_45"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">45</span></span></a> And they no doubt +found it as impossible to conceive that a body should act upon +the earth, at the distance of the sun or moon, as we find it +to conceive an end to space or time, or two straight lines +inclosing a space. Newton himself had not been able to +realize the conception, or we should not have had his hypothesis +of a subtle ether, the occult cause of gravitation; and +his writings prove, that although he deemed the particular +nature of the intermediate agency a matter of conjecture, the +necessity of <em class="tei tei-emph"><span style="font-style: italic">some</span></em> such agency appeared to him indubitable. +It would seem that even now the majority of scientific men +have not completely got over this very difficulty; for though +they have at last learnt to conceive the sun <em class="tei tei-emph"><span style="font-style: italic">attracting</span></em> the +earth without any intervening fluid, they cannot yet conceive +the sun <em class="tei tei-emph"><span style="font-style: italic">illuminating</span></em> the earth without some such medium. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If, then, it be so natural to the human mind, even in a +high state of culture, to be incapable of conceiving, and on +that ground to believe impossible, what is afterwards not +only found to be conceivable but proved to be true; what +wonder if in cases where the association is still older, more +confirmed, and more familiar, and in which nothing ever +occurs to shake our conviction, or even suggest to us any +conception at variance with the association, the acquired +incapacity should continue, and be mistaken for a natural +<span class="tei tei-pb" id="page268">[pg 268]</span><a name="Pg268" id="Pg268" class="tei tei-anchor"></a> +incapacity? It is true, our experience of the varieties in +nature enables us, within certain limits, to conceive other +varieties analogous to them. We can conceive the sun or +moon falling; for although we never saw them fall, nor ever +perhaps imagined them falling, we have seen so many other +things fall, that we have innumerable familiar analogies to assist +the conception; which, after all, we should probably have +some difficulty in framing, were we not well accustomed to see +the sun and moon move, (or appear to move,) so that we are +only called upon to conceive a slight change in the direction +of motion, a circumstance familiar to our experience. But +when experience affords no model on which to shape the +new conception, how is it possible for us to form it? How, +for example, can we imagine an end to space or time? We +never saw any object without something beyond it, nor experienced +any feeling without something following it. When, +therefore, we attempt to conceive the last point of space, we +have the idea irresistibly raised of other points beyond it. +When we try to imagine the last instant of time, we cannot +help conceiving another instant after it. Nor is there any +necessity to assume, as is done by a modern school of metaphysicians, +a peculiar fundamental law of the mind to account +for the feeling of infinity inherent in our conceptions of space +and time; that apparent infinity is sufficiently accounted for +by simpler and universally acknowledged laws. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, in the case of a geometrical axiom, such, for example, +as that two straight lines cannot inclose a space,—a truth +which is testified to us by our very earliest impressions of +the external world,—how is it possible (whether those external +impressions be or be not the ground of our belief) +that the reverse of the proposition <em class="tei tei-emph"><span style="font-style: italic">could</span></em> be otherwise than +inconceivable to us? What analogy have we, what similar +order of facts in any other branch of our experience, to facilitate +to us the conception of two straight lines inclosing a +space? Nor is even this all. I have already called attention +to the peculiar property of our impressions of form, that +the ideas or mental images exactly resemble their prototypes, +and adequately represent them for the purposes of scientific +<span class="tei tei-pb" id="page269">[pg 269]</span><a name="Pg269" id="Pg269" class="tei tei-anchor"></a> +observation. From this, and from the intuitive character of +the observation, which in this case reduces itself to simple +inspection, we cannot so much as call up in our imagination +two straight lines, in order to attempt to conceive them inclosing +a space, without by that very act repeating the scientific +experiment which establishes the contrary. Will it +really be contended that the inconceivableness of the thing, +in such circumstances, proves anything against the experimental +origin of the conviction? Is it not clear that in +whichever mode our belief in the proposition may have +originated, the impossibility of our conceiving the negative +of it must, on either hypothesis, be the same? As, then, +Dr. Whewell exhorts those who have any difficulty in recognising +the distinction held by him between necessary and +contingent truths, to study geometry,—a condition which I +can assure him I have conscientiously fulfilled,—I, in return, +with equal confidence, exhort those who agree with him, to +study the elementary laws of association; being convinced +that nothing more is requisite than a moderate familiarity +with those laws, to dispel the illusion which ascribes a peculiar +necessity to our earliest inductions from experience, +and measures the possibility of things in themselves, by the +human capacity of conceiving them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I hope to be pardoned for adding, that Dr. Whewell himself +has both confirmed by his testimony the effect of habitual +association in giving to an experimental truth the appearance +of a necessary one, and afforded a striking instance of that +remarkable law in his own person. In his <span class="tei tei-hi"><span style="font-style: italic">Philosophy of the +Inductive Sciences</span></span> he continually asserts, that propositions +which not only are not self-evident, but which we know to +have been discovered gradually, and by great efforts of +genius and patience, have, when once established, appeared +so self-evident that, but for historical proof, it would have +been impossible to conceive that they had not been recognised +from the first by all persons in a sound state of their +faculties. <span class="tei tei-q">“We now despise those who, in the Copernican +controversy, could not conceive the apparent motion of the +sun on the heliocentric hypothesis; or those who, in opposition +<span class="tei tei-pb" id="page270">[pg 270]</span><a name="Pg270" id="Pg270" class="tei tei-anchor"></a> +to Galileo, thought that a uniform force might be that +which generated a velocity proportional to the space; or +those who held there was something absurd in Newton's +doctrine of the different refrangibility of differently coloured +rays; or those who imagined that when elements combine, +their sensible qualities must be manifest in the compound; +or those who were reluctant to give up the distinction of vegetables +into herbs, shrubs, and trees. We cannot help thinking +that men must have been singularly dull of comprehension +to find a difficulty in admitting what is to us so plain +and simple. We have a latent persuasion that we in their +place should have been wiser and more clearsighted; that +we should have taken the right side, and given our assent at +once to the truth. Yet in reality such a persuasion is a mere +delusion. The persons who, in such instances as the above, +were on the losing side, were very far in most cases from +being persons more prejudiced, or stupid, or narrow-minded, +than the greater part of mankind now are; and the cause for +which they fought was far from being a manifestly bad one, +till it had been so decided by the result of the war.... +So complete has been the victory of truth in most of these +instances, that at present we can hardly imagine the struggle +to have been necessary. <em class="tei tei-emph"><span style="font-style: italic">The very essence of these triumphs is, +that they lead us to regard the views we reject as not only false +but inconceivable.</span></em>”</span><a id="noteref_46" name="noteref_46" href="#note_46"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">46</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This last proposition is precisely what I contend for; and +I ask no more, in order to overthrow the whole theory of its +author on the nature of the evidence of axioms. For what +is that theory? That the truth of axioms cannot have been +learnt from experience, because their falsity is inconceivable. +But Dr. Whewell himself says, that we are continually led +by the natural progress of thought, to regard as inconceivable +what our forefathers not only conceived but believed, nay +even (he might have added) were unable to conceive the +contrary of. He cannot intend to justify this mode of +thought: he cannot mean to say, that we can be <em class="tei tei-emph"><span style="font-style: italic">right</span></em> in +<span class="tei tei-pb" id="page271">[pg 271]</span><a name="Pg271" id="Pg271" class="tei tei-anchor"></a> +regarding as inconceivable what others have conceived, and +as self-evident what to others did not appear evident at all. +After so complete an admission that inconceivableness is an +accidental thing, not inherent in the phenomenon itself, but +dependent on the mental history of the person who tries to +conceive it, how can he ever call upon us to reject a proposition +as impossible on no other ground than its inconceivableness? +Yet he not only does so, but has unintentionally +afforded some of the most remarkable examples which can +be cited of the very illusion which he has himself so clearly +pointed out. I select as specimens, his remarks on the +evidence of the three laws of motion, and of the atomic +theory. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +With respect to the laws of motion, Dr. Whewell says: +<span class="tei tei-q">“No one can doubt that, in historical fact, these laws were +collected from experience. That such is the case, is no +matter of conjecture. We know the time, the persons, the +circumstances, belonging to each step of each +discovery.”</span><a id="noteref_47" name="noteref_47" href="#note_47"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">47</span></span></a> +After this testimony, to adduce evidence of the fact would be +superfluous. And not only were these laws by no means +intuitively evident, but some of them were originally paradoxes. +The first law was especially so. That a body, once +in motion, would continue for ever to move in the same +direction with undiminished velocity unless acted upon by +some new force, was a proposition which mankind found for +a long time the greatest difficulty in crediting. It stood +opposed to apparent experience of the most familiar kind, +which taught that it was the nature of motion to abate gradually, +and at last terminate of itself. Yet when once the contrary +doctrine was firmly established, mathematicians, as +Dr. Whewell observes, speedily began to believe that laws, +thus contradictory to first appearances, and which, even after +full proof had been obtained, it had required generations to +render familiar to the minds of the scientific world, were +under <span class="tei tei-q">“a demonstrable necessity, compelling them to be +such as they are and no other;”</span> and he himself, though not +<span class="tei tei-pb" id="page272">[pg 272]</span><a name="Pg272" id="Pg272" class="tei tei-anchor"></a> +venturing <span class="tei tei-q">“absolutely to pronounce”</span> that <em class="tei tei-emph"><span style="font-style: italic">all</span></em> these laws <span class="tei tei-q">“can +be rigorously traced to an absolute necessity in the nature +of things,”</span><a id="noteref_48" name="noteref_48" href="#note_48"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">48</span></span></a> +does actually think in that manner of the law +just mentioned; of which he says: <span class="tei tei-q">“Though the discovery +of the first law of motion was made, historically speaking, +by means of experiment, we have now attained a point of +view in which we see that it might have been certainly +known to be true, independently of +experience.”</span><a id="noteref_49" name="noteref_49" href="#note_49"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">49</span></span></a> Can there +be a more striking exemplification than is here afforded, of +the effect of association which we have described? Philosophers, +for generations, have the most extraordinary difficulty +in putting certain ideas together; they at last succeed +in doing so; and after a sufficient repetition of the process, +they first fancy a natural bond between the ideas, then experience +a growing difficulty, which at last, by the continuation +of the same progress, becomes an impossibility, of +severing them from one another. If such be the progress of +an experimental conviction of which the date is of yesterday, +and which is in opposition to first appearances, how +must it fare with those which are conformable to appearances +familiar from the first dawn of intelligence, and of the conclusiveness +of which, from the earliest records of human +thought, no sceptic has suggested even a momentary doubt? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The other instance which I shall quote is a truly astonishing +one, and may be called the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio +ad absurdum</span></span> of the theory of inconceivableness. Speaking of the laws of +chemical composition, Dr. Whewell says:<a id="noteref_50" name="noteref_50" href="#note_50"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">50</span></span></a> <span class="tei tei-q">“That they +could never have been clearly understood, and therefore +never firmly established, without laborious and exact experiments, +is certain; but yet we may venture to say, that being +once known, they possess an evidence beyond that of mere +experiment. <em class="tei tei-emph"><span style="font-style: italic">For how, in fact, can we conceive combinations, +otherwise than as definite in kind and quality?</span></em> If we were +to suppose each element ready to combine with any other +indifferently, and indifferently in any quantity, we should +have a world in which all would be confusion and indefiniteness. +<span class="tei tei-pb" id="page273">[pg 273]</span><a name="Pg273" id="Pg273" class="tei tei-anchor"></a> +There would be no fixed kinds of bodies; salts, and +stones, and ores, would approach to and graduate into each +other by insensible degrees. Instead of this, we know that +the world consists of bodies distinguishable from each other +by definite differences, capable of being classified and named, +and of having general propositions asserted concerning them. +And as <em class="tei tei-emph"><span style="font-style: italic">we cannot conceive a world in which this should not be +the case</span></em>, it would appear that we cannot conceive a state of +things in which the laws of the combination of elements +should not be of that definite and measured kind which we +have above asserted.”</span><a id="noteref_51" name="noteref_51" href="#note_51"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">51</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +That a philosopher of Dr. Whewell's eminence should +gravely assert that we cannot conceive a world in which the +simple elements would combine in other than definite proportions; +that by dint of meditating on a scientific truth, the +original discoverer of which was still living, he should have +rendered the association in his own mind between the idea +of combination and that of constant proportions so familiar +and intimate as to be unable to conceive the one fact without +the other; is so signal an instance of the mental law for +which I am contending, that one word more in illustration +must be superfluous.<a id="noteref_52" name="noteref_52" href="#note_52"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">52</span></span></a> +</p> + +</div> + +<span class="tei tei-pb" id="page277">[pg 277]</span><a name="Pg277" id="Pg277" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc51" id="toc51"></a> +<a name="pdf52" id="pdf52"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VI. THE SAME SUBJECT CONTINUED.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In the examination which formed the subject of +the last chapter, into the nature of the evidence of those +deductive sciences which are commonly represented to be +systems of necessary truth, we have been led to the following +conclusions. The results of those sciences are indeed necessary, +in the sense of necessarily following from certain first +principles, commonly called axioms and definitions; of being +certainly true if those axioms and definitions are so. But +their claim to the character of necessity in any sense beyond +this, as implying an evidence independent of and superior +to observation and experience, must depend on the previous +establishment of such a claim in favour of the definitions and +axioms themselves. With regard to axioms, we found that, +considered as experimental truths, they rest on superabundant +and obvious evidence. We inquired, whether, since +this is the case, it be necessary to suppose any other evidence +of those truths than experimental evidence, any other origin +for our belief of them than an experimental origin. We +decided, that the burden of proof lies with those who maintain +the affirmative, and we examined, at considerable length, +such arguments as they have produced. The examination +having led to the rejection of those arguments, we have +thought ourselves warranted in concluding that axioms are +but a class, the highest class, of inductions from experience; +the simplest and easiest cases of generalization from the +facts furnished to us by our senses or by our internal consciousness. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +While the axioms of demonstrative sciences thus appeared +to be experimental truths, the definitions, as they are +<span class="tei tei-pb" id="page278">[pg 278]</span><a name="Pg278" id="Pg278" class="tei tei-anchor"></a> +incorrectly called, in those sciences, were found by us to +be generalizations from experience which are not even, +accurately speaking, truths; being propositions in which, +while we assert of some kind of object, some property or +properties which observation shows to belong to it, we at +the same time deny that it possesses any other properties, +although in truth other properties do in every individual +instance accompany, and in almost all instances modify, the +property thus exclusively predicated. The denial, therefore, +is a mere fiction, or supposition, made for the purpose of +excluding the consideration of those modifying circumstances, +when their influence is of too trifling amount to be +worth considering, or adjourning it, when important, to a +more convenient moment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From these considerations it would appear that Deductive +or Demonstrative Sciences are all, without exception, +Inductive Sciences; that their evidence is that of experience; +but that they are also, in virtue of the peculiar +character of one indispensable portion of the general formulas +according to which their inductions are made, Hypothetical +Sciences. Their conclusions are only true on certain suppositions, +which are, or ought to be, approximations to the truth, +but are seldom, if ever, exactly true; and to this hypothetical +character is to be ascribed the peculiar certainty, which is +supposed to be inherent in demonstration. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What we have now asserted, however, cannot be received +as universally true of Deductive or Demonstrative Sciences, +until verified by being applied to the most remarkable of all +those sciences, that of Numbers; the theory of the Calculus; +Arithmetic and Algebra. It is harder to believe of the doctrines +of this science than of any other, either that they are +not truths <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, but +experimental truths, or that their peculiar certainty is owing to their being not +absolute but only conditional truths. This, therefore, is a case which +merits examination apart; and the more so, because on this +subject we have a double set of doctrines to contend with; +that of the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> philosophers +on one side; and on the other, a theory the most opposite to theirs, which was +<span class="tei tei-pb" id="page279">[pg 279]</span><a name="Pg279" id="Pg279" class="tei tei-anchor"></a> +at one time very generally received, and is still far from being +altogether exploded among metaphysicians. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. This theory attempts to solve the difficulty apparently +inherent in the case, by representing the propositions +of the science of numbers as merely verbal, and its processes +as simple transformations of language, substitutions of one +expression for another. The proposition, Two and one are +equal to three, according to these writers, is not a truth, +is not the assertion of a really existing fact, but a definition +of the word three; a statement that mankind have agreed to +use the name three as a sign exactly equivalent to two and +one; to call by the former name whatever is called by the +other more clumsy phrase. According to this doctrine, the +longest process in algebra is but a succession of changes in +terminology, by which equivalent expressions are substituted +one for another; a series of translations of the same fact, +from one into another language; though how, after such a +series of translations, the fact itself comes out changed, (as +when we demonstrate a new geometrical theorem by algebra,) +they have not explained; and it is a difficulty which is fatal +to their theory. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It must be acknowledged that there are peculiarities in the +processes of arithmetic and algebra which render the theory +in question very plausible, and have not unnaturally made +those sciences the stronghold of Nominalism. The doctrine +that we can discover facts, detect the hidden processes of +nature, by an artful manipulation of language, is so contrary +to common sense, that a person must have made some +advances in philosophy to believe it; men fly to so paradoxical +a belief to avoid, as they think, some even greater difficulty, +which the vulgar do not see. What has led many to +believe that reasoning is a mere verbal process, is, that no +other theory seemed reconcileable with the nature of the +Science of Numbers. For we do not carry any ideas along +with us when we use the symbols of arithmetic or of +algebra. In a geometrical demonstration we have a mental +diagram, if not one on paper; AB, AC, are present to our +<span class="tei tei-pb" id="page280">[pg 280]</span><a name="Pg280" id="Pg280" class="tei tei-anchor"></a> +imagination as lines, intersecting other lines, forming an +angle with one another, and the like; but not so <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and +<span class="tei tei-hi"><span style="font-style: italic">b</span></span>. These may represent lines or any other magnitudes, but +those magnitudes are never thought of; nothing is realized +in our imagination but <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and <span class="tei tei-hi"><span style="font-style: italic">b</span></span>. The ideas +which, on the particular occasion, they happen to represent, are banished +from the mind during every intermediate part of the process, +between the beginning, when the premisses are translated +from things into signs, and the end, when the conclusion +is translated back from signs into things. Nothing, then, +being in the reasoner's mind but the symbols, what can seem +more inadmissible than to contend that the reasoning process +has to do with anything more? We seem to have come to +one of Bacon's Prerogative Instances; an <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">experimentum crucis</span></span> +on the nature of reasoning itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Nevertheless, it will appear on consideration, that this +apparently so decisive instance is no instance at all; that +there is in every step of an arithmetical or algebraical calculation +a real induction, a real inference of facts from facts; +and that what disguises the induction is simply its comprehensive +nature, and the consequent extreme generality of the +language. All numbers must be numbers of something: +there are no such things as numbers in the abstract. <em class="tei tei-emph"><span style="font-style: italic">Ten</span></em> +must mean ten bodies, or ten sounds, or ten beatings of the +pulse. But though numbers must be numbers of something, +they may be numbers of anything. Propositions, therefore, +concerning numbers, have the remarkable peculiarity that +they are propositions concerning all things whatever; all +objects, all existences of every kind, known to our experience. +All things possess quantity; consist of parts which +can be numbered; and in that character possess all the +properties which are called properties of numbers. That +half of four is two, must be true whatever the word four +represents, whether four men, four miles, or four pounds +weight. We need only conceive a thing divided into four +equal parts, (and all things may be conceived as so divided,) +to be able to predicate of it every property of the number +four, that is, every arithmetical proposition in which the +<span class="tei tei-pb" id="page281">[pg 281]</span><a name="Pg281" id="Pg281" class="tei tei-anchor"></a> +number four stands on one side of the equation. Algebra +extends the generalization still farther: every number represents +that particular number of all things without distinction, +but every algebraical symbol does more, it represents all +numbers without distinction. As soon as we conceive a +thing divided into equal parts, without knowing into what +number of parts, we may call it <span class="tei tei-hi"><span style="font-style: italic">a</span></span> or <span class="tei tei-hi"><span style="font-style: italic">x</span></span>, +and apply to it, without danger of error, every algebraical formula in the +books. The proposition, 2(<span class="tei tei-hi"><span style="font-style: italic">a</span></span> + <span class="tei tei-hi"><span style="font-style: italic">b</span></span>) = +2<span class="tei tei-hi"><span style="font-style: italic">a</span></span> + 2<span class="tei tei-hi"><span style="font-style: italic">b</span></span>, is a truth coextensive +with all nature. Since then algebraical truths +are true of all things whatever, and not, like those of +geometry, true of lines only or angles only, it is no wonder +that the symbols should not excite in our minds ideas of any +things in particular. When we demonstrate the forty-seventh +proposition of Euclid, it is not necessary that the +words should raise in us an image of all right-angled +triangles, but only of some one right-angled triangle: so in +algebra we need not, under the symbol <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, picture to ourselves +all things whatever, but only some one thing; why +not, then, the letter itself? The mere written characters, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">x</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">y</span></span>, <span class="tei tei-hi"><span style="font-style: italic">z</span></span>, serve as well for representatives of +Things in general, as any more complex and apparently more concrete +conception. That we are conscious of them however in +their character of things, and not of mere signs, is evident +from the fact that our whole process of reasoning is carried +on by predicating of them the properties of things. In +resolving an algebraic equation, by what rules do we proceed? +By applying at each step to <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, and +<span class="tei tei-hi"><span style="font-style: italic">x</span></span> the proposition +that equals added to equals make equals; that equals +taken from equals leave equals; and other propositions +founded on these two. These are not properties of language, +or of signs as such, but of magnitudes, which is as +much as to say, of all things. The inferences, therefore, +which are successively drawn, are inferences concerning +things, not symbols; although as any Things whatever will +serve the turn, there is no necessity for keeping the idea of +the Thing at all distinct, and consequently the process of +thought may, in this case, be allowed without danger to do +<span class="tei tei-pb" id="page282">[pg 282]</span><a name="Pg282" id="Pg282" class="tei tei-anchor"></a> +what all processes of thought, when they have been performed +often, will do if permitted, namely, to become +entirely mechanical. Hence the general language of algebra +comes to be used familiarly without exciting ideas, as all +other general language is prone to do from mere habit, +though in no other case than this can it be done with complete +safety. But when we look back to see from whence +the probative force of the process is derived, we find that at +every single step, unless we suppose ourselves to be thinking +and talking of the things, and not the mere symbols, the +evidence fails. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is another circumstance, which, still more than +that which we have now mentioned, gives plausibility to the +notion that the propositions of arithmetic and algebra are +merely verbal. This is, that when considered as propositions +respecting Things, they all have the appearance of +being identical propositions. The assertion, Two and one +are equal to three, considered as an assertion respecting +objects, as for instance <span class="tei tei-q">“Two pebbles and one pebble are +equal to three pebbles,”</span> does not affirm equality between +two collections of pebbles, but absolute identity. It affirms +that if we put one pebble to two pebbles, those very pebbles +are three. The objects, therefore, being the very same, and +the mere assertion that <span class="tei tei-q">“objects are themselves”</span> being insignificant, +it seems but natural to consider the proposition, +Two and one are equal to three, as asserting mere identity +of signification between the two names. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, however, though it looks so plausible, will not bear +examination. The expression <span class="tei tei-q">“two pebbles and one pebble,”</span> +and the expression, <span class="tei tei-q">“three pebbles,”</span> stand indeed for the +same aggregation of objects, but they by no means stand for +the same physical fact. They are names of the same objects, +but of those objects in two different states: though they +<em class="tei tei-emph"><span style="font-style: italic">de</span></em>note the same things, their <em class="tei tei-emph"><span style="font-style: italic">con</span></em>notation is different. Three +pebbles in two separate parcels, and three pebbles in one +parcel, do not make the same impression on our senses; +and the assertion that the very same pebbles may by an +alteration of place and arrangement be made to produce +<span class="tei tei-pb" id="page283">[pg 283]</span><a name="Pg283" id="Pg283" class="tei tei-anchor"></a> +either the one set of sensations or the other, though a +very familiar proposition, is not an identical one. It is a +truth known to us by early and constant experience: an +inductive truth; and such truths are the foundation of the +science of Number. The fundamental truths of that science +all rest on the evidence of sense; they are proved by +showing to our eyes and our fingers that any given number +of objects, ten balls for example, may by separation and +re-arrangement exhibit to our senses all the different sets of +numbers the sum of which is equal to ten. All the improved +methods of teaching arithmetic to children proceed on a +knowledge of this fact. All who wish to carry the child's +<em class="tei tei-emph"><span style="font-style: italic">mind</span></em> along with them in learning arithmetic; all who wish +to teach numbers, and not mere ciphers—now teach it +through the evidence of the senses, in the manner we have +described. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We may, if we please, call the proposition <span class="tei tei-q">“Three is two +and one,”</span> a definition of the number three, and assert that +arithmetic, as it has been asserted that geometry, is a science +founded on definitions. But they are definitions in the +geometrical sense, not the logical; asserting not the meaning +of a term only, but along with it an observed matter of fact. +The proposition, <span class="tei tei-q">“A circle is a figure bounded by a line +which has all its points equally distant from a point within +it,”</span> is called the definition of a circle; but the proposition +from which so many consequences follow, and which is +really a first principle in geometry, is, that figures answering +to this description exist. And thus we may call, <span class="tei tei-q">“Three is +two and one,”</span> a definition of three; but the calculations +which depend on that proposition do not follow from the +definition itself, but from an arithmetical theorem presupposed +in it, namely, that collections of objects exist, which +while they impress the senses thus, [Symbol: three circles, two above one], may be +separated into two parts, thus, [Symbol: two circles, a space, and a third circle]. This +proposition being granted, we term all such parcels Threes, after which the enunciation +of the above-mentioned physical fact will serve also for a +definition of the word Three. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The Science of Number is thus no exception to the conclusion +<span class="tei tei-pb" id="page284">[pg 284]</span><a name="Pg284" id="Pg284" class="tei tei-anchor"></a> +we previously arrived at, that the processes even of +deductive sciences are altogether inductive, and that their +first principles are generalizations from experience. It +remains to be examined whether this science resembles +geometry in the further circumstance, that some of its inductions +are not exactly true; and that the peculiar certainty +ascribed to it, on account of which its propositions are called +Necessary Truths, is fictitious and hypothetical, being true +in no other sense than that those propositions necessarily +follow from the hypothesis of the truth of premisses which +are avowedly mere approximations to truth. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The inductions of arithmetic are of two sorts: first, +those which we have just expounded, such as One and one +are two, Two and one are three, &c., which may be called +the definitions of the various numbers, in the improper or +geometrical sense of the word Definition; and secondly, the +two following axioms: The sums of equals are equal, The +differences of equals are equal. These two are sufficient; +for the corresponding propositions respecting unequals may +be proved from these, by a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio ad +absurdum</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These axioms, and likewise the so-called definitions, are, +as already shown, results of induction; true of all objects +whatever, and, as it may seem, exactly true, without the +hypothetical assumption of unqualified truth where an approximation +to it is all that exists. The conclusions, therefore, +it will naturally be inferred, are exactly true, and the +science of number is an exception to other demonstrative +sciences in this, that the absolute certainty which is predicable +of its demonstrations is independent of all hypothesis. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +On more accurate investigation, however, it will be found +that, even in this case, there is one hypothetical element in +the ratiocination. In all propositions concerning numbers, +a condition is implied, without which none of them would be +true; and that condition is an assumption which may be +false. The condition is, that 1 = 1; that all the numbers +are numbers of the same or of equal units. Let this be +doubtful, and not one of the propositions of arithmetic will +<span class="tei tei-pb" id="page285">[pg 285]</span><a name="Pg285" id="Pg285" class="tei tei-anchor"></a> +hold true. How can we know that one pound and one pound +make two pounds, if one of the pounds may be troy, and the +other avoirdupois? They may not make two pounds of +either, or of any weight. How can we know that a forty-horse +power is always equal to itself, unless we assume that +all horses are of equal strength? It is certain that 1 is always +equal in <em class="tei tei-emph"><span style="font-style: italic">number</span></em> to 1; and where the mere number of +objects, or of the parts of an object, without supposing them +to be equivalent in any other respect, is all that is material, +the conclusions of arithmetic, so far as they go to that alone, +are true without mixture of hypothesis. There are a few such +cases; as, for instance, an inquiry into the amount of the population +of any country. It is indifferent to that inquiry whether +they are grown people or children, strong or weak, tall or +short; the only thing we want to ascertain is their number. +But whenever, from equality or inequality of number, equality +or inequality in any other respect is to be inferred, arithmetic +carried into such inquiries becomes as hypothetical a science +as geometry. All units must be assumed to be equal in that +other respect; and this is never practically true, for one actual +pound weight is not exactly equal to another, nor one mile's +length to another; a nicer balance, or more accurate measuring +instruments, would always detect some difference. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What is commonly called mathematical certainty, therefore, +which comprises the twofold conception of unconditional +truth and perfect accuracy, is not an attribute of all mathematical +truths, but of those only which relate to pure Number, +as distinguished from Quantity in the more enlarged +sense; and only so long as we abstain from supposing that +the numbers are a precise index to actual quantities. The +certainty usually ascribed to the conclusions of geometry, and +even to those of mechanics, is nothing whatever but certainty +of inference. We can have full assurance of particular results +under particular suppositions, but we cannot have the +same assurance that these suppositions are accurately true, +nor that they include all the data which may exercise an +influence over the result in any given instance. +</p> + +<span class="tei tei-pb" id="page286">[pg 286]</span><a name="Pg286" id="Pg286" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. It appears, therefore, that the method of all Deductive +Sciences is hypothetical. They proceed by tracing the +consequences of certain assumptions; leaving for separate +consideration whether the assumptions are true or not, and +if not exactly true, whether they are a sufficiently near +approximation to the truth. The reason is obvious. Since +it is only in questions of pure number that the assumptions +are exactly true, and even there, only so long as no conclusions +except purely numerical ones are to be founded on +them; it must, in all other cases of deductive investigation, +form a part of the inquiry, to determine how much the assumptions +want of being exactly true in the case in hand. This is +generally a matter of observation, to be repeated in every +fresh case; or if it has to be settled by argument instead of +observation, may require in every different case different +evidence, and present every degree of difficulty from the +lowest to the highest. But the other part of the process—namely, +to determine what else may be concluded if we find, +and in proportion as we find, the assumptions to be true—may +be performed once for all, and the results held ready to +be employed as the occasions turn up for use. We thus do +all beforehand that can be so done, and leave the least possible +work to be performed when cases arise and press for a +decision. This inquiry into the inferences which can be +drawn from assumptions, is what properly constitutes Demonstrative +Science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is of course quite as practicable to arrive at new conclusions +from facts assumed, as from facts observed; from +fictitious, as from real, inductions. Deduction, as we have +seen, consists of a series of inferences in this form—<span class="tei tei-hi"><span style="font-style: italic">a</span></span> is a +mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span> of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, therefore <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +is a mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, which last +may be a truth inaccessible to direct observation. In like +manner it is allowable to say, <em class="tei tei-emph"><span style="font-style: italic">Suppose</span></em> that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> were a +mark of <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span> of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +and <span class="tei tei-hi"><span style="font-style: italic">c</span></span> of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +would be a mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, which last +conclusion was not thought of by those who laid down the +premisses. A system of propositions as complicated as geometry +might be deduced from assumptions which are false; +as was done by Ptolemy, Descartes, and others, in their +<span class="tei tei-pb" id="page287">[pg 287]</span><a name="Pg287" id="Pg287" class="tei tei-anchor"></a> +attempts to explain synthetically the phenomena of the solar +system on the supposition that the apparent motions of the +heavenly bodies were the real motions, or were produced in +some way more or less different from the true one. Sometimes +the same thing is knowingly done, for the purpose of +showing the falsity of the assumption; which is called a +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio ad absurdum</span></span>. In such +cases, the reasoning is as follows: <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is a mark of +<span class="tei tei-hi"><span style="font-style: italic">b</span></span>, and <span class="tei tei-hi"><span style="font-style: italic">b</span></span> of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>; now +if <span class="tei tei-hi"><span style="font-style: italic">c</span></span> were also a mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> would be a mark of +<span class="tei tei-hi"><span style="font-style: italic">d</span></span>; but <span class="tei tei-hi"><span style="font-style: italic">d</span></span> is known to be a mark +of the absence of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>; consequently <span class="tei tei-hi"><span style="font-style: italic">a</span></span> would +be a mark of its own absence, which is a contradiction; +therefore <span class="tei tei-hi"><span style="font-style: italic">c</span></span> is not a mark of <span class="tei tei-hi"><span style="font-style: italic">d</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. It has even been held by some writers, that +all ratiocination rests in the last resort on a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio ad absurdum</span></span>; since the way to enforce assent +to it, in case of obscurity, would be to show that if the conclusion be denied +we must deny some one at least of the premisses, which, as +they are all supposed true, would be a contradiction. And +in accordance with this, many have thought that the peculiar +nature of the evidence of ratiocination consisted in the impossibility +of admitting the premisses and rejecting the conclusion +without a contradiction in terms. This theory, however +is inadmissible as an explanation of the grounds on which +ratiocination itself rests. If any one denies the conclusion +notwithstanding his admission of the premisses, he is not +involved in any direct and express contradiction until he is +compelled to deny some premiss; and he can only be forced +to do this by a <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">reductio ad absurdum</span></span>, that is, by another +ratiocination: now, if he denies the validity of the reasoning process +itself, he can no more be forced to assent to the second +syllogism than to the first. In truth, therefore, no one is +ever forced to a contradiction in terms: he can only be forced +to a contradiction (or rather an infringement) of the fundamental +maxim of ratiocination, namely, that whatever has a +mark, has what it is a mark of; or, (in the case of universal +propositions,) that whatever is a mark of anything, is a mark +of whatever else that thing is a mark of. For in the case of +<span class="tei tei-pb" id="page288">[pg 288]</span><a name="Pg288" id="Pg288" class="tei tei-anchor"></a> +every correct argument, as soon as thrown into the syllogistic +form, it is evident without the aid of any other syllogism, +that he who, admitting the premisses, fails to draw the conclusion, +does not conform to the above axiom. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Without attaching exaggerated importance to the distinction +now drawn, I think it enables us to characterize in a +more accurate manner than is usually done, the nature of +demonstrative evidence and of logical necessity. That is +necessary, from which to withhold assent would be to violate +the above axiom. And since the axiom can only be +violated by assenting to premisses and rejecting a legitimate +conclusion from them, nothing is necessary, except the connexion +between a conclusion and premisses; of which doctrine, +the whole of this and the preceding chapter are submitted +as the proof. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We have now proceeded as far in the theory of Deduction +as we can advance in the present stage of our inquiry. +Any further insight into the subject requires that the foundation +shall have been laid of the philosophic theory of Induction +itself; in which theory that of deduction, as a mode of +induction, which we have now shown it to be, will assume +spontaneously the place which belongs to it, and will receive +its share of whatever light may be thrown upon the great +intellectual operation of which it forms so important a part. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We here, therefore, close the Second Book. The theory +of Induction, in the most comprehensive sense of the term, +will form the subject of the Third. +</p> + +</div> + +</div> + +<span class="tei tei-pb" id="page289">[pg 289]</span><a name="Pg289" id="Pg289" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<a name="toc53" id="toc53"></a> +<a name="pdf54" id="pdf54"></a> +<h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">BOOK III. OF INDUCTION.</span></h1> + +<span class="tei tei-pb" id="page290">[pg 290]</span><a name="Pg290" id="Pg290" class="tei tei-anchor"></a> + +<div class="block tei tei-quote" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"> +<span class="tei tei-q"><span style="font-size: 90%">“</span><span style="font-size: 90%">According to the doctrine now stated, the highest, or rather the only +proper object of physics, is to ascertain those established conjunctions of successive +events, which constitute the order of the universe; to record the +phenomena which it exhibits to our observations, or which it discloses to +our experiments; and to refer these phenomena to their general +laws.</span><span style="font-size: 90%">”</span></span><span style="font-size: 90%">—</span><span class="tei tei-hi"><span style="font-size: 90%; font-variant: small-caps">D. Stewart</span></span><span style="font-size: 90%">, </span><span class="tei tei-hi"><span style="font-size: 90%; font-style: italic">Elements of the +Philosophy of the Human Mind</span></span><span style="font-size: 90%">, vol. ii. chap. iv. sect. 1. +</span></div> + +<span class="tei tei-pb" id="page291">[pg 291]</span><a name="Pg291" id="Pg291" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc55" id="toc55"></a> +<a name="pdf56" id="pdf56"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN +GENERAL.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The portion of the present inquiry upon which we +are now about to enter, may be considered as the principal, +both from its surpassing in intricacy all the other branches, +and because it relates to a process which has been shown in +the preceding Book to be that in which the investigation of +nature essentially consists. We have found that all Inference, +consequently all Proof, and all discovery of truths not +self-evident, consists of inductions, and the interpretation of +inductions: that all our knowledge, not intuitive, comes to +us exclusively from that source. What Induction is, therefore, +and what conditions render it legitimate, cannot but be +deemed the main question of the science of logic—the question +which includes all others. It is, however, one which +professed writers on logic have almost entirely passed over. +The generalities of the subject have not been altogether +neglected by metaphysicians; but, for want of sufficient +acquaintance with the processes by which science has actually +succeeded in establishing general truths, their analysis of +the inductive operation, even when unexceptionable as to +correctness, has not been specific enough to be made the +foundation of practical rules, which might be for induction +itself what the rules of the syllogism are for the interpretation +of induction: while those by whom physical science has +been carried to its present state of improvement—and who, +to arrive at a complete theory of the process, needed only to +generalize, and adapt to all varieties of problems, the methods +which they themselves employed in their habitual pursuits—never +until very lately made any serious attempt to philosophize +<span class="tei tei-pb" id="page292">[pg 292]</span><a name="Pg292" id="Pg292" class="tei tei-anchor"></a> +on the subject, nor regarded the mode in which they +arrived at their conclusions as deserving of study, independently +of the conclusions themselves. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. For the purposes of the present inquiry, Induction +may be defined, the operation of discovering and proving +general propositions. It is true that (as already shown) the +process of indirectly ascertaining individual facts, is as truly +inductive as that by which we establish general truths. But +it is not a different kind of induction; it is another form of +the very same process: since, on the one hand, generals are +but collections of particulars, definite in kind but indefinite +in number; and on the other hand, whenever the evidence +which we derive from observation of known cases justifies us +in drawing an inference respecting even one unknown case, +we should on the same evidence be justified in drawing a +similar inference with respect to a whole class of cases. The +inference either does not hold at all, or it holds in all cases +of a certain description; in all cases which, in certain definable +respects, resemble those we have observed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If these remarks are just; if the principles and rules of +inference are the same whether we infer general propositions +or individual facts; it follows that a complete logic of the +sciences would be also a complete logic of practical business +and common life. Since there is no case of legitimate inference +from experience, in which the conclusion may not legitimately +be a general proposition; an analysis of the process +by which general truths are arrived at, is virtually an analysis +of all induction whatever. Whether we are inquiring into a +scientific principle or into an individual fact, and whether +we proceed by experiment or by ratiocination, every step in +the train of inferences is essentially inductive, and the legitimacy +of the induction depends in both cases on the +same conditions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +True it is that in the case of the practical inquirer, who +is endeavouring to ascertain facts not for the purposes of +science but for those of business, such for instance as the +advocate or the judge, the chief difficulty is one in which the +<span class="tei tei-pb" id="page293">[pg 293]</span><a name="Pg293" id="Pg293" class="tei tei-anchor"></a> +principles of induction will afford him no assistance. It lies +not in <em class="tei tei-emph"><span style="font-style: italic">making</span></em> his inductions but in the <em class="tei tei-emph"><span style="font-style: italic">selection</span></em> of them; in +choosing from among all general propositions ascertained to +be true, those which furnish marks by which he may trace +whether the given subject possesses or not the predicate in +question. In arguing a doubtful question of fact before a +jury, the general propositions or principles to which the +advocate appeals are mostly, in themselves, sufficiently trite, +and assented to as soon as stated: his skill lies in bringing +his case under those propositions or principles; in calling to +mind such of the known or received maxims of probability +as admit of application to the case in hand, and selecting +from among them those best adapted to his object. Success +is here dependent on natural or acquired sagacity, aided +by knowledge of the particular subject, and of subjects +allied with it. Invention, though it can be cultivated, +cannot be reduced to rule; there is no science which will +enable a man to bethink himself of that which will suit his +purpose. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But when he <em class="tei tei-emph"><span style="font-style: italic">has</span></em> thought of something, science can tell +him whether that which he has thought of will suit his purpose +or not. The inquirer or arguer must be guided by his +own knowledge and sagacity in the choice of the inductions +out of which he will construct his argument. But the validity +of the argument when constructed, depends on principles +and must be tried by tests which are the same for all descriptions +of inquiries, whether the result be to give A an estate, +or to enrich science with a new general truth. In the one +case and in the other, the senses, or testimony, must decide +on the individual facts; the rules of the syllogism will determine +whether, those facts being supposed correct, the case +really falls within the formulæ of the different inductions +under which it has been successively brought; and finally, +the legitimacy of the inductions themselves must be decided +by other rules, and these it is now our purpose to investigate. +If this third part of the operation be, in many of the questions +of practical life, not the most, but the least arduous +portion of it, we have seen that this is also the case in some +great departments of the field of science; in all those which +<span class="tei tei-pb" id="page294">[pg 294]</span><a name="Pg294" id="Pg294" class="tei tei-anchor"></a> +are principally deductive, and most of all in mathematics; +where the inductions themselves are few in number, and +so obvious and elementary that they seem to stand in no +need of the evidence of experience, while to combine them so +as to prove a given theorem or solve a problem, may call for +the utmost powers of invention and contrivance with which +our species is gifted. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If the identity of the logical processes which prove particular +facts and those which establish general scientific truths, +required any additional confirmation, it would be sufficient to +consider that in many branches of science, single facts have +to be proved, as well as principles; facts as completely individual +as any that are debated in a court of justice; but +which are proved in the same manner as the other truths of +the science, and without disturbing in any degree the homogeneity +of its method. A remarkable example of this is +afforded by astronomy. The individual facts on which that +science grounds its most important deductions, such facts as +the magnitudes of the bodies of the solar system, their distances +from one another, the figure of the earth, and its rotation, +are scarcely any of them accessible to our means of +direct observation: they are proved indirectly, by the aid of +inductions founded on other facts which we can more easily +reach. For example, the distance of the moon from the +earth was determined by a very circuitous process. The +share which direct observation had in the work consisted in +ascertaining, at one and the same instant, the zenith distances +of the moon, as seen from two points very remote from one +another on the earth's surface. The ascertainment of these +angular distances ascertained their supplements; and since +the angle at the earth's centre subtended by the distance +between the two places of observation was deducible by +spherical trigonometry from the latitude and longitude of +those places, the angle at the moon subtended by the same +line became the fourth angle of a quadrilateral of which the +other three angles were known. The four angles being thus +ascertained, and two sides of the quadrilateral being radii of +the earth; the two remaining sides and the diagonal, or in +other words, the moon's distance from the two places of observation +<span class="tei tei-pb" id="page295">[pg 295]</span><a name="Pg295" id="Pg295" class="tei tei-anchor"></a> +and from the centre of the earth, could be ascertained, +at least in terms of the earth's radius, from elementary +theorems of geometry. At each step in this demonstration +we take in a new induction, represented, in the aggregate of +its results, by a general proposition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Not only is the process by which an individual astronomical +fact was thus ascertained, exactly similar to those by +which the same science establishes its general truths, but +also (as we have shown to be the case in all legitimate +reasoning) a general proposition might have been concluded +instead of a single fact. In strictness, indeed, the result of +the reasoning <em class="tei tei-emph"><span style="font-style: italic">is</span></em> a general proposition; a theorem respecting +the distance, not of the moon in particular, but of any inaccessible +object; showing in what relation that distance stands +to certain other quantities. And although the moon is almost +the only heavenly body the distance of which from the earth +can really be thus ascertained, this is merely owing to the +accidental circumstances of the other heavenly bodies, which +render them incapable of affording such data as the application +of the theorem requires; for the theorem itself is as true +of them as it is of the moon.<a id="noteref_53" name="noteref_53" href="#note_53"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">53</span></span></a> +</p> + +<span class="tei tei-pb" id="page296">[pg 296]</span><a name="Pg296" id="Pg296" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We shall fall into no error, then, if in treating of Induction, +we limit our attention to the establishment of general +propositions. The principles and rules of Induction, as +directed to this end, are the principles and rules of all Induction; +and the logic of Science is the universal Logic, applicable +to all inquiries in which man can engage. +</p> + +</div> + +<span class="tei tei-pb" id="page297">[pg 297]</span><a name="Pg297" id="Pg297" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc57" id="toc57"></a> +<a name="pdf58" id="pdf58"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER II. OF INDUCTIONS IMPROPERLY SO CALLED.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. Induction, then, is that operation of the mind, by +which we infer that what we know to be true in a particular +case or cases, will be true in all cases which resemble the +former in certain assignable respects. In other words, +Induction is the process by which we conclude that what is +true of certain individuals of a class is true of the whole +class, or that what is true at certain times will be true in +similar circumstances at all times. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This definition excludes from the meaning of the term +Induction, various logical operations, to which it is not +unusual to apply that name. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Induction, as above defined, is a process of inference; it +proceeds from the known to the unknown; and any operation +involving no inference, any process in which what seems +the conclusion is no wider than the premisses from which it +is drawn, does not fall within the meaning of the term. Yet +in the common books of Logic we find this laid down as the +most perfect, indeed the only quite perfect, form of induction. +In those books, every process which sets out from a less +general and terminates in a more general expression,—which +admits of being stated in the form, <span class="tei tei-q">“This and that +A are B, therefore every A is B,”</span>—is called an induction, +whether anything be really concluded or not; and the +induction is asserted to be not perfect, unless every single +individual of the class A is included in the antecedent, +or premiss: that is, unless what we affirm of the class +has already been ascertained to be true of every individual +in it, so that the nominal conclusion is not really a conclusion, +but a mere reassertion of the premisses. If we +were to say, All the planets shine by the sun's light, from +<span class="tei tei-pb" id="page298">[pg 298]</span><a name="Pg298" id="Pg298" class="tei tei-anchor"></a> +observation of each separate planet, or All the Apostles +were Jews, because this is true of Peter, Paul, John, and +every other apostle,—these, and such as these, would, in the +phraseology in question, be called perfect, and the only +perfect, Inductions. This, however, is a totally different kind +of induction from ours; it is no inference from facts known +to facts unknown, but a mere short-hand registration of facts +known. The two simulated arguments which we have +quoted, are not generalizations; the propositions purporting +to be conclusions from them, are not really general propositions. +A general proposition is one in which the predicate +is affirmed or denied of an unlimited number of individuals; +namely, all, whether few or many, existing or capable of +existing, which possess the properties connoted by the subject +of the proposition. <span class="tei tei-q">“All men are mortal”</span> does not mean +all now living, but all men past, present, and to come. +When the signification of the term is limited so as to render +it a name not for any and every individual falling under a +certain general description, but only for each of a number of +individuals designated as such, and as it were counted off +individually, the proposition, though it may be general in its +language, is no general proposition, but merely that number +of singular propositions, written in an abridged character. +The operation may be very useful, as most forms of abridged +notation are; but it is no part of the investigation of truth, +though often bearing an important part in the preparation of +the materials for that investigation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. A second process which requires to be distinguished +from Induction, is one to which mathematicians sometimes +give that name: and which so far resembles Induction properly +so called, that the propositions it leads to are really +general propositions. For example, when we have proved +with respect to the circle, that a straight line cannot meet it +in more than two points, and when the same thing has been +successively proved of the ellipse, the parabola, and the hyperbola, +it may be laid down as an universal property of the +sections of the cone. In this example there is no induction, +<span class="tei tei-pb" id="page299">[pg 299]</span><a name="Pg299" id="Pg299" class="tei tei-anchor"></a> +because there is no inference: the conclusion is a mere summing +up of what was asserted in the various propositions +from which it is drawn. A case somewhat, though not altogether, +similar, is the proof of a geometrical theorem by +means of a diagram. Whether the diagram be on paper or +only in the imagination, the demonstration (as formerly +observed<a id="noteref_54" name="noteref_54" href="#note_54"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">54</span></span></a>) +does not prove directly the general theorem; it +proves only that the conclusion, which the theorem asserts +generally, is true of the particular triangle or circle exhibited +in the diagram; but since we perceive that in the same way +in which we have proved it of that circle, it might also be +proved of any other circle, we gather up into one general +expression all the singular propositions susceptible of being +thus proved, and embody them in an universal proposition. +Having shown that the three angles of the triangle ABC +are together equal to two right angles, we conclude that +this is true of every other triangle, not because it is true +of ABC, but for the same reason which proved it to be +true of ABC. If this were to be called Induction, an +appropriate name for it would be, induction by parity of +reasoning. But the term cannot properly belong to it; the +characteristic quality of Induction is wanting, since the truth +obtained, though really general, is not believed on the +evidence of particular instances. We do not conclude that +all triangles have the property because some triangles have, +but from the ulterior demonstrative evidence which was the +ground of our conviction in the particular instances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are nevertheless, in mathematics, some examples +of so-called induction, in which the conclusion does bear the +appearance of a generalization grounded on some of the +particular cases included in it. A mathematician, when he +has calculated a sufficient number of the terms of an algebraical +or arithmetical series to have ascertained what is called +the <em class="tei tei-emph"><span style="font-style: italic">law</span></em> of the series, does not hesitate to fill up any number +of the succeeding terms without repeating the calculations. +But I apprehend he only does so when it is apparent from +<span class="tei tei-pb" id="page300">[pg 300]</span><a name="Pg300" id="Pg300" class="tei tei-anchor"></a> +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> considerations +(which might be exhibited in the form of demonstration) that the mode of formation of +the subsequent terms, each from that which preceded it, must be +similar to the formation of the terms which have been already +calculated. And when the attempt has been hazarded without +the sanction of such general considerations, there are +instances on record in which it has led to false results. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is said that Newton discovered the binomial theorem +by induction; by raising a binomial successively to a certain +number of powers, and comparing those powers with one +another until he detected the relation in which the algebraic +formula of each power stands to the exponent of that power, +and to the two terms of the binomial. The fact is not improbable: +but a mathematician like Newton, who seemed to +arrive <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">per saltum</span></span> at principles +and conclusions that ordinary mathematicians only reached by a succession of steps, +certainly could not have performed the comparison in question without being led by +it to the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> ground of the +law; since any one who understands sufficiently the nature of +multiplication to venture upon multiplying several lines of +symbols at one operation, cannot but perceive that in raising +a binomial to a power, the coefficients must depend on the +laws of permutation and combination: and as soon as this is +recognised, the theorem is demonstrated. Indeed, when +once it was seen that the law prevailed in a few of the lower +powers, its identity with the law of permutation would at +once suggest the considerations which prove it to obtain +universally. Even, therefore, such cases as these, are but +examples of what I have called induction by parity of reasoning, +that is, not really induction, because not involving +inference of a general proposition from particular instances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. There remains a third improper use of the term +Induction, which it is of real importance to clear up, because +the theory of induction has been, in no ordinary degree, confused +by it, and because the confusion is exemplified in the +most recent and most elaborate treatise on the inductive +philosophy which exists in our language. The error in +<span class="tei tei-pb" id="page301">[pg 301]</span><a name="Pg301" id="Pg301" class="tei tei-anchor"></a> +question is that of confounding a mere description of a set +of observed phenomena, with an induction from them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Suppose that a phenomenon consists of parts, and that +these parts are only capable of being observed separately, +and as it were piecemeal. When the observations have been +made, there is a convenience (amounting for many purposes +to a necessity) in obtaining a representation of the phenomenon +as a whole, by combining, or as we may say, piecing +these detached fragments together. A navigator sailing in +the midst of the ocean discovers land: he cannot at first, or +by any one observation, determine whether it is a continent +or an island; but he coasts along it, and after a few days +finds himself to have sailed completely round it: he then +pronounces it an island. Now there was no particular time +or place of observation at which he could perceive that this +land was entirely surrounded by water: he ascertained the +fact by a succession of partial observations, and then selected +a general expression which summed up in two or three words +the whole of what he so observed. But is there anything of +the nature of an induction in this process? Did he infer +anything that had not been observed, from something else +which had? Certainly not. He had observed the whole of +what the proposition asserts. That the land in question is +an island, is not an inference from the partial facts which the +navigator saw in the course of his circumnavigation; it is the +facts themselves; it is a summary of those facts; the description +of a complex fact, to which those simpler ones are as the +parts of a whole. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now there is, I conceive, no difference in kind between +this simple operation, and that by which Kepler ascertained +the nature of the planetary orbits: and Kepler's operation, +all at least that was characteristic in it, was not more an +inductive act than that of our supposed navigator. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The object of Kepler was to determine the real path +described by each of the planets, or let us say by the planet +Mars, (for it was of that body that he first established two of +the three great astronomical truths which bear his name.) +To do this there was no other mode than that of direct +<span class="tei tei-pb" id="page302">[pg 302]</span><a name="Pg302" id="Pg302" class="tei tei-anchor"></a> +observation: and all which observation could do was to +ascertain a great number of the successive places of the +planet; or rather, of its apparent places. That the planet +occupied successively all these positions, or at all events, +positions which produced the same impressions on the eye, +and that it passed from one of these to another insensibly, +and without any apparent breach of continuity; thus much +the senses, with the aid of the proper instruments, could +ascertain. What Kepler did more than this, was to find what +sort of a curve these different points would make, supposing +them to be all joined together. He expressed the whole +series of the observed places of Mars by what Dr. Whewell +calls the general conception of an ellipse. This operation +was far from being as easy as that of the navigator who expressed +the series of his observations on successive points +of the coast by the general conception of an island. But it +is the very same sort of operation; and if the one is not an +induction but a description, this must also be true of the +other. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To avoid misapprehension, we must remark that Kepler, +in one respect, performed a real act of induction; namely, +in concluding that because the observed places of Mars were +correctly represented by points in an imaginary ellipse, +therefore Mars would continue to revolve in that same ellipse; +and even in concluding that the position of the planet during +the time which intervened between two observations, must +have coincided with the intermediate points of the curve. +But this really inductive operation requires to be carefully +distinguished from the mere act of bringing the facts actually +observed under a general description. So distinct are these +two operations, that the one might have been performed +without the other. Men might and did make correct inductions +concerning the heavenly motions, before they had +obtained correct general descriptions of them. It was known +that the planets always moved in the same paths, long before +it had been ascertained that those paths were ellipses. +Astronomers early remarked that the same set of apparent +positions returned periodically. When they obtained a new +<span class="tei tei-pb" id="page303">[pg 303]</span><a name="Pg303" id="Pg303" class="tei tei-anchor"></a> +description of the phenomenon, they did not necessarily +make any further induction, nor (which is the true test of a +new general truth) add anything to the power of prediction +which they already possessed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. The descriptive operation which enables a number +of details to be summed up in a single proposition, Dr. +Whewell, by an aptly chosen expression, has termed the +Colligation of Facts.<a id="noteref_55" name="noteref_55" href="#note_55"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">55</span></span></a> In most of his observations concerning +that mental process I fully agree, and would gladly +transfer all that portion of his book into my own pages. I +only think him mistaken in setting up this kind of operation, +which according to the old and received meaning of the +term, is not induction at all, as the type of induction generally; +and laying down, throughout his work, as principles +of induction, the principles of mere colligation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell maintains that the general proposition which +binds together the particular facts, and makes them, as it +were, one fact, is not the mere sum of those facts, but something +more, since there is introduced a conception of the +mind, which did not exist in the facts themselves. <span class="tei tei-q">“The +particular facts,”</span> says he,<a id="noteref_56" name="noteref_56" href="#note_56"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">56</span></span></a> +<span class="tei tei-q">“are not merely brought together, +but there is a new element added to the combination by the +very act of thought by which they are combined.... When +the Greeks, after long observing the motions of the planets, +saw that these motions might be rightly considered as produced +by the motion of one wheel revolving in the inside of +another wheel, these wheels were creations of their minds, +added to the facts which they perceived by sense. And even +if the wheels were no longer supposed to be material, but +were reduced to mere geometrical spheres or circles, they +were not the less products of the mind alone,—something +additional to the facts observed. The same is the case in +all other discoveries. The facts are known, but they are +insulated and unconnected, till the discoverer supplies from +his own store a principle of connexion. The pearls are +<span class="tei tei-pb" id="page304">[pg 304]</span><a name="Pg304" id="Pg304" class="tei tei-anchor"></a> +there, but they will not hang together till some one provides +the string.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +That a conception of the mind is introduced is indeed +undeniable, and I willingly concede, that to hit upon the +right conception is often a far more difficult and more meritorious +achievement, than to prove its applicability when +obtained. But a conception implies, and corresponds to, +something conceived: and though the conception itself is +not in the facts, but in our mind, it must be a conception <em class="tei tei-emph"><span style="font-style: italic">of</span></em> +something which really is in the facts, some property which +they actually possess, and which they would manifest to our +senses, if our senses were able to take cognizance of them. +If, for instance, the planet left behind it in space a visible +track, and if the observer were in a fixed position at such a +distance above the plane of the orbit as would enable him to +see the whole of it at once, he would see it to be an ellipse; +and if gifted with appropriate instruments, and powers of +locomotion, he could prove it to be such by measuring its +different dimensions. These things are indeed impossible +to us, but not impossible in themselves; if they were so, +Kepler's law could not be true. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Subject to the indispensable condition which has just +been stated, I cannot perceive that the part which conceptions +have in the operation of studying facts, has ever been +overlooked or undervalued. No one ever disputed that in +order to reason about anything we must have a conception +of it; or that when we include a multitude of things under a +general expression, there is implied in the expression a +conception of something common to those things. But it +by no means follows that the conception is necessarily pre-existent, +or constructed by the mind out of its own materials. +If the facts are rightly classed under the conception, it is +because there is in the facts themselves something of which +the conception is itself a copy; and which if we cannot +directly perceive, it is because of the limited power of our +organs, and not because the thing itself is not there. The +conception itself is often obtained by abstraction from the +very facts which, in Dr. Whewell's language, it is afterwards +<span class="tei tei-pb" id="page305">[pg 305]</span><a name="Pg305" id="Pg305" class="tei tei-anchor"></a> +called in to connect. This he himself admits, when he +observes, (which he does on several occasions,) how great a +service would be rendered to the science of physiology by +the philosopher <span class="tei tei-q">“who should establish a precise, tenable, +and consistent conception of life.”</span><a id="noteref_57" name="noteref_57" href="#note_57"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">57</span></span></a> Such a conception <em class="tei tei-emph"><span style="font-style: italic">can</span></em> +only be abstracted from the phenomena of life itself; from +the very facts which it is put in requisition to connect. In +other cases (no doubt) instead of collecting the conception +from the very phenomena which we are attempting to colligate, +we select it from among those which have been previously +collected by abstraction from other facts. In the +instance of Kepler's laws, the latter was the case. The facts +being out of the reach of being observed, in any such manner +as would have enabled the senses to identify directly the +path of the planet, the conception requisite for framing a +general description of that path could not be collected by +abstraction from the observations themselves; the mind had +to supply hypothetically, from among the conceptions it +had obtained from other portions of its experience, some one +which would correctly represent the series of the observed +facts. It had to frame a supposition respecting the general +course of the phenomenon, and ask itself, If this be the +general description, what will the details be? and then +compare these with the details actually observed. If they +agreed, the hypothesis would serve for a description of the +phenomenon: if not, it was necessarily abandoned, and +another tried. It is such a case as this which gives rise to +the doctrine that the mind, in framing the descriptions, adds +something of its own which it does not find in the facts. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Yet it is a fact surely, that the planet does describe +an ellipse; and a fact which we could see, if we had adequate +visual organs and a suitable position. Not having these +advantages, but possessing the conception of an ellipse, or +(to express the meaning in less technical language) knowing +what an ellipse was, Kepler tried whether the observed places +of the planet were consistent with such a path. He found +<span class="tei tei-pb" id="page306">[pg 306]</span><a name="Pg306" id="Pg306" class="tei tei-anchor"></a> +they were so; and he, consequently, asserted as a fact that +the planet moved in an ellipse. But this fact, which Kepler +did not add to, but found in, the motions of the planet, +namely, that it occupied in succession the various points in +the circumference of a given ellipse, was the very fact, the +separate parts of which had been separately observed; it was +the sum of the different observations. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Having stated this fundamental difference between my +opinion and that of Dr. Whewell, I must add, that his account +of the manner in which a conception is selected, +suitable to express the facts, appears to me perfectly just. The +experience of all thinkers will, I believe, testify that the +process is tentative; that it consists of a succession of +guesses; many being rejected, until one at last occurs fit to +be chosen. We know from Kepler himself that before hitting +upon the <span class="tei tei-q">“conception”</span> of an ellipse, he tried nineteen +other imaginary paths, which, finding them inconsistent with +the observations, he was obliged to reject. But as Dr. +Whewell truly says, the successful hypothesis, though a +guess, ought generally to be called, not a lucky, but a skilful +guess. The guesses which serve to give mental unity and +wholeness to a chaos of scattered particulars, are accidents +which rarely occur to any minds but those abounding in +knowledge and disciplined in intellectual combinations. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +How far this tentative method, so indispensable as a +means to the colligation of facts for purposes of description, +admits of application to Induction itself, and what functions +belong to it in that department, will be considered in the +chapter of the present Book which relates to Hypotheses. +On the present occasion we have chiefly to distinguish this +process of Colligation from Induction properly so called: and +that the distinction may be made clearer, it is well to advert +to a curious and interesting remark, which is as strikingly +true of the former operation, as it appears to me unequivocally +false of the latter. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In different stages of the progress of knowledge, philosophers +have employed, for the colligation of the same order of +facts, different conceptions. The early rude observations +<span class="tei tei-pb" id="page307">[pg 307]</span><a name="Pg307" id="Pg307" class="tei tei-anchor"></a> +of the heavenly bodies, in which minute precision was neither +attained nor sought, presented nothing inconsistent with the +representation of the path of a planet as an exact circle, +having the earth for its centre. As observations increased +in accuracy, and facts were disclosed which were not reconcileable +with this simple supposition; for the colligation of +those additional facts, the supposition was varied; and varied +again and again as facts became more numerous and precise. +The earth was removed from the centre to some other point +within the circle; the planet was supposed to revolve in a +smaller circle called an epicycle, round an imaginary point +which revolved in a circle round the earth: in proportion as +observation elicited fresh facts contradictory to these representations, +other epicycles and other excentrics were added, +producing additional complication; until at last Kepler swept +all these circles away, and substituted the conception of an +exact ellipse. Even this is found not to represent with complete +correctness the accurate observations of the present +day, which disclose many slight deviations from an orbit +exactly elliptical. Now Dr. Whewell has remarked that +these successive general expressions, though apparently so +conflicting, were all correct: they all answered the purpose +of colligation: they all enabled the mind to represent to itself +with facility, and by a simultaneous glance, the whole body +of facts at that time ascertained; each in its turn served as a +correct description of the phenomena, so far as the senses +had up to that time taken cognizance of them. If a necessity +afterwards arose for discarding one of these general descriptions +of the planet's orbit, and framing a different imaginary +line, by which to express the series of observed positions, it +was because a number of new facts had now been added, +which it was necessary to combine with the old facts into one +general description. But this did not affect the correctness +of the former expression, considered as a general statement +of the only facts which it was intended to represent. And so +true is this, that, as is well remarked by M. Comte, these +ancient generalizations, even the rudest and most imperfect +of them, that of uniform movement in a circle, are so far +<span class="tei tei-pb" id="page308">[pg 308]</span><a name="Pg308" id="Pg308" class="tei tei-anchor"></a> +from being entirely false, that they are even now habitually +employed by astronomers when only a rough approximation +to correctness is required. <span class="tei tei-q">“L'astronomie moderne, en détruisant +sans retour les hypothèses primitives, envisagées +comme lois réelles du monde, a soigneusement maintenu +leur valeur positive et permanente, la propriété de représenter +commodément les phénomènes quand il s'agit d'une +première ébauche. Nos ressources à cet égard sont même +bien plus étendues, precisément à cause que nous ne nous +faisons aucune illusion sur la réalité des hypothèses; ce qui +nous permet d'employer sans scrupule, en chaque cas, celle +que nous jugeons la plus avantageuse.”</span><a id="noteref_58" name="noteref_58" href="#note_58"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">58</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's remark, therefore, is philosophically correct. +Successive expressions for the colligation of observed +facts, or, in other words, successive descriptions of a phenomenon +as a whole, which has been observed only in parts, +may, though conflicting, be all correct as far as they go. But +it would surely be absurd to assert this of conflicting inductions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The scientific study of facts may be undertaken for three +different purposes: the simple description of the facts; their +explanation; or their prediction: meaning by prediction, +the determination of the conditions under which similar facts +may be expected again to occur. To the first of these three +operations the name of Induction does not properly belong: +to the other two it does. Now, Dr. Whewell's observation is +true of the first alone. Considered as a mere description, +the circular theory of the heavenly motions represents perfectly +well their general features: and by adding epicycles +without limit, those motions, even as now known to us, might +be expressed with any degree of accuracy that might be +required. The elliptical theory, as a mere description, would +have a great advantage in point of simplicity, and in the +consequent facility of conceiving it and reasoning about it; +but it would not really be more true than the other. Different +descriptions, therefore, may be all true: but not, surely, +<span class="tei tei-pb" id="page309">[pg 309]</span><a name="Pg309" id="Pg309" class="tei tei-anchor"></a> +different explanations. The doctrine that the heavenly bodies +moved by a virtue inherent in their celestial nature; the +doctrine that they were moved by impact, (which led to the +hypothesis of vortices as the only impelling force capable of +whirling bodies in circles,) and the Newtonian doctrine, that +they are moved by the composition of a centripetal with an +original projectile force; all these are explanations, collected +by real induction from supposed parallel cases; and they +were all successively received by philosophers, as scientific +truths on the subject of the heavenly bodies. Can it be said +of these, as was said of the different descriptions, that they +are all true as far as they go? Is it not clear that one only +can be true in any degree, and the other two must be altogether +false? So much for explanations: let us now compare +different predictions: the first, that eclipses will occur whenever +one planet or satellite is so situated as to cast its shadow +upon another; the second, that they will occur whenever +some great calamity is impending over mankind. Do these +two doctrines only differ in the degree of their truth, as expressing +real facts with unequal degrees of accuracy? +Assuredly the one is true, and the other absolutely false.<a id="noteref_59" name="noteref_59" href="#note_59"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">59</span></span></a> +</p> + +<span class="tei tei-pb" id="page310">[pg 310]</span><a name="Pg310" id="Pg310" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In every way, therefore, it is evident that to explain induction +as the colligation of facts by means of appropriate +conceptions, that is, conceptions which will really express +them, is to confound mere description of the observed facts +with inference from those facts, and ascribe to the latter +what is a characteristic property of the former. +</p> + +<span class="tei tei-pb" id="page311">[pg 311]</span><a name="Pg311" id="Pg311" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is, however, between Colligation and Induction, a +real correlation, which it is important to conceive correctly. +Colligation is not always induction; but induction is always +colligation. The assertion that the planets move in ellipses, was +but a mode of representing observed facts; it was but a colligation; +while the assertion that they are drawn, or tend, +<span class="tei tei-pb" id="page312">[pg 312]</span><a name="Pg312" id="Pg312" class="tei tei-anchor"></a> +towards the sun, was the statement of a new fact, inferred +by induction. But the induction, once made, accomplishes +the purposes of colligation likewise. It brings the same +facts, which Kepler had connected by his conception of an +ellipse, under the additional conception of bodies acted +upon by a central force, and serves therefore as a new bond +of connexion for those facts; a new principle for their +classification. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Further, that general description, which is improperly +confounded with induction, is nevertheless a necessary preparation +for induction; no less necessary than correct observation +of the facts themselves. Without the previous +colligation of detached observations by means of one general +conception, we could never have obtained any basis for an +induction, except in the case of phenomena of very limited +compass. We should not be able to affirm any predicates +at all, of a subject incapable of being observed otherwise +than piecemeal: much less could we extend those predicates +by induction to other similar subjects. Induction, therefore, +always presupposes, not only that the necessary observations +are made with the necessary accuracy, but also that +the results of these observations are, so far as practicable, +connected together by general descriptions, enabling the +mind to represent to itself as wholes whatever phenomena +are capable of being so represented. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. Dr. Whewell has replied at some length to the +preceding observations, re-stating his opinions, but without +(as far as I can perceive) adding anything to his former +arguments. Since, however, mine have not had the good +fortune to make any impression upon him, I will subjoin a +few remarks, tending to shew more clearly in what our +difference of opinion consists, as well as, in some measure, +to account for it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All the definitions of induction, by writers of authority, +make it consist in drawing inferences from known cases to +unknown; affirming of a class, a predicate which has been +found true of some cases belonging to the class; concluding, +<span class="tei tei-pb" id="page313">[pg 313]</span><a name="Pg313" id="Pg313" class="tei tei-anchor"></a> +because some things have a certain property, that other +things which resemble them have the same property—or +because a thing has manifested a property at a certain time, +that it has and will have that property at other times. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It will scarcely be contended that Kepler's operation was +an Induction in this sense of the term. The statement, +that Mars moves in an elliptical orbit, was no generalization +from individual cases to a class of cases. Neither was it an +extension to all time, of what had been found true at some +particular time. The whole amount of generalization which +the case admitted of, was already completed, or might have +been so. Long before the elliptic theory was thought of, it +had been ascertained that the planets returned periodically +to the same apparent places; the series of these places was, +or might have been, completely determined, and the apparent +course of each planet marked out on the celestial globe in an +uninterrupted line. Kepler did not extend an observed +truth to other cases than those in which it had been observed: +he did not widen the <em class="tei tei-emph"><span style="font-style: italic">subject</span></em> of the proposition which +expressed the observed facts. He left the subject as it was; +the alteration he made was in the predicate. Instead of +saying, the successive places of Mars are so and so, he +summed them up in the statement, that the successive places +of Mars are points in an ellipse. It is true, this statement, +as Dr. Whewell says, was not the sum of the observations +<em class="tei tei-emph"><span style="font-style: italic">merely</span></em>; it was the sum of the observations <em class="tei tei-emph"><span style="font-style: italic">seen under a new +point of view</span></em>.<a id="noteref_60" name="noteref_60" href="#note_60"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">60</span></span></a> But it was not the sum of <em class="tei tei-emph"><span style="font-style: italic">more</span></em> than the +observations, as a real induction is. It took in no cases but +those which had been actually observed, or which could have +been inferred from the observations before the new point of +view presented itself. There was not that transition from +known cases to unknown, which constitutes Induction in the +original and acknowledged meaning of the term. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Old definitions, it is true, cannot prevail against new +knowledge: and if the Keplerian operation, as a logical process, +were really identical with what takes place in acknowledged +<span class="tei tei-pb" id="page314">[pg 314]</span><a name="Pg314" id="Pg314" class="tei tei-anchor"></a> +induction, the definition of induction ought to be +so widened as to take it in; since scientific language ought +to adapt itself to the true relations which subsist between +the things it is employed to designate. Here then it is +that I join issue with Dr. Whewell. He does think the +operations identical. He allows of no logical process in +any case of induction, other than what there was in +Kepler's case, namely, guessing until a guess is found +which tallies with the facts: and accordingly, as we shall +see hereafter, he rejects all canons of induction, because +it is not by means of them that we guess. Dr. Whewell's +theory of the logic of science would be very perfect, if it did +not pass over altogether the question of Proof. But in my +apprehension there is such a thing as proof, and inductions +differ altogether from descriptions in their relation to that +element. Induction is proof; it is inferring something +unobserved from something observed: it requires, therefore, +an appropriate test of proof; and to provide that test, is the +special purpose of inductive logic. When, on the contrary, +we merely collate known observations, and, in Dr. Whewell's +phraseology, connect them by means of a new conception; +if the conception does but serve to connect the observations, +we have all we want. As the proposition in which it is +embodied pretends to no other truth than what it may share +with many other modes of representing the same facts, to be +consistent with the facts is all it requires: it neither needs +nor admits of proof; though it may serve to prove other +things, inasmuch as, by placing the facts in mental connexion +with other facts, not previously seen to resemble them, +it assimilates the case to another class of phenomena, concerning +which real Inductions have already been made. +Thus Kepler's so-called law brought the orbit of Mars into +the class ellipse, and by doing so, proved all the properties +of an ellipse to be true of the orbit: but in this proof +Kepler's law supplied the minor premiss, and not (as is the +case with real Inductions) the major. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The mental operation which extracts from a number of +detached observations certain general characters in which +<span class="tei tei-pb" id="page315">[pg 315]</span><a name="Pg315" id="Pg315" class="tei tei-anchor"></a> +the observed phenomena resemble one another, or resemble +other known facts, is what Bacon, Locke, and most subsequent +metaphysicians, have understood by the word Abstraction. +A general expression obtained by abstraction, +connecting known facts by means of common characters, but +without concluding from them to unknown, may, I think, +with strict logical correctness, be termed a Description; nor +do I know in what other way things can ever be described. +My position, however, does not depend on the employment +of that particular word; I am quite content to use Dr. +Whewell's term Colligation, provided it be clearly seen +that the process is not Induction, but something radically +different. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +What more may usefully be said on the subject of Colligation, +or of the correlative expression invented by Dr. +Whewell, the Explication of Conceptions, and generally on +the subject of ideas and mental representations as connected +with the study of facts, will find a more appropriate place in +the Fourth Book, on the Operations Subsidiary to Induction: +to which the reader must refer for the removal of any +difficulty which the present discussion may have left. +</p> + +</div> + +<span class="tei tei-pb" id="page316">[pg 316]</span><a name="Pg316" id="Pg316" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc59" id="toc59"></a> +<a name="pdf60" id="pdf60"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER III. OF THE GROUND OF INDUCTION.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. Induction properly so called, as distinguished +from those mental operations, sometimes though improperly +designated by the name, which I have attempted in the preceding +chapter to characterize, may, then, be summarily +defined as Generalization from Experience. It consists in +inferring from some individual instances in which a phenomenon +is observed to occur, that it occurs in all instances of +a certain class; namely, in all which <em class="tei tei-emph"><span style="font-style: italic">resemble</span></em> the former, in +what are regarded as the material circumstances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In what way the material circumstances are to be distinguished +from those which are immaterial, or why some of +the circumstances are material and others not so, we are not +yet ready to point out. We must first observe, that there is +a principle implied in the very statement of what Induction +is; an assumption with regard to the course of nature and +the order of the universe: namely, that there are such things +in nature as parallel cases; that what happens once, will, +under a sufficient degree of similarity of circumstances, +happen again, and not only again, but as often as the same +circumstances recur. This, I say, is an assumption, involved +in every case of induction. And, if we consult the actual +course of nature, we find that the assumption is warranted. +The universe, we find, is so constituted, that whatever is true +in any one case, is true in all cases of a certain description; +the only difficulty is, to find <em class="tei tei-emph"><span style="font-style: italic">what</span></em> description. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This universal fact, which is our warrant for all inferences +from experience, has been described by different philosophers +in different forms of language: that the course of nature is +uniform; that the universe is governed by general laws; and +the like. One of the most usual of these modes of expression, +<span class="tei tei-pb" id="page317">[pg 317]</span><a name="Pg317" id="Pg317" class="tei tei-anchor"></a> +but also one of the most inadequate, is that which has been +brought into familiar use by the metaphysicians of the school +of Reid and Stewart. The disposition of the human mind +to generalize from experience,—a propensity considered by +these philosophers as an instinct of our nature,—they usually +describe under some such name as <span class="tei tei-q">“our intuitive conviction +that the future will resemble the past.”</span> Now it has been +well pointed out, that (whether the tendency be or not an +original and ultimate element of our nature), Time, in its +modifications of past, present, and future, has no concern +either with the belief itself, or with the grounds of it. We +believe that fire will burn to-morrow, because it burned to-day +and yesterday; but we believe, on precisely the same +grounds, that it burned before we were born, and that it +burns this very day in Cochin-China. It is not from the +past to the future, <em class="tei tei-emph"><span style="font-style: italic">as</span></em> past and future, that we infer, but from +the known to the unknown; from facts observed to facts +unobserved; from what we have perceived, or been directly +conscious of, to what has not come within our experience. +In this last predicament is the whole region of the future; +but also the vastly greater portion of the present and of +the past. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Whatever be the most proper mode of expressing it, the +proposition that the course of nature is uniform, is the fundamental +principle, or general axiom, of Induction. It would +yet be a great error to offer this large generalization as any +explanation of the inductive process. On the contrary, I +hold it to be itself an instance of induction, and induction +by no means of the most obvious kind. Far from being the +first induction we make, it is one of the last, or at all events +one of those which are latest in attaining strict philosophical +accuracy. As a general maxim, indeed, it has scarcely +entered into the minds of any but philosophers; nor even +by them, as we shall have many opportunities of remarking, +have its extent and limits been always very justly conceived. +The truth is, that this great generalization is itself founded +on prior generalizations. The obscurer laws of nature were +discovered by means of it, but the more obvious ones must +<span class="tei tei-pb" id="page318">[pg 318]</span><a name="Pg318" id="Pg318" class="tei tei-anchor"></a> +have been understood and assented to as general truths +before it was ever heard of. We should never have thought +of affirming that all phenomena take place according to +general laws, if we had not first arrived, in the case of a +great multitude of phenomena, at some knowledge of the +laws themselves; which could be done no otherwise than by +induction. In what sense, then, can a principle, which is so +far from being our earliest induction, be regarded as our +warrant for all the others? In the only sense, in which (as +we have already seen) the general propositions which we +place at the head of our reasonings when we throw them +into syllogisms, ever really contribute to their validity. As +Archbishop Whately remarks, every induction is a syllogism +with the major premiss suppressed; or (as I prefer expressing +it) every induction may be thrown into the form of a syllogism, +by supplying a major premiss. If this be actually done, +the principle which we are now considering, that of the uniformity +of the course of nature, will appear as the ultimate +major premiss of all inductions, and will, therefore, stand to +all inductions in the relation in which, as has been shown at +so much length, the major proposition of a syllogism always +stands to the conclusion; not contributing at all to prove it, +but being a necessary condition of its being proved; since +no conclusion is proved for which there cannot be found a +true major premiss. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The statement, that the uniformity of the course of nature is +the ultimate major premiss in all cases of induction, may be +thought to require some explanation. The immediate major +premiss in every inductive argument, it certainly is not. Of +that, Archbishop Whately's must be held to be the correct account. +The induction, <span class="tei tei-q">“John, Peter, &c., are mortal, therefore +all mankind are mortal,”</span> may, as he justly says, be thrown +into a syllogism by prefixing as a major premiss (what is at +any rate a necessary condition of the validity of the argument) +namely, that what is true of John, Peter, &c, is true of all +mankind. But how come we by this major premiss? It is +not self-evident; nay, in all cases of unwarranted generalization, +it is not true. How, then, is it arrived at? Necessarily +<span class="tei tei-pb" id="page319">[pg 319]</span><a name="Pg319" id="Pg319" class="tei tei-anchor"></a> +either by induction or ratiocination; and if by induction, the +process, like all other inductive arguments, may be thrown into +the form of a syllogism. This previous syllogism it is, therefore, +necessary to construct. There is, in the long run, only +one possible construction. The real proof that what is true +of John, Peter, &c., is true of all mankind, can only be, that +a different supposition would be inconsistent with the uniformity +which we know to exist in the course of nature. +Whether there would be this inconsistency or not, may be a +matter of long and delicate inquiry; but unless there would, +we have no sufficient ground for the major of the inductive +syllogism. It hence appears, that if we throw the whole +course of any inductive argument into a series of syllogisms, +we shall arrive by more or fewer steps at an ultimate syllogism, +which will have for its major premiss the principle, or +axiom, of the uniformity of the course of nature.<a id="noteref_61" name="noteref_61" href="#note_61"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">61</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It was not to be expected that in the case of this axiom, +any more than of other axioms, there should be unanimity +among thinkers with respect to the grounds on which it is +to be received as true. I have already stated that I regard +<span class="tei tei-pb" id="page320">[pg 320]</span><a name="Pg320" id="Pg320" class="tei tei-anchor"></a> +it as itself a generalization from experience. Others hold +it to be a principle which, antecedently to any verification +by experience, we are compelled by the constitution of our +thinking faculty to assume as true. Having so recently, and +at so much length, combated a similar doctrine as applied to +the axioms of mathematics, by arguments which are in a +great measure applicable to the present case, I shall defer the +more particular discussion of this controverted point in +regard to the fundamental axiom of induction, until a more +advanced period of our inquiry.<a id="noteref_62" name="noteref_62" href="#note_62"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">62</span></span></a> At present it is of more +importance to understand thoroughly the import of the axiom +itself. For the proposition, that the course of nature is +uniform, possesses rather the brevity suitable to popular, +than the precision requisite in philosophical, language: its +terms require to be explained, and a stricter than their ordinary +signification given to them, before the truth of the +assertion can be admitted. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Every person's consciousness assures him that he +does not always expect uniformity in the course of events; +he does not always believe that the unknown will be similar +to the known, that the future will resemble the past. Nobody +believes that the succession of rain and fine weather will be +the same in every future year as in the present. Nobody +expects to have the same dreams repeated every night. On +the contrary, everybody mentions it as something extraordinary, +if the course of nature is constant, and resembles itself, +in these particulars. To look for constancy where constancy +is not to be expected, as for instance, that a day which has +once brought good fortune will always be a fortunate day, is +justly accounted superstition. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The course of nature, in truth, is not only uniform, it is +also infinitely various. Some phenomena are always seen to +recur in the very same combinations in which we met with +them at first; others seem altogether capricious; while +some, which we had been accustomed to regard as bound +<span class="tei tei-pb" id="page321">[pg 321]</span><a name="Pg321" id="Pg321" class="tei tei-anchor"></a> +down exclusively to a particular set of combinations, we +unexpectedly find detached from some of the elements with +which we had hitherto found them conjoined, and united to +others of quite a contrary description. To an inhabitant of +Central Africa, fifty years ago, no fact probably appeared to +rest on more uniform experience than this, that all human +beings are black. To Europeans, not many years ago, the +proposition, All swans are white, appeared an equally unequivocal +instance of uniformity in the course of nature. Further +experience has proved to both that they were mistaken; but +they had to wait fifty centuries for this experience. During +that long time, mankind believed in an uniformity of the +course of nature where no such uniformity really existed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +According to the notion which the ancients entertained of +induction, the foregoing were cases of as legitimate inference +as any inductions whatever. In these two instances, in +which, the conclusion being false, the ground of inference +must have been insufficient, there was, nevertheless, as much +ground for it as this conception of induction admitted of. +The induction of the ancients has been well described by +Bacon, under the name of <span class="tei tei-q">“Inductio per enumerationem simplicem, +ubi non reperitur instantia contradictoria.”</span> It consists +in ascribing the character of general truths to all +propositions which are true in every instance that we happen +to know of. This is the kind of induction which is natural +to the mind when unaccustomed to scientific methods. The +tendency, which some call an instinct, and which others +account for by association, to infer the future from the past, +the known from the unknown, is simply a habit of expecting +that what has been found true once or several times, and +never yet found false, will be found true again. Whether +the instances are few or many, conclusive or inconclusive, +does not much affect the matter: these are considerations +which occur only on reflection: the unprompted tendency of +the mind is to generalize its experience, provided this points +all in one direction; provided no other experience of a conflicting +character comes unsought. The notion of seeking it, +of experimenting for it, of <em class="tei tei-emph"><span style="font-style: italic">interrogating</span></em> nature (to use Bacon's +<span class="tei tei-pb" id="page322">[pg 322]</span><a name="Pg322" id="Pg322" class="tei tei-anchor"></a> +expression) is of much later growth. The observation of +nature, by uncultivated intellects, is purely passive: they +accept the facts which present themselves, without taking +the trouble of searching for more: it is a superior mind only +which asks itself what facts are needed to enable it to come +to a sure conclusion, and then looks out for these. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But though we have always a propensity to generalize +from unvarying experience, we are not always warranted in +doing so. Before we can be at liberty to conclude that something +is universally true because we have never known an instance +to the contrary, we must have reason to believe that if +there were in nature any instances to the contrary, we should +have known of them. This assurance, in the great majority +of cases, we cannot have, or can have only in a very moderate +degree. The possibility of having it, is the foundation on +which we shall see hereafter that induction by simple enumeration +may in some remarkable cases amount practically to +proof.<a id="noteref_63" name="noteref_63" href="#note_63"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">63</span></span></a> No such assurance, however, can be had, on +any of the ordinary subjects of scientific inquiry. Popular notions +are usually founded on induction by simple enumeration; in +science it carries us but a little way. We are forced to +begin with it; we must often rely on it provisionally, in the +absence of means of more searching investigation. But, for +the accurate study of nature, we require a surer and a more +potent instrument. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It was, above all, by pointing out the insufficiency of this +rude and loose conception of Induction, that Bacon merited +the title so generally awarded to him, of Founder of the Inductive +Philosophy. The value of his own contributions to +a more philosophical theory of the subject has certainly been +exaggerated. Although (along with some fundamental +errors) his writings contain, more or less fully developed, +several of the most important principles of the Inductive +Method, physical investigation has now far outgrown the +Baconian conception of Induction. Moral and political inquiry, +indeed, are as yet far behind that conception. The +<span class="tei tei-pb" id="page323">[pg 323]</span><a name="Pg323" id="Pg323" class="tei tei-anchor"></a> +current and approved modes of reasoning on these subjects +are still of the same vicious description against which Bacon +protested; the method almost exclusively employed by those +professing to treat such matters inductively, is the very +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">inductio +per enumerationem simplicem</span></span> which he condemns; and +the experience which we hear so confidently appealed to by +all sects, parties, and interests, is still, in his own emphatic +words, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">mera palpatio</span></span>. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. In order to a better understanding of the problem +which the logician must solve if he would establish a scientific +theory of Induction, let us compare a few cases of incorrect +inductions with others which are acknowledged to be legitimate. +Some, we know, which were believed for centuries to +be correct, were nevertheless incorrect. That all swans are +white, cannot have been a good induction, since the conclusion +has turned out erroneous. The experience, however, +on which the conclusion rested was genuine. From the +earliest records, the testimony of the inhabitants of the +known world was unanimous on the point. The uniform +experience, therefore, of the inhabitants of the known world, +agreeing in a common result, without one known instance of +deviation from that result, is not always sufficient to establish +a general conclusion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But let us now turn to an instance apparently not very +dissimilar to this. Mankind were wrong, it seems, in concluding +that all swans were white: are we also wrong, when +we conclude that all men's heads grow above their shoulders, +and never below, in spite of the conflicting testimony of the +naturalist Pliny? As there were black swans, though civilized +people had existed for three thousand years on the earth +without meeting with them, may there not also be <span class="tei tei-q">“men +whose heads do grow beneath their shoulders,”</span> notwithstanding +a rather less perfect unanimity of negative testimony +from observers? Most persons would answer No; it was +more credible that a bird should vary in its colour, than that +men should vary in the relative position of their principal +organs. And there is no doubt that in so saying they would +<span class="tei tei-pb" id="page324">[pg 324]</span><a name="Pg324" id="Pg324" class="tei tei-anchor"></a> +be right: but to say why they are right, would be impossible, +without entering more deeply than is usually done, into the +true theory of Induction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Again, there are cases in which we reckon with the most +unfailing confidence upon uniformity, and other cases in which +we do not count upon it at all. In some we feel complete +assurance that the future will resemble the past, the unknown +be precisely similar to the known. In others, however +invariable may be the result obtained from the instances +which have been observed, we draw from them no more than +a very feeble presumption that the like result will hold in all +other cases. That a straight line is the shortest distance +between two points, we do not doubt to be true even in the +region of the fixed stars. When a chemist announces the +existence and properties of a newly-discovered substance, if +we confide in his accuracy, we feel assured that the conclusions +he has arrived at will hold universally, although the +induction be founded but on a single instance. We do not +withhold our assent, waiting for a repetition of the experiment; +or if we do, it is from a doubt whether the one experiment +was properly made, not whether if properly made it would be +conclusive. Here, then, is a general law of nature, inferred +without hesitation from a single instance; an universal proposition +from a singular one. Now mark another case, and +contrast it with this. Not all the instances which have been +observed since the beginning of the world, in support of the +general proposition that all crows are black, would be deemed +a sufficient presumption of the truth of the proposition, to +outweigh the testimony of one unexceptionable witness who +should affirm that in some region of the earth not fully explored, +he had caught and examined a crow, and had found +it to be grey. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Why is a single instance, in some cases, sufficient for a +complete induction, while in others, myriads of concurring +instances, without a single exception known or presumed, go +such a very little way towards establishing an universal proposition? +Whoever can answer this question knows more +of the philosophy of logic than the wisest of the ancients, +and has solved the problem of induction. +</p> + +</div> + +<span class="tei tei-pb" id="page325">[pg 325]</span><a name="Pg325" id="Pg325" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc61" id="toc61"></a> +<a name="pdf62" id="pdf62"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER IV. OF LAWS OF NATURE.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In the contemplation of that uniformity in the course +of nature, which is assumed in every inference from experience, +one of the first observations that present themselves +is, that the uniformity in question is not properly uniformity, +but uniformities. The general regularity results from the +co-existence of partial regularities. The course of nature in +general is constant, because the course of each of the various +phenomena that compose it is so. A certain fact invariably +occurs whenever certain circumstances are present, and does +not occur when they are absent; the like is true of another +fact; and so on. From these separate threads of connexion +between parts of the great whole which we term nature, a +general tissue of connexion unavoidably weaves itself, by +which the whole is held together. If A is always accompanied +by D, B by E, and C by F, it follows that A B is accompanied +by D E, A C by D F, B C by E F, and finally A B C +by D E F; and thus the general character of regularity is +produced, which, along with and in the midst of infinite +diversity, pervades all nature. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The first point, therefore, to be noted in regard to what +is called the uniformity of the course of nature, is, that it is +itself a complex fact, compounded of all the separate uniformities +which exist in respect to single phenomena. These +various uniformities, when ascertained by what is regarded +as a sufficient induction, we call in common parlance, Laws +of Nature. Scientifically speaking, that title is employed in +a more restricted sense, to designate the uniformities when +reduced to their most simple expression. Thus in the illustration +already employed, there were seven uniformities; all +of which, if considered sufficiently certain, would in the more +<span class="tei tei-pb" id="page326">[pg 326]</span><a name="Pg326" id="Pg326" class="tei tei-anchor"></a> +lax application of the term, be called laws of nature. But of +the seven, three alone are properly distinct and independent; +these being pre-supposed, the others follow of course: the +three first, therefore, according to the stricter acceptation, +are called laws of nature, the remainder not; because they +are in truth mere <em class="tei tei-emph"><span style="font-style: italic">cases</span></em> of the three first; virtually included +in them; said, therefore, to <em class="tei tei-emph"><span style="font-style: italic">result</span></em> from them: whoever affirms +those three has already affirmed all the rest. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To substitute real examples for symbolical ones, the following +are three uniformities, or call them laws of nature: +the law that air has weight, the law that pressure on a fluid +is propagated equally in all directions, and the law that pressure +in one direction, not opposed by equal pressure in the +contrary direction, produces motion, which does not cease +until equilibrium is restored. From these three uniformities +we should be able to predict another uniformity, namely, the +rise of the mercury in the Torricellian tube. This, in the +stricter use of the phrase, is not a law of nature. It is a result +of laws of nature. It is a <em class="tei tei-emph"><span style="font-style: italic">case</span></em> of each and every one of +the three laws: and is the only occurrence by which they +could all be fulfilled. If the mercury were not sustained in +the barometer, and sustained at such a height that the column +of mercury were equal in weight to a column of the atmosphere +of the same diameter; here would be a case, either of +the air not pressing upon the surface of the mercury with the +force which is called its weight, or of the downward pressure +on the mercury not being propagated equally in an upward +direction, or of a body pressed in one direction and not in +the direction opposite, either not moving in the direction in +which it is pressed, or stopping before it had attained equilibrium. +If we knew, therefore, the three simple laws, but had +never tried the Torricellian experiment, we might <em class="tei tei-emph"><span style="font-style: italic">deduce</span></em> its +result from those laws. The known weight of the air, combined +with the position of the apparatus, would bring the +mercury within the first of the three inductions; the first induction +would bring it within the second, and the second +within the third, in the manner which we characterized in +treating of Ratiocination. We should thus come to know +<span class="tei tei-pb" id="page327">[pg 327]</span><a name="Pg327" id="Pg327" class="tei tei-anchor"></a> +the more complex uniformity, independently of specific experience, +through our knowledge of the simpler ones from +which it results; although, for reasons which will appear +hereafter, <em class="tei tei-emph"><span style="font-style: italic">verification</span></em> by specific experience would still be +desirable, and might possibly be indispensable. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Complex uniformities which, like this, are mere cases of +simpler ones, and have, therefore, been virtually affirmed in +affirming those, may with propriety be called <em class="tei tei-emph"><span style="font-style: italic">laws</span></em>, but can +scarcely, in the strictness of scientific speech, be termed Laws +of Nature. It is the custom in science, wherever regularity +of any kind can be traced, to call the general proposition +which expresses the nature of that regularity, a <em class="tei tei-emph"><span style="font-style: italic">law</span></em>; as when, +in mathematics, we speak of the law of decrease of the successive +terms of a converging series. But the expression, +<em class="tei tei-emph"><span style="font-style: italic">law of nature</span></em>, has generally been employed with a sort of +tacit reference to the original sense of the word <em class="tei tei-emph"><span style="font-style: italic">law</span></em>, namely, +the expression of the will of a superior. When, therefore, it +appeared that any of the uniformities which were observed +in nature, would result spontaneously from certain other +uniformities, no separate act of creative will being supposed +necessary for the production of the derivative uniformities, +these have not usually been spoken of as laws of nature. +According to another mode of expression, the question, What +are the laws of nature? may be stated thus:—What are the +fewest and simplest assumptions, which being granted, the +whole existing order of nature would result? Another mode +of stating it would be thus: What are the fewest general +propositions from which all the uniformities which exist in +the universe might be deductively inferred? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Every great advance which marks an epoch in the progress +of science, has consisted in a step made towards the +solution of this problem. Even a simple colligation of inductions +already made, without any fresh extension of the +inductive inference, is already an advance in that direction. +When Kepler expressed the regularity which exists in the +observed motions of the heavenly bodies, by the three general +propositions called his laws, he, in so doing, pointed out +three simple suppositions which, instead of a much greater +<span class="tei tei-pb" id="page328">[pg 328]</span><a name="Pg328" id="Pg328" class="tei tei-anchor"></a> +number, would suffice to construct the whole scheme of the +heavenly motions, so far as it was known up to that time. A +similar and still greater step was made when these laws, +which at first did not seem to be included in any more general +truths, were discovered to be cases of the three laws of +motion, as obtaining among bodies which mutually tend towards +one another with a certain force, and have had a certain +instantaneous impulse originally impressed upon them. +After this great discovery, Kepler's three propositions, though +still called laws, would hardly, by any person accustomed to +use language with precision, be termed laws of nature: that +phrase would be reserved for the simpler laws into which +Newton is said to have resolved them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +According to this language, every well-grounded inductive +generalization is either a law of nature, or a result of +laws of nature, capable, if those laws are known, of being +predicted from them. And the problem of Inductive Logic +may be summed up in two questions: how to ascertain the +laws of nature; and how, after having ascertained them, to +follow them into their results. On the other hand, we must +not suffer ourselves to imagine that this mode of statement +amounts to a real analysis, or to anything but a mere verbal +transformation of the problem; for the expression, Laws of +Nature, <em class="tei tei-emph"><span style="font-style: italic">means</span></em> nothing but the uniformities which exist +among natural phenomena (or, in other words, the results +of induction), when reduced to their simplest expression. +It is, however, something, to have advanced so far, as to see +that the study of nature is the study of laws, not <em class="tei tei-emph"><span style="font-style: italic">a</span></em> law; of +uniformities, in the plural number: that the different natural +phenomena have their separate rules or modes of taking +place, which, though much intermixed and entangled with +one another, may, to a certain extent, be studied apart: that +(to resume our former metaphor) the regularity which exists +in nature is a web composed of distinct threads, and only to +be understood by tracing each of the threads separately; for +which purpose it is often necessary to unravel some portion +of the web, and exhibit the fibres apart. The rules of experimental +inquiry are the contrivances for unravelling the web. +</p> + +<span class="tei tei-pb" id="page329">[pg 329]</span><a name="Pg329" id="Pg329" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. In thus attempting to ascertain the general order of +nature by ascertaining the particular order of the occurrence +of each one of the phenomena of nature, the most scientific +proceeding can be no more than an improved form of that +which was primitively pursued by the human understanding, +while undirected by science. When mankind first formed +the idea of studying phenomena according to a stricter and +surer method than that which they had in the first instance +spontaneously adopted, they did not, conformably to the +well meant but impracticable precept of Descartes, set out +from the supposition that nothing had been already ascertained. +Many of the uniformities existing among phenomena +are so constant, and so open to observation, as to force themselves +upon involuntary recognition. Some facts are so +perpetually and familiarly accompanied by certain others, +that mankind learnt, as children learn, to expect the one +where they found the other, long before they knew how to +put their expectation into words by asserting, in a proposition, +the existence of a connexion between those phenomena. +No science was needed to teach that food nourishes, +that water drowns, or quenches thirst, that the sun gives +light and heat, that bodies fall to the ground. The first +scientific inquirers assumed these and the like as known +truths, and set out from them to discover others which were +unknown: nor were they wrong in so doing, subject, however, +as they afterwards began to see, to an ulterior revision +of these spontaneous generalizations themselves, when +the progress of knowledge pointed out limits to them, or +showed their truth to be contingent on some other circumstance +not originally attended to. It will appear, I think, +from the subsequent part of our inquiry, that there is no +logical fallacy in this mode of proceeding; but we may see +already that any other mode is rigorously impracticable: +since it is impossible to frame any scientific method of +induction, or test of the correctness of inductions, unless on +the hypothesis that some inductions deserving of reliance +have been already made. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us revert, for instance, to one of our former illustrations, +<span class="tei tei-pb" id="page330">[pg 330]</span><a name="Pg330" id="Pg330" class="tei tei-anchor"></a> +and consider why it is that, with exactly the same +amount of evidence, both negative and positive, we did not +reject the assertion that there are black swans, while we should +refuse credence to any testimony which asserted that there +were men wearing their heads underneath their shoulders. +The first assertion was more credible than the latter. But +why more credible? So long as neither phenomenon had +been actually witnessed, what reason was there for finding +the one harder to be believed than the other? Apparently, +because there is less constancy in the colours of animals, +than in the general structure of their internal anatomy. But +how do we know this? Doubtless, from experience. It +appears, then, that we need experience to inform us, in what +degree, and in what cases, or sorts of cases, experience is +to be relied on. Experience must be consulted in order +to learn from it under what circumstances arguments from +it will be valid. We have no ulterior test to which we +subject experience in general; but we make experience its +own test. Experience testifies, that among the uniformities +which it exhibits or seems to exhibit, some are more to be +relied on than others; and uniformity, therefore, may be +presumed, from any given number of instances, with a +greater degree of assurance, in proportion as the case belongs +to a class in which the uniformities have hitherto been +found more uniform. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This mode of correcting one generalization by means of +another, a narrower generalization by a wider, which common +sense suggests and adopts in practice, is the real type +of scientific Induction. All that art can do is but to give +accuracy and precision to this process, and adapt it to all +varieties of cases, without any essential alteration in its +principle. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are of course no means of applying such a test +as that above described, unless we already possess a general +knowledge of the prevalent character of the uniformities +existing throughout nature. The indispensable foundation, +therefore, of a scientific formula of induction, must be a +survey of the inductions to which mankind have been conducted +<span class="tei tei-pb" id="page331">[pg 331]</span><a name="Pg331" id="Pg331" class="tei tei-anchor"></a> +in unscientific practice; with the special purpose of +ascertaining what kinds of uniformities have been found +perfectly invariable, pervading all nature, and what are those +which have been found to vary with difference of time, place, +or other changeable circumstances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The necessity of such a survey is confirmed by the +consideration, that the stronger inductions are the touchstone +to which we always endeavour to bring the weaker. +If we find any means of deducing one of the less strong +inductions from stronger ones, it acquires, at once, all the +strength of those from which it is deduced; and even adds +to that strength; since the independent experience on which +the weaker induction previously rested, becomes additional +evidence of the truth of the better established law in which +it is now found to be included. We may have inferred, +from historical evidence, that the uncontrolled power of a +monarch, of an aristocracy, or of the majority, will often be +abused: but we are entitled to rely on this generalization +with much greater assurance when it is shown to be a +corollary from still better established facts; the very low +degree of elevation of character ever yet attained by the +average of mankind, and the little efficacy, for the most part, +of the modes of education hitherto practised, in maintaining +the predominance of reason and conscience over the selfish +propensities. It is at the same time obvious that even these +more general facts derive an accession of evidence from the +testimony which history bears to the effects of despotism. +The strong induction becomes still stronger when a weaker +one has been bound up with it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +On the other hand, if an induction conflicts with stronger +inductions, or with conclusions capable of being correctly +deduced from them, then, unless on re-consideration it should +appear that some of the stronger inductions have been +expressed with greater universality than their evidence +warrants, the weaker one must give way. The opinion +so long prevalent that a comet, or any other unusual appearance +in the heavenly regions, was the precursor of +<span class="tei tei-pb" id="page332">[pg 332]</span><a name="Pg332" id="Pg332" class="tei tei-anchor"></a> +calamities to mankind, or to those at least who witnessed it; +the belief in the veracity of the oracles of Delphi or Dodona; +the reliance on astrology, or on the weather-prophecies in +almanacs; were doubtless inductions supposed to be grounded +on experience:<a id="noteref_64" name="noteref_64" href="#note_64"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">64</span></span></a> and faith in such delusions seems quite +capable of holding out against a great multitude of failures, +provided it be nourished by a reasonable number of casual +coincidences between the prediction and the event. What +has really put an end to these insufficient inductions, is their +inconsistency with the stronger inductions subsequently +obtained by scientific inquiry, respecting the causes on +which terrestrial events really depend; and where those +scientific truths have not yet penetrated, the same or similar +delusions still prevail. +</p> + +<span class="tei tei-pb" id="page333">[pg 333]</span><a name="Pg333" id="Pg333" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It may be affirmed as a general principle, that all inductions, +whether strong or weak, which can be connected by a +ratiocination, are confirmatory of one another: while any +which lead deductively to consequences that are incompatible, +become mutually each other's test, showing that one or other +must be given up, or at least, more guardedly expressed. +In the case of inductions which confirm each other, the one +which becomes a conclusion from ratiocination rises to at +least the level of certainty of the weakest of those from which +it is deduced; while in general all are more or less increased +in certainty. Thus the Torricellian experiment, though a +mere case of three more general laws, not only strengthened +greatly the evidence on which those laws rested, but converted +one of them (the weight of the atmosphere) from a +doubtful generalization into one of the best-established doctrines +in the range of physical science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If, then, a survey of the uniformities which have been +ascertained to exist in nature, should point out some which, +as far as any human purpose requires certainty, may be considered +as quite certain and quite universal; then by means +of these uniformities, we may be able to raise multitudes of +other inductions to the same point in the scale. For if we +can show, with respect to any induction, that either it must +be true, or one of these certain and universal inductions must +admit of an exception; the former generalization will attain +the same certainty, and indefeasibleness within the bounds +assigned to it, which are the attributes of the latter. It will +be proved to be a law; and if not a result of other and +simpler laws, it will be a law of nature. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are such certain and universal inductions; and +it is because there are such, that a Logic of Induction is +possible. +</p> + +</div> + +<span class="tei tei-pb" id="page334">[pg 334]</span><a name="Pg334" id="Pg334" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc63" id="toc63"></a> +<a name="pdf64" id="pdf64"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER V. OF THE LAW OF UNIVERSAL CAUSATION.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The phenomena of nature exist in two distinct +relations to one another; that of simultaneity, and that of +succession. Every phenomenon is related, in an uniform +manner, to some phenomena that coexist with it, and to +some that have preceded or will follow it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of the uniformities which exist among synchronous phenomena, +the most important, on every account, are the laws +of number; and next to them those of space, or in other +words, of extension and figure. The laws of number are +common to synchronous and successive phenomena. That +two and two make four, is equally true whether the second +two follow the first two or accompany them. It is as true of +days and years as of feet and inches. The laws of extension +and figure, (in other words, the theorems of geometry, from +its lowest to its highest branches,) are, on the contrary, laws +of simultaneous phenomena only. The various parts of +space, and of the objects which are said to fill space, coexist; +and the unvarying laws which are the subject of the science +of geometry, are an expression of the mode of their coexistence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This is a class of laws, or in other words, of uniformities, +for the comprehension and proof of which it is not necessary +to suppose any lapse of time, any variety of facts or events +succeeding one another. If all the objects in the universe +were unchangeably fixed, and had remained in that condition +from eternity, the propositions of geometry would still be +true of those objects. All things which possess extension, +or in other words, which fill space, are subject to geometrical +laws. Possessing extension, they possess figure; possessing +figure, they must possess some figure in particular, and +<span class="tei tei-pb" id="page335">[pg 335]</span><a name="Pg335" id="Pg335" class="tei tei-anchor"></a> +have all the properties which geometry assigns to that figure. +If one body be a sphere and another a cylinder, of equal +height and diameter, the one will be exactly two-thirds of +the other, let the nature and quality of the material be what +it will. Again, each body, and each point of a body, must +occupy some place or position among other bodies; and the +position of two bodies relatively to each other, of whatever +nature the bodies be, may be unerringly inferred from the +position of each of them relatively to any third body. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In the laws of number, then, and in those of space, we +recognise, in the most unqualified manner, the rigorous +universality of which we are in quest. Those laws have +been in all ages the type of certainty, the standard of comparison +for all inferior degrees of evidence. Their invariability +is so perfect, that we are unable even to conceive any +exception to them; and philosophers have been led, although +(as I have endeavoured to show) erroneously, to consider +their evidence as lying not in experience, but in the original +constitution of the intellect. If, therefore, from the laws +of space and number, we were able to deduce uniformities +of any other description, this would be conclusive +evidence to us that those other uniformities possessed the +same degree of rigorous certainty. But this we cannot do. +From laws of space and number alone, nothing can be +deduced but laws of space and number. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of all truths relating to phenomena, the most valuable to +us are those which relate to the order of their succession. On +a knowledge of these is founded every reasonable anticipation +of future facts, and whatever power we possess of +influencing those facts to our advantage. Even the laws of +geometry are chiefly of practical importance to us as being +a portion of the premisses from which the order of the succession +of phenomena may be inferred. Inasmuch as the +motion of bodies, the action of forces, and the propagation +of influences of all sorts, take place in certain lines and over +definite spaces, the properties of those lines and spaces are +an important part of the laws to which those phenomena are +themselves subject. Again, motions, forces or other influences, +<span class="tei tei-pb" id="page336">[pg 336]</span><a name="Pg336" id="Pg336" class="tei tei-anchor"></a> +and times, are numerable quantities; and the properties +of number are applicable to them as to all other things. +But though the laws of number and space are important +elements in the ascertainment of uniformities of succession, +they can do nothing towards it when taken by themselves. +They can only be made instrumental to that purpose when +we combine with them additional premisses, expressive of +uniformities of succession already known. By taking, for +instance, as premisses these propositions, that bodies acted +upon by an instantaneous force move with uniform velocity +in straight lines; that bodies acted upon by a continuous +force move with accelerated velocity in straight lines; and +that bodies acted upon by two forces in different directions +move in the diagonal of a parallelogram, whose sides represent +the direction and quantity of those forces; we may by +combining these truths with propositions relating to the properties +of straight lines and of parallelograms, (as that a +triangle is half of a parallelogram of the same base and altitude,) +deduce another important uniformity of succession, +viz. that a body moving round a centre of force describes +areas proportional to the times. But unless there had been +laws of succession in our premisses, there could have been +no truths of succession in our conclusions. A similar remark +might be extended to every other class of phenomena really +peculiar; and, had it been attended to, would have prevented +many chimerical attempts at demonstrations of the indemonstrable, +and explanations which do not explain. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is not, therefore, enough for us that the laws of space, +which are only laws of simultaneous phenomena, and the +laws of number, which though true of successive phenomena +do not relate to their succession, possess the rigorous certainty +and universality of which we are in search. We must +endeavour to find some law of succession which has those +same attributes, and is therefore fit to be made the foundation +of processes for discovering, and of a test for verifying, +all other uniformities of succession. This fundamental law +must resemble the truths of geometry in their most remarkable +<span class="tei tei-pb" id="page337">[pg 337]</span><a name="Pg337" id="Pg337" class="tei tei-anchor"></a> +peculiarity, that of never being, in any instance whatever, +defeated or suspended by any change of circumstances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now among all those uniformities in the succession of +phenomena, which common observation is sufficient to bring +to light, there are very few which have any, even apparent, +pretension to this rigorous indefeasibility: and of those few, +one only has been found capable of completely sustaining +it. In that one, however, we recognise a law which is +universal also in another sense; it is coextensive with the +entire field of successive phenomena, all instances whatever +of succession being examples of it. This law is the Law of +Causation. The truth, that every fact which has a beginning +has a cause, is coextensive with human experience. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This generalization may appear to some minds not to +amount to much, since after all it asserts only this: <span class="tei tei-q">“it is a +law, that every event depends on some law.”</span> We must +not, however, conclude that the generality of the principle is +merely verbal; it will be found on inspection to be no vague +or unmeaning assertion, but a most important and really +fundamental truth. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. The notion of Cause being the root of the whole +theory of Induction, it is indispensable that this idea should, +at the very outset of our inquiry, be, with the utmost practicable +degree of precision, fixed and determined. If, indeed, +it were necessary for the purpose of inductive logic that the +strife should be quelled, which has so long raged among the +different schools of metaphysicians, respecting the origin +and analysis of our idea of causation; the promulgation, or +at least the general reception, of a true theory of induction, +might be considered desperate, for a long time to come. But +the science of the Investigation of Truth by means of +Evidence, is happily independent of many of the controversies +which perplex the science of the ultimate constitution +of the human mind, and is under no necessity of pushing the +analysis of mental phenomena to that extreme limit which +alone ought to satisfy a metaphysician. +</p> + +<span class="tei tei-pb" id="page338">[pg 338]</span><a name="Pg338" id="Pg338" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I premise, then, that when in the course of this inquiry I +speak of the cause of any phenomenon, I do not mean a +cause which is not itself a phenomenon; I make no research +into the ultimate, or ontological cause of anything. To adopt +a distinction familiar in the writings of the Scotch metaphysicians, +and especially of Reid, the causes with which I concern +myself are not <em class="tei tei-emph"><span style="font-style: italic">efficient</span></em>, but <em class="tei tei-emph"><span style="font-style: italic">physical</span></em> causes. They are +causes in that sense alone, in which one physical fact is +said to be the cause of another. Of the efficient causes of +phenomena, or whether any such causes exist at all, I am not +called upon to give an opinion. The notion of causation is +deemed, by the schools of metaphysics most in vogue at the +present moment, to imply a mysterious and most powerful +tie, such as cannot, or at least does not, exist between any +physical fact and that other physical fact on which it is +invariably consequent, and which is popularly termed its +cause: and thence is deduced the supposed necessity of +ascending higher, into the essences and inherent constitution +of things, to find the true cause, the cause which is not only +followed by, but actually <em class="tei tei-emph"><span style="font-style: italic">produces</span></em>, the effect. No such necessity +exists for the purposes of the present inquiry, nor will +any such doctrine be found in the following pages. But +neither will there be found anything incompatible with it. We +are in no way concerned in the question. The only notion +of a cause, which the theory of induction requires, is such a +notion as can be gained from experience. The Law of Causation, +the recognition of which is the main pillar of inductive +science, is but the familiar truth, that invariability of succession +is found by observation to obtain between every fact +in nature and some other fact which has preceded it; independently +of all consideration respecting the ultimate mode +of production of phenomena, and of every other question +regarding the nature of <span class="tei tei-q">“Things in themselves.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Between the phenomena, then, which exist at any +instant, and the phenomena which exist at the succeeding +instant, there is an invariable order of succession; and, +as we said in speaking of the general uniformity of the +course of nature, this web is composed of separate fibres; +<span class="tei tei-pb" id="page339">[pg 339]</span><a name="Pg339" id="Pg339" class="tei tei-anchor"></a> +this collective order is made up of particular sequences, +obtaining invariably among the separate parts. To certain +facts, certain facts always do, and, as we believe, will +continue to, succeed. The invariable antecedent is termed +the cause; the invariable consequent, the effect. And the +universality of the law of causation consists in this, that +every consequent is connected in this manner with some +particular antecedent, or set of antecedents. Let the fact +be what it may, if it has begun to exist, it was preceded by +some fact or facts, with which it is invariably connected. +For every event there exists some combination of objects or +events, some given concurrence of circumstances, positive +and negative, the occurrence of which is always followed by +that phenomenon. We may not have found out what this +concurrence of circumstances may be; but we never doubt +that there is such a one, and that it never occurs without +having the phenomenon in question as its effect or consequence. +On the universality of this truth depends the +possibility of reducing the inductive process to rules. The +undoubted assurance we have that there is a law to be found +if we only knew how to find it, will be seen presently to be +the source from which the canons of the Inductive Logic +derive their validity. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. It is seldom, if ever, between a consequent and +a single antecedent, that this invariable sequence subsists. +It is usually between a consequent and the sum of several +antecedents; the concurrence of all of them being requisite +to produce, that is, to be certain of being followed by, the +consequent. In such cases it is very common to single out +one only of the antecedents under the denomination of +Cause, calling the others merely Conditions. Thus, if a +person eats of a particular dish, and dies in consequence, +that is, would not have died if he had not eaten of it, people +would be apt to say that eating of that dish was the cause of +his death. There needs not, however, be any invariable +connexion between eating of the dish and death; but there +certainly is, among the circumstances which took place, +<span class="tei tei-pb" id="page340">[pg 340]</span><a name="Pg340" id="Pg340" class="tei tei-anchor"></a> +some combination or other on which death is invariably +consequent: as, for instance, the act of eating of the dish, +combined with a particular bodily constitution, a particular +state of present health, and perhaps even a certain state of +the atmosphere; the whole of which circumstances perhaps +constituted in this particular case the <em class="tei tei-emph"><span style="font-style: italic">conditions</span></em> of the phenomenon, +or in other words, the set of antecedents which +determined it, and but for which it would not have happened. +The real Cause, is the whole of these antecedents; +and we have, philosophically speaking, no right to give the +name of cause to one of them, exclusively of the others. +What, in the case we have supposed, disguises the incorrectness +of the expression, is this: that the various conditions, +except the single one of eating the food, were not <em class="tei tei-emph"><span style="font-style: italic">events</span></em> +(that is, instantaneous changes, or successions of instantaneous +changes) but <em class="tei tei-emph"><span style="font-style: italic">states</span></em>, possessing more or less of permanency; +and might therefore have preceded the effect by +an indefinite length of duration, for want of the event which +was requisite to complete the required concurrence of conditions: +while as soon as that event, eating the food, occurs, +no other cause is waited for, but the effect begins immediately +to take place: and hence the appearance is presented +of a more immediate and close connexion between the effect +and that one antecedent, than between the effect and the +remaining conditions. But though we may think proper +to give the name of cause to that one condition, the fulfilment +of which completes the tale, and brings about the effect +without further delay; this condition has really no closer +relation to the effect than any of the other conditions has. +The production of the consequent required that they should +all <em class="tei tei-emph"><span style="font-style: italic">exist</span></em> immediately previous, though not that they should +all <em class="tei tei-emph"><span style="font-style: italic">begin</span></em> to exist immediately previous. The statement of +the cause is incomplete, unless in some shape or other we +introduce all the conditions. A man takes mercury, goes +out of doors, and catches cold. We say, perhaps, that the +cause of his taking cold was exposure to the air. It is clear, +however, that his having taken mercury may have been a +necessary condition of his catching cold; and though it +<span class="tei tei-pb" id="page341">[pg 341]</span><a name="Pg341" id="Pg341" class="tei tei-anchor"></a> +might consist with usage to say that the cause of his attack +was exposure to the air, to be accurate we ought to say that +the cause was exposure to the air while under the effect of +mercury. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If we do not, when aiming at accuracy, enumerate all the +conditions, it is only because some of them will in most +cases be understood without being expressed, or because for +the purpose in view they may without detriment be overlooked. +For example, when we say, the cause of a man's +death was that his foot slipped in climbing a ladder, we +omit as a thing unnecessary to be stated the circumstance of +his weight, though quite as indispensable a condition of the +effect which took place. When we say that the assent of +the crown to a bill makes it law, we mean that the assent, +being never given until all the other conditions are fulfilled, +makes up the sum of the conditions, though no one now +regards it as the principal one. When the decision of a +legislative assembly has been determined by the casting vote +of the chairman, we sometimes say that this one person was +the cause of all the effects which resulted from the enactment. +Yet we do not really suppose that his single vote contributed +more to the result than that of any other person who voted +in the affirmative; but, for the purpose we have in view, +which is to insist on his share of the responsibility, the part +which any other person had in the transaction is not +material. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In all these instances the fact which was dignified by the +name of cause, was the one condition which came last into +existence. But it must not be supposed that in the employment +of the term this or any other rule is always adhered to. +Nothing can better shew the absence of any scientific ground +for the distinction between the cause of a phenomenon and +its conditions, than the capricious manner in which we select +from among the conditions that which we choose to denominate +the cause. However numerous the conditions may +be, there is hardly any of them which may not, according to +the purpose of our immediate discourse, obtain that nominal +pre-eminence. This will be seen by analysing the conditions +<span class="tei tei-pb" id="page342">[pg 342]</span><a name="Pg342" id="Pg342" class="tei tei-anchor"></a> +of some one familiar phenomenon. For example, a +stone thrown into water falls to the bottom. What are the +conditions of this event? In the first place there must be a +stone, and water, and the stone must be thrown into the +water; but, these suppositions forming part of the enunciation +of the phenomenon itself, to include them also among +the conditions would be a vicious tautology, and this class +of conditions, therefore, have never received the name of +cause from any but the schoolmen, by whom they were called +the <em class="tei tei-emph"><span style="font-style: italic">material</span></em> cause, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">causa +materialis</span></span>. The next condition is, +there must be an earth: and accordingly it is often said, that +the fall of a stone is caused by the earth; or by a power or +property of the earth, or a force exerted by the earth, all of +which are merely roundabout ways of saying that it is caused +by the earth; or, lastly, the earth's attraction; which also is +only a technical mode of saying that the earth causes the +motion, with the additional particularity that the motion is +<em class="tei tei-emph"><span style="font-style: italic">towards</span></em> the earth, which is not a character of the cause, but +of the effect. Let us now pass to another condition. It is +not enough that the earth should exist; the body must be +within that distance from it, in which the earth's attraction +preponderates over that of any other body. Accordingly we +may say, and the expression would be confessedly correct, +that the cause of the stone's falling is its being <em class="tei tei-emph"><span style="font-style: italic">within the +sphere</span></em> of the earth's attraction. We proceed to a further +condition. The stone is immersed in water: it is therefore +a condition of its reaching the ground, that its specific gravity +exceed that of the surrounding fluid, or in other words that +it surpass in weight an equal volume of water. Accordingly +any one would be acknowledged to speak correctly who +said, that the cause of the stone's going to the bottom is +its exceeding in specific gravity the fluid in which it is +immersed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus we see that each and every condition of the phenomenon +may be taken in its turn, and, with equal propriety in +common parlance, but with equal impropriety in scientific +discourse, may be spoken of as if it were the entire cause. +And in practice that particular condition is usually styled the +<span class="tei tei-pb" id="page343">[pg 343]</span><a name="Pg343" id="Pg343" class="tei tei-anchor"></a> +cause, whose share in the matter is superficially the most conspicuous +or whose requisiteness to the production of the effect +we happen to be insisting on at the moment. So great is the +force of this last consideration, that it sometimes induces us +to give the name of cause even to one of the negative conditions. +We say, for example, The army was surprised because +the sentinel was off his post. But since the sentinel's +absence was not what created the enemy, or put the soldiers +asleep, how did it cause them to be surprised? All that is +really meant is, that the event would not have happened if +he had been at his duty. His being off his post was no +producing cause, but the mere absence of a preventing cause: +it was simply equivalent to his non-existence. From nothing, +from a mere negation, no consequences can proceed. All +effects are connected, by the law of causation, with some set +of <em class="tei tei-emph"><span style="font-style: italic">positive</span></em> conditions; negative ones, it is true, being almost +always required in addition. In other words, every fact or +phenomenon which has a beginning, invariably arises when +some certain combination of positive facts exists, provided +certain other positive facts do not exist. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is, no doubt, a tendency (which our first example, +that of death from taking a particular food, sufficiently illustrates) +to associate the idea of causation with the proximate +antecedent <em class="tei tei-emph"><span style="font-style: italic">event</span></em>, rather than with any of the antecedent +<em class="tei tei-emph"><span style="font-style: italic">states</span></em>, or permanent facts, which may happen also to be conditions +of the phenomenon; the reason being that the event +not only exists, but begins to exist, immediately previous; +while the other conditions may have preexisted for an indefinite +time. And this tendency shows itself very visibly in +the different logical fictions which are resorted to, even by +men of science, to avoid the necessity of giving the name of +cause to anything which had existed for an indeterminate +length of time before the effect. Thus, rather than say that +the earth causes the fall of bodies, they ascribe it to a <em class="tei tei-emph"><span style="font-style: italic">force</span></em> +exerted by the earth, or an <em class="tei tei-emph"><span style="font-style: italic">attraction</span></em> by the earth, abstractions +which they can represent to themselves as exhausted by each +effort, and therefore constituting at each successive instant a +fresh fact, simultaneous with, or only immediately preceding, +<span class="tei tei-pb" id="page344">[pg 344]</span><a name="Pg344" id="Pg344" class="tei tei-anchor"></a> +the effect. Inasmuch as the coming of the circumstance +which completes the assemblage of conditions, is a change +or event, it thence happens that an event is always the antecedent +in closest apparent proximity to the consequent: and +this may account for the illusion which disposes us to look +upon the proximate event as standing more peculiarly in the +position of a cause than any of the antecedent states. But +even this peculiarity, of being in closer proximity to the +effect than any other of its conditions, is, as we have already +seen, far from being necessary to the common notion of a +cause; with which notion, on the contrary, any one of the +conditions, either positive or negative, is found, on occasion, +completely to accord.<a id="noteref_65" name="noteref_65" href="#note_65"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">65</span></span></a> +</p> + +<span class="tei tei-pb" id="page345">[pg 345]</span><a name="Pg345" id="Pg345" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The cause, then, philosophically speaking, is the sum +total of the conditions, positive and negative taken together; +the whole of the contingencies of every description, which +being realized, the consequent invariably follows. The +negative conditions, however, of any phenomenon, a special +enumeration of which would generally be very prolix, may +be all summed up under one head, namely, the absence of +preventing or counteracting causes. The convenience of +this mode of expression is mainly grounded on the fact, that +the effects of any cause in counteracting another cause may +in most cases be, with strict scientific exactness, regarded as +a mere extension of its own proper and separate effects. If +gravity retards the upward motion of a projectile, and deflects +<span class="tei tei-pb" id="page346">[pg 346]</span><a name="Pg346" id="Pg346" class="tei tei-anchor"></a> +it into a parabolic trajectory, it produces, in so doing, the +very same kind of effect, and even (as mathematicians know) +the same quantity of effect, as it does in its ordinary operation +of causing the fall of bodies when simply deprived of +their support. If an alkaline solution mixed with an acid +destroys its sourness, and prevents it from reddening vegetable +blues, it is because the specific effect of the alkali is to +combine with the acid, and form a compound with totally +different qualities. This property, which causes of all descriptions +possess, of preventing the effects of other causes +by virtue (for the most part) of the same laws according to +<span class="tei tei-pb" id="page347">[pg 347]</span><a name="Pg347" id="Pg347" class="tei tei-anchor"></a> +which they produce their own,<a id="noteref_66" name="noteref_66" href="#note_66"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">66</span></span></a> enables us, by establishing +the general axiom that all causes are liable to be counteracted +in their effects by one another, to dispense with the +consideration of negative conditions entirely, and limit the +notion of cause to the assemblage of the positive conditions +of the phenomenon: one negative condition invariably understood, +and the same in all instances (namely, the absence of +all counteracting causes) being sufficient, along with the sum +of the positive conditions, to make up the whole set of circumstances +on which the phenomenon is dependent. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. Among the positive conditions, as we have seen +that there are some to which, in common parlance, the term +cause is more readily and frequently awarded, so there are +others to which it is, in ordinary circumstances, refused. In +most cases of causation a distinction is commonly drawn between +something which acts, and some other thing which is +acted upon; between an <em class="tei tei-emph"><span style="font-style: italic">agent</span></em> and a <em class="tei tei-emph"><span style="font-style: italic">patient</span></em>. Both of these, +it would be universally allowed, are conditions of the phenomenon; +but it would be thought absurd to call the latter the +cause, that title being reserved for the former. The distinction, +however, vanishes on examination, or rather is found to +be only verbal; arising from an incident of mere expression, +namely, that the object said to be <em class="tei tei-emph"><span style="font-style: italic">acted upon</span></em>, and which is +<span class="tei tei-pb" id="page348">[pg 348]</span><a name="Pg348" id="Pg348" class="tei tei-anchor"></a> +considered as the scene in which the effect takes place, is +commonly included in the phrase by which the effect is +spoken of, so that if it were also reckoned as part of the +cause, the seeming incongruity would arise of its being supposed +to cause itself. In the instance which we have already +had, of falling bodies, the question was thus put:—What is +the cause which makes a stone fall? and if the answer had +been <span class="tei tei-q">“the stone itself,”</span> the expression would have been in +apparent contradiction to the meaning of the word cause. +The stone, therefore, is conceived as the patient, and the +earth (or, according to the common and most unphilosophical +practice, some occult quality of the earth) is represented as +the agent, or cause. But that there is nothing fundamental +in the distinction may be seen from this, that it is quite possible +to conceive the stone as causing its own fall, provided +the language employed be such as to save the mere verbal +incongruity. We might say that the stone moves towards +the earth by the properties of the matter composing it; and +according to this mode of presenting the phenomenon, the +stone itself might without impropriety be called the agent; +although, to save the established doctrine of the inactivity of +matter, men usually prefer here also to ascribe the effect to +an occult quality, and say that the cause is not the stone +itself, but the <em class="tei tei-emph"><span style="font-style: italic">weight</span></em> or <em class="tei tei-emph"><span style="font-style: italic">gravitation</span></em> of the stone. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Those who have contended for a radical distinction between +agent and patient, have generally conceived the agent +as that which causes some state of, or some change in the +state of, another object which is called the patient. But +a little reflection will show that the licence we assume of +speaking of phenomena as <em class="tei tei-emph"><span style="font-style: italic">states</span></em> of the various objects which +take part in them, (an artifice of which so much use has been +made by some philosophers, Brown in particular, for the apparent +explanation of phenomena,) is simply a sort of logical +fiction, useful sometimes as one among several modes of +expression, but which should never be supposed to be the +statement of a scientific truth. Even those attributes of +an object which might seem with greatest propriety to be +called states of the object itself, its sensible qualities, its +<span class="tei tei-pb" id="page349">[pg 349]</span><a name="Pg349" id="Pg349" class="tei tei-anchor"></a> +colour, hardness, shape, and the like, are, in reality, (as no +one has pointed out more clearly than Brown himself,) +phenomena of causation, in which the substance is distinctly +the agent, or producing cause, the patient being our own +organs, and those of other sentient beings. What we call +states of objects, are always sequences into which those +the objects enter, generally as antecedents or causes; and +things are never more active than in the production of those +phenomena in which they are said to be acted upon. Thus, +in the example of a stone falling to the earth, according to +the theory of gravitation the stone is as much an agent as +the earth, which not only attracts, but is itself attracted by, +the stone. In the case of a sensation produced in our organs, +the laws of our organization, and even those of our minds, are +as directly operative in determining the effect produced, as the +laws of the outward object. Though we call prussic acid the +agent of a person's death, the whole of the vital and organic +properties of the patient are as actively instrumental as the +poison, in the chain of effects which so rapidly terminates his +sentient existence. In the process of education, we may +call the teacher the agent, and the scholar only the material +acted upon; yet in truth all the facts which pre-existed in the +scholar's mind exert either co-operating or counteracting +agencies in relation to the teacher's efforts. It is not light +alone which is the agent in vision, but light coupled with the +active properties of the eye and brain, and with those of the +visible object. The distinction between agent and patient is +merely verbal: patients are always agents; in a great proportion, +indeed, of all natural phenomena, they are so to +such a degree as to react forcibly upon the causes which +acted upon them: and even when this is not the case, they +contribute, in the same manner as any of the other conditions, +to the production of the effect of which they are +vulgarly treated as the mere theatre. All the positive conditions +of a phenomenon are alike agents, alike active; and in +any expression of the cause which professes to be a complete +one, none of them can with reason be excluded, except such +as have already been implied in the words used for describing +<span class="tei tei-pb" id="page350">[pg 350]</span><a name="Pg350" id="Pg350" class="tei tei-anchor"></a> +the effect; nor by including even these would there be incurred +any but a merely verbal inconsistency. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. It now remains to advert to a distinction which is +of first-rate importance both for clearing up the notion of +cause, and for obviating a very specious objection often made +against the view which we have taken of the subject. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When we define the cause of anything (in the only sense +in which the present inquiry has any concern with causes) +to be <span class="tei tei-q">“the antecedent which it invariably follows,”</span> we do not +use this phrase as exactly synonymous with <span class="tei tei-q">“the antecedent +which it invariably <em class="tei tei-emph"><span style="font-style: italic">has</span></em> followed in our past experience.”</span> +Such a mode of conceiving causation would be liable to the +objection very plausibly urged by Dr. Reid, namely, that +according to this doctrine night must be the cause of day, +and day the cause of night; since these phenomena have +invariably succeeded one another from the beginning of the +world. But it is necessary to our using the word cause, that +we should believe not only that the antecedent always <em class="tei tei-emph"><span style="font-style: italic">has</span></em> +been followed by the consequent, but that, as long as the +present constitution of things endures, it always <em class="tei tei-emph"><span style="font-style: italic">will</span></em> be so. +And this would not be true of day and night. We do not +believe that night will be followed by day under all imaginable +circumstances, but only that it will be so <em class="tei tei-emph"><span style="font-style: italic">provided</span></em> the +sun rises above the horizon. If the sun ceased to rise, which, +for aught we know, may be perfectly compatible with the +general laws of matter, night would be, or might be, eternal. +On the other hand, if the sun is above the horizon, his light +not extinct, and no opaque body between us and him, we +believe firmly that unless a change takes place in the properties +of matter, this combination of antecedents will be +followed by the consequent, day; that if the combination of +antecedents could be indefinitely prolonged, it would be +always day; and that if the same combination had always +existed, it would always have been day, quite independently +of night as a previous condition. Therefore is it that we do +not call night the cause, nor even a condition, of day. The +existence of the sun (or some such luminous body), and there +<span class="tei tei-pb" id="page351">[pg 351]</span><a name="Pg351" id="Pg351" class="tei tei-anchor"></a> +being no opaque medium in a straight line<a id="noteref_67" name="noteref_67" href="#note_67"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">67</span></span></a> between that +body and the part of the earth where we are situated, are the +sole conditions; and the union of these, without the addition +of any superfluous circumstance, constitutes the cause. This +is what writers mean when they say that the notion of cause +involves the idea of necessity. If there be any meaning +which confessedly belongs to the term necessity, it is <em class="tei tei-emph"><span style="font-style: italic">unconditionalness</span></em>. +That which is necessary, that which <em class="tei tei-emph"><span style="font-style: italic">must</span></em> be, +means that which will be, whatever supposition we may make +in regard to all other things. The succession of day and +night evidently is not necessary in this sense. It is conditional +on the occurrence of other antecedents. That which +will be followed by a given consequent when, and only when, +some third circumstance also exists, is not the cause, even +though no case should have ever occurred in which the +phenomenon took place without it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Invariable sequence, therefore, is not synonymous with +causation, unless the sequence, besides being invariable, is +unconditional. There are sequences, as uniform in past +experience as any others whatever, which yet we do not regard +as cases of causation, but as conjunctions in some sort +accidental. Such, to an accurate thinker, is that of day and +night. The one might have existed for any length of time, +and the other not have followed the sooner for its existence; +it follows only if certain other antecedents exist; and where +those antecedents existed, it would follow in any case. No +one, probably, ever called night the cause of day; mankind +must so soon have arrived at the very obvious generalization, +that the state of general illumination which we call day would +follow the presence of a sufficiently luminous body, whether +darkness had preceded or not. +</p> + +<span class="tei tei-pb" id="page352">[pg 352]</span><a name="Pg352" id="Pg352" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We may define, therefore, the cause of a phenomenon, to +be the antecedent, or the concurrence of antecedents, on +which it is invariably and <em class="tei tei-emph"><span style="font-style: italic">unconditionally</span></em> consequent. Or if +we adopt the convenient modification of the meaning of the +word cause, which confines it to the assemblage of positive +conditions without the negative, then instead of <span class="tei tei-q">“unconditionally,”</span> +we must say, <span class="tei tei-q">“subject to no other than negative +conditions.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is evident, that from a limited number of unconditional +sequences, there will result a much greater number of conditional +ones. Certain causes being given, that is, certain antecedents +which are unconditionally followed by certain consequents; +the mere coexistence of these causes will give rise +to an unlimited number of additional uniformities. If two +causes exist together, the effects of both will exist together; +and if many causes coexist, these causes (by what we shall +term hereafter the intermixture of their laws) will give rise +to new effects, accompanying or succeeding one another in +some particular order, which order will be invariable while +the causes continue to coexist, but no longer. The motion +of the earth in a given orbit round the sun, is a series of +changes which follow one another as antecedents and consequents, +and will continue to do so while the sun's attraction, +and the force with which the earth tends to advance in a +direct line through space, continue to coexist in the same +quantities as at present. But vary either of these causes, +and the unvarying succession of motions would cease to take +place. The series of the earth's motions, therefore, though +a case of sequence invariable within the limits of human +experience, is not a case of causation. It is not unconditional. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This distinction between the relations of succession which +so far as we know are unconditional, and those relations, +whether of succession or of coexistence, which, like the +earth's motions, or the succession of day and night, depend +on the existence or on the coexistence of other antecedent +facts—corresponds to the great division which Dr. Whewell and +other writers have made of the field of science, into the investigation +<span class="tei tei-pb" id="page353">[pg 353]</span><a name="Pg353" id="Pg353" class="tei tei-anchor"></a> +of what they term the Laws of Phenomena, and +the investigation of causes; a phraseology, as I conceive, not +philosophically sustainable, inasmuch as the ascertainment +of causes, such causes as the human faculties <em class="tei tei-emph"><span style="font-style: italic">can</span></em> ascertain, +namely, causes which are themselves phenomena, is, therefore, +merely the ascertainment of other and more universal +Laws of Phenomena. Yet the distinction, however incorrectly +expressed, is not only real, but is one of the fundamental +distinctions in science; indeed it is on this alone, +as we shall hereafter find, that the possibility rests of framing +a rigorous Canon of Induction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. Does a cause always stand with its effect in the +relation of antecedent and consequent? Do we not often +say of two simultaneous facts that they are cause and effect—as +when we say that fire is the cause of warmth, the sun and +moisture the cause of vegetation, and the like? Since a +cause does not necessarily perish because its effect has been +produced, the two things do very generally coexist; and +there are some appearances, and some common expressions, +seeming to imply not only that causes may, but that they +must, be contemporaneous with their effects. <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">Cessante causâ cessat et effectus</span></span>, +has been a dogma of the schools: the necessity +for the continued existence of the cause in order to the +continuance of the effect, seems to have been once a generally +received doctrine. Kepler's numerous attempts to +account for the motions of the heavenly bodies on mechanical +principles, were rendered abortive by his always supposing +that the force which set those bodies in motion must continue +to operate in order to keep up the motion which it at first +produced. Yet there were at all times many familiar instances +of the continuance of effects, long after their causes +had ceased. A <span lang="fr" class="tei tei-foreign" xml:lang="fr"><span style="font-style: italic">coup de soleil</span></span> +gives a person a brain fever: will the fever go off as soon as he is moved out of the +sunshine? A sword is run through his body: must the sword +remain in his body in order that he may continue dead? A +ploughshare once made, remains a ploughshare, without any +continuance of heating and hammering, and even after the man +<span class="tei tei-pb" id="page354">[pg 354]</span><a name="Pg354" id="Pg354" class="tei tei-anchor"></a> +who heated and hammered it has been gathered to his fathers. +On the other hand, the pressure which forces up the mercury +in an exhausted tube must be continued in order to sustain +it in the tube. This (it may be replied) is because another +force is acting without intermission, the force of gravity, +which would restore it to its level, unless counterpoised by +a force equally constant. But again; a tight bandage causes +pain, which pain will sometimes go off as soon as the bandage +is removed. The illumination which the sun diffuses over the +earth ceases when the sun goes down. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is, therefore, a distinction to be drawn. The +conditions which are necessary for the first production of a +phenomenon, are occasionally also necessary for its continuance; +but more commonly its continuance requires no condition +except negative ones. Most things, once produced, +continue as they are, until something changes or destroys +them; but some require the permanent presence of the +agencies which produced them at first. These may, if we +please, be considered as instantaneous phenomena, requiring +to be renewed at each instant by the cause by which they +were at first generated. Accordingly, the illumination of any +given point of space has always been looked upon as an instantaneous +fact, which perishes and is perpetually renewed +as long as the necessary conditions subsist. If we adopt this +language we avoid the necessity of admitting that the continuance +of the cause is ever required to maintain the effect. +We may say, it is not required to maintain, but to reproduce +the effect, or else to counteract some force tending to destroy +it. And this may be a convenient phraseology. But it is +only a phraseology. The fact remains, that in some cases +(though these are a minority) the continuance of the conditions +which produced an effect is necessary to the continuance +of the effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As to the ulterior question, whether it is strictly necessary +that the cause, or assemblage of conditions, should precede, +by ever so short an instant, the production of the effect, (a +question raised and argued with much ingenuity by a writer +<span class="tei tei-pb" id="page355">[pg 355]</span><a name="Pg355" id="Pg355" class="tei tei-anchor"></a> +from whom I have quoted,<a id="noteref_68" name="noteref_68" href="#note_68"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">68</span></span></a>) I think the inquiry an unimportant +one. There certainly are cases in which the effect follows +without any interval perceptible by our faculties; and when +there is an interval, we cannot tell by how many intermediate +links imperceptible to us that interval may really be filled +up. But even granting that an effect may commence simultaneously +with its cause, the view I have taken of causation +is in no way practically affected. Whether the cause and its +effect be necessarily successive or not, causation is still the +law of the succession of phenomena. Everything which +begins to exist must have a cause; what does not begin to +exist does not need a cause; what causation has to account +for is the origin of phenomena, and all the successions of +phenomena must be resolvable into causation. These are +the axioms of our doctrine. If these be granted, we can +afford, though I see no necessity for doing so, to drop the +words antecedent and consequent as applied to cause and +effect. I have no objection to define a cause, the assemblage +of phenomena, which occurring, some other phenomenon invariably +commences, or has its origin. Whether the effect +coincides in point of time with, or immediately follows, the +hindmost of its conditions, is immaterial. At all events it +does not precede it; and when we are in doubt, between +two coexistent phenomena, which is cause and which effect, +we rightly deem the question solved if we can ascertain +which of them preceded the other. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. It continually happens that several different phenomena, +which are not in the slightest degree dependent or +conditional on one another, are found all to depend, as the +phrase is, on one and the same agent; in other words, one +and the same phenomenon is seen to be followed by several +sorts of effects quite heterogeneous, but which go on simultaneously +one with another; provided, of course, that all +other conditions requisite for each of them also exist. Thus, +<span class="tei tei-pb" id="page356">[pg 356]</span><a name="Pg356" id="Pg356" class="tei tei-anchor"></a> +the sun produces the celestial motions, it produces daylight, +and it produces heat. The earth causes the fall of heavy +bodies, and it also, in its capacity of an immense magnet, +causes the phenomena of the magnetic needle. A crystal of +galena causes the sensations of hardness, of weight, of cubical +form, of grey colour, and many others between which we +can trace no interdependence. The purpose to which the +phraseology of Properties and Powers is specially adapted, is +the expression of this sort of cases. When the same phenomenon +is followed (either subject or not to the presence of +other conditions) by effects of different and dissimilar orders, +it is usual to say that each different sort of effect is produced +by a different property of the cause. Thus we distinguish +the attractive or gravitative property of the earth, and its +magnetic property: the gravitative, luminiferous, and calorific +properties of the sun: the colour, shape, weight, and hardness +of a crystal. These are mere phrases, which explain +nothing, and add nothing to our knowledge of the subject; +but, considered as abstract names denoting the connexion +between the different effects produced and the object which +produces them, they are a very powerful instrument of +abridgment, and of that acceleration of the process of +thought which abridgment accomplishes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This class of considerations leads to a conception which +we shall find to be of great importance, that of a Permanent +Cause, or original natural agent. There exist in +nature a number of permanent causes, which have subsisted +ever since the human race has been in existence, +and for an indefinite and probably an enormous length of +time previous. The sun, the earth, and planets, with their +various constituents, air, water, and the other distinguishable +substances, whether simple or compound, of which nature is +made up, are such Permanent Causes. These have existed, +and the effects or consequences which they were fitted to +produce have taken place, (as often as the other conditions +of the production met,) from the very beginning of our experience. +But we can give no account of the origin of the +Permanent Causes themselves. Why these particular natural +<span class="tei tei-pb" id="page357">[pg 357]</span><a name="Pg357" id="Pg357" class="tei tei-anchor"></a> +agents existed originally and no others, or why they are +commingled in such and such proportions, and distributed +in such and such a manner throughout space, is a question +we cannot answer. More than this: we can discover nothing +regular in the distribution itself; we can reduce it to no +uniformity, to no law. There are no means by which, from +the distribution of these causes or agents in one part of +space, we could conjecture whether a similar distribution +prevails in another. The coexistence, therefore, of Primeval +Causes, ranks, to us, among merely casual concurrences: and +all those sequences or coexistences among the effects of +several such causes, which, though invariable while those +causes coexist, would, if the coexistence terminated, terminate +along with it, we do not class as cases of causation, or +laws of nature: we can only calculate on finding these +sequences or coexistences where we know by direct evidence, +that the natural agents on the properties of which +they ultimately depend, are distributed in the requisite +manner. These Permanent Causes are not always objects; +they are sometimes events, that is to say, periodical cycles +of events, that being the only mode in which events can possess +the property of permanence. Not only, for instance, is +the earth itself a permanent cause, or primitive natural +agent, but the earth's rotation is so too: it is a cause which +has produced, from the earliest period, (by the aid of other +necessary conditions,) the succession of day and night, the +ebb and flow of the sea, and many other effects, while, as we +can assign no cause (except conjecturally) for the rotation +itself, it is entitled to be ranked as a primeval cause. It is, +however, only the <em class="tei tei-emph"><span style="font-style: italic">origin</span></em> of the rotation which is mysterious +to us: once begun, its continuance is accounted for by the +first law of motion (that of the permanence of rectilinear +motion once impressed) combined with the gravitation of +the parts of the earth towards one another. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All phenomena without exception which begin to exist, +that is, all except the primeval causes, are effects either +immediate or remote of those primitive facts, or of some +combination of them. There is no Thing produced, no event +<span class="tei tei-pb" id="page358">[pg 358]</span><a name="Pg358" id="Pg358" class="tei tei-anchor"></a> +happening, in the known universe, which is not connected by +an uniformity, or invariable sequence, with some one or more +of the phenomena which preceded it; insomuch that it will +happen again as often as those phenomena occur again, and +as no other phenomenon having the character of a counteracting +cause shall coexist. These antecedent phenomena, +again, were connected in a similar manner with some that +preceded them; and so on, until we reach, as the ultimate +step attainable by us, either the properties of some one +primeval cause, or the conjunction of several. The whole of +the phenomena of nature were therefore the necessary, or in +other words, the unconditional, consequences of some former +collocation of the Permanent Causes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The state of the whole universe at any instant, we believe +to be the consequence of its state at the previous instant; +insomuch that one who knew all the agents which exist at the +present moment, their collocation in space, and their properties, +in other words the laws of their agency, could +predict the whole subsequent history of the universe, at +least unless some new volition of a power capable of controlling +the universe should supervene.<a id="noteref_69" name="noteref_69" href="#note_69"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">69</span></span></a> And if any particular +state of the entire universe could ever recur a second +time, all subsequent states would return too, and history +<span class="tei tei-pb" id="page359">[pg 359]</span><a name="Pg359" id="Pg359" class="tei tei-anchor"></a> +would, like a circulating decimal of many figures, periodically +repeat itself:— +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left">Jam redit et virgo, redeunt Saturnia regna....</div> +<div class="tei tei-l" style="text-align: left">Alter erit tum Tiphys, et altera quæ vehat Argo</div> +<div class="tei tei-l" style="text-align: left">Delectos heroas; erunt quoque altera bella,</div> +<div class="tei tei-l" style="text-align: left">Atque iterum ad Troiam magnus mittetur Achilles.</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And though things do not really revolve in this eternal round, +the whole series of events in the history of the universe, past +and future, is not the less capable, in its own nature, of +being constructed <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +by any one whom we can suppose +acquainted with the original distribution of all natural agents, +and with the whole of their properties, that is, the laws of +succession existing between them and their effects: saving +the more than human powers of combination and calculation +which would be required, even in one possessing the data, +for the actual performance of the task. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 8. Since everything which occurs is determined by +laws of causation and collocations of the original causes, +it follows that the coexistences which are observable +among effects cannot be themselves the subject of any +similar set of laws, distinct from laws of causation. Uniformities +there are, as well of coexistence as of succession, +among effects; but these must in all cases be a mere +result either of the identity or of the coexistence of their +causes: if the causes did not coexist, neither could the +effects. And these causes being also effects of prior causes, +and these of others, until we reach the primeval causes, it +follows that (except in the case of effects which can be +traced immediately or remotely to one and the same cause) +the coexistences of phenomena can in no case be universal, +<span class="tei tei-pb" id="page360">[pg 360]</span><a name="Pg360" id="Pg360" class="tei tei-anchor"></a> +unless the coexistences of the primeval causes to which +the effects are ultimately traceable, can be reduced to an +universal law: but we have seen that they cannot. There +are, accordingly, no original and independent, in other words +no unconditional, uniformities of coexistence between effects +of different causes; if they coexist, it is only because the +causes have casually coexisted. The only independent and +unconditional coexistences which are sufficiently invariable +to have any claim to the character of laws, are between different +and mutually independent effects of the same cause; +in other words, between different properties of the same +natural agent. This portion of the Laws of Nature will be +treated of in the latter part of the present Book, under the +name of the Specific Properties of Kinds. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 9. It is proper in this place to advert to a doctrine at +least as old as Dr. Reid, though propounded by him not as +certain but as probable; which has been revived during the +last few years in several quarters, and at present gives more +signs of life than any other theory of causation at variance +with that set forth in the preceding pages. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +According to the theory in question, Mind, or, to speak +more precisely, Will, is the only cause of phenomena. The +type of Causation, as well as the exclusive source from which +we derive the idea, is our own voluntary agency. Here, and +here only (it is said) we have direct evidence of causation. +We know that we can move our bodies. Respecting the +phenomena of inanimate nature, we have no other direct +knowledge than that of antecedence and sequence. But in +the case of our voluntary actions, it is affirmed that we are +conscious of power, before we have experience of results. +An act of volition, whether followed by an effect or not, is +accompanied by a consciousness of effort, <span class="tei tei-q">“of force exerted, +of power in action, which is necessarily causal, or causative.”</span> +This feeling of energy or force, inherent in an act of will, +is knowledge <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>; +assurance, prior to experience, that +we have the power of causing effects. Volition, therefore, +<span class="tei tei-pb" id="page361">[pg 361]</span><a name="Pg361" id="Pg361" class="tei tei-anchor"></a> +it is asserted, is something more than an unconditional antecedent; +it is a cause, in a different sense from that in which +physical phenomena are said to cause one another: it is an +Efficient Cause. From this the transition is easy to the +further doctrine, that Volition is the <em class="tei tei-emph"><span style="font-style: italic">sole</span></em> Efficient Cause of +all phenomena. <span class="tei tei-q">“It is inconceivable that dead force could +continue unsupported for a moment beyond its creation. +We cannot even conceive of change or phenomena without +the energy of a mind.”</span> <span class="tei tei-q">“The word <em class="tei tei-emph"><span style="font-style: italic">action</span></em> itself,”</span> says +another writer of the same school, <span class="tei tei-q">“has no real significance +except when applied to the doings of an intelligent agent. +Let any one conceive, if he can, of any power, energy, or +force, inherent in a lump of matter.”</span> Phenomena may have +the semblance of being produced by physical causes, but +they are in reality produced, say these writers, by the immediate +agency of mind. All things which do not proceed +from a human (or, I suppose, an animal) will, proceed, they +say, directly from divine will. The earth is not moved by +the combination of a centripetal and a projectile force; this +is but a mode of speaking which serves to facilitate our conceptions. +It is moved by the direct volition of an omnipotent +being, in a path coinciding with that which we deduce +from the hypothesis of these two forces. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As I have so often observed, the general question of the +existence of Efficient Causes does not fall within the limits +of our subject: but a theory which represents them as capable +of being subjects of human knowledge, and which passes +off as efficient causes what are only physical or phenomenal +causes, belongs as much to Logic as to Metaphysics, and is +a fit subject for discussion here. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To my apprehension, a volition is not an efficient, but +simply a physical, cause. Our will causes our bodily actions +in the same sense, and in no other, in which cold causes ice, +or a spark causes an explosion of gunpowder. The volition, +a state of our mind, is the antecedent; the motion of our +limbs in conformity to the volition, is the consequent. This +sequence I conceive to be not a subject of direct consciousness, +<span class="tei tei-pb" id="page362">[pg 362]</span><a name="Pg362" id="Pg362" class="tei tei-anchor"></a> +in the sense intended by the theory. The antecedent, +indeed, and the consequent, are subjects of consciousness. +But the connexion between them is a subject of experience. +I cannot admit that our consciousness of the volition contains +in itself any <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +knowledge that the muscular motion will +follow. If our nerves of motion were paralyzed, or our +muscles stiff and inflexible, and had been so all our lives, I +do not see the slightest ground for supposing that we should +ever (unless by information from other people) have known +anything of volition as a physical power, or been conscious +of any tendency in feelings of our mind to produce motions +of our body, or of other bodies. I will not undertake to say +whether we should in that case have had the physical feeling +which I suppose is meant when these writers speak of <span class="tei tei-q">“consciousness +of effort:”</span> I see no reason why we should not; +since that physical feeling is probably a state of nervous +sensation beginning and ending in the brain, without involving +the motory apparatus; but we certainly should not +have designated it by any term equivalent to effort, since +effort implies consciously aiming at an end, which we should +not only in that case have had no reason to do, but could not +even have had the idea of doing. If conscious at all of this +peculiar sensation, we should have been conscious of it, I +conceive, only as a kind of uneasiness, accompanying our +feelings of desire. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Those against whom I am contending have never produced, +and do not pretend to produce, any positive evidence<a id="noteref_70" name="noteref_70" href="#note_70"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">70</span></span></a> +<span class="tei tei-pb" id="page363">[pg 363]</span><a name="Pg363" id="Pg363" class="tei tei-anchor"></a> +that the power of our will to move our bodies would be +known to us independently of experience. What they have +to say on the subject is, that the production of physical +events by a will, seems to carry its own explanation with it, +while the action of matter upon matter seems to require +something else to explain it; and is even, according to them, +<span class="tei tei-q">“inconceivable”</span> on any other supposition than that some +will intervenes between the apparent cause and its apparent +effect. They thus rest their case on an appeal to the inherent +laws of our conceptive faculty; mistaking, as I apprehend, +for the laws of that faculty its acquired habits, grounded +on the spontaneous tendencies of its uncultured state. The +succession between the will to move a limb and the actual +motion, is one of the most direct and instantaneous of all +sequences which come under our observation, and is familiar +to every moment's experience from our earliest infancy; more +familiar than any succession of events exterior to our bodies, +and especially more so than any other case of the apparent +origination (as distinguished from the mere communication) +of motion. Now, it is the natural tendency of the mind to +be always attempting to facilitate its conception of unfamiliar +facts by assimilating them to others which are familiar. +Accordingly, our voluntary acts, being the most familiar to +us of all cases of causation, are, in the infancy and early +youth of the human race, spontaneously taken as the type +of causation in general, and all phenomena are supposed to +be directly produced by the will of some sentient being. +This original Fetichism I shall not characterize in the words +<span class="tei tei-pb" id="page364">[pg 364]</span><a name="Pg364" id="Pg364" class="tei tei-anchor"></a> +of Hume, or of any follower of Hume, but in those of a religious +metaphysician, Dr. Reid, in order more effectually to +shew the unanimity which exists on the subject among all +competent thinkers. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“When we turn our attention to external objects, and +begin to exercise our rational faculties about them, we find, +that there are some motions and changes in them which we +have power to produce, and that there are many which must +have some other cause. Either the objects must have life +and active power, as we have, or they must be moved or +changed by something that has life and active power, as +external objects are moved by us.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Our first thoughts seem to be, that the objects in which +we perceive such motion have understanding and active power +as we have. <span class="tei tei-q">‘Savages,’</span> says the Abbé Raynal, <span class="tei tei-q">‘wherever +they see motion which they cannot account for, there they +suppose a soul.’</span> All men may be considered as savages in +this respect, until they are capable of instruction, and of +using their faculties in a more perfect manner than savages +do.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“The Abbé Raynal's observation is sufficiently confirmed, +both from fact, and from the structure of all languages.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Rude nations do really believe sun, moon, and stars, +earth, sea, and air, fountains, and lakes, to have understanding +and active power. To pay homage to them, and implore +their favour, is a kind of idolatry natural to savages.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“All languages carry in their structure the marks of their +being formed when this belief prevailed. The distinction of +verbs and participles into active and passive, which is found +in all languages, must have been originally intended to distinguish +what is really active from what is merely passive; +and in all languages, we find active verbs applied to those +objects, in which, according to the Abbé Raynal's observation, +savages suppose a soul.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Thus we say the sun rises and sets, and comes to the +meridian, the moon changes, the sea ebbs and flows, the +winds blow. Languages were formed by men who believed +these objects to have life and active power in themselves. +<span class="tei tei-pb" id="page365">[pg 365]</span><a name="Pg365" id="Pg365" class="tei tei-anchor"></a> +It was therefore proper and natural to express their motions +and changes by active verbs.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“There is no surer way of tracing the sentiments of +nations before they have records, than by the structure of +their language, which, notwithstanding the changes produced +in it by time, will always retain some signatures of +the thoughts of those by whom it was invented. When we +find the same sentiments indicated in the structure of all +languages, those sentiments must have been common to the +human species when languages were invented.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“When a few, of superior intellectual abilities, find leisure +for speculation, they begin to philosophize, and soon discover, +that many of those objects which at first they believed +to be intelligent and active are really lifeless and passive. +This is a very important discovery. It elevates the mind, +emancipates from many vulgar superstitions, and invites to +further discoveries of the same kind.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“As philosophy advances, life and activity in natural +objects retires, and leaves them dead and inactive. Instead +of moving voluntarily we find them to be moved necessarily; +instead of acting, we find them to be acted upon; and Nature +appears as one great machine, where one wheel is turned by +another, that by a third; and how far this necessary succession +may reach, the philosopher does not know.”</span><a id="noteref_71" name="noteref_71" href="#note_71"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">71</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is, then, a spontaneous tendency of the intellect to +account to itself for all cases of causation by assimilating +them to the intentional acts of voluntary agents like itself. +This is the instinctive philosophy of the human mind in its +earliest stage, before it has become familiar with any other +invariable sequences than those between its own volitions +and its voluntary acts. As the notion of fixed laws of succession +among external phenomena gradually establishes +itself, the propensity to refer all phenomena to voluntary +agency slowly gives way before it. The suggestions, however, +of daily life continuing to be more powerful than those +of scientific thought, the original instinctive philosophy +<span class="tei tei-pb" id="page366">[pg 366]</span><a name="Pg366" id="Pg366" class="tei tei-anchor"></a> +maintains its ground in the mind, underneath the growths +obtained by cultivation, and keeps up a constant resistance +to their throwing their roots deep into the soil. The theory +against which I am contending derives its nourishment from +that substratum. Its strength does not lie in argument, but +in its affinity to an obstinate tendency of the infancy of the +human mind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +That this tendency, however, is not the result of an inherent +mental law, is proved by superabundant evidence. +The history of science, from its earliest dawn, shows that +mankind have not been unanimous in thinking either that +the action of matter upon matter was <em class="tei tei-emph"><span style="font-style: italic">not</span></em> conceivable, or that +the action of mind upon matter <em class="tei tei-emph"><span style="font-style: italic">was</span></em>. To some thinkers, and +some schools of thinkers, both in ancient and in modern times, +this last has appeared much more inconceivable than the +former. Sequences entirely physical and material, as soon +as they had become sufficiently familiar to the human mind, +came to be thought perfectly natural, and were regarded not +only as needing no explanation themselves, but as being +capable of affording it to others, and even of serving as the +ultimate explanation of things in general. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +One of the most recent supporters of the Volitional +theory has furnished an explanation, at once historically true +and philosophically acute, of the failure of the Greek philosophers +in physical inquiry, in which, as I conceive, he unconsciously +depicts his own state of mind. <span class="tei tei-q">“Their stumbling-block +was one as to the nature of the evidence they had +to expect for their conviction.... They had not seized the +idea that they must not expect to understand the processes +of outward causes, but only their results: and consequently, +the whole physical philosophy of the Greeks was an attempt +to identify mentally the effect with its cause, to feel after +some not only necessary but natural connexion, where they +meant by natural that which would <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> carry some presumption +to their own mind.... They wanted to see some +<em class="tei tei-emph"><span style="font-style: italic">reason</span></em> why the physical antecedent should produce this particular +consequent, and their only attempts were in directions +<span class="tei tei-pb" id="page367">[pg 367]</span><a name="Pg367" id="Pg367" class="tei tei-anchor"></a> +where they could find such reasons.”</span><a id="noteref_72" name="noteref_72" href="#note_72"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">72</span></span></a> In other words, they +were not content merely to know that one phenomenon was +always followed by another; they thought that they had not +attained the true aim of science, unless they could perceive +something in the nature of the one phenomenon, from which +it might have been known or presumed <em class="tei tei-emph"><span style="font-style: italic">previous to trial</span></em> that +it would be followed by the other: just what the writer, who +has so clearly pointed out their error, thinks that he perceives +in the nature of the phenomenon Volition. And to +complete the statement of the case, he should have added +that these early speculators not only made this their aim, +but were quite satisfied with their success in it; not only +sought for causes which should carry in their mere statement +evidence of their efficiency, but fully believed that they had +found such causes. The reviewer can see plainly that this +was an error, because <em class="tei tei-emph"><span style="font-style: italic">he</span></em> does not believe that there exist +any relations between material phenomena which can account +for their producing one another: but the very fact of the persistency +of the Greeks in this error, shows that their minds +were in a very different state: they were able to derive from +the assimilation of physical facts to other physical facts, the +kind of mental satisfaction which we connect with the word +explanation, and which the reviewer would have us think can +only be found in referring phenomena to a will. When +Thales and Hippo held that moisture was the universal cause, +and eternal element, of which all other things were but the +infinitely various sensible manifestations; when Anaximenes +predicated the same thing of air, Pythagoras of numbers, and +the like, they all thought that they had found a real explanation; +and were content to rest in this explanation as +ultimate. The ordinary sequences of the external universe +appeared to them, no less than to their critic, to be inconceivable +without the supposition of some universal agency to +connect the antecedents with the consequents; but they did +not think that Volition, exerted by minds, was the only agency +which fulfilled this requirement. Moisture, or air, or numbers, +<span class="tei tei-pb" id="page368">[pg 368]</span><a name="Pg368" id="Pg368" class="tei tei-anchor"></a> +carried to their minds a precisely similar impression of +making that intelligible which was otherwise inconceivable, +and gave the same full satisfaction to the demands of their +conceptive faculty. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It was not the Greeks alone, who <span class="tei tei-q">“wanted to see some +reason why the physical antecedent should produce this particular +consequent,”</span> some connexion <span class="tei tei-q">“which would <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> +carry some presumption to their own mind.”</span> Among modern +philosophers, Leibnitz laid it down as a self-evident principle +that all physical causes without exception must contain +in their own nature something which makes it intelligible +that they should be able to produce the effects which +they do produce. Far from admitting Volition as the only +kind of cause which carried internal evidence of its own +power, and as the real bond of connexion between physical +antecedents and their consequents, he demanded some naturally +and <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> efficient physical antecedent as the bond +of connexion between Volition itself and its effects. He distinctly +refused to admit the will of a God as a sufficient explanation +of anything except miracles; and insisted upon finding +something that would account <em class="tei tei-emph"><span style="font-style: italic">better</span></em> for the phenomena +of nature than a mere reference to divine +volition.<a id="noteref_73" name="noteref_73" href="#note_73"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">73</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Again, and conversely, the action of mind upon matter +(which, we are now told, not only needs no explanation itself, +but is the explanation of all other effects), has appeared to +some thinkers to be itself the grand inconceivability. It was +to get over this very difficulty that the Cartesians invented +the system of Occasional Causes. They could not conceive +that thoughts in a mind could produce movements in a body, +or that bodily movements could produce thoughts. They +could see no necessary connexion, no relation +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, between +a motion and a thought. And as the Cartesians, more +than any other school of philosophical speculation before or +since, made their own minds the measure of all things, and +refused, on principle, to believe that Nature had done what +they were unable to see any reason why she must do, they +<span class="tei tei-pb" id="page369">[pg 369]</span><a name="Pg369" id="Pg369" class="tei tei-anchor"></a> +affirmed it to be impossible that a material and a mental fact +could be causes one of another. They regarded them as +mere Occasions on which the real agent, God, thought fit to +exert his power as a Cause. When a man wills to move his +foot, it is not his will that moves it, but God (they said) +moves it on the occasion of his will. God, according to +this system, is the only efficient cause, not <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">quâ</span></span> mind, or <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">quâ</span></span> endowed with volition, but +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">quâ</span></span> omnipotent. This hypothesis +was, as I said, originally suggested by the supposed +inconceivability of any real mutual action between Mind and +Matter: but it was afterwards extended to the action of Matter +upon Matter, for, on a nicer examination they found this +inconceivable too, and therefore, according to their logic, +impossible. The <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">deus ex machinâ</span></span> +was ultimately called in to +produce a spark on the occasion of a flint and steel coming +together, or to break an egg on the occasion of its falling on +the ground. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All this, undoubtedly, shows that it is the disposition of +mankind in general, not to be satisfied with knowing that +one fact is invariably antecedent and another consequent, but +to look out for something which may seem to explain their +being so—something ἄνευ οὕ τὸ αἴτιον οὐκ ἂν ποτ᾽ εἴη αἴτιον. +But we also see that this demand may be completely satisfied +by an agency purely physical, provided it be much more +familiar than that which it is invoked to explain. To Thales +and Anaximenes, it appeared inconceivable that the antecedents +which we see in nature, should produce the consequents; +but perfectly natural that water, or air, should produce them. +The writers whom I oppose declare this inconceivable, but +can conceive that mind, or volition, is <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> an efficient +cause: while the Cartesians could not conceive even that, +but peremptorily declared that no mode of production of any +fact whatever was conceivable, except the direct agency of +an omnipotent being. Thus giving additional proof of what +finds new confirmation in every stage of the history of +science: that both what persons can, and what they cannot, +conceive, is very much an affair of accident, and depends +altogether on their experience, and their habits of thought; +<span class="tei tei-pb" id="page370">[pg 370]</span><a name="Pg370" id="Pg370" class="tei tei-anchor"></a> +that by cultivating the requisite associations of ideas, people +may make themselves unable to conceive any given thing; and +may make themselves able to conceive most things, however +inconceivable these may at first appear: and the same facts +in each person's mental history which determine what is or +is not conceivable to him, determine also which among the +various sequences in nature will appear to him so natural +and plausible, as to need no other proof of their existence; +to be evident by their own light, independent equally of +experience and of explanation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +By what rule is any one to decide between one theory +of this description and another? The theorists do not direct +us to any external evidence; they appeal, each to his own +subjective feelings. One says, the succession C, B, appears +to me more natural, conceivable, and credible <span class="tei tei-hi"><span style="font-style: italic">per se</span></span> than +the succession A, B; you are therefore mistaken in thinking +that B depends upon A; I am certain, though I can give no +other evidence of it, that C comes in between A and B, and +is the real and only cause of B. The other answers—the +successions C, B, and A, B, appear to me equally natural +and conceivable, or the latter more so than the former: A is +quite capable of producing B without any other intervention. +A third agrees with the first in being unable to conceive that +A can produce B, but finds the sequence D, B, still more +natural than C, B, or of nearer kin to the subject matter, and +prefers his D theory to the C theory. It is plain that there +is no universal law operating here, except the law that each +person's conceptions are governed and limited by his individual +experience and habits of thought. We are warranted +in saying of all three, what each of them already believes of +the other two, namely, that they exalt into an original law +of the human intellect and of outward nature, one particular +sequence of phenomena, which appears to them more natural +and more conceivable than other sequences, only because +it is more familiar. And from this judgment I am unable +to except the theory, that Volition is an Efficient Cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I am unwilling to leave the subject without adverting to +the additional fallacy contained in the corollary from this +<span class="tei tei-pb" id="page371">[pg 371]</span><a name="Pg371" id="Pg371" class="tei tei-anchor"></a> +theory; in the inference that because Volition is an efficient +cause therefore it is the only cause, and the direct agent in +producing even what is apparently produced by something +else. Volitions are not known to produce anything directly +except nervous action, for the will influences even the muscles +only through the nerves. Though it were granted, then, +that every phenomenon has an efficient, and not merely a +phenomenal cause, and that volition, in the case of the peculiar +phenomena which are known to be produced by it, is +that efficient cause: are we therefore to say, with these +writers, that since we know of no other efficient cause, and +ought not to assume one without evidence, there <em class="tei tei-emph"><span style="font-style: italic">is</span></em> no other, +and volition is the direct cause of all phenomena? A more +outrageous stretch of inference could hardly be made. Because +among the infinite variety of the phenomena of nature +there is one, namely, a particular mode of action of certain +nerves, which has for its cause, and as we are now supposing +for its efficient cause, a state of our mind; and because this +is the only efficient cause of which we are conscious, being +the only one of which in the nature of the case we <em class="tei tei-emph"><span style="font-style: italic">can</span></em> +be conscious, since it is the only one which exists within +ourselves; does this justify us in concluding that all other +phenomena must have the same kind of efficient cause with +that one eminently special, narrow, and peculiarly human +or animal, phenomenon? It is true there are cases in which, +with acknowledged propriety, we generalize from a single +instance to a multitude of instances. But they must be +instances which resemble the one known instance, and not +such as have no circumstance in common with it except +that of being instances. I have, for example, no direct +evidence that any creature is alive except myself: yet I +attribute, with full assurance, life and sensation to other +human beings and animals. But I do not conclude that all +other things are alive merely because I am. I ascribe to +certain other creatures a life like my own, because they +manifest it by the same sort of indications by which mine +is manifested. I find that their phenomena and mine conform +to the same laws, and it is for this reason that I believe +<span class="tei tei-pb" id="page372">[pg 372]</span><a name="Pg372" id="Pg372" class="tei tei-anchor"></a> +both to arise from a similar cause. Accordingly I do not +extend the conclusion beyond the grounds for it. Earth, +fire, mountains, trees, are remarkable agencies, but their +phenomena do not conform to the same laws as my actions +do, and I therefore do not believe earth or fire, mountains or +trees, to possess animal life. But the supporters of the +Volition Theory ask us to infer that volition causes everything, +for no reason except that it causes one particular +thing; although that one phenomenon, far from being a type +of all natural phenomena, is eminently peculiar; its laws +bearing scarcely any resemblance to those of any other phenomenon, +whether of inorganic or of organic nature.<a id="noteref_74" name="noteref_74" href="#note_74"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">74</span></span></a> +</p> + +</div> + +<span class="tei tei-pb" id="page373">[pg 373]</span><a name="Pg373" id="Pg373" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc65" id="toc65"></a> +<a name="pdf66" id="pdf66"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VI. OF THE COMPOSITION OF CAUSES.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. To complete the general notion of causation on +which the rules of experimental inquiry into the laws of +nature must be founded, one distinction still remains to be +pointed out: a distinction so radical, and of so much importance, +as to require a chapter to itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The preceding discussions have rendered us familiar with +the case in which several agents, or causes, concur as conditions +to the production of an effect; a case, in truth, almost +universal, there being very few effects to the production of +which no more than one agent contributes. Suppose, then, +that two different agents, operating jointly, are followed, +under a certain set of collateral conditions, by a given effect. +If either of these agents, instead of being joined with the +other, had operated alone, under the same set of conditions +in all other respects, some effect would probably have followed; +which would have been different from the joint effect +of the two, and more or less dissimilar to it. Now, if we +happen to know what would be the effects of each cause +when acting separately from the other, we are often able to +arrive deductively, or <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, +at a correct prediction of what +will arise from their conjunct agency. To enable us to do +this, it is only necessary that the same law which expresses +the effect of each cause acting by itself, shall also correctly +express the part due to that cause, of the effect which follows +from the two together. This condition is realised in the +extensive and important class of phenomena commonly +called mechanical, namely the phenomena of the communication +of motion (or of pressure, which is tendency to motion) +from one body to another. In this important class of cases +of causation, one cause never, properly speaking, defeats or +<span class="tei tei-pb" id="page374">[pg 374]</span><a name="Pg374" id="Pg374" class="tei tei-anchor"></a> +frustrates another; both have their full effect. If a body is +propelled in two directions by two forces, one tending to +drive it to the north, and the other to the east, it is caused +to move in a given time exactly as far in <em class="tei tei-emph"><span style="font-style: italic">both</span></em> directions as +the two forces would separately have carried it; and is left +precisely where it would have arrived if it had been acted +upon first by one of the two forces, and afterwards by the +other. This law of nature is called, in dynamics, the principle +of the Composition of Forces: and in imitation of that +well-chosen expression, I shall give the name of the Composition +of Causes to the principle which is exemplified in +all cases in which the joint effect of several causes is identical +with the sum of their separate effects. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This principle, however, by no means prevails in all +departments of the field of nature. The chemical combination +of two substances produces, as is well known, a third +substance with properties entirely different from those of +either of the two substances separately, or both of them +taken together. Not a trace of the properties of hydrogen +or of oxygen is observable in those of their compound, +water. The taste of sugar of lead is not the sum of the +tastes of its component elements, acetic acid and lead or its +oxide; nor is the colour of green vitriol a mixture of the +colours of sulphuric acid and copper. This explains why +mechanics is a deductive or demonstrative science, and +chemistry not. In the one, we can compute the effects of +all combinations of causes, whether real or hypothetical, +from the laws which we know to govern those causes when +acting separately; because they continue to observe the +same laws when in combination which they observed when +separate: whatever would have happened in consequence of +each cause taken by itself, happens when they are together, +and we have only to cast up the results. Not so in the +phenomena which are the peculiar subject of the science of +chemistry. There, most of the uniformities to which the +causes conformed when separate, cease altogether when they +are conjoined; and we are not, at least in the present state +of our knowledge, able to foresee what result will follow +<span class="tei tei-pb" id="page375">[pg 375]</span><a name="Pg375" id="Pg375" class="tei tei-anchor"></a> +from any new combination, until we have tried the specific +experiment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If this be true of chemical combinations, it is still more +true of those far more complex combinations of elements +which constitute organised bodies; and in which those extraordinary +new uniformities arise, which are called the laws +of life. All organised bodies are composed of parts similar +to those composing inorganic nature, and which have even +themselves existed in an inorganic state; but the phenomena +of life, which result from the juxtaposition of those parts in +a certain manner, bear no analogy to any of the effects which +would be produced by the action of the component substances +considered as mere physical agents. To whatever +degree we might imagine our knowledge of the properties of +the several ingredients of a living body to be extended and +perfected, it is certain that no mere summing up of the +separate actions of those elements will ever amount to the +action of the living body itself. The tongue, for instance, +is, like all other parts of the animal frame, composed of +gelatine, fibrin, and other products of the chemistry of digestion, +but from no knowledge of the properties of those substances +could we ever predict that it could taste, unless +gelatine or fibrin could themselves taste; for no elementary +fact can be in the conclusion, which was not first in the +premisses. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are thus two different modes of the conjunct action +of causes; from which arise two modes of conflict, or mutual +interference, between laws of nature. Suppose, at a given +point of time and space, two or more causes, which, if they +acted separately, would produce effects contrary, or at least +conflicting with each other; one of them tending to undo, +wholly or partially, what the other tends to do. Thus, the +expansive force of the gases generated by the ignition of +gunpowder tends to project a bullet towards the sky, while +its gravity tends to make it fall to the ground. A stream +running into a reservoir at one end tends to fill it higher and +higher, while a drain at the other extremity tends to empty +it. Now, in such cases as these, even if the two causes which +<span class="tei tei-pb" id="page376">[pg 376]</span><a name="Pg376" id="Pg376" class="tei tei-anchor"></a> +are in joint action exactly annul one another, still the laws +of both are fulfilled; the effect is the same as if the drain +had been open for half an hour first,<a id="noteref_75" name="noteref_75" href="#note_75"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">75</span></span></a> and the stream had +flowed in for as long afterwards. Each agent produced the +same amount of effect as if it had acted separately, though +the contrary effect which was taking place during the same +time obliterated it as fast as it was produced. Here then, +are two causes, producing by their joint operation an effect +which at first seems quite dissimilar to those which they +produce separately, but which on examination proves to +be really the sum of those separate effects. It will be +noticed that we here enlarge the idea of the sum of two +effects, so as to include what is commonly called their difference, +but which is in reality the result of the addition of +opposites; a conception to which mankind are indebted +for that admirable extension of the algebraical calculus, +which has so vastly increased its powers as an instrument +of discovery, by introducing into its reasonings (with the +sign of subtraction prefixed, and under the name of Negative +Quantities) every description whatever of positive phenomena, +provided they are of such a quality in reference to those previously +introduced, that to add the one is equivalent to subtracting +an equal quantity of the other. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is, then, one mode of the mutual interference of +laws of nature, in which, even when the concurrent causes +annihilate each other's effects, each exerts its full efficacy +according to its own law, its law as a separate agent. But +in the other description of cases, the agencies which are +brought together cease entirely, and a totally different set of +phenomena arise: as in the experiment of two liquids +which, when mixed in certain proportions, instantly become +a solid mass, instead of merely a larger amount of liquid. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. This difference between the case in which the +<span class="tei tei-pb" id="page377">[pg 377]</span><a name="Pg377" id="Pg377" class="tei tei-anchor"></a> +joint effect of causes is the sum of their separate effects, +and the case in which it is heterogeneous to them; between +laws which work together without alteration, and laws which, +when called upon to work together, cease and give place to +others; is one of the fundamental distinctions in nature. +The former case, that of the Composition of Causes, is the +general one; the other is always special and exceptional. +There are no objects which do not, as to some of their phenomena, +obey the principle of the Composition of Causes; +none that have not some laws which are rigidly fulfilled in +every combination into which the objects enter. The weight +of a body, for instance, is a property which it retains in all +the combinations in which it is placed. The weight of a +chemical compound, or of an organized body, is equal to +the sum of the weights of the elements which compose it. +The weight either of the elements or of the compound will +vary, if they be carried farther from their centre of attraction, +or brought nearer to it; but whatever affects the one affects +the other. They always remain precisely equal. So again, +the component parts of a vegetable or animal substance do +not lose their mechanical and chemical properties as separate +agents, when, by a peculiar mode of juxta-position, they, as +an aggregate whole, acquire physiological or vital properties +in addition. Those bodies continue, as before, to obey +mechanical and chemical laws, in so far as the operation of +those laws is not counteracted by the new laws which govern +them as organised beings. When, in short, a concurrence +of causes takes place which calls into action new laws +bearing no analogy to any that we can trace in the separate +operation of the causes, the new laws, while they supersede +one portion of the previous laws, may co-exist with another +portion, and may even compound the effect of those previous +laws with their own. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Again, laws which were themselves generated in the +second mode, may generate others in the first. Though +there be laws which, like those of chemistry and physiology, +owe their existence to a breach of the principle of Composition +of Causes, it does not follow that these peculiar, or as +<span class="tei tei-pb" id="page378">[pg 378]</span><a name="Pg378" id="Pg378" class="tei tei-anchor"></a> +they might be termed, <span class="tei tei-hi"><span style="font-style: italic">heteropathic</span></span> laws, are not capable of +composition with one another. The causes which by one +combination have had their laws altered, may carry their +new laws with them unaltered into their ulterior combinations. +And hence there is no reason to despair of ultimately raising +chemistry and physiology to the condition of deductive +sciences; for though it is impossible to deduce all chemical +and physiological truths from the laws or properties of +simple substances or elementary agents, they may possibly +be deducible from laws which commence when these elementary +agents are brought together into some moderate number +of not very complex combinations. The Laws of Life will +never be deducible from the mere laws of the ingredients, +but the prodigiously complex Facts of Life may all be deducible +from comparatively simple laws of life; which laws, +(depending indeed on combinations, but on comparatively +simple combinations, of antecedents) may, in more complex +circumstances, be strictly compounded with one another, +and with the physical and chemical laws of the ingredients. +The details of the vital phenomena even now afford innumerable +exemplifications of the Composition of Causes; and +in proportion as these phenomena are more accurately +studied, there appears more reason to believe that the same +laws which operate in the simpler combinations of circumstances +do, in fact, continue to be observed in the more +complex. This will be found equally true in the phenomena +of mind; and even in social and political phenomena, +the result of the laws of mind. It is in the case of chemical +phenomena that the least progress has yet been made in +bringing the special laws under general ones from which +they may be deduced; but there are even in chemistry many +circumstances to encourage the hope that such general laws +will hereafter be discovered. The different actions of a +chemical compound will never, undoubtedly, be found to be +the sums of the actions of its separate elements; but there +may exist, between the properties of the compound and +those of its elements, some constant relation, which, if discoverable +by a sufficient induction, would enable us to foresee +<span class="tei tei-pb" id="page379">[pg 379]</span><a name="Pg379" id="Pg379" class="tei tei-anchor"></a> +the sort of compound which will result from a new combination +before we have actually tried it, and to judge of what +sort of elements some new substance is compounded before +we have analysed it. The law of definite proportions, +first discovered in its full generality by Dalton, is a complete +solution of this problem in one, though but a +secondary aspect, that of quantity: and in respect to +quality, we have already some partial generalizations sufficient +to indicate the possibility of ultimately proceeding +farther. We can predicate some common properties of the +kind of compounds which result from the combination, in +each of the small number of possible proportions, of any +acid whatever with any base. We have also the curious +law, discovered by Berthollet, that two soluble salts mutually +decompose one another whenever the new combinations +which result produce an insoluble compound, or one +less soluble than the two former. Another uniformity is +that called the law of isomorphism; the identity of the +crystalline forms of substances which possess in common +certain peculiarities of chemical composition. Thus it +appears that even heteropathic laws, such laws of combined +agency as are not compounded of the laws of the +separate agencies, are yet, at least in some cases, derived +from them according to a fixed principle. There may, +therefore, be laws of the generation of laws from others +dissimilar to them; and in chemistry, these undiscovered +laws of the dependence of the properties of the compound +on the properties of its elements, may, together with the +laws of the elements themselves, furnish the premisses by +which the science is perhaps destined one day to be rendered +deductive. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It would seem, therefore, that there is no class of phenomena +in which the Composition of Causes does not obtain: +that as a general rule, causes in combination produce exactly +the same effects as when acting singly: but that this rule, +though general, is not universal: that in some instances, +at some particular points in the transition from separate +to united action, the laws change, and an entirely new +<span class="tei tei-pb" id="page380">[pg 380]</span><a name="Pg380" id="Pg380" class="tei tei-anchor"></a> +set of effects are either added to, or take the place of, +those which arise from the separate agency of the same +causes: the laws of these new effects being again susceptible +of composition, to an indefinite extent, like the laws which +they superseded. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. That effects are proportional to their causes is laid +down by some writers as an axiom in the theory of causation; +and great use is sometimes made of this principle in +reasonings respecting the laws of nature, though it is +incumbered with many difficulties and apparent exceptions, +which much ingenuity has been expended in showing not +to be real ones. This proposition, in so far as it is true, +enters as a particular case into the general principle of the +Composition of Causes: the causes compounded being, in +this instance, homogeneous; in which case, if in any, their +joint effect might be expected to be identical with the sum +of their separate effects. If a force equal to one hundred +weight will raise a certain body along an inclined plane, +a force equal to two hundred weight will raise two bodies +exactly similar, and thus the effect is proportional to the +cause. But does not a force equal to two hundred weight, +actually contain in itself two forces each equal to one +hundred weight, which, if employed apart, would separately +raise the two bodies in question? The fact, therefore, +that when exerted jointly they raise both bodies at once, +results from the Composition of Causes, and is a mere +instance of the general fact that mechanical forces are subject +to the law of Composition. And so in every other case +which can be supposed. For the doctrine of the proportionality +of effects to their causes cannot of course be applicable +to cases in which the augmentation of the cause alters the +<em class="tei tei-emph"><span style="font-style: italic">kind</span></em> of effect; that is, in which the surplus quantity super-added +to the cause does not become compounded with it, +but the two together generate an altogether new phenomenon. +Suppose that the application of a certain quantity +of heat to a body merely increases its bulk, that a double +quantity melts it, and a triple quantity decomposes it: these +<span class="tei tei-pb" id="page381">[pg 381]</span><a name="Pg381" id="Pg381" class="tei tei-anchor"></a> +three effects being heterogeneous, no ratio, whether corresponding +or not to that of the quantities of heat applied, can +be established between them. Thus the supposed axiom of +the proportionality of effects to their causes fails at the precise +point where the principle of the Composition of Causes +also fails; viz. where the concurrence of causes is such as +to determine a change in the properties of the body generally, +and render it subject to new laws, more or less +dissimilar to those to which it conformed in its previous +state. The recognition, therefore, of any such law of +proportionality, is superseded by the more comprehensive +principle, in which as much of it as is true is implicitly +asserted. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The general remarks on causation, which seemed necessary +as an introduction to the theory of the inductive process, +may here terminate. That process is essentially an +inquiry into cases of causation. All the uniformities which +exist in the succession of phenomena, and most of the +uniformities in their coexistence, are either, as we have seen, +themselves laws of causation, or consequences resulting +from, and corollaries capable of being deduced from, such +laws. If we could determine what causes are correctly +assigned to what effects, and what effects to what causes, we +should be virtually acquainted with the whole course of +nature. All those uniformities which are mere results of +causation, might then be explained and accounted for; and +every individual fact or event might be predicted, provided +we had the requisite data, that is, the requisite knowledge +of the circumstances which, in the particular instance, preceded +it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To ascertain, therefore, what are the laws of causation +which exist in nature; to determine the effects of every +cause, and the causes of all effects,—is the main business of +Induction; and to point out how this is done is the chief +object of Inductive Logic. +</p> + +</div> + +<span class="tei tei-pb" id="page382">[pg 382]</span><a name="Pg382" id="Pg382" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc67" id="toc67"></a> +<a name="pdf68" id="pdf68"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VII. OF OBSERVATION AND EXPERIMENT.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. It results from the preceding exposition, that the +process of ascertaining what consequents, in nature, are invariably +connected with what antecedents, or in other words +what phenomena are related to each other as causes and +effects, is in some sort a process of analysis. That every +fact which begins to exist has a cause, and that this cause +must be found somewhere among the facts which immediately +preceded the occurrence, may be taken for certain. +The whole of the present facts are the infallible result of all +past facts, and more immediately of all the facts which +existed at the moment previous. Here, then, is a great +sequence, which we know to be uniform. If the whole prior +state of the entire universe could again recur, it would again +be followed by the present state. The question is, how to +resolve this complex uniformity into the simpler uniformities +which compose it, and assign to each portion of the vast +antecedent the portion of the consequent which is attendant +on it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This operation, which we have called analytical, inasmuch +as it is the resolution of a complex whole into the +component elements, is more than a merely mental analysis. +No mere contemplation of the phenomena, and partition of +them by the intellect alone, will of itself accomplish the end +we have now in view. Nevertheless, such a mental partition +is an indispensable first step. The order of nature, as perceived +at a first glance, presents at every instant a chaos +followed by another chaos. We must decompose each chaos +into single facts. We must learn to see in the chaotic antecedent +a multitude of distinct antecedents, in the chaotic +consequent a multitude of distinct consequents. This, supposing +<span class="tei tei-pb" id="page383">[pg 383]</span><a name="Pg383" id="Pg383" class="tei tei-anchor"></a> +it done, will not of itself tell us on which of the +antecedents each consequent is invariably attendant. To +determine that point, we must endeavour to effect a separation +of the facts from one another, not in our minds only, +but in nature. The mental analysis, however, must take +place first. And every one knows that in the mode of performing +it, one intellect differs immensely from another. +It is the essence of the act of observing; for the observer is +not he who merely sees the thing which is before his eyes, +but he who sees what parts that thing is composed of. To +do this well is a rare talent. One person, from inattention, +or attending only in the wrong place, overlooks half of what +he sees; another sets down much more than he sees, confounding +it with what he imagines, or with what he infers; +another takes note of the <em class="tei tei-emph"><span style="font-style: italic">kind</span></em> of all the circumstances, but +being inexpert in estimating their degree, leaves the quantity +of each vague and uncertain; another sees indeed the whole, +but makes such an awkward division of it into parts, +throwing things into one mass which require to be separated, +and separating others which might more conveniently be +considered as one, that the result is much the same, sometimes +even worse, than if no analysis had been attempted at +all. It would be possible to point out what qualities of +mind, and modes of mental culture, fit a person for being a +good observer; that, however, is a question not of Logic, +but of the theory of Education, in the most enlarged sense +of the term. There is not properly an Art of Observing. +There may be rules for observing. But these, like rules for +inventing, are properly instructions for the preparation of +one's own mind; for putting it into the state in which it will +be most fitted to observe, or most likely to invent. They +are, therefore, essentially rules of self-education, which is a +different thing from Logic. They do not teach how to do +the thing, but how to make ourselves capable of doing it. +They are an art of strengthening the limbs, not an art of +using them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The extent and minuteness of observation which may be +requisite, and the degree of decomposition to which it may be +<span class="tei tei-pb" id="page384">[pg 384]</span><a name="Pg384" id="Pg384" class="tei tei-anchor"></a> +necessary to carry the mental analysis, depend on the particular +purpose in view. To ascertain the state of the whole +universe at any particular moment is impossible, but would +also be useless. In making chemical experiments, we do +not think it necessary to note the position of the planets; +because experience has shown, as a very superficial experience +is sufficient to show, that in such cases that circumstance +is not material to the result: and, accordingly, in the +ages when men believed in the occult influences of the heavenly +bodies, it might have been unphilosophical to omit +ascertaining the precise condition of those bodies at the +moment of the experiment. As to the degree of minuteness +of the mental subdivision; if we were obliged to break +down what we observe into its very simplest elements, that +is, literally into single facts, it would be difficult to say +where we should find them: we can hardly ever affirm that +our divisions of any kind have reached the ultimate unit. +But this, too, is fortunately unnecessary. The only object +of the mental separation is to suggest the requisite physical +separation, so that we may either accomplish it ourselves, or +seek for it in nature; and we have done enough when we +have carried the subdivision as far as the point at which +we are able to see what observations or experiments we +require. It is only essential, at whatever point our mental +decomposition of facts may for the present have stopped, +that we should hold ourselves ready and able to carry it +farther as occasion requires, and should not allow the freedom +of our discriminating faculty to be imprisoned by the +swathes and bands of ordinary classification; as was the +case with all early speculative inquirers, not excepting the +Greeks, to whom it hardly ever occurred that what was called +by one abstract name might, in reality, be several phenomena, +or that there was a possibility of decomposing the +facts of the universe into any elements but those which ordinary +language already recognised. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. The different antecedents and consequents being, +then, supposed to be, so far as the case requires, ascertained +<span class="tei tei-pb" id="page385">[pg 385]</span><a name="Pg385" id="Pg385" class="tei tei-anchor"></a> +and discriminated from one another; we are to inquire which +is connected with which. In every instance which comes +under our observation, there are many antecedents and many +consequents. If those antecedents could not be severed +from one another except in thought, or if those consequents +never were found apart, it would be impossible for us to distinguish +(<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à posteriori</span></span> +at least) the real laws, or to assign to +any cause its effect, or to any effect its cause. To do so, we +must be able to meet with some of the antecedents apart +from the rest, and observe what follows from them; or some +of the consequents, and observe by what they are preceded. +We must, in short, follow the Baconian rule of <em class="tei tei-emph"><span style="font-style: italic">varying the +circumstances</span></em>. This is, indeed, only the first rule of physical +inquiry, and not, as some have thought, the sole rule; but it +is the foundation of all the rest. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For the purpose of varying the circumstances, we may +have recourse (according to a distinction commonly made) +either to observation or to experiment; we may either <em class="tei tei-emph"><span style="font-style: italic">find</span></em> +an instance in nature, suited to our purposes, or, by an artificial +arrangement of circumstances, <em class="tei tei-emph"><span style="font-style: italic">make</span></em> one. The value of +the instance depends on what it is in itself, not on the mode +in which it is obtained: its employment for the purposes of +induction depends on the same principles in the one case +and in the other; as the uses of money are the same whether +it is inherited or acquired. There is, in short, no difference +in kind, no real logical distinction, between the two processes +of investigation. There are, however, practical distinctions +to which it is of considerable importance to advert. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The first and most obvious distinction between Observation +and Experiment is, that the latter is an immense +extension of the former. It not only enables us to produce +a much greater number of variations in the circumstances +than nature spontaneously offers, but also, in thousands of +cases, to produce the precise <em class="tei tei-emph"><span style="font-style: italic">sort</span></em> of variation which we are +in want of for discovering the law of the phenomenon; a service +which nature, being constructed on a quite different +scheme from that of facilitating our studies, is seldom so +<span class="tei tei-pb" id="page386">[pg 386]</span><a name="Pg386" id="Pg386" class="tei tei-anchor"></a> +friendly as to bestow upon us. For example, in order to ascertain +what principle in the atmosphere enables it to sustain +life, the variation we require is that a living animal should +be immersed in each component element of the atmosphere +separately. But nature does not supply either oxygen or +azote in a separate state. We are indebted to artificial experiment +for our knowledge that it is the former, and not the +latter, which supports respiration; and for our knowledge +of the very existence of the two ingredients. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus far the advantage of experimentation over simple +observation is universally recognised: all are aware that it +enables us to obtain innumerable combinations of circumstances +which are not to be found in nature, and so add to +nature's experiments a multitude of experiments of our own. +But there is another superiority (or, as Bacon would have +expressed it, another prerogative) of instances artificially obtained +over spontaneous instances,—of our own experiments +over even the same experiments when made by nature,—which +is not of less importance, and which is far from being +felt and acknowledged in the same degree. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When we can produce a phenomenon artificially, we can +take it, as it were, home with us, and observe it in the midst +of circumstances with which in all other respects we are +accurately acquainted. If we desire to know what are the +effects of the cause A, and are able to produce A by means +at our disposal, we can generally determine at our own +discretion, so far as is compatible with the nature of the +phenomenon A, the whole of the circumstances which shall +be present along with it: and thus, knowing exactly the +simultaneous state of everything else which is within the +reach of A's influence, we have only to observe what alteration +is made in that state by the presence of A. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For example, by the electric machine we can produce +in the midst of known circumstances, the phenomena which +nature exhibits on a grander scale in the form of lightning +and thunder. Now let any one consider what amount +of knowledge of the effects and laws of electric agency mankind +could have obtained from the mere observation of thunder-storms, +<span class="tei tei-pb" id="page387">[pg 387]</span><a name="Pg387" id="Pg387" class="tei tei-anchor"></a> +and compare it with that which they have gained, +and may expect to gain, from electrical and galvanic experiments. +This example is the more striking, now that we have +reason to believe that electric action is of all natural phenomena +(except heat) the most pervading and universal, which, +therefore, it might antecedently have been supposed could +stand least in need of artificial means of production to enable +it to be studied; while the fact is so much the contrary, that +without the electric machine, the voltaic battery, and the +Leyden jar, we probably should never have suspected the +existence of electricity as one of the great agents in nature; +the few electric phenomena we should have known of would +have continued to be regarded either as supernatural, or as +a sort of anomalies and eccentricities in the order of the +universe. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When we have succeeded in insulating the phenomenon +which is the subject of inquiry, by placing it among known +circumstances, we may produce further variations of circumstances +to any extent, and of such kinds as we think best +calculated to bring the laws of the phenomenon into a clear +light. By introducing one well defined circumstance after +another into the experiment, we obtain assurance of the manner +in which the phenomenon behaves under an indefinite +variety of possible circumstances. Thus, chemists, after +having obtained some newly-discovered substance in a pure +state, (that is, having made sure that there is nothing present +which can interfere with and modify its agency,) introduce +various other substances, one by one, to ascertain whether it +will combine with them, or decompose them, and with what +result; and also apply heat, or electricity, or pressure, to +discover what will happen to the substance under each of +these circumstances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But if, on the other hand, it is out of our power to produce +the phenomenon, and we have to seek for instances in +which nature produces it, the task before us is very different. +Instead of being able to choose what the concomitant circumstances +shall be, we now have to discover what they are; +which, when we go beyond the simplest and most accessible +<span class="tei tei-pb" id="page388">[pg 388]</span><a name="Pg388" id="Pg388" class="tei tei-anchor"></a> +cases, it is next to impossible to do, with any precision and +completeness. Let us take, as an exemplification of a phenomenon +which we have no means of fabricating artificially, +a human mind. Nature produces many; but the consequence +of our not being able to produce it by art is, that in +every instance in which we see a human mind developing +itself, or acting upon other things, we see it surrounded and +obscured by an indefinite multitude of unascertainable circumstances, +rendering the use of the common experimental +methods almost delusive. We may conceive to what extent +this is true, if we consider, among other things, that whenever +nature produces a human mind, she produces, in close +connexion with it, also a body; that is, a vast complication +of physical facts, in no two cases perhaps exactly similar, +and most of which (except the mere structure, which we can +examine in a sort of coarse way after it has ceased to act), +are radically out of the reach of our means of exploration. +If, instead of a human mind, we suppose the subject of investigation +to be a human society or State, all the same difficulties +recur in a greatly augmented degree. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We have thus already come within sight of a conclusion, +which the progress of the inquiry will, I think, bring before +us with the clearest evidence: namely, that in the sciences +which deal with phenomena in which artificial experiments +are impossible (as in the case of astronomy,) or in which +they have a very limited range (as in physiology, mental +philosophy, and the social science,) induction from direct +experience is practised at a disadvantage generally equivalent +to impracticability: from which it follows that the methods +of those sciences, in order to accomplish anything worthy of +attainment, must be to a great extent, if not principally, deductive. +This is already known to be the case with the first +of the sciences we have mentioned, astronomy; that it is not +generally recognised as true of the others, is probably one of +the reasons why they are still in their infancy. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. If what is called pure observation is at so great a +disadvantage, compared with artificial experimentation, in one +<span class="tei tei-pb" id="page389">[pg 389]</span><a name="Pg389" id="Pg389" class="tei tei-anchor"></a> +department of the direct exploration of phenomena, there is +another branch in which the advantage is all on the side of +the former. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Inductive inquiry having for its object to ascertain what +causes are connected with what effects, we may begin this +search at either end of the road which leads from the one point +to the other: we may either inquire into the effects of a +given cause, or into the causes of a given effect. The fact +that light blackens chloride of silver might have been discovered +either by experiments on light, trying what effect it +would produce on various substances, or by observing that +portions of the chloride had repeatedly become black, and +inquiring into the circumstances. The effect of the urali +poison might have become known either by administering +it to animals, or by examining how it happened that the +wounds which the Indians of Guiana inflict with their arrows +prove so uniformly mortal. Now it is manifest from the mere +statement of the examples, without any theoretical discussion, +that artificial experimentation is applicable only to the former +of these modes of investigation. We can take a cause, +and try what it will produce: but we cannot take an effect, +and try what it will be produced by. We can only watch +till we see it produced, or are enabled to produce it by accident. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This would be of little importance, if it always depended +on our choice from which of the two ends of the sequence +we would undertake our inquiries. But we have seldom any +option. As we can only travel from the known to the unknown, +we are obliged to commence at whichever end we +are best acquainted with. If the agent is more familiar to +us than its effects, we watch for, or contrive, instances of the +agent, under such varieties of circumstances as are open to +us, and observe the result. If, on the contrary, the conditions +on which a phenomenon depends are obscure, but the +phenomenon itself familiar, we must commence our inquiry +from the effect. If we are struck with the fact that chloride +of silver has been blackened, and have no suspicion of the +cause, we have no resource but to compare instances in which +<span class="tei tei-pb" id="page390">[pg 390]</span><a name="Pg390" id="Pg390" class="tei tei-anchor"></a> +the fact has chanced to occur, until by that comparison we +discover that in all those instances the substance had been +exposed to light. If we knew nothing of the Indian arrows +but their fatal effect, accident alone could turn our attention +to experiments on the urali: in the regular course of investigation, +we could only inquire, or try to observe, what had +been done to the arrows in particular instances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Wherever, having nothing to guide us to the cause, we +are obliged to set out from the effect, and to apply the rule +of varying the circumstances to the consequents, not the +antecedents, we are necessarily destitute of the resource of +artificial experimentation. We cannot, at our choice, obtain +consequents, as we can antecedents, under any set of circumstances +compatible with their nature. There are no +means of producing effects but through their causes, and by +the supposition the causes of the effect in question are not +known to us. We have therefore no expedient but to study +it where it offers itself spontaneously. If nature happens to +present us with instances sufficiently varied in their circumstances, +and if we are able to discover, either among the +proximate antecedents or among some other order of antecedents, +something which is always found when the effect is +found, however various the circumstances, and never found +when it is not; we may discover, by mere observation without +experiment, a real uniformity in nature. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But though this is certainly the most favourable case +for sciences of pure observation, as contrasted with those in +which artificial experiments are possible, there is in reality +no case which more strikingly illustrates the inherent imperfection +of direct induction when not founded on experimentation. +Suppose that, by a comparison of cases of the +effect, we have found an antecedent which appears to be, and +perhaps is, invariably connected with it: we have not yet +proved that antecedent to be the cause, until we have reversed +the process, and produced the effect by means of that +antecedent. If we can produce the antecedent artificially, +and if, when we do so, the effect follows, the induction is +<span class="tei tei-pb" id="page391">[pg 391]</span><a name="Pg391" id="Pg391" class="tei tei-anchor"></a> +complete; that antecedent is the cause of that consequent.<a id="noteref_76" name="noteref_76" href="#note_76"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">76</span></span></a> +But we have then added the evidence of experiment to that +of simple observation. Until we had done so, we had only +proved <em class="tei tei-emph"><span style="font-style: italic">invariable</span></em> antecedence, but not <em class="tei tei-emph"><span style="font-style: italic">unconditional</span></em> +antecedence, or causation. Until it had been shown by the actual +production of the antecedent under known circumstances, +and the occurrence thereupon of the consequent, that the +antecedent was really the condition on which it depended; +the uniformity of succession which was proved to exist between +them might, for aught we knew, be (like the succession +of day and night) no case of causation at all; both antecedent +and consequent might be successive stages of the effect of an +ulterior cause. Observation, in short, without experiment +(supposing no aid from deduction) can ascertain sequences +and coexistences, but cannot prove causation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In order to see these remarks verified by the actual state +of the sciences, we have only to think of the condition of natural +history. In zoology, for example, there is an immense +number of uniformities ascertained, some of coexistence, +others of succession, to many of which, notwithstanding considerable +variations of the attendant circumstances, we know +not any exception: but the antecedents, for the most part, +are such as we cannot artificially produce; or if we can, it +is only by setting in motion the exact process by which +nature produces them; and this being to us a mysterious +process, of which the main circumstances are not only unknown +but unobservable, the name of experimentation would +here be completely misapplied. Such are the facts: and +what is the result? That on this vast subject, which affords +so much and such varied scope for observation, we have not, +properly speaking, ascertained a single cause, a single unconditional +uniformity. We know not, in the case of most +<span class="tei tei-pb" id="page392">[pg 392]</span><a name="Pg392" id="Pg392" class="tei tei-anchor"></a> +of the phenomena that we find conjoined, which is the condition +of the other; which is cause, and which effect, or +whether either of them is so, or they are not rather conjunct +effects of causes yet to be discovered, complex results of laws +hitherto unknown. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although some of the foregoing observations may be, in +technical strictness of arrangement, premature in this place, +it seemed that a few general remarks on the difference +between sciences of mere observation and sciences of experimentation, +and the extreme disadvantage under which +directly inductive inquiry is necessarily carried on in the +former, were the best preparation for discussing the methods +of direct induction; a preparation rendering superfluous much +that must otherwise have been introduced, with some inconvenience, +into the heart of that discussion. To the consideration +of these methods we now proceed. +</p> + +</div> + +<span class="tei tei-pb" id="page393">[pg 393]</span><a name="Pg393" id="Pg393" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc69" id="toc69"></a> +<a name="pdf70" id="pdf70"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER VIII. OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The simplest and most obvious modes of singling +out from among the circumstances which precede or follow a +phenomenon, those with which it is really connected by an +invariable law, are two in number. One is, by comparing +together different instances in which the phenomenon occurs. +The other is, by comparing instances in which the phenomenon +does occur, with instances in other respects similar +in which it does not. These two methods may be respectively +denominated, the Method of Agreement, and the +Method of Difference. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In illustrating these methods it will be necessary to bear +in mind the two-fold character of inquiries into the laws of +phenomena; which may be either inquiries into the cause of +a given effect, or into the effects or properties of a given cause. +We shall consider the methods in their application to either +order of investigation, and shall draw our examples equally +from both. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We shall denote antecedents by the large letters of the +alphabet, and the consequents corresponding to them by the +small. Let A, then, be an agent or cause, and let the object +of our inquiry be to ascertain what are the effects of this +cause. If we can either find, or produce, the agent A in such +varieties of circumstances, that the different cases have no +circumstance in common except A; then whatever effect we +find to be produced in all our trials, is indicated as the effect +of A. Suppose, for example, that A is tried along with B +and C, and that the effect is <span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">b</span></span> +<span class="tei tei-hi"><span style="font-style: italic">c</span></span>; and suppose that A is next +tried with D and E, but without B and C, and that the effect +is <span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">d</span></span> <span class="tei tei-hi"><span style="font-style: italic">e</span></span>. +Then we may reason thus: <span class="tei tei-hi"><span style="font-style: italic">b</span></span> and <span class="tei tei-hi"><span style="font-style: italic">c</span></span> +are not effects +of A, for they were not produced by it in the second experiment; +<span class="tei tei-pb" id="page394">[pg 394]</span><a name="Pg394" id="Pg394" class="tei tei-anchor"></a> +nor are <span class="tei tei-hi"><span style="font-style: italic">d</span></span> and <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, +for they were not produced in the first. +Whatever is really the effect of A must have been produced +in both instances; now this condition is fulfilled by no circumstance +except <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. The phenomenon <span class="tei tei-hi"><span style="font-style: italic">a</span></span> cannot have been +the effect of B or C, since it was produced where they were +not; nor of D or E, since it was produced where they were +not. Therefore it is the effect of A. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For example, let the antecedent A be the contact of an +alkaline substance and an oil. This combination being tried +under several varieties of circumstance, resembling each +other in nothing else, the results agree in the production of +a greasy and detersive or saponaceous substance: it is therefore +concluded that the combination of an oil and an alkali +causes the production of a soap. It is thus we inquire, by +the Method of Agreement, into the effect of a given cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In a similar manner we may inquire into the cause of a +given effect. Let <span class="tei tei-hi"><span style="font-style: italic">a</span></span> be the effect. Here, as shown in the last +chapter, we have only the resource of observation without +experiment: we cannot take a phenomenon of which we +know not the origin, and try to find its mode of production +by producing it: if we succeeded in such a random trial it +could only be by accident. But if we can observe <span class="tei tei-hi"><span style="font-style: italic">a</span></span> in two +different combinations, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">b</span></span> +<span class="tei tei-hi"><span style="font-style: italic">c</span></span>, and <span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">d</span></span> +<span class="tei tei-hi"><span style="font-style: italic">e</span></span>; and if we know, or +can discover, that the antecedent circumstances in these cases +respectively were A B C and A D E; we may conclude by +a reasoning similar to that in the preceding example, that A +is the antecedent connected with the consequent <span class="tei tei-hi"><span style="font-style: italic">a</span></span> by a law +of causation. B and C, we may say, cannot be causes of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, +since on its second occurrence they were not present; nor +are D and E, for they were not present on its first occurrence. +A, alone of the five circumstances, was found among the antecedents +of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> in both instances. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For example, let the effect <span class="tei tei-hi"><span style="font-style: italic">a</span></span> be crystallization. We +compare instances in which bodies are known to assume +crystalline structure, but which have no other point of agreement; +and we find them to have one, and as far as we can +observe, only one, antecedent in common: the deposition of +a solid matter from a liquid state, either a state of fusion or +<span class="tei tei-pb" id="page395">[pg 395]</span><a name="Pg395" id="Pg395" class="tei tei-anchor"></a> +of solution. We conclude, therefore, that the solidification +of a substance from a liquid state is an invariable antecedent +of its crystallization. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In this example we may go farther, and say, it is not only +the invariable antecedent but the cause; or at least the proximate +event which completes the cause. For in this case +we are able, after detecting the antecedent A, to produce it +artificially, and by finding that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> follows it, verify the result +of our induction. The importance of thus reversing +the proof was strikingly manifested when by keeping a +phial of water charged with siliceous particles undisturbed +for years, a chemist (I believe Dr. Wollaston) succeeded in +obtaining crystals of quartz; and in the equally interesting +experiment in which Sir James Hall produced artificial +marble, by the cooling of its materials from fusion under +immense pressure: two admirable examples of the light +which may be thrown upon the most secret processes of +nature by well-contrived interrogation of her. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But if we cannot artificially produce the phenomenon A, +the conclusion that it is the cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> remains subject to +very considerable doubt. Though an invariable, it may not +be the unconditional antecedent of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, but may precede it as +day precedes night or night day. This uncertainty arises +from the impossibility of assuring ourselves that A is the <em class="tei tei-emph"><span style="font-style: italic">only</span></em> +immediate antecedent common to both the instances. If we +could be certain of having ascertained all the invariable antecedents, +we might be sure that the unconditional invariable +antecedent, or cause, must be found somewhere among them. +Unfortunately it is hardly ever possible to ascertain all the +antecedents, unless the phenomenon is one which we can +produce artificially. Even then, the difficulty is merely +lightened, not removed: men knew how to raise water in +pumps long before they adverted to what was really the +operating circumstance in the means they employed, namely, +the pressure of the atmosphere on the open surface of the +water. It is, however, much easier to analyse completely +a set of arrangements made by ourselves, than the whole +complex mass of the agencies which nature happens to be +<span class="tei tei-pb" id="page396">[pg 396]</span><a name="Pg396" id="Pg396" class="tei tei-anchor"></a> +exerting at the moment of the production of a given phenomenon. +We may overlook some of the material circumstances +in an experiment with an electrical machine; but +we shall, at the worst, be better acquainted with them than +with those of a thunder-storm. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The mode of discovering and proving laws of nature, +which we have now examined, proceeds on the following +axiom: Whatever circumstance can be excluded, without +prejudice to the phenomenon, or can be absent notwithstanding +its presence, is not connected with it in the way of +causation. The casual circumstances being thus eliminated, +if only one remains, that one is the cause which we are in +search of: if more than one, they either are, or contain +among them, the cause: and so, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">mutatis mutandis</span></span>, of the +effect. As this method proceeds by comparing different +instances to ascertain in what they agree, I have termed it +the Method of Agreement: and we may adopt as its regulating +principle the following canon:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">First Canon.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<em class="tei tei-emph"><span style="font-style: italic">If two or more instances of the phenomenon under investigation +have only one circumstance in common, the circumstance in +which alone all the instances agree, is the cause (or effect) of the +given phenomenon.</span></em> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Quitting for the present the Method of Agreement, to +which we shall almost immediately return, we proceed to a +still more potent instrument of the investigation of nature, +the Method of Difference. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. In the Method of Agreement, we endeavoured to +obtain instances which agreed in the given circumstance but +differed in every other: in the present method we require, +on the contrary, two instances resembling one another in +every other respect, but differing in the presence or absence +of the phenomenon we wish to study. If our object be to +discover the effects of an agent A, we must procure A in +some set of ascertained circumstances, as A B C, and having +<span class="tei tei-pb" id="page397">[pg 397]</span><a name="Pg397" id="Pg397" class="tei tei-anchor"></a> +noted the effects produced, compare them with the effect +of the remaining circumstances B C, when A is absent. If +the effect of A B C is <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, and the effect of B C, +<span class="tei tei-hi"><span style="font-style: italic">b c</span></span>, it is +evident that the effect of A is <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. So again, if we begin at +the other end, and desire to investigate the cause of an +effect <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, we must select an instance, as +<span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, in which the +effect occurs, and in which the antecedents were A B C, and +we must look out for another instance in which the remaining +circumstances, <span class="tei tei-hi"><span style="font-style: italic">b c</span></span>, occur without <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. +If the antecedents, in +that instance, are B C, we know that the cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> must be +A: either A alone, or A in conjunction with some of the +other circumstances present. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is scarcely necessary to give examples of a logical +process to which we owe almost all the inductive conclusions +we draw in daily life. When a man is shot through the +heart, it is by this method we know that it was the gun-shot +which killed him: for he was in the fulness of life immediately +before, all circumstances being the same, except the +wound. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The axioms implied in this method are evidently the +following. Whatever antecedent cannot be excluded without +preventing the phenomenon, is the cause, or a condition, of +that phenomenon: Whatever consequent can be excluded, +with no other difference in the antecedents than the absence +of a particular one, is the effect of that one. Instead of +comparing different instances of a phenomenon, to discover +in what they agree, this method compares an instance of its +occurrence with an instance of its non-occurrence, to discover +in what they differ. The canon which is the regulating +principle of the Method of Difference may be expressed as +follows:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Second Canon.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<em class="tei tei-emph"><span style="font-style: italic">If an instance in which the phenomenon under investigation +occurs, and an instance in which it does not occur, have every +circumstance in common save one, that one occurring only in the +former; the circumstance in which alone the two instances differ, +is the effect, or cause, or a necessary part of the cause, of the +phenomenon</span></em>. +</p> + +<span class="tei tei-pb" id="page398">[pg 398]</span><a name="Pg398" id="Pg398" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The two methods which we have now stated have +many features of resemblance, but there are also many distinctions +between them. Both are methods of <em class="tei tei-emph"><span style="font-style: italic">elimination.</span></em> +This term (employed in the theory of equations to denote +the process by which one after another of the elements of +a question is excluded, and the solution made to depend +on the relation between the remaining elements only) is well +suited to express the operation, analogous to this, which has +been understood since the time of Bacon to be the foundation +of experimental inquiry: namely, the successive exclusion +of the various circumstances which are found to +accompany a phenomenon in a given instance, in order to +ascertain what are those among them which can be absent +consistently with the existence of the phenomenon. The +Method of Agreement stands on the ground that whatever +can be eliminated, is not connected with the phenomenon +by any law. The Method of Difference has for its foundation, +that whatever can <em class="tei tei-emph"><span style="font-style: italic">not</span></em> be eliminated, <em class="tei tei-emph"><span style="font-style: italic">is</span></em> connected with +the phenomenon by a law. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of these methods, that of Difference is more particularly +a method of artificial experiment; while that of Agreement +is more especially the resource employed where experimentation +is impossible. A few reflections will prove the fact, +and point out the reason of it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is inherent in the peculiar character of the Method of +Difference, that the nature of the combinations which it +requires is much more strictly defined than in the Method +of Agreement. The two instances which are to be compared +with one another must be exactly similar, in all circumstances +except the one which we are attempting to investigate: +they must be in the relation of A B C and B C, or +of <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span> and <span class="tei tei-hi"><span style="font-style: italic">b c</span></span>. +It is true that this similarity of circumstances +needs not extend to such as are already known to +be immaterial to the result. And in the case of most phenomena +we learn at once, from the commonest experience, +that most of the coexistent phenomena of the universe may +be either present or absent without affecting the given +phenomenon; or, if present, are present indifferently when +<span class="tei tei-pb" id="page399">[pg 399]</span><a name="Pg399" id="Pg399" class="tei tei-anchor"></a> +the phenomenon does not happen, and when it does. Still, +even limiting the identity which is required between the two +instances, A B C and B C, to such circumstances as are not +already known to be indifferent; it is very seldom that +nature affords two instances, of which we can be assured +that they stand in this precise relation to one another. In +the spontaneous operations of nature there is generally such +complication and such obscurity, they are mostly either on +so overwhelmingly large or on so inaccessibly minute a scale, +we are so ignorant of a great part of the facts which really +take place, and even those of which we are not ignorant are +so multitudinous, and therefore so seldom exactly alike in +any two cases, that a spontaneous experiment, of the kind +required by the Method of Difference, is commonly not to be +found. When, on the contrary, we obtain a phenomenon +by an artificial experiment, a pair of instances such as the +method requires is obtained almost as a matter of course, +provided the process does not last a long time. A certain +state of surrounding circumstances existed before we commenced +the experiment; this is B C. We then introduce +A; say, for instance, by merely bringing an object from +another part of the room, before there has been time for any +change in the other elements. It is, in short, (as M. Comte +observes,) the very nature of an experiment, to introduce +into the pre-existing state of circumstances a change perfectly +definite. We choose a previous state of things with +which we are well acquainted, so that no unforeseen alteration +in that state is likely to pass unobserved; and into this +we introduce, as rapidly as possible, the phenomenon which +we wish to study; so that in general we are entitled to feel +complete assurance, that the pre-existing state, and the +state which we have produced, differ in nothing except the +presence or absence of that phenomenon. If a bird is taken +from a cage, and instantly plunged into carbonic acid gas, +the experimentalist may be fully assured (at all events after +one or two repetitions) that no circumstance capable of +causing suffocation had supervened in the interim, except +the change from immersion in the atmosphere to immersion +<span class="tei tei-pb" id="page400">[pg 400]</span><a name="Pg400" id="Pg400" class="tei tei-anchor"></a> +in carbonic acid gas. There is one doubt, indeed, which +may remain in some cases of this description; the effect +may have been produced not by the change, but by the +means employed to produce the change. The possibility, +however, of this last supposition generally admits of being +conclusively tested by other experiments. It thus appears +that in the study of the various kinds of phenomena which +we can, by our voluntary agency, modify or control, we can +in general satisfy the requisitions of the Method of Difference; +but that by the spontaneous operations of nature +those requisitions are seldom fulfilled. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The reverse of this is the case with the Method of Agreement. +We do not here require instances of so special and +determinate a kind. Any instances whatever, in which +nature presents us with a phenomenon, may be examined +for the purposes of this method; and if <em class="tei tei-emph"><span style="font-style: italic">all</span></em> such instances +agree in anything, a conclusion of considerable value is +already attained. We can seldom, indeed, be sure that the +one point of agreement is the only one; but this ignorance +does not, as in the Method of Difference, vitiate the conclusion; +the certainty of the result, as far as it goes, is not +affected. We have ascertained one invariable antecedent +or consequent, however many other invariable antecedents +or consequents may still remain unascertained. If A B C, +A D E, A F G, are all equally followed by <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, then +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> is an invariable consequent of A. If +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">b</span></span> <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">d</span></span> <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> <span class="tei tei-hi"><span style="font-style: italic">f</span></span> <span class="tei tei-hi"><span style="font-style: italic">g</span></span>, all number +A among their antecedents, then A is connected as an antecedent, +by some invariable law, with <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. But to determine +whether this invariable antecedent is a cause, or this invariable +consequent an effect, we must be able, in addition, to +produce the one by means of the other; or, at least, to +obtain that which alone constitutes our assurance of having +produced anything, namely, an instance in which the effect, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span>, has come into existence, +with no other change in the pre-existing +circumstances than the addition of A. And this, if +we can do it, is an application of the Method of Difference, +not of the Method of Agreement. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It thus appears to be by the Method of Difference alone +<span class="tei tei-pb" id="page401">[pg 401]</span><a name="Pg401" id="Pg401" class="tei tei-anchor"></a> +that we can ever, in the way of direct experience, arrive with +certainty at causes. The Method of Agreement leads only +to laws of phenomena, (as some writers call them, but improperly, +since laws of causation are also laws of phenomena): +that is, to uniformities which either are not laws of +causation, or in which the question of causation must for the +present remain undecided. The Method of Agreement is +chiefly to be resorted to, as a means of suggesting applications +of the Method of Difference (as in the last example +the comparison of A B C, A D E, A F G, suggested that A +was the antecedent on which to try the experiment whether +it could produce <span class="tei tei-hi"><span style="font-style: italic">a</span></span>); or as an inferior resource, in case +the Method of Difference is impracticable; which, as we +before showed, generally arises from the impossibility of +artificially producing the phenomena. And hence it is that +the Method of Agreement, though applicable in principle to +either case, is more emphatically the method of investigation +on those subjects where artificial experimentation is impossible; +because on those it is, generally, our only resource of +a directly inductive nature; while, in the phenomena which +we can produce at pleasure, the Method of Difference generally +affords a more efficacious process, which will ascertain +causes as well as mere laws. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. There are, however, many cases in which, though +our power of producing the phenomenon is complete, the +Method of Difference either cannot be made available at +all, or not without a previous employment of the Method of +Agreement. This occurs when the agency by which we can +produce the phenomenon is not that of one single antecedent, +but of a combination of antecedents, which we have no power +of separating from each other and exhibiting apart. For instance, +suppose the subject of inquiry to be the cause of the +double refraction of light. We can produce this phenomenon +at pleasure, by employing any one of the many substances +which are known to refract light in that peculiar manner. +But if, taking one of those substances, as Iceland spar for +example, we wish to determine on which of the properties of +<span class="tei tei-pb" id="page402">[pg 402]</span><a name="Pg402" id="Pg402" class="tei tei-anchor"></a> +Iceland spar this remarkable phenomenon depends, we can +make no use, for that purpose, of the Method of Difference; +for we cannot find another substance precisely resembling +Iceland spar except in some one property. The only mode, +therefore, of prosecuting this inquiry is that afforded by the +Method of Agreement; by which, in fact, through a comparison +of all the known substances which have the property of +doubly refracting light, it was ascertained that they agree +in the circumstance of being crystalline substances; and +though the converse does not hold, though all crystalline +substances have not the property of double refraction, it +was concluded, with reason, that there is a real connexion +between these two properties; that either crystalline structure, +or the cause which gives rise to that structure, is one +of the conditions of double refraction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Out of this employment of the Method of Agreement +arises a peculiar modification of that method, which is sometimes +of great avail in the investigation of nature. In cases +similar to the above, in which it is not possible to obtain +the precise pair of instances which our second canon requires—instances +agreeing in every antecedent except A, or +in every consequent except <span class="tei tei-hi"><span style="font-style: italic">a</span></span>; we may yet be able, by a +double employment of the Method of Agreement, to discover +in what the instances which contain A or <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, differ from those +which do not. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If we compare various instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> occurs, and +find that they all have in common the circumstance A, and +(as far as can be observed) no other circumstance, the +Method of Agreement, so far, bears testimony to a connexion +between A and <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. In order to convert this evidence +of connexion into proof of causation by the direct Method +of Difference, we ought to be able in some one of these +instances, as for example A B C, to leave out A, and observe +whether by doing so, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is prevented. Now supposing +(what is often the case) that we are not able to try this +decisive experiment; yet, provided we can by any means +discover what would be its result if we could try it, the +advantage will be the same. Suppose, then, that as we +<span class="tei tei-pb" id="page403">[pg 403]</span><a name="Pg403" id="Pg403" class="tei tei-anchor"></a> +previously examined a variety of instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +occurred, and found them to agree in containing A, so we +now observe a variety of instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> does not +occur, and find them agree in not containing A; which establishes, +by the Method of Agreement, the same connexion +between the absence of A and the absence of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, which was +before established between their presence. As, then, it had +been shown that whenever A is present <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is present, so it +being now shown that when A is taken away <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is removed +along with it, we have by the one proposition A B C, <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, +by the other B C, <span class="tei tei-hi"><span style="font-style: italic">b c</span></span>, the positive and negative instances +which the Method of Difference requires. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This method may be called the Indirect Method of +Difference, or the Joint Method of Agreement and Difference; +and consists in a double employment of the Method of +Agreement, each proof being independent of the other, and +corroborating it. But it is not equivalent to a proof by the +direct Method of Difference. For the requisitions of the +Method of Difference are not satisfied, unless we can be +quite sure either that the instances affirmative of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> agree in +no antecedent whatever but A, or that the instances negative +of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> agree in nothing but the negation of A. Now if it were +possible, which it never is, to have this assurance, we should +not need the joint method; for either of the two sets of +instances separately would then be sufficient to prove causation. +This indirect method, therefore, can only be regarded +as a great extension and improvement of the Method of +Agreement, but not as participating in the more cogent +nature of the Method of Difference. The following may +be stated as its canon:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Third Canon.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<em class="tei tei-emph"><span style="font-style: italic">If two or more instances in which the phenomenon occurs +have only one circumstance in common, while two or more instances +in which it does not occur have nothing in common save +the absence of that circumstance; the circumstance in which alone +the two sets of instances differ, is the effect, or cause, or a necessary +part of the cause, of the phenomenon.</span></em> +</p> + +<span class="tei tei-pb" id="page404">[pg 404]</span><a name="Pg404" id="Pg404" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We shall presently see that the Joint Method of Agreement +and Difference constitutes, in another respect not yet +adverted to, an improvement upon the common Method of +Agreement, namely, in being unaffected by a characteristic +imperfection of that method, the nature of which still remains +to be pointed out. But as we cannot enter into this exposition +without introducing a new element of complexity into +this long and intricate discussion, I shall postpone it to a +subsequent chapter, and shall at once proceed to the statement +of two other methods, which will complete the enumeration +of the means which mankind possess for exploring the +laws of nature by specific observation and experience. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. The first of these has been aptly denominated the +Method of Residues. Its principle is very simple. Subducting +from any given phenomenon all the portions which, +by virtue of preceding inductions, can be assigned to known +causes, the remainder will be the effect of the antecedents +which had been overlooked, or of which the effect was as yet +an unknown quantity. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Suppose, as before, that we have the antecedents A B C, +followed by the consequents <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, +and that by previous inductions, (founded, we will suppose, on the Method of Difference,) +we have ascertained the causes of some of these +effects, or the effects of some of these causes; and are by +this means apprised that the effect of A is <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, and that the +effect of B is <span class="tei tei-hi"><span style="font-style: italic">b</span></span>. Subtracting the sum of these effects from +the total phenomenon, there remains <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, which now, without +any fresh experiment, we may know to be the effect of C. +This Method of Residues is in truth a peculiar modification +of the Method of Difference. If the instance A B C, <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, +could have been compared with a single instance A B, <span class="tei tei-hi"><span style="font-style: italic">a b</span></span>, +we should have proved C to be the cause of <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, by the common +process of the Method of Difference. In the present +case, however, instead of a single instance A B, we have had +to study separately the causes A and B, and to infer from +the effects which they produce separately, what effect they +must produce in the case A B C where they act together. +</p> + +<span class="tei tei-pb" id="page405">[pg 405]</span><a name="Pg405" id="Pg405" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of the two instances, therefore, which the Method of Difference +requires,—the one positive, the other negative,—the +negative one, or that in which the given phenomenon is absent, +is not the direct result of observation and experiment, +but has been arrived at by deduction. As one of the forms +of the Method of Difference, the Method of Residues partakes +of its rigorous certainty, provided the previous inductions, +those which gave the effects of A and B, were obtained +by the same infallible method, and provided we are certain +that C is the <em class="tei tei-emph"><span style="font-style: italic">only</span></em> antecedent to which the residual phenomenon +<span class="tei tei-hi"><span style="font-style: italic">c</span></span> can be referred; the only agent of which we had +not already calculated and subducted the effect. But as we +can never be quite certain of this, the evidence derived from +the Method of Residues is not complete unless we can obtain +C artificially and try it separately, or unless its agency, +when once suggested, can be accounted for, and proved +deductively, from known laws. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Even with these reservations, the Method of Residues is +one of the most important among our instruments of discovery. +Of all the methods of investigating laws of nature, +this is the most fertile in unexpected results; often informing +us of sequences in which neither the cause nor the effect +were sufficiently conspicuous to attract of themselves the +attention of observers. The agent C may be an obscure +circumstance, not likely to have been perceived unless sought +for, nor likely to have been sought for until attention had +been awakened by the insufficiency of the obvious causes to +account for the whole of the effect. And <span class="tei tei-hi"><span style="font-style: italic">c</span></span> may be so disguised +by its intermixture with <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +that it would scarcely have presented itself spontaneously as a subject of separate +study. Of these uses of the method, we shall presently cite +some remarkable examples. The canon of the Method of +Residues is as follows:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Fourth Canon.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<em class="tei tei-emph"><span style="font-style: italic">Subduct from any phenomenon such part as is known by previous +inductions to be the effect of certain antecedents, and the residue +of the phenomenon is the effect of the remaining antecedents.</span></em> +</p> + +<span class="tei tei-pb" id="page406">[pg 406]</span><a name="Pg406" id="Pg406" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. There remains a class of laws which it is impracticable +to ascertain by any of the three methods which I have +attempted to characterize; namely, the laws of those Permanent +Causes, or indestructible natural agents, which it is +impossible either to exclude or to isolate; which we can +neither hinder from being present, nor contrive that they +shall be present alone. It would appear at first sight that +we could by no means separate the effects of these agents +from the effects of those other phenomena with which they +cannot be prevented from coexisting. In respect, indeed, to +most of the permanent causes, no such difficulty exists; since +though we cannot eliminate them as coexisting facts, we can +eliminate them as influencing agents, by simply trying our +experiment in a local situation beyond the limits of their +influence. The pendulum, for example, has its oscillations +disturbed by the vicinity of a mountain: we remove the pendulum +to a sufficient distance from the mountain, and the +disturbance ceases: from these data we can determine by the +Method of Difference, the amount of effect due to the mountain; +and beyond a certain distance everything goes on precisely +as it would do if the mountain exercised no influence +whatever, which, accordingly, we, with sufficient reason, conclude +to be the fact, +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The difficulty, therefore, in applying the methods already +treated of to determine the effects of Permanent Causes, is +confined to the cases in which it is impossible for us to get +out of the local limits of their influence. The pendulum can +be removed from the influence of the mountain, but it cannot +be removed from the influence of the earth: we cannot take +away the earth from the pendulum, nor the pendulum from +the earth, to ascertain whether it would continue to vibrate +if the action which the earth exerts upon it were withdrawn. +On what evidence, then, do we ascribe its vibrations to the +earth's influence? Not on any sanctioned by the Method of +Difference; for one of the two instances, the negative instance, +is wanting. Nor by the Method of Agreement; for +though all pendulums agree in this, that during their oscillations +the earth is always present, why may we not as well +<span class="tei tei-pb" id="page407">[pg 407]</span><a name="Pg407" id="Pg407" class="tei tei-anchor"></a> +ascribe the phenomenon to the sun, which is equally a coexistent +fact in all the experiments? It is evident that to +establish even so simple a fact of causation as this, there was +required some method over and above those which we have +yet examined. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As another example, let us take the phenomenon Heat. +Independently of all hypothesis as to the real nature of the +agency so called, this fact is certain, that we are unable to +exhaust any body of the whole of its heat. It is equally +certain, that no one ever perceived heat not emanating from +a body. Being unable, then, to separate Body and Heat, +we cannot effect such a variation of circumstances as the +foregoing three methods require; we cannot ascertain, by +those methods, what portion of the phenomena exhibited by +any body are due to the heat contained in it. If we could +observe a body with its heat, and the same body entirely +divested of heat, the Method of Difference would show the +effect due to the heat, apart from that due to the body. If +we could observe heat under circumstances agreeing in +nothing but heat, and therefore not characterized also by +the presence of a body, we could ascertain the effects of +heat, from an instance of heat with a body and an instance +of heat without a body, by the Method of Agreement; or we +could determine by the Method of Difference what effect +was due to the body, when the remainder which was due to +the heat would be given by the Method of Residues. But +we can do none of these things; and without them the application +of any of the three methods to the solution of this +problem would be illusory. It would be idle, for instance, +to attempt to ascertain the effect of heat by subtracting from +the phenomena exhibited by a body, all that is due to its +other properties; for as we have never been able to observe +any bodies without a portion of heat in them, the effects due +to that heat might form a part of the very results, which we +were affecting to subtract in order that the effect of heat +might be shown by the residue. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If, therefore, there were no other methods of experimental +investigation than these three, we should be unable to determine +<span class="tei tei-pb" id="page408">[pg 408]</span><a name="Pg408" id="Pg408" class="tei tei-anchor"></a> +the effects due to heat as a cause. But we have still +a resource. Though we cannot exclude an antecedent +altogether, we may be able to produce, or nature may produce +for us, some modification in it. By a modification +is here meant, a change in it, not amounting to its total +removal. If some modification in the antecedent A is +always followed by a change in the consequent <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, the other +consequents <span class="tei tei-hi"><span style="font-style: italic">b</span></span> and <span class="tei tei-hi"><span style="font-style: italic">c</span></span> +remaining the same; or, <span class="tei tei-hi"><span style="font-style: italic">vice versâ</span></span>, if +every change in <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is found to have been preceded by some +modification in A, none being observable in any of the other +antecedents; we may safely conclude that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is, wholly or in +part, an effect traceable to A, or at least in some way connected +with it through causation. For example, in the case +of heat, though we cannot expel it altogether from any body, +we can modify it in quantity, we can increase or diminish +it; and doing so, we find by the various methods of experimentation +or observation already treated of, that such increase +or diminution of heat is followed by expansion or +contraction of the body. In this manner we arrive at the +conclusion, otherwise unattainable by us, that one of the +effects of heat is to enlarge the dimensions of bodies; or +what is the same thing in other words, to widen the distances +between their particles. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A change in a thing, not amounting to its total removal, +that is, a change which leaves it still the same thing it was, +must be a change either in its quantity, or in some of its +relations to other things, of which relations the principal is +its position in space. In the previous example, the modification +which was produced in the antecedent was an alteration +in its quantity. Let us now suppose the question to be, +what influence the moon exerts on the surface of the earth. +We cannot try an experiment in the absence of the moon, +so as to observe what terrestrial phenomena her annihilation +would put an end to; but when we find that all the variations +in the <em class="tei tei-emph"><span style="font-style: italic">position</span></em> of the moon are followed by corresponding +variations in the time and place of high water, the place being +always either the part of the earth which is nearest to, or that +which is most remote from, the moon, we have ample evidence +<span class="tei tei-pb" id="page409">[pg 409]</span><a name="Pg409" id="Pg409" class="tei tei-anchor"></a> +that the moon is, wholly or partially, the cause which determines +the tides. It very commonly happens, as it does in this +instance, that the variations of an effect are correspondent, +or analogous, to those of its cause; as the moon moves +further towards the east, the high water point does the same: +but this is not an indispensable condition; as may be seen +in the same example, for along with that high water point, +there is at the same instant another high water point diametrically +opposite to it, and which, therefore, of necessity, +moves towards the west as the moon followed by the nearer +of the tide waves advances towards the east: and yet both +these motions are equally effects of the moon's motion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +That the oscillations of the pendulum are caused by the +earth, is proved by similar evidence. Those oscillations take +place between equidistant points on the two sides of a line, +which, being perpendicular to the earth, varies with every +variation in the earth's position, either in space or relatively +to the object. Speaking accurately, we only know by the +method now characterized, that all terrestrial bodies tend to +the earth, and not to some unknown fixed point lying in the +same direction. In every twenty-four hours, by the earth's +rotation, the line drawn from the body at right angles to the +earth coincides successively with all the radii of a circle, and +in the course of six months the place of that circle varies by +nearly two hundred millions of miles; yet in all these changes +of the earth's position, the line in which bodies tend to fall +continues to be directed towards it: which proves that terrestrial +gravity is directed to the earth, and not, as was once +fancied by some, to a fixed point of space. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The method by which these results were obtained, may +be termed the Method of Concomitant Variations: it is regulated +by the following canon:— +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-hi"><span style="font-variant: small-caps">Fifth Canon.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<em class="tei tei-emph"><span style="font-style: italic">Whatever phenomenon varies in any manner whenever another +phenomenon varies in some particular manner, is either a cause +or an effect of that phenomenon, or is connected with it through +some fact of causation.</span></em> +</p> + +<span class="tei tei-pb" id="page410">[pg 410]</span><a name="Pg410" id="Pg410" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The last clause is subjoined, because it by no means +follows when two phenomena accompany each other in their +variations, that the one is cause and the other effect. The +same thing may, and indeed must happen, supposing them +to be two different effects of a common cause: and by this +method alone it would never be possible to ascertain which +of the suppositions is the true one. The only way to solve the +doubt would be that which we have so often adverted to, viz. +by endeavouring to ascertain whether we can produce the +one set of variations by means of the other. In the case of +heat, for example, by increasing the temperature of a body +we increase its bulk, but by increasing its bulk we do not +increase its temperature; on the contrary, (as in the rarefaction +of air under the receiver of an air-pump,) we generally +diminish it: therefore heat is not an effect, but a cause, of +increase of bulk. If we cannot ourselves produce the variations, +we must endeavour, though it is an attempt which is +seldom successful, to find them produced by nature in some +case in which the pre-existing circumstances are perfectly +known to us. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is scarcely necessary to say, that in order to ascertain +the uniform concomitance of variations in the effect with variations +in the cause, the same precautions must be used as in +any other case of the determination of an invariable sequence. +We must endeavour to retain all the other antecedents unchanged, +while that particular one is subjected to the requisite +series of variations; or in other words, that we may be warranted +in inferring causation from concomitance of variations, +the concomitance itself must be proved by the Method of +Difference. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It might at first appear that the Method of Concomitant +Variations assumes a new axiom, or law of causation in +general, namely, that every modification of the cause is followed +by a change in the effect. And it does usually happen +that when a phenomenon A causes a phenomenon <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, any +variation in the quantity or in the various relations of A, is +uniformly followed by a variation in the quantity or relations +of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. To take a familiar instance, that of gravitation. The +<span class="tei tei-pb" id="page411">[pg 411]</span><a name="Pg411" id="Pg411" class="tei tei-anchor"></a> +sun causes a certain tendency to motion in the earth; here +we have cause and effect; but that tendency is <em class="tei tei-emph"><span style="font-style: italic">towards</span></em> the +sun, and therefore varies in direction as the sun varies in the +relation of position; and moreover the tendency varies in +intensity, in a certain numerical ratio to the sun's distance +from the earth, that is, according to another relation of the +sun. Thus we see that there is not only an invariable connexion +between the sun and the earth's gravitation, but that +two of the relations of the sun, its position with respect to the +earth and its distance from the earth, are invariably connected +as antecedents with the quantity and direction of the earth's +gravitation. The cause of the earth's gravitating at all, is +simply the sun; but the cause of its gravitating with a given +intensity and in a given direction, is the existence of the sun +in a given direction and at a given distance. It is not strange +that a modified cause, which is in truth a different cause, +should produce a different effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although it is for the most part true that a modification +of the cause is followed by a modification of the effect, the +Method of Concomitant Variations does not, however, presuppose +this as an axiom. It only requires the converse +proposition; that anything on whose modifications, modifications +of an effect are invariably consequent, must be the +cause (or connected with the cause) of that effect; a proposition, +the truth of which is evident; for if the thing itself +had no influence on the effect, neither could the modifications +of the thing have any influence. If the stars have no power +over the fortunes of mankind, it is implied in the very terms, +that the conjunctions or oppositions of different stars can +have no such power. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Although the most striking applications of the Method of +Concomitant Variations take place in the cases in which the +Method of Difference, strictly so called, is impossible, its use +is not confined to those cases; it may often usefully follow +after the Method of Difference, to give additional precision to +a solution which that has found. When by the Method of +Difference it has first been ascertained that a certain object +produces a certain effect, the Method of Concomitant Variations +<span class="tei tei-pb" id="page412">[pg 412]</span><a name="Pg412" id="Pg412" class="tei tei-anchor"></a> +may be usefully called in to determine according to +what law the quantity or the different relations of the effect +follow those of the cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. The case in which this method admits of the most +extensive employment, is that in which the variations of the +cause are variations of quantity. Of such variations we may +in general affirm with safety, that they will be attended not +only with variations, but with similar variations, of the effect: +the proposition, that more of the cause is followed by more +of the effect, being a corollary from the principle of the +Composition of Causes, which, as we have seen, is the general +rule of causation; cases of the opposite description, in which +causes change their properties on being conjoined with one +another, being, on the contrary, special and exceptional. +Suppose, then, that when A changes in quantity, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> also +changes in quantity, and in such a manner that we can trace +the numerical relation which the changes of the one bear to +such changes of the other as take place within our limits of +observation. We may then, with certain precautions, safely +conclude that the same numerical relation will hold beyond +those limits. If, for instance, we find that when A is double, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +is double; that when A is treble or quadruple, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is treble or +quadruple; we may conclude that if A were a half or a third, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +would be a half or a third, and finally, that if A were annihilated, +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> would be annihilated, and that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +is wholly the effect of A, or wholly the effect of the same cause with A. And so +with any other numerical relation according to which A and +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> would vanish simultaneously; as for instance +if <span class="tei tei-hi"><span style="font-style: italic">a</span></span> were proportional +to the square of A. If, on the other hand, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is not +wholly the effect of A, but yet varies when A varies, it is probably +a mathematical function not of A alone but of A and something +else: its changes, for example, may be such as would occur +if part of it remained constant, or varied on some other principle, +and the remainder varied in some numerical relation to +the variations of A. In that case, when A diminishes, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> will +seem to approach not towards zero, but towards some other +limit: and when the series of variations is such as to indicate +<span class="tei tei-pb" id="page413">[pg 413]</span><a name="Pg413" id="Pg413" class="tei tei-anchor"></a> +what that limit is, if constant, or the law of its variation if +variable, the limit will exactly measure how much of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is the +effect of some other and independent cause, and the remainder +will be the effect of A (or of the cause of A). +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These conclusions, however, must not be drawn without +certain precautions. In the first place, the possibility of +drawing them at all, manifestly supposes that we are +acquainted not only with the variations, but with the absolute +quantities, both of A and <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. If we do not know the +total quantities, we cannot, of course, determine the real +numerical relation according to which those quantities vary. +It is therefore an error to conclude, as some have concluded, +that because increase of heat expands bodies, that is, increases +the distance between their particles, therefore the +distance is wholly the effect of heat, and that if we could +entirely exhaust the body of its heat, the particles would +be in complete contact. This is no more than a guess, +and of the most hazardous sort, not a legitimate induction: +for since we neither know how much heat there is in any +body, nor what is the real distance between any two of its +particles, we cannot judge whether the contraction of the +distance does or does not follow the diminution of the quantity +of heat according to such a numerical relation that the +two quantities would vanish simultaneously. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In contrast with this, let us consider a case in which the +absolute quantities are known; the case contemplated in the +first law of motion; viz. that all bodies in motion continue +to move in a straight line with uniform velocity until acted +upon by some new force. This assertion is in open opposition +to first appearances; all terrestrial objects, when in +motion, gradually abate their velocity and at last stop; which +accordingly the ancients, with their <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">inductio per enumerationem +simplicem</span></span>, imagined to be the law. Every moving body, +however, encounters various obstacles, as friction, the resistance +of the atmosphere, &c., which we know by daily +experience to be causes capable of destroying motion. It +was suggested that the whole of the retardation might be +owing to these causes. How was this inquired into? If the +<span class="tei tei-pb" id="page414">[pg 414]</span><a name="Pg414" id="Pg414" class="tei tei-anchor"></a> +obstacles could have been entirely removed, the case would +have been amenable to the Method of Difference. They +could not be removed, they could only be diminished, and +the case, therefore, admitted only of the Method of Concomitant +Variations. This accordingly being employed, it +was found that every diminution of the obstacles diminished +the retardation of the motion: and inasmuch as in this case +(unlike the case of heat) the total quantities both of the antecedent +and of the consequent were known; it was practicable +to estimate, with an approach to accuracy, both the amount +of the retardation and the amount of the retarding causes, or +resistances, and to judge how near they both were to being +exhausted; and it appeared that the effect dwindled as +rapidly, and at each step was as far on the road towards annihilation, +as the cause was. The simple oscillation of a weight +suspended from a fixed point, and moved a little out of the +perpendicular, which in ordinary circumstances lasts but a +few minutes, was prolonged in Borda's experiments to more +than thirty hours, by diminishing as much as possible the +friction at the point of suspension, and by making the body +oscillate in a space exhausted as nearly as possible of its air. +There could therefore be no hesitation in assigning the whole +of the retardation of motion to the influence of the obstacles: +and since, after subducting this retardation from the total +phenomenon, the remainder was an uniform velocity, the +result was the proposition known as the first law of motion. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is also another characteristic uncertainty affecting +the inference that the law of variation which the quantities +observe within our limits of observation, will hold beyond +those limits. There is of course, in the first instance, the +possibility that beyond the limits, and in circumstances +therefore of which we have no direct experience, some +counteracting cause might develop itself; either a new +agent, or a new property of the agents concerned, which +lies dormant in the circumstances we are able to observe. +This is an element of uncertainty which enters largely into +all our predictions of effects; but it is not peculiarly applicable +to the Method of Concomitant Variations. The uncertainty, +<span class="tei tei-pb" id="page415">[pg 415]</span><a name="Pg415" id="Pg415" class="tei tei-anchor"></a> +however, of which I am about to speak, is characteristic +of that method; especially in the cases in which the +extreme limits of our observation are very narrow, in comparison +with the possible variations in the quantities of the +phenomena. Any one who has the slightest acquaintance +with mathematics, is aware that very different laws of variation +may produce numerical results which differ but slightly +from one another within narrow limits; and it is often only +when the absolute amounts of variation are considerable, +that the difference between the results given by one law and +by another becomes appreciable. When, therefore, such +variations in the quantity of the antecedents as we have the +means of observing, are small in comparison with the total +quantities, there is much danger lest we should mistake the +numerical law, and be led to miscalculate the variations +which would take place beyond the limits; a miscalculation +which would vitiate any conclusion respecting the +dependence of the effect upon the cause, that could be +founded on those variations. Examples are not wanting of +such mistakes. <span class="tei tei-q">“The formulæ,”</span> says Sir John +Herschel,<a id="noteref_77" name="noteref_77" href="#note_77"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">77</span></span></a> +<span class="tei tei-q">“which have been empirically deduced for the elasticity of +steam, (till very recently,) and those for the resistance of +fluids, and other similar subjects,”</span> when relied on beyond +the limits of the observations from which they were deduced, +<span class="tei tei-q">“have almost invariably failed to support the theoretical +structures which have been erected on them.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In this uncertainty, the conclusion we may draw from +the concomitant variations of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and A, to the existence of an +invariable and exclusive connexion between them, or to the +permanency of the same numerical relation between their +variations when the quantities are much greater or smaller +than those which we have had the means of observing, cannot +be considered to rest on a complete induction. All that +in such a case can be regarded as proved on the subject of +causation is, that there is some connexion between the two +phenomena; that A, or something which can influence A, +<span class="tei tei-pb" id="page416">[pg 416]</span><a name="Pg416" id="Pg416" class="tei tei-anchor"></a> +must be <em class="tei tei-emph"><span style="font-style: italic">one</span></em> of the causes which collectively determine +<span class="tei tei-hi"><span style="font-style: italic">a</span></span>. +We may, however, feel assured that the relation which we +have observed to exist between the variations of A and <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, +will hold true in all cases which fall between the same +extreme limits; that is, wherever the utmost increase or +diminution in which the result has been found by observation +to coincide with the law, is not exceeded. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The four methods which it has now been attempted to +describe, are the only possible modes of experimental inquiry, +of direct induction <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à +posteriori</span></span>, as distinguished from deduction: +at least, I know not, nor am able to imagine, any +others. And even of these, the Method of Residues, as we +have seen, is not independent of deduction; though, as it +also requires specific experience, it may, without impropriety, +be included among methods of direct observation and +experiment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These, then, with such assistance as can be obtained +from Deduction, compose the available resources of the +human mind for ascertaining the laws of the succession of +phenomena. Before proceeding to point out certain circumstances, +by which the employment of these methods is +subjected to an immense increase of complication and of +difficulty, it is expedient to illustrate the use of the methods +by suitable examples drawn from actual physical investigations. +These, accordingly, will form the subject of the succeeding +chapter. +</p> + +</div> + +<span class="tei tei-pb" id="page417">[pg 417]</span><a name="Pg417" id="Pg417" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc71" id="toc71"></a> +<a name="pdf72" id="pdf72"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER IX. MISCELLANEOUS EXAMPLES OF THE FOUR METHODS.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. I shall select, as a first example, an interesting +speculation of one of the most eminent of theoretical chemists, +Professor Liebig. The object in view, is to ascertain the +immediate cause of the death produced by metallic poisons. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Arsenious acid, and the salts of lead, bismuth, copper, +and mercury, if introduced into the animal organism, except +in the smallest doses, destroy life. These facts have long +been known, as insulated truths of the lowest order of +generalization; but it was reserved for Liebig, by an apt +employment of the first two of our methods of experimental +inquiry, to connect these truths together by a higher induction, +pointing out what property, common to all these deleterious +substances, is the really operating cause of their +fatal effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When solutions of these substances are placed in sufficiently +close contact with many animal products, albumen, +milk, muscular fibre, and animal membranes, the acid or +salt leaves the water in which it was dissolved, and enters +into combination with the animal substance: which substance, +after being thus acted upon, is found to have lost its +tendency to spontaneous decomposition, or putrefaction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Observation also shows, in cases where death has been +produced by these poisons, that the parts of the body with +which the poisonous substances have been brought into +contact, do not afterwards putrefy. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And, finally, when the poison has been supplied in too +small a quantity to destroy life, eschars are produced, that +is, certain superficial portions of the tissues are destroyed, +which are afterwards thrown off by the reparative process +taking place in the healthy parts. +</p> + +<span class="tei tei-pb" id="page418">[pg 418]</span><a name="Pg418" id="Pg418" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These three sets of instances admit of being treated +according to the Method of Agreement. In all of them the +metallic compounds are brought into contact with the substances +which compose the human or animal body; and the +instances do not seem to agree in any other circumstance. +The remaining antecedents are as different, and even opposite, +as they could possibly be made; for in some the animal +substances exposed to the action of the poisons are in a +state of life, in others only in a state of organization, in +others not even in that. And what is the result which +follows in all the cases? The conversion of the animal +substance (by combination with the poison) into a chemical +compound, held together by so powerful a force as to resist +the subsequent action of the ordinary causes of decomposition. +Now, organic life (the necessary condition of sensitive +life) consisting in a continual state of decomposition and +recomposition of the different organs and tissues; whatever +incapacitates them for this decomposition destroys life. +And thus the proximate cause of the death produced by this +description of poisons, is ascertained, as far as the Method +of Agreement can ascertain it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us now bring our conclusion to the test of the Method +of Difference. Setting out from the cases already mentioned, +in which the antecedent is the presence of substances +forming with the tissues a compound incapable of putrefaction, +(and <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à fortiori</span></span> +incapable of the chemical actions which +constitute life,) and the consequent is death, either of the +whole organism, or of some portion of it; let us compare +with these cases other cases, as much resembling them as +possible, but in which that effect is not produced. And, +first, <span class="tei tei-q">“many insoluble basic salts of arsenious acid are +known not to be poisonous. The substance called alkargen, +discovered by Bunsen, which contains a very large quantity +of arsenic, and approaches very closely in composition to +the organic arsenious compounds found in the body, has not +the slightest injurious action upon the organism.”</span> Now +when these substances are brought into contact with the +tissues in any way, they do not combine with them; they +<span class="tei tei-pb" id="page419">[pg 419]</span><a name="Pg419" id="Pg419" class="tei tei-anchor"></a> +do not arrest their progress to decomposition. As far, +therefore, as these instances go, it appears that when the +effect is absent, it is by reason of the absence of that antecedent +which we had already good ground for considering +as the proximate cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +But the rigorous conditions of the Method of Difference +are not yet satisfied; for we cannot be sure that these unpoisonous +bodies agree with the poisonous substances in +every property, except the particular one, of entering into a +difficultly decomposable compound with the animal tissues. +To render the method strictly applicable, we need an +instance, not of a different substance, but of one of the very +same substances, in circumstances which would prevent +it from forming, with the tissues, the sort of compound in +question; and then, if death does not follow, our case is +made out. Now such instances are afforded by the antidotes +to these poisons. For example, in case of poisoning by +arsenious acid, if hydrated peroxide of iron is administered, +the destructive agency is instantly checked. Now this peroxide +is known to combine with the acid, and form a compound, +which, being insoluble, cannot act at all on animal +tissues. So, again, sugar is a well-known antidote to +poisoning by salts of copper; and sugar reduces those salts +either into metallic copper, or into the red suboxide, neither +of which enters into combination with animal matter. The +disease called painter's colic, so common in manufactories of +white lead, is unknown where the workmen are accustomed +to take, as a preservative, sulphuric-acid-lemonade (a solution +of sugar rendered acid by sulphuric acid). Now diluted +sulphuric acid has the property of decomposing all compounds +of lead with organic matter, or of preventing them from +being formed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is another class of instances, of the nature required +by the Method of Difference, which seem at first sight to +conflict with the theory. Soluble salts of silver, such for +instance as the nitrate, have the same stiffening antiseptic +effect on decomposing animal substances as corrosive sublimate +and the most deadly metallic poisons; and when +<span class="tei tei-pb" id="page420">[pg 420]</span><a name="Pg420" id="Pg420" class="tei tei-anchor"></a> +applied to the external parts of the body, the nitrate is a +powerful caustic, depriving those parts of all active vitality, +and causing them to be thrown off by the neighbouring +living structures, in the form of an eschar. The nitrate +and the other salts of silver ought, then, it would seem, if +the theory be correct, to be poisonous; yet they may be +administered internally with perfect impunity. From this +apparent exception arises the strongest confirmation which +the theory has yet received. Nitrate of silver, in spite of its +chemical properties, does not poison when introduced into +the stomach; but in the stomach, as in all animal liquids, +there is common salt; and in the stomach there is also free +muriatic acid. These substances operate as natural antidotes, +combining with the nitrate, and if its quantity is not +too great, immediately converting it into chloride of silver; +a substance very slightly soluble, and therefore incapable of +combining with the tissues, although to the extent of its +solubility it has a medicinal influence, through an entirely +different class of organic actions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The preceding instances have afforded an induction of a +high order of conclusiveness, illustrative of the two simplest +of our four methods; although not rising to the maximum +of certainty which the Method of Difference, in its most perfect +exemplification, is capable of affording. For (let us not +forget) the positive instance and the negative one which the +rigour of that method requires, ought to differ only in the +presence or absence of one single circumstance. Now, in +the preceding argument, they differ in the presence or +absence not of a single <em class="tei tei-emph"><span style="font-style: italic">circumstance</span></em>, but of a single +<em class="tei tei-emph"><span style="font-style: italic">substance</span></em>: and as every substance has innumerable properties, there is +no knowing what number of real differences are involved in +what is nominally and apparently only one difference. It is +conceivable that the antidote, the peroxide of iron for example, +may counteract the poison through some other of its +properties than that of forming an insoluble compound with +it; and if so, the theory would fall to the ground, so far as +it is supported by that instance. This source of uncertainty, +which is a serious hindrance to all extensive generalizations +<span class="tei tei-pb" id="page421">[pg 421]</span><a name="Pg421" id="Pg421" class="tei tei-anchor"></a> +in chemistry, is however reduced in the present case to +almost the lowest degree possible, when we find that not +only one substance, but many substances, possess the capacity +of acting as antidotes to metallic poisons, and that all +these agree in the property of forming insoluble compounds +with the poisons, while they cannot be ascertained to agree +in any other property whatsoever. We have thus, in favour +of the theory, all the evidence which can be obtained by +what we termed the Indirect Method of Difference, or the +Joint Method of Agreement and Difference; the evidence of +which, though it never can amount to that of the Method +of Difference properly so called, may approach indefinitely +near to it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Let the object be<a id="noteref_78" name="noteref_78" href="#note_78"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">78</span></span></a> to ascertain the law of what is +termed <em class="tei tei-emph"><span style="font-style: italic">induced</span></em> electricity; to find under what conditions +any electrified body, whether positively or negatively electrified, +gives rise to a contrary electric state in some other +body adjacent to it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The most familiar exemplification of the phenomenon to +be investigated, is the following. Around the prime conductors +of an electrical machine, the atmosphere to some +distance, or any conducting surface suspended in that atmosphere, +is found to be in an electric condition opposite to that +of the prime conductor itself. Near and around the positive +prime conductor there is negative electricity, and near and +around the negative prime conductor there is positive electricity. +When pith balls are brought near to either of the +conductors, they become electrified with the opposite electricity +to it; either receiving a share from the already +electrified atmosphere by conduction, or acted upon by the +direct inductive influence of the conductor itself: they are +then attracted by the conductor to which they are in opposition; +or, if withdrawn in their electrified state, they will be +attracted by any other oppositely charged body. In like +manner the hand, if brought near enough to the conductor, +<span class="tei tei-pb" id="page422">[pg 422]</span><a name="Pg422" id="Pg422" class="tei tei-anchor"></a> +receives or gives an electric discharge; now we have no +evidence that a charged conductor can be suddenly discharged +unless by the approach of a body oppositely electrified. +In the case, therefore, of the electrical machine, it +appears that the accumulation of electricity in an insulated +conductor is always accompanied by the excitement of the +contrary electricity in the surrounding atmosphere, and in +every conductor placed near the former conductor. It does +not seem possible, in this case, to produce one electricity by +itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us now examine all the other instances which we can +obtain, resembling this instance in the given consequent, +namely, the evolution of an opposite electricity in the neighbourhood +of an electrified body. As one remarkable instance +we have the Leyden jar; and after the splendid experiments +of Faraday in complete and final establishment of the substantial +identity of magnetism and electricity, we may cite +the magnet, both the natural and the electro-magnet, in neither +of which is it possible to produce one kind of electricity by +itself, or to charge one pole without charging an opposite +pole with the contrary electricity at the same time. We +cannot have a magnet with one pole: if we break a natural +loadstone into a thousand pieces, each piece will have its +two oppositely electrified poles complete within itself. In +the voltaic circuit, again, we cannot have one current without +its opposite. In the ordinary electric machine, the glass +cylinder or plate, and the rubber, acquire opposite electricities. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +From all these instances, treated by the Method of Agreement, +a general law appears to result. The instances embrace +all the known modes in which a body can become charged +with electricity; and in all of them there is found, as a concomitant +or consequent, the excitement of the opposite electric +state in some other body or bodies. It seems to follow +that the two facts are invariably connected, and that the +excitement of electricity in any body has for one of its +necessary conditions the possibility of a simultaneous excitement +<span class="tei tei-pb" id="page423">[pg 423]</span><a name="Pg423" id="Pg423" class="tei tei-anchor"></a> +of the opposite electricity in some neighbouring +body. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +As the two contrary electricities can only be produced +together, so they can only cease together. This may be +shown by an application of the Method of Difference to the +example of the Leyden jar. It needs scarcely be here +remarked that in the Leyden jar, electricity can be accumulated +and retained in considerable quantity, by the contrivance +of having two conducting surfaces of equal extent, +and parallel to each other through the whole of that extent, +with a non-conducting substance such as glass between them. +When one side of the jar is charged positively, the other is +charged negatively, and it was by virtue of this fact that the +Leyden jar served just now as an instance in our employment +of the Method of Agreement. Now it is impossible +to discharge one of the coatings unless the other can be +discharged at the same time. A conductor held to the positive +side cannot convey away any electricity unless an equal +quantity be allowed to pass from the negative side: if one +coating be perfectly insulated, the charge is safe. The dissipation +of one must proceed <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">pari passu</span></span> +with that of the other. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The law thus strongly indicated admits of corroboration +by the Method of Concomitant Variations. The Leyden jar +is capable of receiving a much higher charge than can ordinarily +be given to the conductor of an electrical machine. +Now in the case of the Leyden jar, the metallic surface which +receives the induced electricity is a conductor exactly similar +to that which receives the primary charge, and is therefore +as susceptible of receiving and retaining the one electricity, +as the opposite surface of receiving and retaining the other; +but in the machine, the neighbouring body which is to be +oppositely electrified is the surrounding atmosphere, or any +body casually brought near to the conductor; and as these +are generally much inferior in their capacity of becoming +electrified, to the conductor itself, their limited power imposes +a corresponding limit to the capacity of the conductor +for being charged. As the capacity of the neighbouring body +<span class="tei tei-pb" id="page424">[pg 424]</span><a name="Pg424" id="Pg424" class="tei tei-anchor"></a> +for supporting the opposition increases, a higher charge becomes +possible: and to this appears to be owing the great +superiority of the Leyden jar. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A further and most decisive confirmation by the Method +of Difference, is to be found in one of Faraday's experiments +in the course of his researches on the subject of induced +electricity. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Since common or machine electricity, and voltaic electricity, +may be considered for the present purpose to be +identical, Faraday wished to know whether, as the prime +conductor develops opposite electricity upon a conductor in +its vicinity, so a voltaic current running along a wire would +induce an opposite current upon another wire laid parallel +to it at a short distance. Now this case is similar to the +cases previously examined, in every circumstance except the +one to which we have ascribed the effect. We found in the +former instances that whenever electricity of one kind was +excited in one body, electricity of the opposite kind must be +excited in a neighbouring body. But in Faraday's experiment +this indispensable opposition exists within the wire +itself. From the nature of a voltaic charge, the two opposite +currents necessary to the existence of each other are both +accommodated in one wire; and there is no need of another +wire placed beside it to contain one of them, in the same way +as the Leyden jar must have a positive and a negative surface. +The exciting cause can and does produce all the effect +which its laws require, independently of any electric excitement +of a neighbouring body. Now the result of the experiment +with the second wire was, that no opposite current +was produced. There was an instantaneous effect at the +closing and breaking of the voltaic circuit; electric inductions +appeared when the two wires were moved to and from +one another; but these are phenomena of a different class. +There was no induced electricity in the sense in which this is +predicated of the Leyden jar; there was no sustained current +running up the one wire while an opposite current ran down +the neighbouring wire; and this alone would have been a +true parallel case to the other. +</p> + +<span class="tei tei-pb" id="page425">[pg 425]</span><a name="Pg425" id="Pg425" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It thus appears by the combined evidence of the Method +of Agreement, the Method of Concomitant Variations, and +the most rigorous form of the Method of Difference, that +neither of the two kinds of electricity can be excited without +an equal excitement of the other and opposite kind: that +both are effects of the same cause; that the possibility of the +one is a condition of the possibility of the other, and the +quantity of the one an impassable limit to the quantity of the +other. A scientific result of considerable interest in itself, +and illustrating those three methods in a manner both characteristic +and easily intelligible.<a id="noteref_79" name="noteref_79" href="#note_79"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">79</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. Our third example shall be extracted from Sir John +Herschel's <span class="tei tei-hi"><span style="font-style: italic">Discourse on the Study of Natural Philosophy</span></span>, a +work replete with happily-selected exemplifications of inductive +processes from almost every department of physical +science, and in which alone, of all books which I have met +with, the four methods of induction are distinctly recognised, +though not so clearly characterized and defined, nor their +correlation so fully shown, as has appeared to me desirable. +The present example is described by Sir John Herschel as +<span class="tei tei-q">“one of the most beautiful specimens”</span> which can be cited +<span class="tei tei-q">“of inductive experimental inquiry lying within a moderate +compass;”</span> the theory of dew, first promulgated by the late +Dr. Wells, and now universally adopted by scientific authorities. +The passages in inverted commas are extracted verbatim +from the <span class="tei tei-q">“Discourse.”</span><a id="noteref_80" name="noteref_80" href="#note_80"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">80</span></span></a> +</p> + +<span class="tei tei-pb" id="page426">[pg 426]</span><a name="Pg426" id="Pg426" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Suppose <em class="tei tei-emph"><span style="font-style: italic">dew</span></em> were the phenomenon proposed, whose +cause we would know. In the first place”</span> we must determine +precisely what we mean by dew: what the fact really +is, whose cause we desire to investigate. <span class="tei tei-q">“We must separate +dew from rain, and the moisture of fogs, and limit the +application of the term to what is really meant, which is, the +spontaneous appearance of moisture on substances exposed +in the open air when no rain or <em class="tei tei-emph"><span style="font-style: italic">visible</span></em> wet is falling.”</span> This +answers to a preliminary operation which will be characterized +in the ensuing book, treating of operations subsidiary to +induction.<a id="noteref_81" name="noteref_81" href="#note_81"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">81</span></span></a> The state of the question being fixed, we come +to the solution. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Now, here we have analogous phenomena in the moisture +which bedews a cold metal or stone when we breathe +upon it; that which appears on a glass of water fresh from +the well in hot weather; that which appears on the inside of +windows when sudden rain or hail chills the external air; +that which runs down our walls when, after a long frost, a +warm moist thaw comes on.”</span> Comparing these cases, we +find that they all contain the phenomenon which was proposed +as the subject of investigation. Now <span class="tei tei-q">“all these instances +agree in one point, the coldness of the object dewed, +in comparison with the air in contact with it.”</span> But there +still remains the most important case of all, that of nocturnal +dew: does the same circumstance exist in this case? <span class="tei tei-q">“Is it +a fact that the object dewed <em class="tei tei-emph"><span style="font-style: italic">is</span></em> colder than the air? Certainly +not, one would at first be inclined to say; for what is to <em class="tei tei-emph"><span style="font-style: italic">make</span></em> +it so? But ... the experiment is easy: we have only to +lay a thermometer in contact with the dewed substance, and +hang one at a little distance above it, out of reach of its influence. +The experiment has been therefore made; the question +has been asked, and the answer has been invariably in +the affirmative. Whenever an object contracts dew, it <em class="tei tei-emph"><span style="font-style: italic">is</span></em> +colder than the air.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Here then is a complete application of the Method of +Agreement, establishing the fact of an invariable connexion +<span class="tei tei-pb" id="page427">[pg 427]</span><a name="Pg427" id="Pg427" class="tei tei-anchor"></a> +between the deposition of dew on a surface, and the coldness +of that surface compared with the external air. But which +of these is cause, and which effect? or are they both effects +of something else? On this subject the Method of Agreement +can afford us no light: we must call in a more potent +method. <span class="tei tei-q">“We must collect more facts, or, which comes to +the same thing, vary the circumstances; since every instance +in which the circumstances differ is a fresh fact: and especially, +we must note the contrary or negative cases, <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span>, where +no dew is produced:”</span> for a comparison between instances of +dew and instances of no dew, is the condition necessary to +bring the Method of Difference into play. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Now, first, no dew is produced on the surface of polished +metals, but it <em class="tei tei-emph"><span style="font-style: italic">is</span></em> very copiously on glass, both exposed with +their faces upwards, and in some cases the under side of a +horizontal plate of glass is also dewed.”</span> Here is an instance +in which the effect is produced, and another instance in which +it is not produced; but we cannot yet pronounce, as the +canon of the Method of Difference requires, that the latter +instance agrees with the former in all its circumstances except +one; for the differences between glass and polished +metals are manifold, and the only thing we can as yet be sure +of is, that the cause of dew will be found among the circumstances +by which the former substance is distinguished from +the latter. But if we could be sure that glass, and the various +other substances on which dew is deposited, have only <em class="tei tei-emph"><span style="font-style: italic">one</span></em> +quality in common, and that polished metals and the other +substances on which dew is <em class="tei tei-emph"><span style="font-style: italic">not</span></em> deposited have also nothing +in common but the one circumstance, of <em class="tei tei-emph"><span style="font-style: italic">not</span></em> having the one +quality which the others have; the requisitions of the Method +of Difference would be completely satisfied, and we should +recognise, in that quality of the substances, the cause of dew. +This, accordingly, is the path of inquiry which is next to be +pursued. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“In the cases of polished metal and polished glass, the +contrast shows evidently that the <em class="tei tei-emph"><span style="font-style: italic">substance</span></em> has much to do +with the phenomenon; therefore let the substance <em class="tei tei-emph"><span style="font-style: italic">alone</span></em> be +diversified as much as possible, by exposing polished surfaces +<span class="tei tei-pb" id="page428">[pg 428]</span><a name="Pg428" id="Pg428" class="tei tei-anchor"></a> +of various kinds. This done, a <em class="tei tei-emph"><span style="font-style: italic">scale of intensity</span></em> becomes +obvious. Those polished substances are found to be most +strongly dewed which conduct heat worst; while those which +conduct well, resist dew most effectually.”</span> The complication +increases; here is the Method of Concomitant Variations +called to our assistance; and no other method was +practicable on this occasion; for the quality of conducting +heat could not be excluded, since all substances conduct +heat in some degree. The conclusion obtained is, that +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">cæteris paribus</span></span> +the deposition of dew is in some proportion to +the power which the body possesses of resisting the passage +of heat; and that this, therefore, (or something connected +with this,) must be at least one of the causes which assist in +producing the deposition of dew on the surface. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“But if we expose rough surfaces instead of polished, +we sometimes find this law interfered with. Thus, roughened +iron, especially if painted over or blackened, becomes +dewed sooner than varnished paper: the kind of <em class="tei tei-emph"><span style="font-style: italic">surface</span></em>, +therefore, has a great influence. Expose, then, the <em class="tei tei-emph"><span style="font-style: italic">same</span></em> +material in very diversified states as to surface,”</span> (that is, +employ the Method of Difference to ascertain concomitance +of variations,) <span class="tei tei-q">“and another scale of intensity becomes at +once apparent; those <em class="tei tei-emph"><span style="font-style: italic">surfaces</span></em> which <em class="tei tei-emph"><span style="font-style: italic">part with their heat</span></em> most +readily by radiation, are found to contract dew most copiously.”</span> +Here, therefore, are the requisites for a second +employment of the Method of Concomitant Variations; +which in this case also is the only method available, since +all substances radiate heat in some degree or other. The +conclusion obtained by this new application of the method +is, that <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">cæteris paribus</span></span> +the deposition of dew is also in some +proportion to the power of radiating heat; and that the +quality of doing this abundantly (or some cause on which +that quality depends) is another of the causes which promote +the deposition of dew on the substance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Again, the influence ascertained to exist of <em class="tei tei-emph"><span style="font-style: italic">substance</span></em> +and <em class="tei tei-emph"><span style="font-style: italic">surface</span></em> leads us to consider that of <em class="tei tei-emph"><span style="font-style: italic">texture</span></em>: and here, +again, we are presented on trial with remarkable differences, +and with a third scale of intensity, pointing out substances +<span class="tei tei-pb" id="page429">[pg 429]</span><a name="Pg429" id="Pg429" class="tei tei-anchor"></a> +of a close firm texture, such as stones, metals, &c., as unfavourable, +but those of a loose one, as cloth, velvet, wool, eiderdown, +cotton, &c., as eminently favourable to the contraction +of dew.”</span> The Method of Concomitant Variations is here, +for the third time, had recourse to; and, as before, from +necessity, since the texture of no substance is absolutely +firm or absolutely loose. Looseness of texture, therefore, +or something which is the cause of that quality, is another +circumstance which promotes the deposition of dew; but +this third cause resolves itself into the first, viz. the quality +of resisting the passage of heat: for substances of loose +texture <span class="tei tei-q">“are precisely those which are best adapted for +clothing, or for impeding the free passage of heat from the +skin into the air, so as to allow their outer surfaces to be +very cold, while they remain warm within;”</span> and this last is, +therefore, an induction (from fresh instances) simply <em class="tei tei-emph"><span style="font-style: italic">corroborative</span></em> +of a former induction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It thus appears that the instances in which much dew is +deposited, which are very various, agree in this, and, so far as +we are able to observe, in this only, that they either radiate +heat rapidly or conduct it slowly: qualities between which +there is no other circumstance of agreement, than that by +virtue of either, the body tends to lose heat from the surface +more rapidly than it can be restored from within. The +instances, on the contrary, in which no dew, or but a small +quantity of it, is formed, and which are also extremely +various, agree (so far as we can observe) in nothing except +in <em class="tei tei-emph"><span style="font-style: italic">not</span></em> having this same property. We seem, therefore, to +have detected the characteristic difference between the substances +on which dew is produced, and those on which it is +not produced. And thus have been realized the requisitions +of what we have termed the Indirect Method of Difference, +or the Joint Method of Agreement and Difference. The +example afforded of this indirect method, and of the manner +in which the data are prepared for it by the Methods of +Agreement and of Concomitant Variations, is the most +important of all the illustrations of induction afforded by +this interesting speculation. +</p> + +<span class="tei tei-pb" id="page430">[pg 430]</span><a name="Pg430" id="Pg430" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We might now consider the question, on what the +deposition of dew depends, to be completely solved, if we +could be quite sure that the substances on which dew is +produced differ from those on which it is not, in <em class="tei tei-emph"><span style="font-style: italic">nothing</span></em> but +in the property of losing heat from the surface faster than +the loss can be repaired from within. And though we +never can have that complete certainty, this is not of so +much importance as might at first be supposed; for we +have, at all events, ascertained that even if there be any other +quality hitherto unobserved which is present in all the substances +which contract dew, and absent in those which do +not, this other property must be one which, in all that great +number of substances, is present or absent exactly where the +property of being a better radiator than conductor is present +or absent; an extent of coincidence which affords a +strong presumption of a community of cause, and a consequent +invariable coexistence between the two properties; +so that the property of being a better radiator than conductor, +if not itself the cause, almost certainly always accompanies +the cause, and for purposes of prediction, no error is +likely to be committed by treating it as if it were really such. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Reverting now to an earlier stage of the inquiry, let us +remember that we had ascertained that, in every instance +where dew is formed, there is actual coldness of the surface +below the temperature of the surrounding air; but we were +not sure whether this coldness was the cause of dew, or its +effect. This doubt we are now able to resolve. We have +found that, in every such instance, the substance must be +one which, by its own properties or laws, would, if exposed +in the night, become colder than the surrounding air. The +coldness therefore, being accounted for independently of the +dew, while it is proved that there is a connexion between +the two, it must be the dew which depends on the coldness; +or in other words, the coldness is the cause of the dew. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This law of causation, already so amply established, +admits, however, of efficient additional corroboration in +no less than three ways. First, by deduction from the +known laws of aqueous vapour when diffused through air +<span class="tei tei-pb" id="page431">[pg 431]</span><a name="Pg431" id="Pg431" class="tei tei-anchor"></a> +or any other gas; and though we have not yet come to +the Deductive Method, we will not omit what is necessary +to render this speculation complete. It is known by direct +experiment that only a limited quantity of water can remain +suspended in the state of vapour at each degree of temperature, +and that this maximum grows less and less as the +temperature diminishes. From this it follows, deductively, +that if there is already as much vapour suspended as the air +will contain at its existing temperature, any lowering of that +temperature will cause a portion of the vapour to be condensed, +and become water. But, again, we know deductively, +from the laws of heat, that the contact of the air with +a body colder than itself, will necessarily lower the temperature +of the stratum of air immediately applied to its surface; +and will therefore cause it to part with a portion of its water, +which accordingly will, by the ordinary laws of gravitation +or cohesion, attach itself to the surface of the body, thereby +constituting dew. This deductive proof, it will have been +seen, has the advantage of proving at once, causation as +well as coexistence; and it has the additional advantage that +it also accounts for the <em class="tei tei-emph"><span style="font-style: italic">exceptions</span></em> to the occurrence of the +phenomenon, the cases in which, although the body is colder +than the air, yet no dew is deposited; by showing that this +will necessarily be the case when the air is so under-supplied +with aqueous vapour, comparatively to its temperature, that +even when somewhat cooled by the contact of the colder +body, it can still continue to hold in suspension all the +vapour which was previously suspended in it: thus in a very +dry summer there are no dews, in a very dry winter no hoar +frost. Here, therefore, is an additional condition of the production +of dew, which the methods we previously made use +of failed to detect, and which might have remained still +undetected, if recourse had not been had to the plan of +deducing the effect from the ascertained properties of the +agents known to be present. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The second corroboration of the theory is by direct experiment, +according to the canon of the Method of Difference. +We can, by cooling the surface of any body, find in all cases +<span class="tei tei-pb" id="page432">[pg 432]</span><a name="Pg432" id="Pg432" class="tei tei-anchor"></a> +some temperature, (more or less inferior to that of the surrounding +air, according to its hygrometric condition), at which +dew will begin to be deposited. Here, too, therefore, the +causation is directly proved. We can, it is true, accomplish +this only on a small scale; but we have ample reason to conclude +that the same operation, if conducted in Nature's great +laboratory, would equally produce the effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And, finally, even on that great scale we are able to verify +the result. The case is one of those rare cases, as we have +shown them to be, in which nature works the experiment for +us in the same manner in which we ourselves perform it; +introducing into the previous state of things a single and perfectly +definite new circumstance, and manifesting the effect +so rapidly that there is not time for any other material change +in the pre-existing circumstances. <span class="tei tei-q">“It is observed that dew +is never copiously deposited in situations much screened +from the open sky, and not at all in a cloudy night; but <em class="tei tei-emph"><span style="font-style: italic">if +the clouds withdraw even for a few minutes, and leave a clear +opening, a deposition of dew presently begins</span></em>, and goes on increasing.... +Dew formed in clear intervals will often even +evaporate again when the sky becomes thickly overcast.”</span> +The proof, therefore, is complete, that the presence or absence +of an uninterrupted communication with the sky causes the +deposition or non-deposition of dew. Now, since a clear sky +is nothing but the absence of clouds, and it is a known property +of clouds, as of all other bodies between which and any +given object nothing intervenes but an elastic fluid, that they +tend to raise or keep up the superficial temperature of the +object by radiating heat to it, we see at once that the disappearance +of clouds will cause the surface to cool; so that +Nature, in this case, produces a change in the antecedent by +definite and known means, and the consequent follows accordingly: +a natural experiment which satisfies the requisitions +of the Method of Difference.<a id="noteref_82" name="noteref_82" href="#note_82"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">82</span></span></a> +</p> + +<span class="tei tei-pb" id="page433">[pg 433]</span><a name="Pg433" id="Pg433" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The accumulated proof of which the Theory of Dew has +been found susceptible, is a striking instance of the fulness +of assurance which the inductive evidence of laws of causation +may attain, in cases in which the invariable sequence is +by no means obvious to a superficial view. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. The last example will have conveyed to any one +by whom it has been duly followed, so clear a conception of +the use and practical management of three of the four methods +of experimental inquiry, as to supersede the necessity +of any further exemplification of them. The remaining +method, that of Residues, not having found any place either +in this or in the two preceding investigations, I shall extract +from Sir John Herschel some examples of that method, with +the remarks by which they are introduced. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“It is by this process, in fact, that science, in its present +advanced state, is chiefly promoted. Most of the phenomena +which Nature presents are very complicated; and when +the effects of all known causes are estimated with exactness, +and subducted, the residual facts are constantly appearing in +the form of phenomena altogether new, and leading to the +most important conclusions.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“For example: the return of the comet predicted by Professor +<span class="tei tei-pb" id="page434">[pg 434]</span><a name="Pg434" id="Pg434" class="tei tei-anchor"></a> +Encke, a great many times in succession, and the +general good agreement of its calculated with its observed +place during any one of its periods of visibility, would lead +us to say that its gravitation towards the sun and planets is +the sole and sufficient cause of all the phenomena of its orbitual +motion: but when the effect of this cause is strictly calculated +and subducted from the observed motion, there is +found to remain behind a <em class="tei tei-emph"><span style="font-style: italic">residual phenomenon</span></em>, which would +never have been otherwise ascertained to exist, which is a +small anticipation of the time of its reappearance, or a diminution +of its periodic time, which cannot be accounted for by +gravity, and whose cause is therefore to be inquired into. +Such an anticipation would be caused by the resistance of a +medium disseminated through the celestial regions; and as +there are other good reasons for believing this to be a +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">vera +causa</span></span>,”</span> (an actually existing antecedent,) <span class="tei tei-q">“it has therefore +been ascribed to such a resistance.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“M. Arago, having suspended a magnetic needle by a silk +thread, and set it in vibration, observed, that it came much +sooner to a state of rest when suspended over a plate of copper, +than when no such plate was beneath it. Now, in both +cases there were two <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">veræ +causæ</span></span></span> (antecedents known to +exist) <span class="tei tei-q">“why it <em class="tei tei-emph"><span style="font-style: italic">should</span></em> come at length to rest, viz. the resistance +of the air, which opposes, and at length destroys, all +motions performed in it; and the want of perfect mobility in +the silk thread. But the effect of these causes being exactly +known by the observation made in the absence of the copper, +and being thus allowed for and subducted, a residual phenomenon +appeared, in the fact that a retarding influence was +exerted by the copper itself; and this fact, once ascertained, +speedily led to the knowledge of an entirely new and unexpected +class of relations." This example belongs, however, +not to the Method of Residues but to the Method of Difference, +the law being ascertained by a direct comparison of +the results of two experiments, which differed in nothing but +the presence or absence of the plate of copper. To have +made it exemplify the Method of Residues, the effect of the +resistance of the air and that of the rigidity of the silk should +<span class="tei tei-pb" id="page435">[pg 435]</span><a name="Pg435" id="Pg435" class="tei tei-anchor"></a> +have been calculated <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, +from the laws obtained by +separate and foregone experiments.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Unexpected and peculiarly striking confirmations of +inductive laws frequently occur in the form of residual phenomena, +in the course of investigations of a widely different +nature from those which gave rise to the inductions themselves. +A very elegant example may be cited in the unexpected +confirmation of the law of the development of heat in +elastic fluids by compression, which is afforded by the phenomena +of sound. The inquiry into the cause of sound had +led to conclusions respecting its mode of propagation, from +which its velocity in the air could be precisely calculated. +The calculations were performed; but, when compared with +fact, though the agreement was quite sufficient to show the +general correctness of the cause and mode of propagation +assigned, yet the <em class="tei tei-emph"><span style="font-style: italic">whole</span></em> velocity could not be shown to arise +from this theory. There was still a residual velocity to be +accounted for, which placed dynamical philosophers for a +long time in a great dilemma. At length Laplace struck on +the happy idea, that this might arise from the <em class="tei tei-emph"><span style="font-style: italic">heat</span></em> developed +in the act of that condensation which necessarily takes place +at every vibration by which sound is conveyed. The matter +was subjected to exact calculation, and the result was at once +the complete explanation of the residual phenomenon, and a +striking confirmation of the general law of the development +of heat by compression, under circumstances beyond artificial +imitation.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Many of the new elements of chemistry have been +detected in the investigation of residual phenomena. Thus +Arfwedson discovered lithia by perceiving an excess of +weight in the sulphate produced from a small portion of +what he considered as magnesia present in a mineral he +had analysed. It is on this principle, too, that the small +concentrated residues of great operations in the arts are +almost sure to be the lurking places of new chemical ingredients: +witness iodine, brome, selenium, and the new metals +accompanying platina in the experiments of Wollaston and +<span class="tei tei-pb" id="page436">[pg 436]</span><a name="Pg436" id="Pg436" class="tei tei-anchor"></a> +Tennant. It was a happy thought of Glauber to examine +what everybody else threw away.”</span><a id="noteref_83" name="noteref_83" href="#note_83"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">83</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Almost all the greatest discoveries in Astronomy,”</span> says +the same author,<a id="noteref_84" name="noteref_84" href="#note_84"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">84</span></span></a> <span class="tei tei-q">“have resulted from the consideration of +residual phenomena of a quantitative or numerical kind.... +It was thus that the grand discovery of the precession of +the equinoxes resulted as a residual phenomenon, from the +imperfect explanation of the return of the seasons by the +return of the sun to the same apparent place among the +fixed stars. Thus, also, aberration and nutation resulted as +residual phenomena from that portion of the changes of the +apparent places of the fixed stars which was left unaccounted +for by precession. And thus again the apparent +proper motions of the stars are the observed residues of +their apparent movements outstanding and unaccounted for +by strict calculation of the effects of precession, nutation, and +aberration. The nearest approach which human theories +can make to perfection is to diminish this residue, this +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">caput +mortuum</span></span> of observation, as it may be considered, as much as +practicable, and, if possible, to reduce it to nothing, either +by showing that something has been neglected in our estimation +of known causes, or by reasoning upon it as a new fact, +and on the principle of the inductive philosophy ascending +from the effect to its cause or causes.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The disturbing effects mutually produced by the earth +and planets upon each other's motions were first brought to +light as residual phenomena, by the difference which appeared +between the observed places of those bodies, and the +places calculated on a consideration solely of their gravitation +towards the sun. It was this which determined astronomers +to consider the law of gravitation as obtaining between +all bodies whatever, and therefore between all particles of +matter; their first tendency having been to regard it as a +force acting only between each planet or satellite and the +central body to whose system it belonged. Again, the +catastrophists, in geology, be their opinion right or wrong, +<span class="tei tei-pb" id="page437">[pg 437]</span><a name="Pg437" id="Pg437" class="tei tei-anchor"></a> +support it on the plea, that after the effect of all causes +now in operation has been allowed for, there remains in the +existing constitution of the earth a large residue of facts, +proving the existence at former periods either of other forces, +or of the same forces in a much greater degree of intensity. +To add one more example: those who assert, what no one +has ever shewn any real ground for believing, that there is +in one human individual, one sex, or one race of mankind +over another, an inherent and inexplicable superiority in +mental faculties, could only substantiate their proposition by +subtracting from the differences of intellect which we in fact +see, all that can be traced by known laws either to the ascertained +differences of physical organization, or to the differences +which have existed in the outward circumstances in +which the subjects of the comparison have hitherto been +placed. What these causes might fail to account for, would +constitute a residual phenomenon, which and which alone +would be evidence of an ulterior original distinction, and +the measure of its amount. But the assertors of such supposed +differences have not provided themselves with these +necessary logical conditions of the establishment of their +doctrine. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The spirit of the Method of Residues being, it is hoped, +sufficiently intelligible from these examples, and the other +three methods having been so aptly exemplified in the +inductive processes which produced the Theory of Dew, we +may here close our exposition of the four methods, considered +as employed in the investigation of the simpler and +more elementary order of the combinations of phenomena.<a id="noteref_85" name="noteref_85" href="#note_85"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">85</span></span></a> +</p> + +</div> + +<span class="tei tei-pb" id="page441">[pg 441]</span><a name="Pg441" id="Pg441" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc73" id="toc73"></a> +<a name="pdf74" id="pdf74"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER X. OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE +OF EFFECTS.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. In the preceding exposition of the four methods of +observation and experiment, by which we contrive to distinguish +among a mass of coexistent phenomena the particular +effect due to a given cause, or the particular cause +which gave birth to a given effect; it has been necessary to +suppose, in the first instance, for the sake of simplification, +that this analytical operation is encumbered by no other +difficulties than what are essentially inherent in its nature; +and to represent to ourselves, therefore, every effect, on the +one hand as connected exclusively with a single cause, and +on the other hand as incapable of being mixed and confounded +with any other coexistent effect. We have regarded +<span class="tei tei-hi"><span style="font-style: italic">a b c d e</span></span>, the aggregate of the phenomena existing at any +moment, as consisting of dissimilar facts, <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, <span class="tei tei-hi"><span style="font-style: italic">d</span></span>, +and <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, +for each of which one, and only one, cause needs be sought; +the difficulty being only that of singling out this one cause +from the multitude of antecedent circumstances, A, B, C, +D, and E. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If such were the fact, it would be comparatively an easy +task to investigate the laws of nature. But the supposition +does not hold, in either of its parts. In the first place, it is +not true that the same phenomenon is always produced by +the same cause: the effect <span class="tei tei-hi"><span style="font-style: italic">a</span></span> may sometimes arise from A, +sometimes from B. And, secondly, the effects of different +causes are often not dissimilar, but homogeneous, and marked +out by no assignable boundaries from one another: A and +B may produce not <span class="tei tei-hi"><span style="font-style: italic">a</span></span> and <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +but different portions of an +effect <span class="tei tei-hi"><span style="font-style: italic">a</span></span>. The obscurity and difficulty of the investigation of +the laws of phenomena is singularly increased by the necessity +<span class="tei tei-pb" id="page442">[pg 442]</span><a name="Pg442" id="Pg442" class="tei tei-anchor"></a> +of adverting to these two circumstances; Intermixture +of Effects, and Plurality of Causes. To the latter, being the +simpler of the two considerations, we shall first direct our +attention. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is not true, then, that one effect must be connected with +only one cause, or assemblage of conditions; that each phenomenon +can be produced only in one way. There are often +several independent modes in which the same phenomenon +could have originated. One fact may be the consequent in +several invariable sequences; it may follow, with equal uniformity, +any one of several antecedents, or collections of +antecedents. Many causes may produce motion: many +causes may produce some kinds of sensation: many causes +may produce death. A given effect may really be produced +by a certain cause, and yet be perfectly capable of being +produced without it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. One of the principal consequences of this fact of +Plurality of Causes is, to render the first of the inductive +methods, that of Agreement, uncertain. To illustrate that +method, we supposed two instances, A B C followed by <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, +and A D E followed by <span class="tei tei-hi"><span style="font-style: italic">a d e</span></span>. From these instances it might +be concluded that A is an invariable antecedent of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, and +even that it is the unconditional invariable antecedent, or +cause, if we could be sure that there is no other antecedent +common to the two cases. That this difficulty may not stand +in the way, let us suppose the two cases positively ascertained +to have no antecedent in common except A. The moment, +however, that we let in the possibility of a plurality of causes, +the conclusion fails. For it involves a tacit supposition, that +<span class="tei tei-hi"><span style="font-style: italic">a</span></span> must have been produced in both instances by the same +cause. If there can possibly have been two causes, those +two may, for example, be C and E: the one may have been +the cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span> in the former of the instances, the other in the +latter, A having no influence in either case. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Suppose, for example, that two great artists, or great +philosophers, that two extremely selfish, or extremely generous +characters, were compared together as to the circumstances +<span class="tei tei-pb" id="page443">[pg 443]</span><a name="Pg443" id="Pg443" class="tei tei-anchor"></a> +of their education and history, and the two cases +were found to agree only in one circumstance: would it +follow that this one circumstance was the cause of the quality +which characterized both those individuals? Not at all; for +the causes which may produce any type of character are +innumerable; and the two persons might equally have +agreed in their character, though there had been no manner +of resemblance in their previous history. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This, therefore, is a characteristic imperfection of the +Method of Agreement; from which imperfection the Method +of Difference is free. For if we have two instances, A B C +and B C, of which B C gives <span class="tei tei-hi"><span style="font-style: italic">b c</span></span>, and A being added converts +it into <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span>, it is certain that in this instance at least, A was +either the cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, or an indispensable portion of its cause, +even though the cause which produces it in other instances +may be altogether different. Plurality of Causes, therefore, +not only does not diminish the reliance due to the Method +of Difference, but does not even render a greater number of +observations or experiments necessary: two instances, the +one positive and the other negative, are still sufficient for the +most complete and rigorous induction. Not so, however, +with the Method of Agreement. The conclusions which that +yields, when the number of instances compared is small, are +of no real value, except as, in the character of suggestions, +they may lead either to experiments bringing them to the +test of the Method of Difference, or to reasonings which may +explain and verify them deductively. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is only when the instances, being indefinitely multiplied +and varied, continue to suggest the same result, that this result +acquires any high degree of independent value. If there +are but two instances, A B C and A D E, although these +instances have no antecedent in common except A, yet as +the effect may possibly have been produced in the two cases +by different causes, the result is at most only a slight probability +in favour of A; there may be causation, but it is +almost equally probable that there was only a coincidence. +But the oftener we repeat the observation, varying the circumstances, +the more we advance towards a solution of this +<span class="tei tei-pb" id="page444">[pg 444]</span><a name="Pg444" id="Pg444" class="tei tei-anchor"></a> +doubt. For if we try A F G, A H K, &c., all unlike one +another except in containing the circumstance A, and if we +find the effect <span class="tei tei-hi"><span style="font-style: italic">a</span></span> entering into the result in all these cases, +we must suppose one of two things, either that it is caused +by A, or that it has as many different causes as there are +instances. With each addition, therefore, to the number of +instances, the presumption is strengthened in favour of A. +The inquirer, of course, will not neglect, if an opportunity +present itself, to exclude A from some one of these combinations, +from A H K for instance, and by trying H K separately, +appeal to the Method of Difference in aid of the Method of +Agreement. By the Method of Difference alone can it be +ascertained that A is the cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>; but that it is either the +cause or another effect of the same cause, may be placed +beyond any reasonable doubt by the Method of Agreement, +provided the instances are very numerous, as well as sufficiently +various. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After how great a multiplication, then, of varied instances, +all agreeing in no other antecedent except A, is the supposition +of a plurality of causes sufficiently rebutted, and the +conclusion that <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is +the effect of A divested of the characteristic +imperfection and reduced to a virtual certainty? This +is a question which we cannot be exempted from answering; +but the consideration of it belongs to what is called the +Theory of Probability, which will form the subject of a +chapter hereafter. It is seen, however, at once, that the +conclusion does amount to a practical certainty after a sufficient +number of instances, and that the method, therefore, +is not radically vitiated by the characteristic imperfection. +The result of these considerations is only, in the first place, +to point out a new source of inferiority in the Method of +Agreement as compared with other modes of investigation, +and new reasons for never resting contented with the results +obtained by it, without attempting to confirm them either by +the Method of Difference, or by connecting them deductively +with some law or laws already ascertained by that superior +method. And, in the second place, we learn from this the true +theory of the value of mere <em class="tei tei-emph"><span style="font-style: italic">number</span></em> of instances in inductive inquiry. +The Plurality of Causes is the only reason why mere +<span class="tei tei-pb" id="page445">[pg 445]</span><a name="Pg445" id="Pg445" class="tei tei-anchor"></a> +number is of any importance. The tendency of unscientific +inquirers is to rely too much on number, without analysing +the instances; without looking closely enough into their nature, +to ascertain what circumstances are or are not eliminated by +means of them. Most people hold their conclusions with a +degree of assurance proportioned to the mere <em class="tei tei-emph"><span style="font-style: italic">mass</span></em> of the +experience on which they appear to rest; not considering +that by the addition of instances to instances, all of the same +kind, that is, differing from one another only in points already +recognised as immaterial, nothing whatever is added to the +evidence of the conclusion. A single instance eliminating +some antecedent which existed in all the other cases, is of +more value than the greatest multitude of instances which +are reckoned by their number alone. It is necessary, no +doubt, to assure ourselves, by a repetition of the observation +or experiment, that no error has been committed concerning +the individual facts observed; and until we have assured +ourselves of this, instead of varying the circumstances, we +cannot too scrupulously repeat the same experiment or +observation without any change. But when once this assurance +has been obtained, the multiplication of instances +which do not exclude any more circumstances would be +entirely useless, were it not for the Plurality of Causes. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is of importance to remark, that the peculiar modification +of the Method of Agreement which, as partaking in +some degree of the nature of the Method of Difference, I +have called the Joint Method of Agreement and Difference, +is not affected by the characteristic imperfection now pointed +out. For, in the joint method, it is supposed not only that +the instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is, agree only in containing A, but +also that the instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> is not, agree only in not +containing A. Now, if this be so, A must be not only the +cause of <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, but the only possible cause: for if there were +another, as for example B, then in the instances in which <span class="tei tei-hi"><span style="font-style: italic">a</span></span> +is not, B must have been absent as well as A, and it would +not be true that these instances agree <em class="tei tei-emph"><span style="font-style: italic">only</span></em> in not containing +A. This, therefore, constitutes an immense advantage of the +joint method over the simple Method of Agreement. It may +seem, indeed, that the advantage does not belong so much +<span class="tei tei-pb" id="page446">[pg 446]</span><a name="Pg446" id="Pg446" class="tei tei-anchor"></a> +to the joint method, as to one of its two premisses, (if they +may be so called,) the negative premiss. The Method of +Agreement, when applied to negative instances, or those in +which a phenomenon does <em class="tei tei-emph"><span style="font-style: italic">not</span></em> take place, is certainly free +from the characteristic imperfection which affects it in the +affirmative case. The negative premiss, it might therefore +be supposed, could be worked as a simple case of the +Method of Agreement, without requiring an affirmative premiss +to be joined with it. But although this is true in +principle, it is generally altogether impossible to work the +Method of Agreement by negative instances without positive +ones: it is so much more difficult to exhaust the field of +negation than that of affirmation. For instance, let the +question be, what is the cause of the transparency of bodies; +with what prospect of success could we set ourselves to +inquire directly in what the multifarious substances which +are <em class="tei tei-emph"><span style="font-style: italic">not</span></em> transparent, agree? But we might hope much sooner +to seize some point of resemblance among the comparatively +few and definite species of objects which <em class="tei tei-emph"><span style="font-style: italic">are</span></em> transparent; +and this being attained, we should quite naturally be put +upon examining whether the <em class="tei tei-emph"><span style="font-style: italic">absence</span></em> of this one circumstance +be not precisely the point in which all opaque substances +will be found to resemble. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The Joint Method of Agreement and Difference, therefore, +or, as I have otherwise called it, the Indirect Method of +Difference (because, like the Method of Difference properly +so called, it proceeds by ascertaining how and in what the +cases where the phenomenon is present, differ from those in +which it is absent) is, after the direct Method of Difference, +the most powerful of the remaining instruments of inductive +investigation; and in the sciences which depend on pure +observation, with little or no aid from experiment, this +method, so well exemplified in the speculation on the cause +of dew, is the primary resource, so far as direct appeals to +experience are concerned. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. We have thus far treated Plurality of Causes only +as a possible supposition, which, until removed, renders our +<span class="tei tei-pb" id="page447">[pg 447]</span><a name="Pg447" id="Pg447" class="tei tei-anchor"></a> +inductions uncertain, and have only considered by what +means, where the plurality does not really exist, we may be +enabled to disprove it. But we must also consider it as a +case actually occurring in nature, and which, as often as it +does occur, our methods of induction ought to be capable of +ascertaining and establishing. For this, however, there is +required no peculiar method. When an effect is really producible +by two or more causes, the process for detecting them +is in no way different from that by which we discover single +causes. They may (first) be discovered as separate sequences, +by separate sets of instances. One set of observations +or experiments shows that the sun is a cause of heat, +another that friction is a source of it, another that percussion, +another that electricity, another that chemical action is +such a source. Or (secondly) the plurality may come to +light in the course of collating a number of instances, when +we attempt to find some circumstance in which they all +agree, and fail in doing so. We find it impossible to trace, +in all the cases in which the effect is met with, any common +circumstance. We find that we can eliminate <em class="tei tei-emph"><span style="font-style: italic">all</span></em> the antecedents; +that no one of them is present in all the instances, +no one of them indispensable to the effect. On closer +scrutiny, however, it appears that though no one is always +present, one or other of several always is. If, on further +analysis, we can detect in these any common element, we +may be able to ascend from them to some one cause which +is the really operative circumstance in them all. Thus it +might, and perhaps will, be discovered, that in the production +of heat by friction, percussion, chemical action, &c., the +ultimate source is one and the same. But if (as continually +happens) we cannot take this ulterior step, the different +antecedents must be set down provisionally as distinct +causes, each sufficient of itself to produce the effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +We here close our remarks on the Plurality of Causes, +and proceed to the still more peculiar and more complex +case of the Intermixture of Effects, and the interference of +causes with one another: a case constituting the principal +part of the complication and difficulty of the study of nature; +<span class="tei tei-pb" id="page448">[pg 448]</span><a name="Pg448" id="Pg448" class="tei tei-anchor"></a> +and with which the four only possible methods of directly +inductive investigation by observation and experiment, are +for the most part, as will appear presently, quite unequal to +cope. The instrument of Deduction alone is adequate to +unravel the complexities proceeding from this source; and +the four methods have little more in their power than to +supply premisses for, and a verification of, our deductions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. A concurrence of two or more causes, not separately +producing each its own effect, but interfering with or +modifying the effects of one another, takes place, as has +already been explained, in two different ways. In the one, +which is exemplified by the joint operation of different forces +in mechanics, the separate effects of all the causes continue +to be produced, but are compounded with one another, and +disappear in one total. In the other, illustrated by the case +of chemical action, the separate effects cease entirely, and are +succeeded by phenomena altogether different, and governed +by different laws. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of these cases the former is by far the more frequent, +and this case it is which, for the most part, eludes the grasp +of our experimental methods. The other and exceptional +case is essentially amenable to them. When the laws of the +original agents cease entirely, and a phenomenon makes its +appearance, which, with reference to those laws, is quite +heterogeneous; when, for example, two gaseous substances, +hydrogen and oxygen, on being brought together, throw off +their peculiar properties, and produce the substance called +water; in such cases the new fact may be subjected to +experimental inquiry, like any other phenomenon; and the +elements which are said to compose it may be considered +as the mere agents of its production; the conditions on +which it depends, the facts which make up its cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The <em class="tei tei-emph"><span style="font-style: italic">effects</span></em> of the new phenomenon, the <em class="tei tei-emph"><span style="font-style: italic">properties</span></em> of +water, for instance, are as easily found by experiment as the +effects of any other cause. But to discover the <em class="tei tei-emph"><span style="font-style: italic">cause</span></em> of it, +that is, the particular conjunction of agents from which it +results, is often difficult enough. In the first place, the +<span class="tei tei-pb" id="page449">[pg 449]</span><a name="Pg449" id="Pg449" class="tei tei-anchor"></a> +origin and actual production of the phenomenon are most +frequently inaccessible to our observation. If we could not +have learned the composition of water until we found instances +in which it was actually produced from oxygen and +hydrogen, we should have been forced to wait until the +casual thought struck some one of passing an electric spark +through a mixture of the two gases, or inserting a lighted +taper into it, merely to try what would happen. Further, +even if we could have ascertained, by the Method of Agreement, +that oxygen and hydrogen were both present when +water is produced, no experimentation on oxygen and +hydrogen separately, no knowledge of their laws, could have +enabled us deductively to infer that they would produce +water. We require a specific experiment on the two combined. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Under these difficulties, we should generally have been +indebted for our knowledge of the causes of this class of +effects, not to any inquiry directed specifically towards that +end, but either to accident, or to the gradual progress of +experimentation on the different combinations of which the +producing agents are susceptible; if it were not for a peculiarity +belonging to effects of this description, that they often, +under some particular combination of circumstances, reproduce +their causes. If water results from the juxtaposition +of hydrogen and oxygen whenever this can be made +sufficiently close and intimate, so, on the other hand, if water +itself be placed in certain situations, hydrogen and oxygen +are reproduced from it: an abrupt termination is put to the +new laws, and the agents reappear separately with their +own properties as at first. What is called chemical analysis +is the process of searching for the causes of a phenomenon +among its effects, or rather among the effects produced by +the action of some other causes upon it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Lavoisier, by heating mercury to a high temperature in +a close vessel containing air, found that the mercury increased +in weight and became what was then called red +precipitate, while the air, on being examined after the experiment, +proved to have lost weight, and to have become +<span class="tei tei-pb" id="page450">[pg 450]</span><a name="Pg450" id="Pg450" class="tei tei-anchor"></a> +incapable of supporting life or combustion. When red +precipitate was exposed to a still greater heat, it became +mercury again, and gave off a gas which did support life +and flame. Thus the agents which by their combination +produced red precipitate, namely the mercury and the gas, +reappear as effects resulting from that precipitate when acted +upon by heat. So, if we decompose water by means of iron +filings, we produce two effects, rust and hydrogen: now rust +is already known by experiments upon the component substances, +to be an effect of the union of iron and oxygen: the +iron we ourselves supplied, but the oxygen must have been +produced from the water. The result therefore is that +water has disappeared, and hydrogen and oxygen have +appeared in its stead: or in other words, the original laws +of these gaseous agents, which had been suspended by the +superinduction of the new laws called the properties of +water, have again started into existence, and the causes of +water are found among its effects. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Where two phenomena, between the laws or properties +of which considered in themselves no connexion can be +traced, are thus reciprocally cause and effect, each capable +in its turn of being produced from the other, and each, when +it produces the other, ceasing itself to exist (as water is produced +from oxygen and hydrogen, and oxygen and hydrogen +are reproduced from water); this causation of the two phenomena +by one another, each being generated by the other's +destruction, is properly transformation. The idea of chemical +composition is an idea of transformation, but of a +transformation which is incomplete; since we consider the +oxygen and hydrogen to be present in the water <em class="tei tei-emph"><span style="font-style: italic">as</span></em> oxygen +and hydrogen, and capable of being discovered in it if our +senses were sufficiently keen: a supposition (for it is no +more) grounded solely on the fact, that the weight of the +water is the sum of the separate weights of the two ingredients. +If there had not been this exception to the entire +disappearance, in the compound, of the laws of the separate +ingredients; if the combined agents had not, in this one +particular of weight, preserved their own laws, and produced +<span class="tei tei-pb" id="page451">[pg 451]</span><a name="Pg451" id="Pg451" class="tei tei-anchor"></a> +a joint result equal to the sum of their separate results; we +should never, probably, have had the notion now implied by +the words chemical composition: and, in the fact of water +produced from hydrogen and oxygen and hydrogen and +oxygen produced from water, as the transformation would +have been complete, we should have seen only a transformation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In these cases, then, when the heteropathic effect (as we +called it in a former chapter)<a id="noteref_86" name="noteref_86" href="#note_86"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">86</span></span></a> is but a transformation of its +cause, or in other words, when the effect and its cause are +reciprocally such, and mutually convertible into each other; +the problem of finding the cause resolves itself into the far +easier one of finding an effect, which is the kind of inquiry +that admits of being prosecuted by direct experiment. But +there are other cases of heteropathic effects to which this +mode of investigation is not applicable. Take, for instance, +the heteropathic laws of mind; that portion of the phenomena +of our mental nature which are analogous to chemical +rather than to dynamical phenomena; as when a complex +passion is formed by the coalition of several elementary +impulses, or a complex emotion by several simple pleasures +or pains, of which it is the result without being the aggregate, +or in any respect homogeneous with them. The +product, in these cases, is generated by its various factors; +but the factors cannot be reproduced from the product: just +as a youth can grow into an old man, but an old man +cannot grow into a youth. We cannot ascertain from what +simple feelings any of our complex states of mind are +generated, as we ascertain the ingredients of a chemical +compound, by making it, in its turn, generate them. We +can only, therefore, discover these laws by the slow process +of studying the simple feelings themselves, and ascertaining +synthetically, by experimenting on the various combinations +of which they are susceptible, what they, by their mutual +action upon one another, are capable of generating. +</p> + +<span class="tei tei-pb" id="page452">[pg 452]</span><a name="Pg452" id="Pg452" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. It might have been supposed that the other, and +apparently simpler variety of the mutual interference of +causes, where each cause continues to produce its own proper +effect according to the same laws to which it conforms in its +separate state, would have presented fewer difficulties to the +inductive inquirer than that of which we have just finished +the consideration. It, presents, however, so far as direct induction +apart from deduction is concerned, infinitely greater +difficulties. When a concurrence of causes gives rise to a +new effect, bearing no relation to the separate effects of those +causes, the resulting phenomenon stands forth undisguised, +inviting attention to its peculiarity, and presenting no obstacle +to our recognising its presence or absence among any number +of surrounding phenomena. It admits therefore of being easily +brought under the canons of induction, provided instances +can be obtained such as those canons require: and the non-occurrence +of such instances, or the want of means to produce +them artificially, is the real and only difficulty in such investigations; +a difficulty not logical, but in some sort physical. +It is otherwise with cases of what, in a preceding chapter, has +been denominated the Composition of Causes. There, the +effects of the separate causes do not terminate and give place +to others, thereby ceasing to form any part of the phenomenon +to be investigated; on the contrary, they still take place, +but are intermingled with, and disguised by, the homogeneous +and closely allied effects of other causes. They are no longer +<span class="tei tei-hi"><span style="font-style: italic">a</span></span>, <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, <span class="tei tei-hi"><span style="font-style: italic">c</span></span>, +<span class="tei tei-hi"><span style="font-style: italic">d</span></span>, <span class="tei tei-hi"><span style="font-style: italic">e</span></span>, existing side by side, +and continuing to be separately discernible; they are + <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, +- <span class="tei tei-hi"><span style="font-style: italic">a</span></span>, 1/2 <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, - <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, +2 <span class="tei tei-hi"><span style="font-style: italic">b</span></span>, &c., some +of which cancel one another, while many others do not appear +distinguishably, but merge in one sum: forming altogether a +result, between which and the causes whereby it was produced +there is often an insurmountable difficulty in tracing by +observation any fixed relation whatever. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The general idea of the Composition of Causes has been +seen to be, that although two or more laws interfere with one +another, and apparently frustrate or modify one another's +operation, yet in reality all are fulfilled, the collective effect +being the exact sum of the effects of the causes taken separately. +<span class="tei tei-pb" id="page453">[pg 453]</span><a name="Pg453" id="Pg453" class="tei tei-anchor"></a> +A familiar instance is that of a body kept in equilibrium +by two equal and contrary forces. One of the forces +if acting alone would carry it in a given time a certain distance +to the west, the other if acting alone would carry it +exactly as far towards the east; and the result is the same +as if it had been first carried to the west as far as the one +force would carry it, and then back towards the east as far as +the other would carry it, that is, precisely the same distance; +being ultimately left where it was found at first. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All laws of causation are liable to be in this manner +counteracted, and seemingly frustrated, by coming into conflict +with other laws, the separate result of which is opposite +to theirs, or more or less inconsistent with it. And hence, +with almost every law, many instances in which it really is +entirely fulfilled, do not, at first sight, appear to be cases of +its operation at all. It is so in the example just adduced: a +force, in mechanics, means neither more nor less than a cause +of motion, yet the sum of the effects of two causes of motion +may be rest. Again, a body solicited by two forces in directions +making an angle with one another, moves in the diagonal; +and it seems a paradox to say that motion in the diagonal +is the sum of two motions in two other lines. Motion, however, +is but change of place, and at every instant the body is +in the exact place it would have been in if the forces had +acted during alternate instants instead of acting in the same +instant; (saving that if we suppose two forces to act successively +which are in truth simultaneous, we must of course +allow them double the time.) It is evident, therefore, that +each force has had, during each instant, all the effect which +belonged to it; and that the modifying influence which one +of two concurrent causes is said to exercise with respect to +the other, may be considered as exerted not over the action +of the cause itself, but over the effect after it is completed. +For all purposes of predicting, calculating, or explaining +their joint result, causes which compound their effects may +be treated as if they produced simultaneously each of them +its own effect, and all these effects coexisted visibly. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Since the laws of causes are as really fulfilled when the +<span class="tei tei-pb" id="page454">[pg 454]</span><a name="Pg454" id="Pg454" class="tei tei-anchor"></a> +causes are said to be counteracted by opposing causes, as +when they are left to their own undisturbed action, we must +be cautious not to express the laws in such terms as would +render the assertion of their being fulfilled in those cases a +contradiction. If, for instance, it were stated as a law of +nature that a body to which a force is applied moves in the +direction of the force, with a velocity proportioned to the +force directly, and to its own mass inversely; when in point +of fact some bodies to which a force is applied do not move +at all, and those which do move are, from the very first, +retarded by the action of gravity and other resisting forces, +and at last stopped altogether; it is clear that the general +proposition, though it would be true under a certain hypothesis, +would not express the facts as they actually occur. To +accommodate the expression of the law to the real phenomena, +we must say, not that the object moves, but that it <em class="tei tei-emph"><span style="font-style: italic">tends</span></em> +to move, in the direction and with the velocity specified. We +might, indeed, guard our expression in a different mode, by +saying that the body moves in that manner unless prevented, +or except in so far as prevented, by some counteracting +cause. But the body does not only move in that manner +unless counteracted; it <em class="tei tei-emph"><span style="font-style: italic">tends</span></em> to move in that manner even +when counteracted; it still exerts, in the original direction, +the same energy of movement as if its first impulse had been +undisturbed, and produces, by that energy, an exactly equivalent +quantity of effect. This is true even when the force +leaves the body as it found it, in a state of absolute rest; as +when we attempt to raise a body of three tons weight with +a force equal to one ton. For if, while we are applying this +force, wind or water or any other agent supplies an additional +force just exceeding two tons, the body will be raised; thus +proving that the force we applied exerted its full effect, by neutralizing +an equivalent portion of the weight which it was insufficient +altogether to overcome. And if, while we are exerting +this force of one ton upon the object in a direction contrary +to that of gravity, it be put into a scale and weighed, it will +be found to have lost a ton of its weight, or in other words, to +<span class="tei tei-pb" id="page455">[pg 455]</span><a name="Pg455" id="Pg455" class="tei tei-anchor"></a> +press downwards with a force only equal to the difference of +the two forces. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These facts are correctly indicated by the expression +<em class="tei tei-emph"><span style="font-style: italic">tendency</span></em>. All laws of causation, in consequence of their +liability to be counteracted, require to be stated in words +affirmative of tendencies only, and not of actual results. In +those sciences of causation which have an accurate nomenclature, +there are special words which signify a tendency to +the particular effect with which the science is conversant; +thus <em class="tei tei-emph"><span style="font-style: italic">pressure</span></em>, in mechanics, is synonymous with tendency to +motion, and forces are not reasoned on as causing actual +motion, but as exerting pressure. A similar improvement +in terminology would be very salutary in many other branches +of science. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The habit of neglecting this necessary element in the +precise expression of the laws of nature, has given birth to +the popular prejudice that all general truths have exceptions; +and much unmerited distrust has thence accrued to the conclusions +of science, when they have been submitted to the +judgment of minds insufficiently disciplined and cultivated. +The rough generalizations suggested by common observation +usually have exceptions; but principles of science, or in +other words, laws of causation, have not. <span class="tei tei-q">“What is +thought to be an exception to a principle,”</span> (to quote words +used on a different occasion,) <span class="tei tei-q">“is always some other and +distinct principle cutting into the former; some other force +which impinges<a id="noteref_87" name="noteref_87" href="#note_87"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">87</span></span></a> +against the first force, and deflects it from its +direction. There are not a law and an exception to that law, +the law acting in ninety-nine cases and the exception in one. +There are two laws, each possibly acting in the whole hundred +cases, and bringing about a common effect by their conjunct +operation. If the force which, being the less conspicuous +of the two, is called the <span class="tei tei-hi"><span style="font-style: italic">disturbing</span></span> force, prevails sufficiently +<span class="tei tei-pb" id="page456">[pg 456]</span><a name="Pg456" id="Pg456" class="tei tei-anchor"></a> +over the other force in some one case, to constitute +that case what is commonly called an exception, the same +disturbing force probably acts as a modifying cause in many +other cases which no one will call exceptions.</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Thus if it were stated to be a law of nature that all +heavy bodies fall to the ground, it would probably be said +that the resistance of the atmosphere, which prevents a balloon +from falling, constitutes the balloon an exception to that +pretended law of nature. But the real law is, that all heavy +bodies <em class="tei tei-emph"><span style="font-style: italic">tend</span></em> to fall; and to this there is no exception, not even +the sun and moon; for even they, as every astronomer knows, +tend towards the earth, with a force exactly equal to that +with which the earth tends towards them. The resistance of +the atmosphere might, in the particular case of the balloon, +from a misapprehension of what the law of gravitation is, be +said to <em class="tei tei-emph"><span style="font-style: italic">prevail over</span></em> the law; but its disturbing effect is quite +as real in every other case, since though it does not prevent, +it retards the fall of all bodies whatever. The rule, and the +so-called exception, do not divide the cases between them; +each of them is a comprehensive rule extending to all cases. +To call one of these concurrent principles an exception to +the other, is superficial, and contrary to the correct principles +of nomenclature and arrangement. An effect of precisely +the same kind, and arising from the same cause, ought not to +be placed in two different categories, merely as there does or +does not exist another cause preponderating over +it.”</span><a id="noteref_88" name="noteref_88" href="#note_88"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">88</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. We have now to consider according to what method +these complex effects, compounded of the effects of many +causes, are to be studied; how we are enabled to trace each +effect to the concurrence of causes in which it originated, and +ascertain the conditions of its recurrence, the circumstances +in which it maybe expected again to occur. The conditions +of a phenomenon which arises from a composition of causes, +may be investigated either deductively or experimentally. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The case, it is evident, is naturally susceptible of the +<span class="tei tei-pb" id="page457">[pg 457]</span><a name="Pg457" id="Pg457" class="tei tei-anchor"></a> +deductive mode of investigation. The law of an effect of this +description is a result of the laws of the separate causes on +the combination of which it depends, and is therefore in +itself capable of being deduced from these laws. This is +called the method <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>. +The other, or <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à posteriori</span></span> method, +professes to proceed according to the canons of experimental +inquiry. Considering the whole assemblage of concurrent +causes which produced the phenomenon, as one single cause, +it attempts to ascertain that cause in the ordinary manner, by +a comparison of instances. This second method subdivides +itself into two different varieties. If it merely collates instances +of the effect, it is a method of pure observation. If +it operates upon the causes, and tries different combinations +of them, in hopes of ultimately hitting the precise combination +which will produce the given total effect, it is a method +of experiment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In order more completely to clear up the nature of each +of these three methods, and determine which of them deserves +the preference, it will be expedient (conformably to a +favourite maxim of Lord Chancellor Eldon, to which, though +it has often incurred philosophical ridicule, a deeper philosophy +will not refuse its sanction) to <span class="tei tei-q">“clothe them in circumstances.”</span> +We shall select for this purpose a case which as +yet furnishes no very brilliant example of the success of any +of the three methods, but which is all the more suited to +illustrate the difficulties inherent in them. Let the subject +of inquiry be, the conditions of health and disease in the +human body; or (for greater simplicity) the conditions of +recovery from a given disease; and in order to narrow the +question still more, let it be limited, in the first instance, to +this one inquiry: Is, or is not some particular medicament +(mercury, for instance) a remedy for that disease. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, the deductive method would set out from known +properties of mercury, and known laws of the human body, +and by reasoning from these, would attempt to discover +whether mercury will act upon the body when in the morbid +condition supposed, in such a manner as to restore health. +The experimental method would simply administer mercury +<span class="tei tei-pb" id="page458">[pg 458]</span><a name="Pg458" id="Pg458" class="tei tei-anchor"></a> +in as many cases as possible, noting the age, sex, temperament, +and other peculiarities of bodily constitution, the particular +form or variety of the disease, the particular stage of +its progress, &c., remarking in which of these cases it produced +a salutary effect, and with what circumstances it was +on those occasions combined. The method of simple observation +would compare instances of recovery, to find whether +they agreed in having been preceded by the administration +of mercury; or would compare instances of recovery with +instances of failure, to find cases which, agreeing in all other +respects, differed only in the fact that mercury had been administered, +or that it had not. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. That the last of these three modes of investigation +is applicable to the case, no one has ever seriously contended. +No conclusions of value, on a subject of such intricacy, ever +were obtained in that way. The utmost that could result +would be a vague general impression for or against the +efficacy of mercury, of no avail for guidance unless confirmed +by one of the other two methods. Not that the results, +which this method strives to obtain, would not be of the +utmost possible value if they could be obtained. If all the +cases of recovery which presented themselves, in an examination +extending to a great number of instances, were cases in +which mercury had been administered, we might generalize +with confidence from this experience, and should have obtained +a conclusion of real value. But no such basis for +generalization can we, in a case of this description, hope to +obtain. The reason is that which we have so often spoken +of as constituting the characteristic imperfection of the Method +of Agreement; Plurality of Causes. Supposing even that +mercury does tend to cure the disease, so many other causes, +both natural and artificial, also tend to cure it, that there are +sure to be abundant instances of recovery, in which mercury +has not been administered: unless, indeed, the practice be +to administer it in all cases; on which supposition it will +equally be found in the cases of failure. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +When an effect results from the union of many causes, +<span class="tei tei-pb" id="page459">[pg 459]</span><a name="Pg459" id="Pg459" class="tei tei-anchor"></a> +the share which each has in the determination of the effect +cannot in general be great: and the effect is not likely, even +in its presence or absence, still less in its variations, to follow, +even approximatively, any one of the causes. Recovery +from a disease is an event to which, in every case, many +influences must concur. Mercury may be one such influence; +but from the very fact that there are many other such, it will +necessarily happen that although mercury is administered, +the patient, for want of other concurring influences, will +often not recover, and that he often will recover when it is +not administered, the other favourable influences being +sufficiently powerful without it. Neither, therefore, will the +instances of recovery agree in the administration of mercury, +nor will the instances of failure agree in its non-administration. +It is much if, by multiplied and accurate returns +from hospitals and the like, we can collect that there are +rather more recoveries and rather fewer failures when +mercury is administered than when it is not; a result of very +secondary value even as a guide to practice, and almost +worthless as a contribution to the theory of the subject. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 8. The inapplicability of the method of simple observation +to ascertain the conditions of effects dependent on +many concurring causes, being thus recognised; we shall +next inquire whether any greater benefit can be expected +from the other branch of the <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à +posteriori</span></span> method, that which +proceeds by directly trying different combinations of causes, +either artificially produced or found in nature, and taking +notice what is their effect: as, for example, by actually +trying the effect of mercury, in as many different circumstances +as possible. This method differs from the one +which we have just examined, in turning our attention +directly to the causes or agents, instead of turning it to the +effect, recovery from the disease. And since, as a general +rule, the effects of causes are far more accessible to our +study than the causes of effects, it is natural to think that +this method has a much better chance of proving successful +than the former. +</p> + +<span class="tei tei-pb" id="page460">[pg 460]</span><a name="Pg460" id="Pg460" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The method now under consideration is called the Empirical +Method; and in order to estimate it fairly, we must +suppose it to be completely, not incompletely, empirical. +We must exclude from it everything which partakes of the +nature not of an experimental but of a deductive operation. +If for instance we try experiments with mercury upon a +person in health, in order to ascertain the general laws of +its action upon the human body, and then reason from these +laws to determine how it will act upon persons affected with +a particular disease, this may be a really effectual method, +but this is deduction. The experimental method does not +derive the law of a complex case from the simpler laws +which conspire to produce it, but makes its experiments +directly upon the complex case. We must make entire +abstraction of all knowledge of the simpler tendencies, the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">modi operandi</span></span> +of mercury in detail. Our experimentation +must aim at obtaining a direct answer to the specific question, +Does or does not mercury tend to cure the particular +disease? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us see, therefore, how far the case admits of the +observance of those rules of experimentation, which it is found +necessary to observe in other cases. When we devise an +experiment to ascertain the effect of a given agent, there are +certain precautions which we never, if we can help it, omit. +In the first place, we introduce the agent into the midst of +a set of circumstances which we have exactly ascertained. +It needs hardly be remarked how far this condition is from +being realized in any case connected with the phenomena of +life; how far we are from knowing what are all the circumstances +which pre-exist in any instance in which mercury is +administered to a living being. This difficulty, however, +though insuperable in most cases, may not be so in all; +there are sometimes (though I should think never in physiology) +concurrences of many causes, in which we yet know +accurately what the causes are. But when we have got +clear of this obstacle we encounter another still more serious. +In other cases, when we intend to try an experiment, we do +not reckon it enough that there be no circumstance in the +<span class="tei tei-pb" id="page461">[pg 461]</span><a name="Pg461" id="Pg461" class="tei tei-anchor"></a> +case, the presence of which is unknown to us. We require +also that none of the circumstances which we do know, +shall have effects susceptible of being confounded with those +of the agent whose properties we wish to study. We take +the utmost pains to exclude all causes capable of composition +with the given cause; or if forced to let in any such causes, +we take care to make them such, that we can compute and +allow for their influence, so that the effect of the given cause +may, after the subduction of those other effects, be apparent +as a residual phenomenon. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These precautions are inapplicable to such cases as we +are now considering. The mercury of our experiment being +tried with an unknown multitude (or even let it be a known +multitude) of other influencing circumstances, the mere fact +of their being influencing circumstances implies that they +disguise the effect of the mercury, and preclude us from +knowing whether it has any effect or no. Unless we already +knew what and how much is owing to every other circumstance, +(that is, unless we suppose the very problem solved +which we are considering the means of solving,) we cannot +tell that those other circumstances may not have produced +the whole of the effect, independently or even in spite of the +mercury. The Method of Difference, in the ordinary mode +of its use, namely by comparing the state of things following +the experiment with the state which preceded it, is thus, in +the case of intermixture of effects, entirely unavailing; +because other causes than that whose effect we are seeking +to determine, have been operating during the transition. As +for the other mode of employing the Method of Difference, +namely by comparing, not the same case at two different +periods, but different cases, this in the present instance is +quite chimerical. In phenomena so complicated it is questionable +if two cases similar in all respects but one ever +occurred; and were they to occur, we could not possibly +know that they were so exactly similar. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Anything like a scientific use of the method of experiment, +in these complicated cases, is therefore out of the +question. We can in the most favourable cases only discover, +<span class="tei tei-pb" id="page462">[pg 462]</span><a name="Pg462" id="Pg462" class="tei tei-anchor"></a> +by a succession of trials, that a certain cause is <em class="tei tei-emph"><span style="font-style: italic">very +often</span></em> followed by a certain effect. For, in one of these conjunct +effects, the portion which is determined by any one of +the influencing agents, is generally, as we before remarked, +but small; and it must be a more potent cause than most, +if even the tendency which it really exerts is not thwarted by +other tendencies in nearly as many cases as it is fulfilled. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If so little can be done by the experimental method to +determine the conditions of an effect of many combined +causes, in the case of medical science, still less is this +method applicable to a class of phenomena, more complicated +than even those of physiology, the phenomena of +politics and history. There, Plurality of Causes exists in +almost boundless excess, and the effects are, for the most +part, inextricably interwoven with one another. To add to +the embarrassment, most of the inquiries in political science +relate to the production of effects of a most comprehensive +description, such as the public wealth, public security, +public morality, and the like: results liable to be affected +directly or indirectly either in <em class="tei tei-emph"><span style="font-style: italic">plus</span></em> or in <em class="tei tei-emph"><span style="font-style: italic">minus</span></em> by nearly +every fact which exists, or event which occurs, in human +society. The vulgar notion, that the safe methods on political +subjects are those of Baconian induction, that the true +guide is not general reasoning, but specific experience, will +one day be quoted as among the most unequivocal marks of +a low state of the speculative faculties in any age in which +it is accredited. Nothing can be more ludicrous than the +sort of parodies on experimental reasoning which one is +accustomed to meet with, not in popular discussion only, +but in grave treatises, when the affairs of nations are the +theme. <span class="tei tei-q">“How,”</span> it is asked, <span class="tei tei-q">“can an institution be bad, +when the country has prospered under it?”</span> <span class="tei tei-q">“How can +such or such causes have contributed to the prosperity of +one country, when another has prospered without them?”</span> +Whoever makes use of an argument of this kind, not intending +to deceive, should be sent back to learn the elements +of some one of the more easy physical sciences. Such +reasoners ignore the fact of Plurality of Causes in the very +<span class="tei tei-pb" id="page463">[pg 463]</span><a name="Pg463" id="Pg463" class="tei tei-anchor"></a> +case which affords the most signal example of it. So little +could be concluded, in such a case, from any possible +collation of individual instances, that even the impossibility, +in social phenomena, of making artificial experiments, a +circumstance otherwise so prejudicial to directly inductive +inquiry, hardly affords, in this case, additional reason of +regret. For even if we could try experiments upon a nation +or upon the human race, with as little scruple as M. +Majendie tries them upon dogs or rabbits, we should never +succeed in making two instances identical in every respect +except the presence or absence of some one indefinite circumstance. +The nearest approach to an experiment in the +philosophical sense, which takes place in politics, is the +introduction of a new operative element into national affairs +by some special and assignable measure of government, +such as the enactment or repeal of a particular law. But +where there are so many influences at work, it requires some +time for the influence of any new cause upon national +phenomena to become apparent; and as the causes operating +in so extensive a sphere are not only infinitely +numerous, but in a state of perpetual alteration, it is always +certain that before the effect of the new cause becomes +conspicuous enough to be a subject of induction, so many +of the other influencing circumstances will have changed as +to vitiate the experiment. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Two, therefore, of the three possible methods for the +study of phenomena resulting from the composition of many +causes, being, from the very nature of the case, inefficient +and illusory; there remains only the third,—that which considers +the causes separately, and computes the effect from +the balance of the different tendencies which produce it: +in short, the deductive, or <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à +priori</span></span> method. The more +particular consideration of this intellectual process requires +a chapter to itself. +</p> + +</div> + +<span class="tei tei-pb" id="page464">[pg 464]</span><a name="Pg464" id="Pg464" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc75" id="toc75"></a> +<a name="pdf76" id="pdf76"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER XI. OF THE DEDUCTIVE METHOD.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The mode of investigation which, from the proved +inapplicability of direct methods of observation and experiment, +remains to us as the main source of the knowledge we +possess or can acquire respecting the conditions, and laws +of recurrence, of the more complex phenomena, is called, in +its most general expression, the Deductive Method; and +consists of three operations: the first, one of direct induction; +the second, of ratiocination; and the third, of verification. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I call the first step in the process an inductive operation, +because there must be a direct induction as the basis of the +whole; although in many particular investigations the place +of the induction may be supplied by a prior deduction; but +the premisses of this prior deduction must have been derived +from induction. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The problem of the Deductive Method is, to find the +law of an effect, from the laws of the different tendencies of +which it is the joint result. The first requisite, therefore, is +to know the laws of those tendencies; the law of each of the +concurrent causes: and this supposes a previous process of +observation or experiment upon each cause separately; or +else a previous deduction, which also must depend for its +ultimate premisses on observation or experiment. Thus, +if the subject be social or historical phenomena, the premisses +of the Deductive Method must be the laws of the +causes which determine that class of phenomena; and those +causes are human actions, together with the general outward +circumstances under the influence of which mankind are +placed, and which constitute man's position on the earth. +The Deductive Method, applied to social phenomena, must +<span class="tei tei-pb" id="page465">[pg 465]</span><a name="Pg465" id="Pg465" class="tei tei-anchor"></a> +begin, therefore, by investigating, or must suppose to have +been already investigated, the laws of human action, and +those properties of outward things by which the actions of +human beings in society are determined. Some of these +general truths will naturally be obtained by observation and +experiment, others by deduction: the more complex laws of +human action, for example, may be deduced from the simpler +ones; but the simple or elementary laws will always, and +necessarily, have been obtained by a directly inductive +process. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To ascertain, then, the laws of each separate cause which +takes a share in producing the effect, is the first desideratum +of the Deductive Method. To know what the causes are, +which must be subjected to this process of study, may or +may not be difficult. In the case last mentioned, this first +condition is of easy fulfilment. That social phenomena +depend on the acts and mental impressions of human beings, +never could have been a matter of any doubt, however imperfectly +it may have been known either by what laws those +impressions and actions are governed, or to what social consequences +their laws naturally lead. Neither, again, after +physical science had attained a certain development, could +there be any real doubt where to look for the laws on which +the phenomena of life depend, since they must be the mechanical +and chemical laws of the solid and fluid substances +composing the organised body and the medium in which it +subsists, together with the peculiar vital laws of the different +tissues constituting the organic structure. In other cases, +really far more simple than these, it was much less obvious +in what quarter the causes were to be looked for: as in the +case of the celestial phenomena. Until, by combining the +laws of certain causes, it was found that those laws explained +all the facts which experience had proved concerning the +heavenly motions, and led to predictions which it always +verified, mankind never knew that those <em class="tei tei-emph"><span style="font-style: italic">were</span></em> the causes. +But whether we are able to put the question before, or not +until after, we have become capable of answering it, in either +<span class="tei tei-pb" id="page466">[pg 466]</span><a name="Pg466" id="Pg466" class="tei tei-anchor"></a> +case it must be answered; the laws of the different causes +must be ascertained, before we can proceed to deduce from +them the conditions of the effect. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The mode of ascertaining those laws neither is, nor can +be, any other than the fourfold method of experimental inquiry, +already discussed. A few remarks on the application +of that method to cases of the Composition of Causes, are all +that is requisite. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is obvious that we cannot expect to find the law of a +tendency, by an induction from cases in which the tendency +is counteracted. The laws of motion could never have been +brought to light from the observation of bodies kept at rest +by the equilibrium of opposing forces. Even where the tendency +is not, in the ordinary sense of the word, counteracted, +but only modified, by having its effects compounded with the +effects arising from some other tendency or tendencies, we +are still in an unfavourable position for tracing, by means of +such cases, the law of the tendency itself. It would have +been difficult to discover the law that every body in motion +tends to continue moving in a straight line, by an induction +from instances in which the motion is deflected into a curve, +by being compounded with the effect of an accelerating force. +Notwithstanding the resources afforded in this description of +cases by the Method of Concomitant Variations, the principles +of a judicious experimentation prescribe that the law +of each of the tendencies should be studied, if possible, in +cases in which that tendency operates alone, or in combination +with no agencies but those of which the effect can, from +previous knowledge, be calculated and allowed for. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Accordingly, in the cases, unfortunately very numerous and +important, in which the causes do not suffer themselves to +be separated and observed apart, there is much difficulty in +laying down with due certainty the inductive foundation +necessary to support the deductive method. This difficulty +is most of all conspicuous in the case of physiological phenomena; +it being impossible to separate the different agencies +which collectively compose an organised body, without destroying +<span class="tei tei-pb" id="page467">[pg 467]</span><a name="Pg467" id="Pg467" class="tei tei-anchor"></a> +the very phenomena which it is our object to investigate: +</p> + +<div class="tei tei-lg" style="margin-bottom: 1.00em; margin-top: 1.00em"> +<div class="tei tei-l" style="text-align: left; margin-left: 4.00em">following life, in creatures we dissect,</div> +<div class="tei tei-l" style="text-align: left">We lose it, in the moment we detect.</div> +</div> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And for this reason I am inclined to the opinion, that physiology +is embarrassed by greater natural difficulties, and is +probably susceptible of a less degree of ultimate perfection, +than even the social science; inasmuch as it is possible to +study the laws and operations of one human mind apart from +other minds, much less imperfectly than we can study the +laws of one organ or tissue of the human body apart from +the other organs or tissues. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It has been judiciously remarked that pathological facts, +or, to speak in common language, diseases in their different +forms and degrees, afford in the case of physiological investigation +the most available equivalent to experimentation +properly so called; inasmuch as they often exhibit to us a +definite disturbance in some one organ or organic function, +the remaining organs and functions being, in the first instance +at least, unaffected. It is true that from the perpetual actions +and reactions which are going on among all parts of the +organic economy, there can be no prolonged disturbance in +any one function without ultimately involving many of the +others; and when once it has done so, the experiment for +the most part loses its scientific value. All depends on +observing the early stages of the derangement; which, unfortunately, +are of necessity the least marked. If, however, +the organs and functions not disturbed in the first instance, +become affected in a fixed order of succession, some light is +thereby thrown upon the action which one organ exercises +over another; and we occasionally obtain a series of effects +which we can refer with some confidence to the original +local derangement; but for this it is necessary that we should +know that the original derangement <em class="tei tei-emph"><span style="font-style: italic">was</span></em> local. If it was what +is termed constitutional, that is, if we do not know in what +part of the animal economy it took its rise, or the precise +nature of the disturbance which took place in that part, we +<span class="tei tei-pb" id="page468">[pg 468]</span><a name="Pg468" id="Pg468" class="tei tei-anchor"></a> +are unable to determine which of the various derangements +was cause and which effect; which of them were produced +by one another, and which by the direct, though perhaps +tardy, action of the original cause. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Besides natural pathological facts, we can produce pathological +facts artificially; we can try experiments, even in the +popular sense of the term, by subjecting the living being to some +external agent, such as the mercury of our former example. +As this experimentation is not intended to obtain a direct +solution of any practical question, but to discover general +laws, from which afterwards the conditions of any particular +effect may be obtained by deduction; the best cases to select +are those of which the circumstances can be best ascertained: +and such are generally not those in which there is any practical +object in view. The experiments are best tried, not in +a state of disease, which is essentially a changeable state, +but in the condition of health, comparatively a fixed state. +In the one, unusual agencies are at work, the results of which +we have no means of predicting; in the other, the course +of the accustomed physiological phenomena would, it may +generally be presumed, remain undisturbed, were it not for +the disturbing cause which we introduce. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Such, with the occasional aid of the method of Concomitant +Variations, (the latter not less encumbered than +the more elementary methods by the peculiar difficulties of +the subject,) are our inductive resources for ascertaining the +laws of the causes considered separately, when we have it not +in our power to make trial of them in a state of actual separation. +The insufficiency of these resources is so glaring, that +no one can be surprised at the backward state of the science +of physiology; in which indeed our knowledge of causes is +so imperfect, that we can neither explain, nor could without +specific experience have predicted, many of the facts which +are certified to us by the most ordinary observation. Fortunately, +we are much better informed as to the empirical laws +of the phenomena, that is, the uniformities respecting which +we cannot yet decide whether they are cases of causation or +mere results of it. Not only has the order in which the facts +<span class="tei tei-pb" id="page469">[pg 469]</span><a name="Pg469" id="Pg469" class="tei tei-anchor"></a> +of organization and life successively manifest themselves, +from the first germ of existence to death, been found to be +uniform, and very accurately ascertainable; but, by a +great application of the Method of Concomitant Variations +to the entire facts of comparative anatomy and physiology, +the conditions of organic structure corresponding to each class +of functions have been determined with considerable precision. +Whether these organic conditions are the whole of +the conditions, and indeed whether they are conditions at all, +or mere collateral effects of some common cause, we are +quite ignorant: nor are we ever likely to know, unless we +could construct an organized body, and try whether it would +live. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Under such disadvantages do we, in cases of this description, +attempt the initial, or inductive step, in the application +of the Deductive Method to complex phenomena. But such, +fortunately, is not the common case. In general, the laws of +the causes on which the effect depends may be obtained by +an induction from comparatively simple instances, or, at the +worst, by deduction from the laws of simpler causes so +obtained. By simple instances are meant, of course, those +in which the action of each cause was not intermixed or interfered +with, or not to any great extent, by other causes whose +laws were unknown. And only when the induction which furnished +the premisses to the Deductive Method rested on such +instances, has the application of such a method to the ascertainment +of the laws of a complex effect, been attended with +brilliant results. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. When the laws of the causes have been ascertained, +and the first stage of the great logical operation now under +discussion satisfactorily accomplished, the second part follows; +that of determining, from the laws of the causes, what +effect any given combination of those causes will produce. +This is a process of calculation, in the wider sense of the +term; and very often involves processes of calculation in the +narrowest sense. It is a ratiocination; and when our knowledge +of the causes is so perfect, as to extend to the exact +<span class="tei tei-pb" id="page470">[pg 470]</span><a name="Pg470" id="Pg470" class="tei tei-anchor"></a> +numerical laws which they observe in producing their effects, +the ratiocination may reckon among its premisses the theorems +of the science of number, in the whole immense extent +of that science. Not only are the highest truths of mathematics +often required to enable us to compute an effect, the +numerical law of which we already know; but, even by the +aid of those highest truths, we can go but a little way. In so +simple a case as the common problem of three bodies +gravitating towards one another, with a force directly as their +mass and inversely as the square of the distance, all the +resources of the calculus have not hitherto sufficed to obtain +any general solution but an approximate one. In a case +a little more complex, but still one of the simplest which +arise in practice, that of the motion of a projectile, the causes +which affect the velocity and range (for example) of a cannon-ball +may be all known and estimated; the force of the gunpowder, +the angle of elevation, the density of the air, the +strength and direction of the wind; but it is one of the +most difficult of mathematical problems to combine all +these, so as to determine the effect resulting from their collective +action. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Besides the theorems of number, those of geometry also +come in as premisses, where the effects take place in space, +and involve motion and extension, as in mechanics, optics, +acoustics, astronomy. But when the complication increases, +and the effects are under the influence of so many and such +shifting causes as to give no room either for fixed numbers, +or for straight lines and regular curves, (as in the case of +physiological, to say nothing of mental and social phenomena,) +the laws of number and extension are applicable, if +at all, only on that large scale on which precision of details +becomes unimportant; and although these laws play a conspicuous +part in the most striking examples of the investigation +of nature by the Deductive Method, as for example +in the Newtonian theory of the celestial motions, they are +by no means an indispensable part of every such process. +All that is essential in it is, reasoning from a general law to a +particular case, that is, determining by means of the particular +<span class="tei tei-pb" id="page471">[pg 471]</span><a name="Pg471" id="Pg471" class="tei tei-anchor"></a> +circumstances of that case, what result is required in +that instance to fulfil the law. Thus in the Torricellian experiment, +if the fact that air has weight had been previously +known, it would have been easy, without any numerical data, +to deduce from the general law of equilibrium, that the mercury +would stand in the tube at such a height that the column +of mercury would exactly balance a column of the atmosphere +of equal diameter; because, otherwise, equilibrium +would not exist. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +By such ratiocinations from the separate laws of the +causes, we may, to a certain extent, succeed in answering +either of the following questions: Given a certain combination +of causes, what effect will follow? and, What combination +of causes, if it existed, would produce a given +effect? In the one case, we determine the effect to be +expected in any complex circumstances of which the different +elements are known: in the other case we learn, according +to what law—under what antecedent conditions—a given +complex effect will occur. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. But (it may here be asked) are not the same arguments +by which the methods of direct observation and experiment +were set aside as illusory when applied to the laws of +complex phenomena, applicable with equal force against the +Method of Deduction? When in every single instance a +multitude, often an unknown multitude of agencies, are clashing +and combining, what security have we that in our computation +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +have taken all these into our reckoning? +How many must we not generally be ignorant of? Among +those which we know, how probable that some have been +overlooked; and even were all included, how vain the pretence +of summing up the effects of many causes, unless we +know accurately the numerical law of each,—a condition in +most cases not to be fulfilled; and even when fulfilled, to +make the calculation transcends, in any but very simple +cases, the utmost power of mathematical science with its most +modern improvements. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These objections have real weight, and would be altogether +<span class="tei tei-pb" id="page472">[pg 472]</span><a name="Pg472" id="Pg472" class="tei tei-anchor"></a> +unanswerable, if there were no test by which, when we +employ the Deductive Method, we might judge whether an +error of any of the above descriptions had been committed +or not. Such a test however there is: and its application +forms, under the name of Verification, the third essential +component part of the Deductive Method; without which all +the results it can give have little other value than that of +guess-work. To warrant reliance on the general conclusions +arrived at by deduction, these conclusions must be found, on +careful comparison, to accord with the results of direct observation +wherever it can be had. If, when we have experience +to compare with them, this experience confirms them, we may +safely trust to them in other cases of which our specific experience +is yet to come. But if our deductions have led to +the conclusion that from a particular combination of causes +a given effect would result, then in all known cases where +that combination can be shown to have existed, and where +the effect has not followed, we must be able to show (or at +least to make a probable surmise) what frustrated it: if we +cannot, the theory is imperfect, and not yet to be relied upon. +Nor is the verification complete, unless some of the cases in +which the theory is borne out by the observed result, are of +at least equal complexity with any other cases in which its +application could be called for. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It needs scarcely be observed, that,—if direct observation +and collation of instances have furnished us with any empirical +laws of the effect, whether true in all observed cases or +only true for the most part,—the most effectual verification +of which the theory could be susceptible would be, that it +led deductively to those empirical laws; that the uniformities, +whether complete or incomplete, which were observed +to exist among the phenomena, were <em class="tei tei-emph"><span style="font-style: italic">accounted for</span></em> by the +laws of the causes—were such as could not <em class="tei tei-emph"><span style="font-style: italic">but</span></em> exist if those +be really the causes by which the phenomena are produced. +Thus it was very reasonably deemed an essential requisite of +any true theory of the causes of the celestial motions, that it +should lead by deduction to Kepler's laws: which, accordingly, +the Newtonian theory did. +</p> + +<span class="tei tei-pb" id="page473">[pg 473]</span><a name="Pg473" id="Pg473" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In order, therefore, to facilitate the verification of theories +obtained by deduction, it is important that as many as possible +of the empirical laws of the phenomena should be ascertained, +by a comparison of instances, conformably to the +Method of Agreement: as well as (it must be added) that +the phenomena themselves should be described, in the most +comprehensive as well as accurate manner possible; by collecting +from the observation of parts, the simplest possible +correct expressions for the corresponding wholes: as when +the series of the observed places of a planet was first expressed +by a circle, then by a system of epicycles, and subsequently +by an ellipse. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is worth remarking, that complex instances which +would have been of no use for the discovery of the simple +laws into which we ultimately analyse their phenomena, +nevertheless, when they have served to verify the analysis, +become additional evidence of the laws themselves. Although +we could not have got at the law from complex cases, still +when the law, got at otherwise, is found to be in accordance +with the result of a complex case, that case becomes a new +experiment on the law, and helps to confirm what it did +not assist to discover. It is a new trial of the principle in +a different set of circumstances; and occasionally serves +to eliminate some circumstance not previously excluded, +and the exclusion of which might require an experiment +impossible to be executed. This was strikingly conspicuous +in the example formerly quoted, in which the difference +between the observed and the calculated velocity of sound +was ascertained to result from the heat extricated by the +condensation which takes place in each sonorous vibration. +This was a trial, in new circumstances, of the law of the +development of heat by compression; and it added materially +to the proof of the universality of that law. Accordingly any +law of nature is deemed to have gained in point of certainty, +by being found to explain some complex case which had +not previously been thought of in connexion with it; and this +indeed is a consideration to which it is the habit of scientific +inquirers to attach rather too much value than too little. +</p> + +<span class="tei tei-pb" id="page474">[pg 474]</span><a name="Pg474" id="Pg474" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To the Deductive Method, thus characterised in its three +constituent parts, Induction, Ratiocination, and Verification, +the human mind is indebted for its most conspicuous +triumphs in the investigation of nature. To it we owe all +the theories by which vast and complicated phenomena are +embraced under a few simple laws, which, considered as the +laws of those great phenomena, could never have been detected +by their direct study. We may form some conception +of what the method has done for us, from the case of the +celestial motions; one of the simplest among the greater instances +of the Composition of Causes, since (except in a few +cases not of primary importance) each of the heavenly bodies +may be considered, without material inaccuracy, to be never +at one time influenced by the attraction of more than two +bodies, the sun and one other planet or satellite, making +with the reaction of the body itself, and the tangential force +(as I see no objection to calling the force generated by the +body's own motion, and acting in the direction of the +tangent<a id="noteref_89" name="noteref_89" href="#note_89"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">89</span></span></a>) +only four different agents on the concurrence of which +the motions of that body depend; a much smaller number, +no doubt, than that by which any other of the great phenomena +of nature is determined or modified. Yet how could +we ever have ascertained the combination of forces on which +the motions of the earth and planets are dependent, by merely +comparing the orbits, or velocities, of different planets, or the +different velocities or positions of the same planet? Notwithstanding +the regularity which manifests itself in those +motions, in a degree so rare among the effects of a concurrence +of causes; although the periodical recurrence of exactly +the same effect, affords positive proof that all the combinations +of causes which occur at all, recur periodically; we +should not have known what the causes were, if the existence +of agencies precisely similar on our own earth had not, fortunately, +brought the causes themselves within the reach of +<span class="tei tei-pb" id="page475">[pg 475]</span><a name="Pg475" id="Pg475" class="tei tei-anchor"></a> +experimentation under simple circumstances. As we shall +have occasion to analyse, further on, this great example of +the Method of Deduction, we shall not occupy any time with +it here, but shall proceed to that secondary application of the +Deductive Method, the result of which is not to prove laws +of phenomena, but to explain them. +</p> + +</div> + +<span class="tei tei-pb" id="page476">[pg 476]</span><a name="Pg476" id="Pg476" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc77" id="toc77"></a> +<a name="pdf78" id="pdf78"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER XII. OF THE EXPLANATION OF LAWS OF NATURE.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. The deductive operation by which we derive the +law of an effect from the laws of the causes, of which the +concurrence gives rise to it, may be undertaken either for the +purpose of discovering the law, or of explaining a law already +discovered. The word <em class="tei tei-emph"><span style="font-style: italic">explanation</span></em> occurs so continually +and holds so important a place in philosophy, that a little +time spent in fixing the meaning of it will be profitably +employed. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +An individual fact is said to be explained, by pointing out +its cause, that is, by stating the law or laws of causation, of +which its production is an instance. Thus, a conflagration +is explained, when it is proved to have arisen from a spark +falling into the midst of a heap of combustibles. And in a +similar manner, a law or uniformity in nature is said to be +explained, when another law or laws are pointed out, of +which that law itself is but a case, and from which it could +be deduced. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. There are three distinguishable sets of circumstances +in which a law of causation may be explained from, +or, as it also is often expressed, resolved into, other laws. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The first is the case already so fully considered; an +intermixture of laws, producing a joint effect equal to the +sum of the effects of the causes taken separately. The law +of the complex effects is explained, by being resolved into +the separate laws of the causes which contribute to it. Thus, +the law of the motion of a planet is resolved into the law of +the tangential force, which tends to produce an uniform +motion in the tangent, and the law of the centripetal force, +<span class="tei tei-pb" id="page477">[pg 477]</span><a name="Pg477" id="Pg477" class="tei tei-anchor"></a> +which tends to produce an accelerating motion towards the +sun; the real motion being a compound of the two. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is necessary here to remark, that in this resolution of +the law of a complex effect, the laws of which it is compounded +are not the only elements. It is resolved into the +laws of the separate causes, together with the fact of their +co-existence. The one is as essential an ingredient as the +other; whether the object be to discover the law of the effect, +or only to explain it. To deduce the laws of the heavenly +motions, we require not only to know the law of a rectilineal +and that of a gravitative force, but the existence of both these +forces in the celestial regions, and even their relative amount. +The complex laws of causation are thus resolved into two +distinct kinds of elements: the one, simpler laws of causation, +the other (in the aptly selected language of Dr. +Chalmers) collocations; the collocations consisting in the +existence of certain agents or powers, in certain circumstances +of place and time. We shall hereafter have occasion +to return to this distinction, and to dwell on it at such a +length as dispenses with the necessity of further insisting on +it here. The first mode, then, of the explanation of Laws of +Causation, is when the law of an effect is resolved into the +various tendencies of which it is the result, and into the laws +of those tendencies. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. A second case is when, between what seemed the +cause and what was supposed to be its effect, further observation +detects an immediate link; a fact caused by the antecedent, +and in its turn causing the consequent; so that the +cause at first assigned is but the remote cause, operating +through the intermediate phenomenon. A seemed the cause +of C, but it subsequently appeared that A was only the cause +of B, and that it is B which was the cause of C. For example: +mankind were aware that the act of touching an outward +object caused a sensation. It was, however, at last discovered, +that after we have touched the object, and before we +experience the sensation, some change takes place in a kind +of thread called a nerve, which extends from our outward +<span class="tei tei-pb" id="page478">[pg 478]</span><a name="Pg478" id="Pg478" class="tei tei-anchor"></a> +organs to the brain. Touching the object, therefore, is only +the remote cause of our sensation; that is, not the cause, +properly speaking, but the cause of the cause;—the real +cause of the sensation is the change in the state of the nerve. +Future experience may not only give us more knowledge +than we now have of the particular nature of this change, but +may also interpolate another link: between the contact (for +example) of the object with our outward organs, and the +production of the change of state in the nerve, there may +take place some electric phenomenon; or some phenomenon +of a nature not resembling the effects of any known agency. +Hitherto, however, no such intermediate link has been discovered; +and the touch of the object must be considered, +provisionally at least, as the proximate cause of the affection +of the nerve. The sequence, therefore, of a sensation of +touch on contact with an object, is ascertained not to be an +ultimate law; it is resolved, as the phrase is, into two other +laws,—the law, that contact with an object produces an +affection of the nerve; and the law, that an affection of the +nerve produces sensation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +To take another example: the more powerful acids corrode +or blacken organic compounds. This is a case of +causation, but of remote causation; and is said to be explained +when it is shown that there is an intermediate link, namely, +the separation of some of the chemical elements of the organic +structure from the rest, and their entering into combination +with the acid. The acid causes this separation of the elements, +and the separation of the elements causes the disorganization, +and often the charring of the structure. So, again, chlorine +extracts colouring matters, (whence its efficacy in bleaching,) +and purifies the air from infection. This law is resolved +into the two following laws. Chlorine has a powerful affinity +for bases of all kinds, particularly metallic bases and hydrogen. +Such bases are essential elements of colouring matters +and contagious compounds: which substances, therefore, are +decomposed and destroyed by chlorine. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. It is of importance to remark, that when a sequence +<span class="tei tei-pb" id="page479">[pg 479]</span><a name="Pg479" id="Pg479" class="tei tei-anchor"></a> +of phenomena is thus resolved into other laws, they are +always laws more general than itself. The law that A is +followed by C, is less general than either of the laws which +connect B with C and A with B. This will appear from +very simple considerations. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +All laws of causation are liable to be counteracted or +frustrated, by the non-fulfilment of some negative condition: +the tendency, therefore, of B to produce C may be defeated. +Now the law that A produces B, is equally fulfilled whether +B is followed by C or not; but the law that A produces C +by means of B, is of course only fulfilled when B is really +followed by C, and is therefore less general than the law +that A produces B. It is also less general than the law that +B produces C. For B may have other causes besides A; +and as A produces C only by means of B, while B produces +C whether it has itself been produced by A or by anything +else, the second law embraces a greater number of +instances, covers as it were a greater space of ground, than +the first. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus, in our former example, the law that the contact +of an object causes a change in the state of the nerve, is +more general than the law that contact with an object causes +sensation, since, for aught we know, the change in the nerve +may equally take place when, from a counteracting cause, as +for instance, strong mental excitement, the sensation does +not follow; as in a battle, where wounds are often received +without any consciousness of receiving them. And again, +the law that change in the state of a nerve produces sensation, +is more general than the law that contact with an +object produces sensation; since the sensation equally follows +the change in the nerve when not produced by contact +with an object, but by some other cause; as in the well-known +case, when a person who has lost a limb feels the +same sensation which he has been accustomed to call a pain +in the limb. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Not only are the laws of more immediate sequence into +which the law of a remote sequence is resolved, laws of +greater generality than that law is, but (as a consequence +<span class="tei tei-pb" id="page480">[pg 480]</span><a name="Pg480" id="Pg480" class="tei tei-anchor"></a> +of, or rather as implied in, their greater generality) +they are more to be relied on; there are fewer chances of +their being ultimately found not to be universally true. +From the moment when the sequence of A and C is shown +not to be immediate, but to depend on an intervening +phenomenon, then, however constant and invariable the +sequence of A and C has hitherto been found, possibilities +arise of its failure, exceeding those which can affect either +of the more immediate sequences, A, B, and B, C. The +tendency of A to produce C may be defeated by whatever +is capable of defeating either the tendency of A to produce +B, or the tendency of B to produce C; it is therefore twice +as liable to failure as either of those more elementary +tendencies; and the generalization that A is always followed +by C, is twice as likely to be found erroneous. And +so of the converse generalization, that C is always preceded +and caused by A; which will be erroneous not only if there +should happen to be a second immediate mode of production +of C itself, but moreover if there be a second mode +of production of B, the immediate antecedent of C in the +sequence. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The resolution of the one generalization into the other +two, not only shows that there are possible limitations of +the former, from which its two elements are exempt, but +shows also where these are to be looked for. As soon as +we know that B intervenes between A and C, we also know +that if there be cases in which the sequence of A and C +does not hold, these are most likely to be found by studying +the effects or the conditions of the phenomenon B. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It appears, then, that in the second of the three modes in +which a law may be resolved into other laws, the latter are +more general, that is, extend to more cases, and are also +less likely to require limitation from subsequent experience, +than the law which they serve to explain. They are more +nearly unconditional; they are defeated by fewer contingencies; +they are a nearer approach to the universal +truth of nature. The same observations are still more evidently +true with regard to the first of the three modes of +<span class="tei tei-pb" id="page481">[pg 481]</span><a name="Pg481" id="Pg481" class="tei tei-anchor"></a> +resolution. When the law of an effect of combined causes +is resolved into the separate laws of the causes, the nature +of the case implies that the law of the effect is less general +than the law of any of the causes, since it only holds when +they are combined; while the law of any one of the causes +holds good both then, and also when that cause acts apart +from the rest. It is also manifest that the complex law is +liable to be oftener unfulfilled than any one of the simpler +laws of which it is the result, since every contingency which +defeats any of the laws prevents so much of the effect as +depends on it, and thereby defeats the complex law. +The mere rusting, for example, of some small part of a +great machine, often suffices entirely to prevent the effect +which ought to result from the joint action of all the parts. +The law of the effect of a combination of causes is always +subject to the whole of the negative conditions which attach +to the action of all the causes severally. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is another and a still stronger reason why the law +of a complex effect must be less general than the laws of +the causes which conspire to produce it. The same causes, +acting according to the same laws, and differing only in the +proportions in which they are combined, often produce +effects which differ not merely in quantity, but in kind. +The combination of a centripetal with a projectile force, in +the proportions which obtain in all the planets and satellites +of our solar system, gives rise to an elliptical motion; but if +the ratio of the two forces to each other were slightly altered, +it is demonstrable that the motion produced would be in a +circle, or a parabola, or an hyperbola: and it has been surmised +that in the case of some comets one of these is really +the fact. Yet the law of the parabolic motion would be +resolvable into the very same simple laws into which that +of the elliptical motion is revolved, namely, the law of the +permanence of rectilineal motion, and the law of gravitation. +If, therefore, in the course of ages, some circumstance +were to manifest itself which, without defeating the law +of either of those forces, should merely alter their proportion +to one another, (such as the shock of a comet, +<span class="tei tei-pb" id="page482">[pg 482]</span><a name="Pg482" id="Pg482" class="tei tei-anchor"></a> +or even the accumulating effect of the resistance of the +medium in which astronomers have been led to surmise that +the motions of the heavenly bodies take place;) the elliptical +motion might be changed into a motion in some other +conic section; and the complex law, that the heavenly +motions take place in ellipses, would be deprived of its +universality, though the discovery would not at all detract +from the universality of the simpler laws into which that +complex law is resolved. The law, in short, of each of the +concurrent causes remains the same, however their collocations +may vary; but the law of their joint effect varies with +every difference in the collocations. There needs no more +to show how much more general the elementary laws must +be, than any of the complex laws which are derived from +them. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. Besides the two modes which have been treated +of, there is a third mode in which laws are resolved into one +another; and in this it is self-evident that they are resolved +into laws more general than themselves. This third mode +is the <span class="tei tei-hi"><span style="font-style: italic">subsumption</span></span> (as it has been called) of one law under +another: or (what comes to the same thing) the gathering +up of several laws into one more general law which includes +them all. The most splendid example of this operation was +when terrestrial gravity and the central force of the solar +system were brought together under the general law of gravitation. +It had been proved antecedently that the earth +and the other planets tend to the sun; and it had been +known from the earliest times that terrestrial bodies tend +towards the earth. These were similar phenomena; and to +enable them both to be subsumed under one law, it was +only necessary to prove that, as the effects were similar in +quality, so also they, as to quantity, conform to the same +rules. This was first shown to be true of the moon, which +agreed with terrestrial objects not only in tending to a centre, +but in the fact that this centre was the earth. The tendency +of the moon towards the earth being ascertained to vary as +the inverse square of the distance, it was deduced from this, +<span class="tei tei-pb" id="page483">[pg 483]</span><a name="Pg483" id="Pg483" class="tei tei-anchor"></a> +by direct calculation, that if the moon were as near to the +earth as terrestrial objects are, and the tangential force were +suspended, the moon would fall towards the earth through +exactly as many feet in a second as those objects do by +virtue of their weight. Hence the inference was irresistible, +that the moon also tends to the earth by virtue of its weight: +and that the two phenomena, the tendency of the moon to +the earth and the tendency of terrestrial objects to the earth, +being not only similar in quality, but, when in the same +circumstances, identical in quantity, are cases of one and +the same law of causation. But the tendency of the moon +to the earth and the tendency of the earth and planets to the +sun, were already known to be cases of the same law of +causation: and thus the law of all these tendencies, and the +law of terrestrial gravity, were recognized as identical, or in +other words, were subsumed under one general law, that of +gravitation. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In a similar manner, the laws of magnetic phenomena +have recently been subsumed under known laws of electricity. +It is thus that the most general laws of nature are +usually arrived at: we mount to them by successive steps. +For, to arrive by correct induction at laws which hold under +such an immense variety of circumstances, laws so general +as to be independent of any varieties of space or time which +we are able to observe, requires for the most part many distinct +sets of experiments or observations, conducted at different +times and by different people. One part of the law +is first ascertained, afterwards another part: one set of +observations teaches us that the law holds good under some +conditions, another that it holds good under other conditions, +by combining which observations we find that it holds +good under conditions much more general, or even universally. +The general law, in this case, is literally the sum of +all the partial ones; it is the recognition of the same +sequence in different sets of instances; and may, in fact, be +regarded as merely one step in the process of elimination. +That tendency of bodies towards one another, which we now +call gravity, had at first been observed only on the earth's +<span class="tei tei-pb" id="page484">[pg 484]</span><a name="Pg5484" id="Pg5484" class="tei tei-anchor"></a> +surface, where it manifested itself only as a tendency of all +bodies towards the earth, and might, therefore, be ascribed +to a peculiar property of the earth itself: one of the circumstances, +namely, the proximity of the earth, had not been +eliminated. To eliminate this circumstance required a fresh +set of instances in other parts of the universe: these we +could not ourselves create; and though nature had created +them for us, we were placed in very unfavourable circumstances +for observing them. To make these observations, +fell naturally to the lot of a different set of persons from +those who studied terrestrial phenomena, and had, indeed, +been a matter of great interest at a time when the idea of +explaining celestial facts by terrestrial laws was looked upon +as the confounding of an indefeasible distinction. When, +however, the celestial motions were accurately ascertained, +and the deductive processes performed from which it appeared +that their laws and those of terrestrial gravity corresponded, +those celestial observations became a set of instances +which exactly eliminated the circumstance of proximity to +the earth; and proved that in the original case, that of terrestrial +objects, it was not the earth, as such, that caused the +motion or the pressure, but the circumstance common to that +case with the celestial instances, namely, the presence of +some great body within certain limits of distance. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. There are, then, three modes of explaining laws of +causation, or, which is the same thing, resolving them into other +laws. First, when the law of an effect of combined causes is +resolved into the separate laws of the causes, together with +the fact of their combination. Secondly, when the law which +connects any two links, not proximate, in a chain of causation, +is resolved into the laws which connect each with the +intermediate links. Both of these are cases of resolving one +law into two or more; in the third, two or more are resolved +into one: when, after the law has been shown to hold good +in several different classes of cases, we decide that what is +true in each of these classes of cases, is true under some +more general supposition, consisting of what all those classes +<span class="tei tei-pb" id="page485">[pg 485]</span><a name="Pg485" id="Pg485" class="tei tei-anchor"></a> +of cases have in common. We may here remark that this +last operation involves none of the uncertainties attendant +on induction by the Method of Agreement, since we need +not suppose the result to be extended by way of inference to +any new class of cases, different from those by the comparison +of which it was engendered. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In all these three processes, laws are, as we have seen, +resolved into laws more general than themselves; laws extending +to all the cases which the former extend to, and +others besides. In the first two modes they are also resolved +into laws more certain, in other words, more universally true +than themselves; they are, in fact, proved not to be themselves +laws of nature, the character of which is to be universally +true, but <em class="tei tei-emph"><span style="font-style: italic">results</span></em> of laws of nature, which may be only true +conditionally, and for the most part. No difference of this +sort exists in the third case; since here the partial laws are, +in fact, the very same law as the general one, and any exception +to them would be an exception to it too. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +By all the three processes, the range of deductive science +is extended; since the laws, thus resolved, may be thenceforth +deduced demonstratively from the laws into which they +are resolved. As already remarked, the same deductive process +which proves a law or fact of causation if unknown, +serves to explain it when known. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The word explanation is here used in its philosophical +sense. What is called explaining one law of nature by +another, is but substituting one mystery for another; and +does nothing to render the general course of nature other +than mysterious: we can no more assign a <em class="tei tei-emph"><span style="font-style: italic">why</span></em> for the more +extensive laws than for the partial ones. The explanation +may substitute a mystery which has become familiar, and +has grown to <em class="tei tei-emph"><span style="font-style: italic">seem</span></em> not mysterious, for one which is still +strange. And this is the meaning of explanation, in common +parlance. But the process with which we are here concerned +often does the very contrary: it resolves a phenomenon with +which we are familiar, into one of which we previously knew +little or nothing; as when the common fact of the fall of +heavy bodies is resolved into a tendency of all particles of +<span class="tei tei-pb" id="page486">[pg 486]</span><a name="Pg486" id="Pg486" class="tei tei-anchor"></a> +matter towards one another. It must be kept constantly in +view, therefore, that in science, those who speak of explaining +any phenomenon mean (or should mean) pointing +out not some more familiar, but merely some more general, +phenomenon, of which it is a partial exemplification; +or some laws of causation which produce it by their joint +or successive action, and from which, therefore, its conditions +may be determined deductively. Every such operation +brings us a step nearer towards answering the question +which was stated in a previous chapter as comprehending +the whole problem of the investigation of nature, viz. What +are the fewest assumptions, which being granted, the order +of nature as it exists would be the result? What are the +fewest general propositions from which all the uniformities +existing in nature could be deduced? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The laws, thus explained or resolved, are sometimes said +to be <em class="tei tei-emph"><span style="font-style: italic">accounted for</span></em>; but the expression is incorrect, if taken +to mean anything more than what has been already stated. +In minds not habituated to accurate thinking, there is often +a confused notion that the general laws are the <em class="tei tei-emph"><span style="font-style: italic">causes</span></em> of the +partial ones; that the law of general gravitation, for example, +causes the phenomenon of the fall of bodies to the earth. But +to assert this, would be a misuse of the word cause: terrestrial +gravity is not an effect of general gravitation, but a <em class="tei tei-emph"><span style="font-style: italic">case</span></em> +of it; that is, one kind of the particular instances in which +that general law obtains. To account for a law of nature +means, and can mean, nothing more than to assign other laws +more general, together with collocations, which laws and +collocations being supposed, the partial law follows without +any additional supposition. +</p> + +</div> + +<span class="tei tei-pb" id="page487">[pg 487]</span><a name="Pg487" id="Pg487" class="tei tei-anchor"></a> + +<hr class="page" /><div class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"> +<a name="toc79" id="toc79"></a> +<a name="pdf80" id="pdf80"></a> +<h2 class="tei tei-head" style="text-align: left; margin-bottom: 2.88em; margin-top: 2.88em"><span style="font-size: 144%">CHAPTER XIII. MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF +LAWS OF NATURE.</span></h2> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 1. Some of the most remarkable instances which have +occurred since the great Newtonian generalization, of the +explanation of laws of causation subsisting among complex +phenomena, by resolving them into simpler and more general +laws, are to be found among the speculations of Liebig in +organic chemistry. These speculations, though they have +not yet been sufficiently long before the world to entitle +us positively to assume that no well-grounded objection can +be made to any part of them, afford, however, so admirable +an example of the spirit of the Deductive Method, that I may +be permitted to present some specimens of them here. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It had been observed in certain cases, that chemical +action is, as it were, contagious; that is to say, a substance +which would not of itself yield to a particular chemical attraction, +(the force of the attraction not being sufficient to overcome +cohesion, or to destroy some chemical combination in +which the substance was already held), will nevertheless do +so if placed in contact with some other body which is in the +act of yielding to the same force. Nitric acid, for example, +does not dissolve pure platinum, which may <span class="tei tei-q">“be boiled with +this acid without being oxidized by it, even when in a state +of such fine division that it no longer reflects light.”</span> But the +same acid easily dissolves silver. Now if an alloy of silver +and platinum be treated with nitric acid, the acid does not, +as might naturally be expected, separate the two metals, +dissolving the silver, and leaving the platinum; it dissolves +both: the platinum as well as the silver becomes oxidized, +and in that state combines with the undecomposed portion +of the acid. In like manner, <span class="tei tei-q">“copper does not decompose +water, even when boiled in dilute sulphuric acid; but an alloy +<span class="tei tei-pb" id="page488">[pg 488]</span><a name="Pg488" id="Pg488" class="tei tei-anchor"></a> +of copper, zinc, and nickel, dissolves easily in this acid with +evolution of hydrogen gas.”</span> These phenomena cannot be +explained by the laws of what is termed chemical affinity. +They point to a peculiar law, by which the oxidation which +one body suffers, causes another, in contact with it, to submit +to the same change. And not only chemical composition, +but chemical decomposition, is capable of being similarly +propagated. The peroxide of hydrogen, a compound formed +by hydrogen with a greater amount of oxygen than the +quantity necessary to form water, is held together by a +chemical attraction of so weak a nature, that the slightest +circumstance is sufficient to decompose it; and it even, +though very slowly, gives off oxygen and is reduced to water +spontaneously (being, I presume, decomposed by the tendency +of its oxygen to absorb heat and assume the gaseous state). +Now it has been observed, that if this decomposition of the +peroxide of hydrogen takes place in contact with some +metallic oxides, as those of silver, and the peroxides of lead +and manganese, it superinduces a corresponding chemical +action upon those substances; they also give forth the whole +or a portion of their oxygen, and are reduced to the metal or +to the protoxide; although they do not undergo this change +spontaneously, and there is no chemical affinity at work to +make them do so. Other similar phenomena are mentioned +by Liebig. <span class="tei tei-q">“Now no other explanation,”</span> he observes, <span class="tei tei-q">“of +these phenomena can be given, than that a body in the act +of combination or decomposition enables another body, with +which it is in contact, to enter into the same state.”</span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Here, therefore, is a law of nature of great simplicity, but +which, owing to the extremely special and limited character +of the phenomena in which alone it can be detected experimentally, +(because in them alone its results are not intermixed +and blended with those of other laws,) had been very +little recognised by chemists, and no one could have ventured, +on experimental evidence, to affirm it as a law common +to all chemical action; owing to the impossibility of a rigorous +employment of the Method of Difference where the +properties of different kinds of substance are involved, an +<span class="tei tei-pb" id="page489">[pg 489]</span><a name="Pg489" id="Pg489" class="tei tei-anchor"></a> +impossibility which we noticed and characterized in a previous +chapter.<a id="noteref_90" name="noteref_90" href="#note_90"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">90</span></span></a> +Now this extremely special and apparently precarious +generalization has, in the hands of Liebig, been +converted, by a masterly employment of the Deductive +Method, into a law pervading all nature, in the same way +as gravitation assumed that character in the hands of Newton; +and has been found to explain, in the most unexpected +manner, numerous detached generalizations of a more limited +kind, reducing the phenomena concerned in those generalizations +into mere cases of itself. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The contagious influence of chemical action is not a +powerful force, and is only capable of overcoming weak +affinities: we, may, therefore, expect to find it principally +exemplified in the decomposition of substances which are +held together by weak chemical forces. Now the force which +holds a compound substance together is generally weaker, +the more compound the substance is; and organic products +are the most compound substances known, those which have +the most complex atomic constitution. It is, therefore, upon +such substances that the self-propagating power of chemical +action is likely to exert itself in the most marked manner. +Accordingly, first, it explains the remarkable laws of fermentation, +and some of those of putrefaction. <span class="tei tei-q">“A little leaven,”</span> +that is, dough in a certain state of chemical action, impresses +a similar chemical action upon <span class="tei tei-q">“the whole lump.”</span> The contact +of any decaying substance, occasions the decay of matter +previously sound. Again, yeast is a substance actually in a +process of decomposition from the action of air and water, +evolving carbonic acid gas. Sugar is a substance which, +from the complexity of its composition, has no great energy +of coherence in its existing form, and is capable of being +easily converted (by combination with the elements of water) +into carbonic acid and alcohol. Now the mere presence of +yeast, the mere proximity of a substance of which the elements +are separating from each other, and combining with the +elements of water, causes sugar to undergo the same change, +<span class="tei tei-pb" id="page490">[pg 490]</span><a name="Pg490" id="Pg490" class="tei tei-anchor"></a> +giving out carbonic acid gas, and becoming alcohol. It is +not the elements contained in the yeast which do this. <span class="tei tei-q">“An +aqueous infusion of yeast may be mixed with a solution of +sugar, and preserved in vessels from which the air is excluded, +without either experiencing the slightest change.”</span> Neither +does the insoluble residue of the yeast, after being treated +with water, possess the power of exciting fermentation. (Here +we have the method of Difference). It is not the yeast itself, +therefore; it is the yeast in a state of decomposition. The +sugar, which would not decompose and oxidize by the mere +presence of oxygen and water, is induced to do so when +another oxidation is at work in the midst of it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +By the same principle Liebig is enabled to explain many +cases of malaria; the pernicious influence of putrid substances; +a variety of poisons; contagious diseases; and other +phenomena. Of all substances, those composing the animal +body are the most complex in their composition, and are in +the least stable condition of union. The blood, in particular, +is the most unstable compound known. It is, therefore, not +surprising that gaseous or other substances, in the act of undergoing +the chemical changes which constitute, for instance, +putrefaction, should, when brought into contact with the tissues +by respiration or otherwise, and still more when introduced +by inoculation into the blood itself, impress upon some +of the particles a chemical action similar to its own; which is +propagated in like manner to other particles, until the whole +system is placed in a state of chemical action more or less +inconsistent with the chemical conditions of vitality. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Of the three modes in which we observed in the last chapter +that the resolution of a special law into more general +ones may take place, this speculation exemplifies the second. +The laws explained are such as this, that yeast puts sugar +into a state of fermentation. Between the remote cause, the +presence of yeast, and the consequent fermentation of the +sugar, there has been interpolated a proximate cause, the +chemical action between the particles of the yeast and the +elements of air and water. The special law is thus resolved +into two others, more general than itself: the first, that yeast +<span class="tei tei-pb" id="page491">[pg 491]</span><a name="Pg491" id="Pg491" class="tei tei-anchor"></a> +is decomposed by the presence of air and water; the second, +that matter undergoing chemical action has a tendency to +produce similar chemical action in other matter in contact +with it. But while the investigation thus aptly exhibits the +second mode of the resolution of a complex law, it no less +happily exemplifies the third; the subsumption of special +laws under a more general law, by gathering them up into +one more comprehensive expression which includes them all. +For the curious fact of the contagious nature of chemical action +is only raised into a law of <em class="tei tei-emph"><span style="font-style: italic">all</span></em> chemical action by these +very investigations; just as the Newtonian attraction was +only recognised as a law of all matter when it was found +to explain the phenomena of terrestrial gravity. Previously +to Liebig's investigations, the property in question had only +been observed in a few special cases of chemical action; but +when his deductive reasonings have established that innumerable +effects produced upon weak compounds, by substances +none of whose known peculiarities would account for +their having such a power, might be explained by considering +the supposed special property to exist in all those cases, +these numerous generalizations on separate substances are +brought together into one law of chemical action in general: +the peculiarities of the various substances being, in fact, eliminated, +just as the Newtonian deduction eliminated from +the instances of terrestrial gravity the circumstance of proximity +to the earth. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 2. Another speculation of the same chemist, which, if +it should ultimately be found to agree with all the facts of the +extremely complicated phenomenon to which it relates, will +constitute one of the finest examples of the Deductive Method +on record, is his theory of respiration. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The facts of respiration, or in other words the special +laws which it is attempted to explain from, and resolve into, +more general ones, are, that the blood in passing through the +lungs absorbs oxygen and gives out carbonic acid gas, changing +thereby its colour from a blackish purple to a brilliant +red. The absorption and exhalation are evidently chemical +<span class="tei tei-pb" id="page492">[pg 492]</span><a name="Pg492" id="Pg492" class="tei tei-anchor"></a> +phenomena; and the carbon of the carbonic acid must have +been derived from the body, that is, must have been absorbed +by the blood from the substances with which it came into +contact in its passage through the organism. Required to +find the intermediate links—the precise nature of the two +chemical actions which take place; first, the absorption of +the carbon or of the carbonic acid by the blood, in its circulation +through the body; next, the excretion of the carbon, +or the exchange of the carbonic acid for oxygen, in its passage +through the lungs. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Liebig believes himself to have found the solution of +this <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">vexata quæstio</span></span> +in a class of chemical actions in which +scarcely any less acute and penetrating inquirer would have +thought of looking for it. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Blood is composed of two parts, the serum and the globules. +The serum absorbs and holds in solution carbonic +acid in great quantity, but has no tendency either to part +with it or to absorb oxygen. The globules, therefore, are +concluded to be the portion of the blood which is operative +in respiration. These globules contain a certain quantity of +iron, which from chemical tests is inferred to be in the state +of oxide. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Liebig recognised, in the known chemical properties +of the oxides of iron, laws which, if followed out deductively, +would lead to the prediction of the precise series of phenomena +which respiration exhibits. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There are two oxides of iron, a protoxide and a peroxide. +In the arterial blood the iron is in the form of +peroxide: in the venous blood we have no direct evidence +which of the oxides is present, but the considerations to be +presently stated lead to the conclusion that it is the protoxide. +As arterial and venous blood are in a perpetual +state of alternate conversion into one another, the question +arises, in what circumstances the protoxide of iron is capable +of being converted into the peroxide, and <span class="tei tei-hi"><span style="font-style: italic">vice versâ</span></span>. Now +the protoxide readily combines with oxygen in the presence +of water, forming the hydrated peroxide: these conditions +it finds in passing through the lungs; it derives oxygen +<span class="tei tei-pb" id="page493">[pg 493]</span><a name="Pg493" id="Pg493" class="tei tei-anchor"></a> +from the air, and finds water in the blood itself. This +would already explain one portion of the phenomena of +respiration. But the arterial blood, in quitting the lungs, +is charged with hydrated peroxide: in what manner is the +peroxide brought back to its former state? +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The chemical conditions for the reduction of the hydrated +peroxide into the state of protoxide, are precisely those which +the blood meets with in circulating through the body; namely, +contact with organic compounds. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Hydrated peroxide of iron, when treated with organic +compounds (where no sulphur is present) gives forth oxygen +and water, which oxygen, attracting the carbon from the +organic substance, becomes carbonic acid; while the peroxide, +being reduced to the state of protoxide, combines +with the carbonic acid, and becomes a carbonate. Now this +carbonate needs only come again into contact with oxygen +and water to be decomposed; the carbonic acid being given +off, and the protoxide, by the absorption of oxygen and +water, becoming again the hydrated peroxide. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The mysterious chemical phenomena connected with +respiration can now, by a beautiful deductive process, be +completely explained. The arterial blood, containing iron +in the form of hydrated peroxide, passes into the capillaries, +where it meets with the decaying tissues, receiving also in +its course certain non-azotised but highly carbonised animal +products, in particular the bile. In these it finds the precise +conditions required for decomposing the peroxide into +oxygen and the protoxide. The oxygen combines with the +carbon of the decaying tissues, and forms carbonic acid, +which, though insufficient in amount to neutralize the whole +of the protoxide, combines with a portion (one-fourth) of +it, and returns in the form of a carbonate, along with the +other three-fourths of the protoxide, through the venous +system into the lungs. There it again meets with oxygen +and water: the free protoxide becomes hydrated peroxide: +the carbonate of protoxide parts with its carbonic acid, and +by absorbing oxygen and water, enters also into the state of +hydrated peroxide. The heat evolved in the transition from +<span class="tei tei-pb" id="page494">[pg 494]</span><a name="Pg494" id="Pg494" class="tei tei-anchor"></a> +protoxide to peroxide, as well as in the previous oxidation +of the carbon contained in the tissues, is considered by +Liebig as the cause which sustains the temperature of the +body. But into this portion of the speculation we need not +enter.<a id="noteref_91" name="noteref_91" href="#note_91"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">91</span></span></a> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This example displays the second mode of resolving +complex laws, by the interpolation of intermediate links in +the chain of causation; and some of the steps of the deduction +exhibit cases of the first mode, that which infers the +joint effect of two or more causes from their separate effects; +but to trace out in detail these exemplifications may be left +to the intelligence of the reader. The third mode is not +employed in this example, since the simpler laws into which +those of respiration are resolved (the laws of the chemical +action of the oxides of iron) were laws already known, and +do not acquire any additional generality from their employment +in the present case. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 3. The property which salt possesses of preserving +animal substances from putrefaction is resolved by Liebig +into two more general laws, the strong attraction of salt for +water, and the necessity of the presence of water as a condition +of putrefaction. The intermediate phenomenon which +is interpolated between the remote cause and the effect, can +here be not merely inferred but seen; for it is a familiar +fact, that flesh upon which salt has been thrown is speedily +found swimming in brine. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The second of the two factors (as they may be termed) +<span class="tei tei-pb" id="page495">[pg 495]</span><a name="Pg495" id="Pg495" class="tei tei-anchor"></a> +into which the preceding law has been resolved, the necessity +of water to putrefaction, itself affords an additional example +of the Resolution of Laws. The law itself is proved by the +Method of Difference, since flesh completely dried and kept +in a dry atmosphere does not putrefy, as we see in the case +of dried provisions, and human bodies in very dry climates. +A deductive explanation of this same law results from +Liebig's speculations. The putrefaction of animal and other +azotised bodies is a chemical process, by which they are +gradually dissipated in a gaseous form, chiefly in that of +carbonic acid and ammonia; now to convert the carbon of +the animal substance into carbonic acid requires oxygen, +and to convert the azote into ammonia requires hydrogen, +which are the elements of water. The extreme rapidity of +the putrefaction of azotised substances, compared with the +gradual decay of non-azotised bodies (such as wood and the +like) by the action of oxygen alone, he explains from the +general law that substances are much more easily decomposed +by the action of two different affinities upon two of +their elements, than by the action of only one. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The purgative effect of salts with alkaline bases, when +administered in concentrated solutions, is explained from +the two following principles: Animal tissues (such as the +stomach) do <em class="tei tei-emph"><span style="font-style: italic">not</span></em> absorb concentrated solutions of alkaline +salts; and such solutions <em class="tei tei-emph"><span style="font-style: italic">do</span></em> dissolve the solids contained in +the intestines. The simpler laws into which the complex +law is here resolved, are the second of the two foregoing +principles combined with a third, namely that the peristaltic +contraction acts easily upon substances in a state of solution. +The negative general proposition, that animal substances do +not absorb these salts, contributes to the explanation by +accounting for the absence of a counteracting cause, namely, +absorption by the stomach, which in the case of other substances +possessed of the requisite chemical properties, interferes +to prevent them from reaching the substances which +they are destined to dissolve. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 4. From the foregoing and similar instances, we may +<span class="tei tei-pb" id="page496">[pg 496]</span><a name="Pg496" id="Pg496" class="tei tei-anchor"></a> +see the importance, when a law of nature previously unknown +has been brought to light, or when new light has been thrown +upon a known law by experiment, of examining all cases +which present the conditions necessary for bringing that law +into action; a process fertile in demonstrations of special +laws previously unsuspected, and explanations of others +already empirically known. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For instance, Faraday discovered by experiment, that +voltaic electricity could be evolved from a natural magnet, +provided a conducting body were set in motion at right +angles to the direction of the magnet: and, this he found to +hold not only of small magnets, but of that great magnet, the +earth. The law being thus established experimentally, that +electricity is evolved, by a magnet, and a conductor moving +at right angles to the direction of its poles, we may now look +out for fresh instances in which these conditions meet. +Wherever a conductor moves or revolves at right angles to +the direction of the earth's magnetic poles, there we may expect +an evolution of electricity. In the northern regions, +where the polar direction is nearly perpendicular to the +horizon, all horizontal motions of conductors will produce electricity; +horizontal wheels, for example, made of metal; likewise +all running streams will evolve a current of electricity +which will circulate round them; and the air thus charged +with electricity may be one of the causes of the Aurora Borealis. +In the equatorial regions, on the contrary, upright +wheels placed parallel to the equator will originate a voltaic +circuit, and waterfalls will naturally become electric. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +For a second example; it has recently been found, chiefly +by the researches of Professor Graham, that gases have a +strong tendency to permeate animal membranes, and diffuse +themselves through the spaces which such membranes inclose, +notwithstanding the presence of other gases in those +spaces. Proceeding from this general law, and reviewing a +variety of cases in which gases lie contiguous to membranes, +we are enabled to demonstrate or to explain the following +more special laws: 1st. The human or animal body, when +surrounded with any gas not already contained within the +<span class="tei tei-pb" id="page497">[pg 497]</span><a name="Pg497" id="Pg497" class="tei tei-anchor"></a> +body, absorbs it rapidly; such, for instance, as the gases of +putrefying matters: which helps to explain malaria. 2nd. +The carbonic acid gas of effervescing drinks, evolved in the +stomach, permeates its membranes, and rapidly spreads +through the system, where, as suggested in a former note, it +probably combines with the iron contained in the blood. +3rd. Alcohol taken into the stomach passes into vapour +and spreads through the system with great rapidity; +(which, combined with the high combustibility of alcohol, +or in other words its ready combination with oxygen, may +perhaps help to explain the bodily warmth immediately +consequent on drinking spirituous liquors.) 4th. In any +state of the body in which peculiar gases are formed within +it, these will rapidly exhale through all parts of the body; +and hence the rapidity with which, in certain states of disease, +the surrounding atmosphere becomes tainted. 5th. The +putrefaction of the interior parts of a carcase will proceed as +rapidly as that of the exterior, from the ready passage outwards +of the gaseous products. 6th. The exchange of oxygen +and carbonic acid in the lungs is not prevented, but rather +promoted, by the intervention of the membrane of the lungs +and the coats of the blood vessels between the blood and the +air. It is necessary, however, that there should be a substance +in the blood with which the oxygen of the air may +immediately combine; otherwise instead of passing into the +blood, it would permeate the whole organism: and it is necessary +that the carbonic acid, as it is formed in the capillaries, +should also find a substance in the blood with which +it can combine; otherwise it would leave the body at all +points, instead of being discharged through the lungs. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 5. The following is a deduction which confirms, by +explaining, the old but not undisputed empirical generalization, +that soda powders weaken the human system. These +powders, consisting of a mixture of tartaric acid with bicarbonate +of soda, from which the carbonic acid is set free, must +pass into the stomach as tartrate of soda. Now, neutral tartrates, +citrates, and acetates of the alkalis are found, in their +<span class="tei tei-pb" id="page498">[pg 498]</span><a name="Pg498" id="Pg498" class="tei tei-anchor"></a> +passage through the system, to be changed into carbonates; +and to convert a tartrate into a carbonate requires an additional +quantity of oxygen, the abstraction of which must +lessen the oxygen destined for assimilation with the blood, +on the quantity of which the vigorous action of the human +system partly depends. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The instances of new theories agreeing with and explaining +old empiricisms, are innumerable. All the just remarks +made by experienced persons on human character and conduct, +are so many special laws, which the general laws of the +human mind explain and resolve. The empirical generalizations +on which the operations of the arts have usually been +founded, are continually justified and confirmed on the one +hand, or corrected and improved on the other, by the discovery +of the simpler scientific laws on which the efficacy of +those operations depends. The effects of the rotation of +crops, of the various manures, and other processes of improved +agriculture, have been for the first time resolved in +our own day into known laws of chemical and organic action, +by Davy and Liebig. The processes of the medical art are +even now mostly empirical: their efficacy is concluded, in +each instance, from a special and most precarious experimental +generalization: but as science advances in discovering +the simple laws of chemistry and physiology, progress is +made in ascertaining the intermediate links in the series of +phenomena, and the more general laws on which they depend; +and thus, while the old processes are either exploded, +or their efficacy, in so far as real, explained, better processes, +founded on the knowledge of proximate causes, are +continually suggested and brought into use.<a id="noteref_92" name="noteref_92" href="#note_92"><span class="tei tei-noteref"><span style="font-size: 60%; vertical-align: super">92</span></span></a> Many even of +<span class="tei tei-pb" id="page499">[pg 499]</span><a name="Pg499" id="Pg499" class="tei tei-anchor"></a> +the truths of geometry were generalizations from experience +before they were deduced from first principles. The quadrature +of the cycloid is said to have been first effected by +measurement, or rather by weighing a cycloidal card, and +comparing its weight with that of a piece of similar card of +known dimensions. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 6. To the foregoing examples from physical science, +let us add another from mental. The following is one of the +simple laws of mind: Ideas of a pleasurable or painful character +form associations more easily and strongly than other +ideas, that is, they become associated after fewer repetitions, +and the association is more durable. This is an experimental +law, grounded on the Method of Difference. By deduction +from this law, many of the more special laws which experience +shows to exist among particular mental phenomena +may be demonstrated and explained:—the ease and rapidity, +for instance, with which thoughts connected with our passions +or our more cherished interests are excited, and the firm +hold which the facts relating to them have on our memory; +the vivid recollection we retain of minute circumstances +which accompanied any object or event that deeply interested +us, and of the times and places in which we have been very +happy or very miserable; the horror with which we view the +accidental instrument of any occurrence which shocked us, +or the locality where it took place, and the pleasure we derive +from any memorial of past enjoyment; all these effects being +proportional to the sensibility of the individual mind, and to +the consequent intensity of the pain or pleasure from which +the association originated. It has been suggested by the +able writer of a biographical sketch of Dr. Priestley in a +monthly periodical, that the same elementary law of our +mental constitution, suitably followed out, would explain a +variety of mental phenomena hitherto inexplicable, and in +<span class="tei tei-pb" id="page500">[pg 500]</span><a name="Pg500" id="Pg500" class="tei tei-anchor"></a> +particular some of the fundamental diversities of human +character and genius. Associations being of two sorts, +either between synchronous, or between successive impressions; +and the influence of the law which renders associations +stronger in proportion to the pleasurable or painful character +of the impressions, being felt with peculiar force in the +synchronous class of associations; it is remarked by the +writer referred to, that in minds of strong organic sensibility +synchronous associations will be likely to predominate, producing +a tendency to conceive things in pictures and in the +concrete, richly clothed in attributes and circumstances, a +mental habit which is commonly called Imagination, and is +one of the peculiarities of the painter and the poet; while +persons of more moderate susceptibility to pleasure and pain +will have a tendency to associate facts chiefly in the order of +their succession, and such persons, if they possess mental superiority, +will addict themselves to history or science rather than +to creative art. This interesting speculation the author of the +present work has endeavoured, on another occasion, to pursue +farther, and to examine how far it will avail towards explaining +the peculiarities of the poetical temperament. It +is at least an example which may serve, instead of many +others, to show the extensive scope which exists for deductive +investigation in the important and hitherto so imperfect +Science of Mind. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +§ 7. The copiousness with which I have exemplified +the discovery and explanation of special laws of phenomena +by deduction from simpler and more general ones, was +prompted by a desire to characterize clearly, and place in its +due position of importance, the Deductive Method; which +in the present state of knowledge is destined henceforth +irrevocably to predominate in the course of scientific investigation. +A revolution is peaceably and progressively +effecting itself in philosophy, the reverse of that to which +Bacon has attached his name. That great man changed the +method of the sciences from deductive to experimental, and it +is now rapidly reverting from experimental to deductive. But +<span class="tei tei-pb" id="page501">[pg 501]</span><a name="Pg501" id="Pg501" class="tei tei-anchor"></a> +the deductions which Bacon abolished were from premisses +hastily snatched up, or arbitrarily assumed. The principles +were neither established by legitimate canons of experimental +inquiry, nor the results tested by that indispensable element +of a rational Deductive Method, verification by specific experience. +Between the primitive method of Deduction and +that which I have attempted to characterize, there is all the +difference which exists between the Aristotelian physics and +the Newtonian theory of the heavens. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It would, however, be a mistake to expect that those great +generalizations, from which the subordinate truths of the more +backward sciences will probably at some future period be +deduced by reasoning (as the truths of astronomy are deduced +from the generalities of the Newtonian theory,) will be +found, in all, or even in most cases, among truths now known +and admitted. We may rest assured, that many of the most +general laws of nature are as yet entirely unthought of; and +that many others, destined hereafter to assume the same character, +are known, if at all, only as laws or properties of some +limited class of phenomena; just as electricity, now recognised +as one of the most universal of natural agencies, was once +known only as a curious property which certain substances +acquired by friction, of first attracting and then repelling +light bodies. If the theories of heat, cohesion, crystallization, +and chemical action, are destined, as there can be little +doubt that they are, to become deductive, the truths which +will then be regarded as the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">principia</span></span> of those sciences would +probably, if now announced, appear quite as novel as the +law of gravitation appeared to the cotemporaries of Newton; +possibly even more so, since Newton's law, after all, was but +an extension of the law of weight—that is, of a generalization +familiar from of old, and which already comprehended +a not inconsiderable body of natural phenomena. The +general laws, of a similarly commanding character, which +we still look forward to the discovery of, may not always +find so much of their foundations already laid. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +These general truths will doubtless make their first appearance +in the character of hypotheses; not proved, nor +<span class="tei tei-pb" id="page502">[pg 502]</span><a name="Pg502" id="Pg502" class="tei tei-anchor"></a> +even admitting of proof, in the first instance, but assumed +as premisses for the purpose of deducing from them the +known laws of concrete phenomena. But this, though +their initial, cannot be their final state. To entitle an hypothesis +to be received as one of the truths of nature, and not +as a mere technical help to the human faculties, it must be +capable of being tested by the canons of legitimate induction, +and must actually have been submitted to that test. When +this shall have been done, and done successfully, premisses +will have been obtained from which all the other propositions +of the science will thenceforth be presented as conclusions, +and the science will, by means of a new and unexpected +Induction, be rendered Deductive. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +END OF VOL. I. +</p> +</div> + +</div> + +<span class="tei tei-pb" id="page503">[pg 503]</span><a name="Pg503" id="Pg503" class="tei tei-anchor"></a> + +<div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +BOOKS PUBLISHED BY +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +John W. Parker, West Strand, London. +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. J. S. Mill's Principles of Political Economy. Second +Edition. 2 vols. Octavo. 30<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. J. S. Mill's Essays on some Unsettled Questions of Political +Economy. Octavo. 6<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Archbishop Whately's Introductory Lectures on Political +Economy. Third Edition. Octavo, 8<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. Cornewall Lewis on the Influence of Authority in Matters +of Opinion. Octavo, 10<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. E. G. Wakefield's View of the Art of Colonization. +Octavo, 12<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The Evils of England, Social and Economical. By a London +Physician. 2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Wayland's Elements of Political Economy. 2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Easy Lessons on Money Matters. Tenth Edition. 1<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's History of the Inductive Sciences. Second +Edition, revised and continued. Three vols. +2<span class="tei tei-hi"><span style="font-style: italic">l.</span></span> 2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's Philosophy of the Inductive Sciences. Second +Edition, revised. Two Vols. Octavo. 30<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's Indications of the Creator. Theological Extracts +from <span class="tei tei-q">“The History and the Philosophy of the Inductive Sciences.”</span> New Edition, +with Preface, 5<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell on Induction, with especial reference to Mr. Mill's +System of Logic. 2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Archbishop Whately's Elements of Logic. With all the +Author's Additions and Emendations. Cheap Edition; Crown Octavo, +4<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> Library +Edition; Demy Octavo, 10<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Archbishop Whately's Elements of Rhetoric. With all the +Author's Additions and Emendations. Cheap Edition; Crown Octavo, +4<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> Library +Edition; Demy Octavo, 10<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Easy Lessons on Reasoning. Fifth Edition. 1<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<span class="tei tei-pb" id="page504">[pg 504]</span><a name="Pg504" id="Pg504" class="tei tei-anchor"></a> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's Elements of Morality, including Polity. +Second Edition, reduced in size and price. Two Vols. 15<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell's Lectures on Systematic Morality. +7<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Butler's Six Sermons on Moral Subjects. Edited by Dr. +<span class="tei tei-hi"><span style="font-variant: small-caps">Whewell</span></span>. With a Preface and Syllabus. +3<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Butler's Three Sermons on Human Nature. Edited by Dr. +<span class="tei tei-hi"><span style="font-variant: small-caps">Whewell</span></span>. With Preface and Syllabus. +Second Edition. 3<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Professor Brande's Manual of Chemistry. Sixth Edition, +almost wholly re-written, considerably enlarged, and embodying all the recent discoveries +in the science up to the present time. 2 vols. Octavo. +2<span class="tei tei-hi"><span style="font-style: italic">l.</span></span> 5<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. T. Griffiths's Recreations in Chemistry. Second Edition, +much enlarged. 5<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. Trimmer's Practical Chemistry for Farmers and Land-owners. +5<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Todd's and Mr. Bowman's Physiological Anatomy and +Physiology of Man. Vol. I. 15<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> Part III. +7<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. Tomes's Lectures on Dental Physiology and Surgery. +Octavo. With upwards of 100 Illustrations. 12<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Lord's Popular Physiology. Second Edition. 7<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +House I Live In; or Popular Illustrations of the Structure +and Functions of the Human Body. Fifth Edition. +2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. Trimmer's Practical Geology and Mineralogy. With +Two Hundred Illustrations. Octavo, 12<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Miss Zornlin's Recreations in Geology. Second Edition. +4<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Colonel Jackson's Minerals and their Uses. With Coloured +Frontispiece. 7<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Miss Zornlin's Recreations in Physical Geography; or the +Earth as It Is. Third Edition, 6<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Captain Smyth's Cycle of Celestial Objects. Two Vols. +Octavo. With numerous Illustrations. 2<span class="tei tei-hi"><span style="font-style: italic">l.</span></span> +2<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Rev. H. Moseley's Lectures on Astronomy. Third Edition. +5<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> + +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Rev. L. Tomlinson's Recreations in Astronomy. With Illustrations. +Third Edition. 4<span class="tei tei-hi"><span style="font-style: italic">s.</span></span> 6<span class="tei tei-hi"><span style="font-style: italic">d.</span></span> +</p> +</div> +</div> +<hr class="doublepage" /><div class="tei tei-back" style="margin-bottom: 2.00em; margin-top: 6.00em"> + <div id="footnotes" class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> + <a name="toc81" id="toc81"></a> + <a name="pdf82" id="pdf82"></a> + <h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">Footnotes</span></h1> + <dl class="tei tei-list-footnotes"><dt class="tei tei-notelabel"><a id="note_1" name="note_1" href="#noteref_1">1.</a></dt><dd class="tei tei-notetext">In the later editions of Archbishop Whately's +<span class="tei tei-hi"><span style="font-style: italic">Logic</span></span> and <span class="tei tei-hi"><span style="font-style: italic">Rhetoric</span></span> there are +some expressions, which, though indefinite, resemble +a disclaimer of the opinion here ascribed to him. If I have +imputed that opinion to him erroneously, I am glad to find myself +mistaken; but he has not altered the passages in which the opinion +appeared to me to be conveyed, and which I still think inconsistent +with the belief that Induction can be reduced to strict rules.</dd><dt class="tei tei-notelabel"><a id="note_2" name="note_2" href="#noteref_2">2.</a></dt><dd class="tei tei-notetext">Archbishop Whately.</dd><dt class="tei tei-notelabel"><a id="note_3" name="note_3" href="#noteref_3">3.</a></dt><dd class="tei tei-notetext">This important theory has recently been +called in question by a writer of deserved reputation, Mr. Samuel Bailey; +but I do not conceive that the grounds on which it has been admitted as an established +doctrine for a century past, have been at all shaken by that gentleman's objections. +I have elsewhere said what appeared to me necessary in reply to his arguments +(<span class="tei tei-hi"><span style="font-style: italic">Westminster Review, for October 1842</span></span>.) It may be necessary +to add, that some other processes of comparison than those described in the text +(but equally the result of experience), appear occasionally to enter into our +judgment of distances by the eye.</dd><dt class="tei tei-notelabel"><a id="note_4" name="note_4" href="#noteref_4">4.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Computation or +Logic</span></span>, chap. ii.</dd><dt class="tei tei-notelabel"><a id="note_5" name="note_5" href="#noteref_5">5.</a></dt><dd class="tei tei-notetext">In the original, <span class="tei tei-q">“had, <span class="tei tei-hi"><span style="font-style: italic">or had +not</span></span>.”</span> These last words, as involving a +subtlety foreign to our present purpose, I have forborne to quote.</dd><dt class="tei tei-notelabel"><a id="note_6" name="note_6" href="#noteref_6">6.</a></dt><dd class="tei tei-notetext">It would, perhaps, be more correct to +say that inflected cases are names and something more; and that this addition prevents +them from being used as the subjects of propositions. But the purposes of our inquiry +do not demand that we should enter with scrupulous accuracy into similar minutiæ.</dd><dt class="tei tei-notelabel"><a id="note_7" name="note_7" href="#noteref_7">7.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Notare</span></span> +to mark; <span class="tei tei-hi"><span style="font-style: italic">con</span></span>notare, to mark <em class="tei tei-emph"><span style="font-style: italic">along with</span></em>; +to mark one thing <em class="tei tei-emph"><span style="font-style: italic">with</span></em> or <em class="tei tei-emph"><span style="font-style: italic">in addition to</span></em> another.</dd><dt class="tei tei-notelabel"><a id="note_8" name="note_8" href="#noteref_8">8.</a></dt><dd class="tei tei-notetext">Archbishop Whately, who in the more recent editions of his +<span class="tei tei-hi"><span style="font-style: italic">Elements of Logic</span></span> has aided in reviving the important +distinction treated of in the text, proposes the term <span class="tei tei-q">“Attributive”</span> as a +substitute for <span class="tei tei-q">“Connotative,”</span> (p. 122, 9th ed.) The expression is, in itself, +appropriate; but, as it has not the advantage of being connected with any verb, of so +markedly distinctive a character as <span class="tei tei-q">“to connote,”</span> it is not, I think, fitted to +supply the place of the word Connotative in scientific use.</dd><dt class="tei tei-notelabel"><a id="note_9" name="note_9" href="#noteref_9">9.</a></dt><dd class="tei tei-notetext">It +would be well if this degeneracy of language took place only in the +hands of the untaught vulgar; but some of the most remarkable instances +are to be found in terms of art, and among technically educated persons, such +as English lawyers. <span class="tei tei-hi"><span style="font-style: italic">Felony</span></span>, for example, is a law term, +with the sound of which all are familiar; but there is no lawyer who would undertake +to tell what a felony is, otherwise than by enumerating the various offences which are so +called. Originally the word felony had a meaning; it denoted all offences, the +penalty of which included forfeiture of lands or goods; but subsequent acts of +parliament have declared various offences to be felonies without enjoining that +penalty, and have taken away the penalty from others which continue nevertheless +to be called felonies, insomuch that the acts so called have now no property +whatever in common, save that of being unlawful and punishable.</dd><dt class="tei tei-notelabel"><a id="note_10" name="note_10" href="#noteref_10">10.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Before +quitting the subject of connotative names, it is proper to observe, +that the first writer who, in our own times, has adopted from the schoolmen the +word <span class="tei tei-hi"><span style="font-style: italic">to connote</span></span>, Mr. Mill, in his <span class="tei tei-hi"><span style="font-style: italic">Analysis of +the Phenomena of the Human Mind</span></span>, employs it in a signification different from that +in which it is here used. He uses the word in a sense coextensive with its etymology, +applying it to every case in which a name, while pointing directly to one thing, (which +is consequently termed its signification,) includes also a tacit reference to some other +thing. In the case considered in the text, that of concrete general names, his +language and mine are the converse of one another. Considering (very justly) +the signification of the name to lie in the attribute, he speaks of the word as +<em class="tei tei-emph"><span style="font-style: italic">noting</span></em> the attribute, and <em class="tei tei-emph"><span style="font-style: italic">connoting</span></em> the things possessing the +attribute. And he describes abstract names as being properly concrete names with their +connotation dropped: whereas, in my view, it is the <em class="tei tei-emph"><span style="font-style: italic">de</span></em>notation which would +be said to be dropped, what was previously connoted becoming the whole signification. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +In adopting a phraseology at variance with that which so high an authority, +and one which I am less likely than any other person to undervalue, has deliberately +sanctioned, I have been influenced by the urgent necessity for a term +exclusively appropriated to express the manner in which a concrete general +name serves to mark the attributes which are involved in its signification. This +necessity can scarcely be felt in its full force by any one who has not found by +experience, how vain is the attempt to communicate clear ideas on the philosophy +of language without such a word. It is hardly an exaggeration to say, +that some of the most prevalent of the errors with which logic has been infected, +and a large part of the cloudiness and confusion of ideas which have enveloped +it, would, in all probability, have been avoided, if a term had been in common use +to express exactly what I have signified by the term <span class="tei tei-hi"><span style="font-style: italic">to connote</span></span>. +And the schoolmen, to whom we are indebted for the greater part of our logical language, +gave us this also, and in this very sense. For although some of their general +expressions countenance the use of the word in the more extensive and vague +acceptation in which it is taken by Mr. Mill, yet when they had to define it +specifically as a technical term, and to fix its meaning as such, with that admirable +precision which always characterizes their definitions, they clearly explained +that nothing was said to be connoted except <em class="tei tei-emph"><span style="font-style: italic">forms</span></em>, which word may +generally, in their writings, be understood as synonymous with <em class="tei tei-emph"><span style="font-style: italic">attributes</span></em>. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Now, if the word <span class="tei tei-hi"><span style="font-style: italic">to connote</span></span>, so well suited to the purpose to +which they applied it, be diverted from that purpose by being taken to fulfil another, +for which it does not seem to me to be at all required; I am unable to find any +expression to replace it, but such as are commonly employed in a sense so much +more general, that it would be useless attempting to associate them peculiarly +with this precise idea. Such are the words, to involve, to imply, &c. By employing +these, I should fail of attaining the object for which alone the name is +needed, namely, to distinguish this particular kind of involving and implying +from all other kinds, and to assure to it the degree of habitual attention which +its importance demands. +</p></dd><dt class="tei tei-notelabel"><a id="note_11" name="note_11" href="#noteref_11">11.</a></dt><dd class="tei tei-notetext">Or +rather, all objects except itself and the percipient mind; for, as we +shall see hereafter, to ascribe any attribute to an object necessarily implies a +mind to perceive it.</dd><dt class="tei tei-notelabel"><a id="note_12" name="note_12" href="#noteref_12">12.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Philosophy of the Inductive Sciences</span></span>, vol. +i. p. 40.</dd><dt class="tei tei-notelabel"><a id="note_13" name="note_13" href="#noteref_13">13.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">This doctrine is laid down in the clearest and +strongest terms by M. Cousin, whose observations on the subject are the more worthy of +attention, as, in consequence of the ultra-German and ontological character of his +philosophy considered generally, they may be regarded as the admissions of an +opponent. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Nous savons qu'il existe quelque chose hors de nous, parceque nous ne +pouvons expliquer nos perceptions sans les rattacher à des causes distinctes de +nous-mêmes; nous savons de plus que ces causes, dont nous ne connaissons pas +d'ailleurs l'essence, produisent les effets les plus variables, les plus divers, et +même les plus contraires, selon qu'elles rencontrent telle nature ou telle disposition +du sujet. Mais savons-nous quelque chose de plus? et même, vu le +caractère indéterminé des causes que nous concevons dans les corps, y a-t-il +quelque chose de plus à savoir? Y a-t-il lieu de nous enquérir si nous percevons +les choses telles qu'elles sont? Non évidemment.... Je ne dis +pas que le problème est insoluble, <em class="tei tei-emph"><span style="font-style: italic">je dis qu'il est absurde et enferme une +contradiction</span></em>. Nous <em class="tei tei-emph"><span style="font-style: italic">ne savons pas ce que ces causes sont en +elles-mêmes</span></em>, et la raison nous défend de chercher à le connaître: mais il est +bien évident <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, +qu'<em class="tei tei-emph"><span style="font-style: italic">elles ne sont pas en +elles-mêmes ce quelles sont par rapport à nous</span></em>, puisque la présence du sujet +modifie nécessairement leur action. Supprimez tout sujet sentant, il est certain que +ces causes agiraient encore puisqu'elles continueraient d'exister; mais elles agiraient +autrement; elles seraient encore des qualités et des propriétés, mais qui ne +resembleraient à rien de ce que nous connaissons. +Le feu ne manifesterait plus aucune des propriétés que nous lui connaissons: que +serait-il? C'est ce que nous ne saurons jamais. <em class="tei tei-emph"><span style="font-style: italic">C'est d'ailleurs peut-être un +problème qui ne répugne pas seulement à la nature de notre esprit, mais à l'essence +même des choses.</span></em> Quand même en effet on supprimerait par la pensée tous les +sujets sentants, il faudrait encore admettre que nul corps ne manifesterait ses +propriétés autrement qu'en relation avec un sujet quelconque, et dans ce cas +<em class="tei tei-emph"><span style="font-style: italic">ses propriétés ne seraient encore que relatives</span></em>: en sorte qu'il me paraît +fort raisonnable d'admettre que les propriétés déterminées des corps n'existent pas +independamment d'un sujet quelconque, et que quand on demande si les propriétés +de la matière sont telles que nous les percevons, il faudrait voir auparavant +si elles sont en tant que déterminées, et dans quel sens il est vrai de dire +qu'elles sont.”</span>—<span class="tei tei-hi"><span style="font-style: italic">Cours d'Histoire de la Philosophie Morale au +18me siècle</span></span>, 8me leçon. +</p></dd><dt class="tei tei-notelabel"><a id="note_14" name="note_14" href="#noteref_14">14.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">An attempt, indeed, has been made by +Reid and others, to establish that although some of the properties we ascribe to objects +exist only in our sensations, others exist in the things themselves, being such as +cannot possibly be copies of any impression upon the senses; and they ask, from what +sensations our notions of extension and figure have been derived? The gauntlet thrown +down by Reid was taken up by Brown, who, applying greater powers of analysis +than had previously been applied to the notions of extension and figure, +showed clearly what are the sensations from which those notions are derived, +viz. sensations of touch, combined with sensations of a class previously too +little adverted to by metaphysicians, those which have their seat in our muscular +frame. Whoever wishes to be more particularly acquainted with this +excellent specimen of metaphysical analysis, may consult the first volume of +Brown's <span class="tei tei-hi"><span style="font-style: italic">Lectures</span></span>, or Mill's <span class="tei tei-hi"><span style="font-style: italic">Analysis of the +Mind</span></span>. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +On this subject also, M. Cousin may be quoted in favour of conclusions +rejected by some of the most eminent thinkers of the school to which he belongs. +M. Cousin recognises, in opposition to Reid, the essential <em class="tei tei-emph"><span style="font-style: italic">subjectivity</span></em> +of our conceptions of the primary qualities of matter, as extension, solidity, &c., +equally with those of colour, heat, and the remainder of what are called +secondary qualities.—<span class="tei tei-hi"><span style="font-style: italic">Cours</span></span>, ut supra, 9me leçon. +</p></dd><dt class="tei tei-notelabel"><a id="note_15" name="note_15" href="#noteref_15">15.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Analysis of the Human Mind</span></span>, i. +126 et seqq.</dd><dt class="tei tei-notelabel"><a id="note_16" name="note_16" href="#noteref_16">16.</a></dt><dd class="tei tei-notetext">Dr. +Whewell (<span class="tei tei-hi"><span style="font-style: italic">Of Induction</span></span>, p. 10) questions this statement, and asks, +<span class="tei tei-q">“Are we to say that a mole cannot dig the ground, except he has an idea of +the ground, and of the snout and paws with which he digs it?”</span> I thought it +had been evident that I was here speaking of rational digging, and not of +digging by instinct.</dd><dt class="tei tei-notelabel"><a id="note_17" name="note_17" href="#noteref_17">17.</a></dt><dd class="tei tei-notetext"><span class="tei tei-q">“From hence also this may be deduced, that +the first truths were arbitrarily made by those that first of all imposed names upon +things, or received them from the imposition of others. For it is true (for example) +that <em class="tei tei-emph"><span style="font-style: italic">man is a living creature</span></em>, but it is for this reason, that it pleased +men to impose both these names on the same +thing.”</span>—<span class="tei tei-hi"><span style="font-style: italic">Computation or Logic</span></span>, ch. iii. sect. 8.</dd><dt class="tei tei-notelabel"><a id="note_18" name="note_18" href="#noteref_18">18.</a></dt><dd class="tei tei-notetext"><span class="tei tei-q">“Men are subject to err not only in affirming and denying, +but also in perception, and in silent cogitation.... Tacit errors, or the errors of +sense and cogitation, are made by passing from one imagination to the imagination of +another different thing; or by feigning that to be past, or future, which never +was, nor ever shall be; as when, by seeing the image of the sun in water, we +imagine the sun itself to be there; or by seeing swords, that there has been +or shall be, fighting, because it uses to be so for the most part; or when from +promises we feign the mind of the promiser to be such and such; or, lastly, +when from any sign we vainly imagine something to be signified which is not. +And errors of this sort are common to all things that have +sense.”</span>—<span class="tei tei-hi"><span style="font-style: italic">Computation or Logic</span></span>, ch. v., sect. 1.</dd><dt class="tei tei-notelabel"><a id="note_19" name="note_19" href="#noteref_19">19.</a></dt><dd class="tei tei-notetext">Ch. iii. sect. 3.</dd><dt class="tei tei-notelabel"><a id="note_20" name="note_20" href="#noteref_20">20.</a></dt><dd class="tei tei-notetext">Book iv. ch. vii.</dd><dt class="tei tei-notelabel"><a id="note_21" name="note_21" href="#noteref_21">21.</a></dt><dd class="tei tei-notetext">Καθόλου μὲν οὖν πᾱσα διαφορὰ προγινομένη τινὶ ἑτεροῖον ποιεῖ; +ἀλλ᾽ αἱ μὲν κοινῶς τε καὶ ἰδίως (differences in the accidental properties) ἀλλοῖον +ποιοῦσιν; αἱ δὲ ἰδιαίτατα (differences in the essential properties) +ἄλλο—<span class="tei tei-hi"><span style="font-style: italic">Isag.</span></span> cap. iii.</dd><dt class="tei tei-notelabel"><a id="note_22" name="note_22" href="#noteref_22">22.</a></dt><dd class="tei tei-notetext">Few among the great names in mental +science have met with a harder measure of justice from the present generation than +Locke; the unquestioned founder of the analytic philosophy of mind, but whose doctrines +were first caricatured, then, when the reaction arrived, cast off by the prevailing +school even with contumely, and who is now regarded by one of the conflicting parties +in philosophy as an apostle of heresy and sophistry, while among those who +still adhere to the standard which he raised, there has been a disposition in +later times to sacrifice his reputation in favour of Hobbes; a great writer, and +a great thinker for his time, but inferior to Locke not only in sober judgment +but even in profundity and original genius. Locke, the most candid of philosophers, +and one whose speculations bear on every subject the strongest marks +of having been wrought out from the materials of his own mind, has been mistaken +for an unworthy plagiarist, while Hobbes has been extolled as having +anticipated many of his leading doctrines. He did anticipate many of them, +and the present is an instance in what manner it was generally done. They +both rejected the scholastic doctrine of essences; but Locke understood and +explained what these supposed essences really were; Hobbes, instead of explaining +the distinction between essential and accidental properties, and between +essential and accidental propositions, jumped over it, and gave a definition +which suits at most only essential propositions, and scarcely those, as the definition +of Proposition in general.</dd><dt class="tei tei-notelabel"><a id="note_23" name="note_23" href="#noteref_23">23.</a></dt><dd class="tei tei-notetext">The always acute and often profound author of +<span class="tei tei-hi"><span style="font-style: italic">An Outline of Sematology</span></span> +(Mr. B. H. Smart) justly says, <span class="tei tei-q">“Locke will be much more intelligible if, in +the majority of places, we substitute <span class="tei tei-q">‘the knowledge of’</span> for what he calls <span class="tei tei-q">‘the +idea of’</span> ”</span> (p. 10). Among the many criticisms on Locke's use of the word +Idea, this is the only one which, as it appears to me, precisely hits the mark; +and I quote it for the additional reason that it precisely expresses the point of +difference respecting the import of Propositions, between my view and what I +have spoken of as the Conceptualist view of them. Where a Conceptualist +says that a name or a proposition expresses our Idea of a thing, I should +generally say (instead of our Idea) our Knowledge, or Belief, concerning the +thing itself.</dd><dt class="tei tei-notelabel"><a id="note_24" name="note_24" href="#noteref_24">24.</a></dt><dd class="tei tei-notetext">If we allow a differentia +to what is not really a species. For the distinction +of Kinds, in the sense explained by us, not being in any way applicable +to attributes, it of course follows that although attributes may be put into +classes, those classes can be admitted to be genera or species only by courtesy.</dd><dt class="tei tei-notelabel"><a id="note_25" name="note_25" href="#noteref_25">25.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">In the fuller discussion which +Archbishop Whately has given to this subject in his later editions, he almost ceases to +regard the definitions of names and those of things as, in any important sense, distinct. +He seems (9th ed. p. 145) to limit the notion of a Real Definition to one which +<span class="tei tei-q">“explains anything <em class="tei tei-emph"><span style="font-style: italic">more</span></em> of the nature of the thing than is implied in the +name;”</span> (including under the word <span class="tei tei-q">“implied,”</span> not only what the name connotes, but +everything which can be deduced by reasoning from the attributes connoted). Even this, +as he adds, is usually called, not a Definition, but a Description; and (as it seems +to me) rightly so called. A Description, I conceive, can only be ranked among +Definitions, when taken (as in the case of the zoological definition of man) to +fulfil the true office of a Definition, by declaring the connotation given to a +word in some special use, as a term of science or art; which special connotation +of course would <em class="tei tei-emph"><span style="font-style: italic">not</span></em> be expressed by the proper definition of the word in +its ordinary employment. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately, understands +by a Real Definition one which contains <em class="tei tei-emph"><span style="font-style: italic">less</span></em> than the Nominal Definition, +provided only that what it contains is sufficient for distinction. <span class="tei tei-q">“By +<em class="tei tei-emph"><span style="font-style: italic">real</span></em> definition I mean such an explanation of the word, be it the whole of +the meaning or only part, as will be sufficient to separate the things contained +under that word from all others. Thus the following, I believe, is a complete +definition of an elephant: An animal which naturally drinks by drawing the water +into its nose, and then spirting it into its mouth.”</span>—<span class="tei tei-hi"><span style="font-style: italic">Formal +Logic</span></span>, p. 36. Mr. De Morgan's general proposition and his example are at variance; +for the peculiar mode of drinking of the elephant certainly forms no part of the meaning +of the word elephant. It could not be said, because a person happened to +be ignorant of this property, that he did not know what an elephant means.</p></dd><dt class="tei tei-notelabel"><a id="note_26" name="note_26" href="#noteref_26">26.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">In the only attempt which, so far as I know, +has been made to refute the preceding argumentation, it is maintained that in the +first form of the syllogism, +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +A dragon is a thing which breathes flame,<br /> +A dragon is a serpent,<br /> +Therefore some serpent or serpents breathe flame, +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“there is just as much truth in the conclusion as there is in the premisses, or +rather, no more in the latter than in the former. If the general name serpent +includes both real and imaginary serpents, there is no falsity in the conclusion; +if not, there is falsity in the minor premiss.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us, then, try to set out the syllogism on the hypothesis that the name +serpent includes imaginary serpents. We shall find that it is now necessary +to alter the predicates; for it cannot be asserted that an imaginary creature +breathes flame: in predicating of it such a fact, we assert by the most positive +implication that it is real and not imaginary. The conclusion must run thus, +<span class="tei tei-q">“Some serpent or serpents either do or are <em class="tei tei-emph"><span style="font-style: italic">imagined</span></em> to breathe flame.”</span> +And to prove this conclusion by the instance of dragons, the premisses must be, +A dragon is <em class="tei tei-emph"><span style="font-style: italic">imagined</span></em> as breathing flame, A dragon is a (real or imaginary) +serpent: from which it undoubtedly follows, that there are serpents which are +imagined to breathe flame; but the major premiss is not a definition, nor part +of a definition; which is all that I am concerned to prove. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Let us now examine the other assertion—that if the word serpent stands for +none but real serpents, the minor premiss (A dragon is a serpent) is false. This +is exactly what I have myself said of the premiss, considered as a statement of +fact: but it is not false as part of the definition of a dragon; and since the +premisses, or one of them, <em class="tei tei-emph"><span style="font-style: italic">must</span></em> be false, (the conclusion being so,) the +real premiss cannot be the definition, which is true, but the statement of fact, which +is false. +</p></dd><dt class="tei tei-notelabel"><a id="note_27" name="note_27" href="#noteref_27">27.</a></dt><dd class="tei tei-notetext"><span class="tei tei-q">“Few +people”</span> (I have said in another place) <span class="tei tei-q">“have reflected how great +a knowledge of Things is required to enable a man to affirm that any given +argument turns wholly upon words. There is, perhaps, not one of the leading +terms of philosophy which is not used in almost innumerable shades of meaning, +to express ideas more or less widely different from one another. Between +two of these ideas a sagacious and penetrating mind will discern, as it were +intuitively, an unobvious link of connexion, upon which, though perhaps +unable to give a logical account of it, he will found a perfectly valid argument, +which his critic, not having so keen an insight into the Things, will +mistake for a fallacy turning on the double meaning of a term. And the +greater the genius of him who thus safely leaps over the chasm, the greater +will probably be the crowing and vain-glory of the mere logician, who, +hobbling after him, evinces his own superior wisdom by pausing on its brink, +and giving up as desperate his proper business of bridging it over.”</span></dd><dt class="tei tei-notelabel"><a id="note_28" name="note_28" href="#noteref_28">28.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Contraries:<br /> +All A is B<br /> +No A is B +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Subtraries:<br /> +Some A is B<br /> +Some A is not B +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Contradictories:<br /> +All A is B<br /> +Some A is not B +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Also contradictories:<br /> +No A is B<br /> +Some A is B +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Respectively subalternate:<br /> +All A is B; No A is B<br /> +Some A is B; and Some A is not B +</p></dd><dt class="tei tei-notelabel"><a id="note_29" name="note_29" href="#noteref_29">29.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">His conclusions are, +<span class="tei tei-q">“The first figure is suited to the discovery or proof +of the properties of a thing; the second to the discovery or proof of the distinctions +between things; the third to the discovery or proof of instances and +exceptions; the fourth to the discovery, or exclusion, of the different species +of a genus.”</span> The reference of syllogisms in the last three figures to the +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de omni et nullo</span></span> is, +in Lambert's opinion, strained and unnatural: to each of the three belongs, according +to him, a separate axiom, co-ordinate and of equal authority with that +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum</span></span>, and to which he gives +the names of <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de diverso</span></span> +for the second figure, <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum de +exemplo</span></span> for the third, and <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">dictum +de reciproco</span></span> for the fourth. See part i. or +<span class="tei tei-hi"><span style="font-style: italic">Dianoiologie</span></span>, chap. iv. § 229 <span class="tei tei-hi"><span style="font-style: italic">et seqq.</span></span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Mr. De Morgan's <span class="tei tei-q">“Formal Logic, or the Calculus of Inference, Necessary +and Probable,”</span> (a work published since the statement in the text was made,) +far exceeds in elaborate minuteness Lambert's treatise on the syllogism. Mr. De +Morgan's principal object is to bring within strict technical rules the cases in +which a conclusion can be drawn from premisses of a form usually classed as +particular. He observes, very justly, that from the premisses Most Bs are Cs, +most Bs are As, it may be concluded with certainty that some As are Cs, +since two portions of the class B, each of them comprising more than half, +must necessarily in part consist of the same individuals. Following out this +line of thought, it is equally evident that if we knew exactly what proportion +the <span class="tei tei-q">“most”</span> in each of the premisses bear to the entire class B, we could increase +in a corresponding degree the definiteness of the conclusion. Thus if 60 +per cent of B are included in C, and 70 per cent in A, 30 per cent at least +must be common to both; in other words, the number of As which are Cs, +and of Cs which are As, must be at least equal to 30 per cent of the class B. +Proceeding on this conception of <span class="tei tei-q">“numerically definite propositions,”</span> and extending +it to such forms as these:—<span class="tei tei-q">“45 Xs (or more) are each of them one of +70 Ys,”</span> or <span class="tei tei-q">“45 Xs (or more), are no one of them to be found among 70 Ys,”</span> +and examining what inferences admit of being drawn from the various combinations +which may be made of premisses of this description, Mr. De Morgan +establishes universal formulæ for such inferences; creating for that purpose +not only a new technical language, but a formidable array of symbols analogous +to those of algebra. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Since it is undeniable that inferences, in the cases examined by Mr. De +Morgan, can legitimately be drawn, and that the ordinary theory takes no +account of them, I will not say that it was not worth while to show in detail +how these also could be reduced to formulae as rigorous as those of Aristotle. +What Mr. De Morgan has done was worth doing once (perhaps more than +once, as a school exercise); but I question if its results are worth studying +and mastering for any practical purpose. The practical use of technical forms +of reasoning is to bar out fallacies: but the fallacies which require to be +guarded against in ratiocination properly so called, arise from the incautious +use of the common forms of language; and the logician must track the fallacy +into that territory, instead of waiting for it on a territory of his own. While +he remains among propositions which have acquired the numerical precision +of the Calculus of Probabilities, the enemy is left in possession of the only +ground on which he can be formidable. The <span class="tei tei-q">“quantification of the predicate,”</span> +an invention to which Sir William Hamilton attaches so much importance as +to have raised an angry dispute with Mr. De Morgan respecting its authorship, +appears to me, I confess, as an accession to the art of Logic, of singularly small +value. It is of course true, that <span class="tei tei-q">“All men are mortal”</span> is equivalent to <span class="tei tei-q">“Every +man is <em class="tei tei-emph"><span style="font-style: italic">some</span></em> mortal.”</span> But as mankind certainly will not be persuaded to +<span class="tei tei-q">“quantify”</span> their predicates in common discourse, they want a logic which will +teach them to reason correctly with propositions in the usual form, by furnishing +them with a type of ratiocination to which propositions can be referred, retaining +that form. Not to mention that the quantification of the predicate, instead of being +a means of bringing out more clearly the meaning of the proposition, actually +leads the mind out of the proposition, into another order of ideas. For when we +say, All men are mortal, we simply mean to affirm the attribute mortality of all +men; without thinking at all of the <em class="tei tei-emph"><span style="font-style: italic">class</span></em> mortal in the concrete, or +troubling ourselves about whether it contains any other beings or not. It is only for +some artificial purpose that we ever look at the proposition in the aspect in +which the predicate also is thought of as a class-name, either including the +subject only, or the subject and something more. +</p></dd><dt class="tei tei-notelabel"><a id="note_30" name="note_30" href="#noteref_30">30.</a></dt><dd class="tei tei-notetext">Suprà, p. +<a href="#Pg129" class="tei tei-ref">129</a>.</dd><dt class="tei tei-notelabel"><a id="note_31" name="note_31" href="#noteref_31">31.</a></dt><dd class="tei tei-notetext">Logic, p. 239 +(9th ed.)</dd><dt class="tei tei-notelabel"><a id="note_32" name="note_32" href="#noteref_32">32.</a></dt><dd class="tei tei-notetext">It is hardly necessary to say, that +I am not contending for any such absurdity as that we <em class="tei tei-emph"><span style="font-style: italic">actually</span></em> <span class="tei tei-q">“ought to +have known”</span> and considered the case of every individual man, past, present, and +future, before affirming that all men are mortal: although this interpretation has been, +strangely enough, put upon the preceding observations. There is no difference between me +and Archbishop Whately, or any other defender of the syllogism, on the practical part of +the matter; I am only pointing out an inconsistency in the logical theory of it, as +conceived by almost all writers. I do not say that a person who affirmed, before +the Duke of Wellington was born, that all men are mortal, <em class="tei tei-emph"><span style="font-style: italic">knew</span></em> that the +Duke of Wellington was mortal; but I do say, that he <em class="tei tei-emph"><span style="font-style: italic">asserted</span></em> it; and I ask +for an explanation of the apparent logical fallacy, of adducing in proof of the +Duke of Wellington's mortality, a general statement which presupposes it. +Finding no sufficient resolution of this difficulty in any of the writers on +Logic, I have attempted to supply one.</dd><dt class="tei tei-notelabel"><a id="note_33" name="note_33" href="#noteref_33">33.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Of Induction</span></span>, p. 85.</dd><dt class="tei tei-notelabel"><a id="note_34" name="note_34" href="#noteref_34">34.</a></dt><dd class="tei tei-notetext">For August 1846.</dd><dt class="tei tei-notelabel"><a id="note_35" name="note_35" href="#noteref_35">35.</a></dt><dd class="tei tei-notetext">There is a +striking passage in the Metaphysics of Aristotle (commencement +of chap. iii.) on the necessity of beginning the study of a subject by a +clear perception of its difficulties. Εστί τοῖς εὐπορῆσαι βουλομένοις προῦργου +τὸ διαπορῆσαι καλῶς. ἡ γὰρ ὕστερον εὐπορία λύσις των πρότερον ἀπορουμένων +ἐστί. λύειν δ᾽ οὐκ ἔστιν ἀγνοοῦντα τὸν δεσμόν: ἀλλ᾽ ἡ της διανοίας ἀπορία +δηλοῖ τοῦτο περὶ τοῦ πράγματος ... διὸ δεῖ τὰς δυσχερείας τελεωρηκέναι πάσας +πρότερον, τούτων τε χάριν καὶ διὰ τὸ τοὺς ζητοῦντας ἄνευ τοῦ διαπορῆσαι +πρῶτον, ὁμοίους εἰναὶ τοῖς ποῖ δει βαδίζειν ἀγνοοῦσι: καὶ πρὸς τούτοις, οὐδ᾽ ἐί +ποτε τὸ ζητούμενον εὕρηκεν ἣ μὴ, γενώσκειν. τὸ γὰρ τέλος τούτῳ μὲν οὐ δῆλον, +τῳ δὲ καλῶς προηπορκότι δῆλον.</dd><dt class="tei tei-notelabel"><a id="note_36" name="note_36" href="#noteref_36">36.</a></dt><dd class="tei tei-notetext">The reviewer misunderstands +me when he supposes me to say that <span class="tei tei-q">“the conclusion must be admitted <em class="tei tei-emph"><span style="font-style: italic">before</span></em> +we can admit the major premiss.”</span> What I say is, that there must be ground for +admitting it <em class="tei tei-emph"><span style="font-style: italic">simultaneously</span></em>, or else the major premise is +not proved.</dd><dt class="tei tei-notelabel"><a id="note_37" name="note_37" href="#noteref_37">37.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Mechanical Euclid</span></span>, pp. 149 +<span class="tei tei-hi"><span style="font-style: italic">et seqq.</span></span></dd><dt class="tei tei-notelabel"><a id="note_38" name="note_38" href="#noteref_38">38.</a></dt><dd class="tei tei-notetext">We might, it is true, insert this property +into the definition of parallel lines, framing the definition so as to require, +<em class="tei tei-emph"><span style="font-style: italic">both</span></em> that when produced indefinitely they shall never meet, and +<em class="tei tei-emph"><span style="font-style: italic">also</span></em> that any straight line which intersects one of them shall, if +prolonged, meet the other. But by doing this we by no means get rid of the +assumption; we are still obliged to take for granted the +geometrical truth, that all straight lines in the same plane, which have the +former of these properties, have also the latter. For if it were possible that +they should not, that is, if any straight lines other than those which are parallel +according to the definition, had the property of never meeting although indefinitely +produced, the demonstrations of the subsequent portions of the theory of +parallels could not be maintained.</dd><dt class="tei tei-notelabel"><a id="note_39" name="note_39" href="#noteref_39">39.</a></dt><dd class="tei tei-notetext">Whewell's +<span class="tei tei-hi"><span style="font-style: italic">Philosophy of the Inductive Sciences</span></span>, i. 130.</dd><dt class="tei tei-notelabel"><a id="note_40" name="note_40" href="#noteref_40">40.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Dr. Whewell +(<span class="tei tei-hi"><span style="font-style: italic">Of Induction</span></span> p. 84) thinks it unreasonable to contend that +we know by experience, that our idea of a line exactly resembles a real line. +<span class="tei tei-q">“It does not appear,”</span> he says, <span class="tei tei-q">“how we can compare our ideas with the realities, +since we know the realities only by our ideas.”</span> We know the realities (I +conceive) by our eyes. Dr. Whewell surely does not hold the <span class="tei tei-q">“doctrine of perception +by means of ideas,”</span> which Reid gave himself so much trouble to refute. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell also says, that it does not appear why this resemblance of ideas +to the sensations of which they are copies, should be spoken of as if it were a +peculiarity of one class of ideas, those of space. My reply is, that I do not so +speak of it. The peculiarity I contend for is only one of degree. All our ideas +of sensation of course resemble the corresponding sensations, but they do so +with very different degrees of exactness and of reliability. No one, I presume, +can recall in imagination a colour or an odour with the same distinctness and +accuracy with which almost every one can mentally reproduce an image of a +straight line or a triangle. To the extent, however, of their capabilities of +accuracy, our recollections of colours or of odours may serve as subjects of +experimentation, as well as those of lines and spaces, and may yield conclusions +which will be true of their external prototypes. A person in whom, +either from natural gift or from cultivation, the impressions of colour were +peculiarly vivid and distinct, if asked which of two blue flowers was of the +darkest tinge, though he might never have compared the two, or even looked +at them together, might be able to give a confident answer on the faith of his +distinct recollection of the colours; that is, he might examine his mental pictures, +and find there a property of the outward objects. But in hardly any +case except that of simple geometrical forms, could this be done by mankind +generally, with a degree of assurance equal to that which is given by a contemplation +of the objects themselves. Persons differ most widely in the precision +of their recollection, even of forms: one person, when he has looked any one +in the face for half a minute, can draw an accurate likeness of him from memory; +another may have seen him every day for six months, and hardly know whether +his nose is long or short. But everybody has a perfectly distinct mental image +of a straight line, a circle, or a rectangle. And every one concludes confidently +from these mental images to the corresponding outward things. +</p></dd><dt class="tei tei-notelabel"><a id="note_41" name="note_41" href="#noteref_41">41.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. Ind. Sc.</span></span> i. 59-61.</dd><dt class="tei tei-notelabel"><a id="note_42" name="note_42" href="#noteref_42">42.</a></dt><dd class="tei tei-notetext">Ibid. 57.</dd><dt class="tei tei-notelabel"><a id="note_43" name="note_43" href="#noteref_43">43.</a></dt><dd class="tei tei-notetext">Ibid. 54, 55.</dd><dt class="tei tei-notelabel"><a id="note_44" name="note_44" href="#noteref_44">44.</a></dt><dd class="tei tei-notetext"><span class="tei tei-q">“If all mankind had spoken one +language, we cannot doubt that there would have been a powerful, perhaps a universal, +school of philosophers, who would have believed in the inherent connexion between names +and things, who would have taken the sound <em class="tei tei-emph"><span style="font-style: italic">man</span></em> to be the mode of agitating +the air which is essentially communicative of the ideas of reason, cookery, +bipedality, &c.”</span> De Morgan, <span class="tei tei-hi"><span style="font-style: italic">Formal Logic</span></span>, p. 246.</dd><dt class="tei tei-notelabel"><a id="note_45" name="note_45" href="#noteref_45">45.</a></dt><dd class="tei tei-notetext">It would be difficult to name a +man more remarkable at once for the greatness +and the wide range of his mental accomplishments, than Leibnitz. Yet +this eminent man gave as a reason for rejecting Newton's scheme of the solar +system, that God <em class="tei tei-emph"><span style="font-style: italic">could not</span></em> make a body revolve round a distant centre, +unless either by some impelling mechanism, or by miracle:—<span class="tei tei-q">“Tout ce qui n'est pas +explicable,”</span> says he in a letter to the Abbé Conti, <span class="tei tei-q">“par la nature des créatures, +est miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de nature; +donc la chose est naturelle. Il faut que la loi soit exécutable par les natures +des créatures. Si Dieu donnait cette loi, par exemple, à un corps libre, de +tourner à l'entour d'un certain centre, <em class="tei tei-emph"><span style="font-style: italic">il faudrait ou qu'il y joignît d'autres +corps qui par leur impulsion l'obligeassent de rester toujours dans son orbite +circulaire, ou quil mît un ange à ses trousses, ou enfin il faudrait qu'il y concourût +extraordinairement</span></em>; car naturellement il s'écartera par la +tangente.”</span>—<span class="tei tei-hi"><span style="font-style: italic">Works of Leibnitz</span></span>, +ed. Dutens, iii. 446.</dd><dt class="tei tei-notelabel"><a id="note_46" name="note_46" href="#noteref_46">46.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. Ind. Sc.</span></span> ii. +174.</dd><dt class="tei tei-notelabel"><a id="note_47" name="note_47" href="#noteref_47">47.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. Ind. Sc.</span></span> i., 238.</dd><dt class="tei tei-notelabel"><a id="note_48" name="note_48" href="#noteref_48">48.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. Ind. Sc.</span></span> i. 237.</dd><dt class="tei tei-notelabel"><a id="note_49" name="note_49" href="#noteref_49">49.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Ibid.</span></span> 213.</dd><dt class="tei tei-notelabel"><a id="note_50" name="note_50" href="#noteref_50">50.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Ibid.</span></span> +384, 385.</dd><dt class="tei tei-notelabel"><a id="note_51" name="note_51" href="#noteref_51">51.</a></dt><dd class="tei tei-notetext">In his recent pamphlet (p. 81), Dr. Whewell +greatly attenuates the opinion here quoted, reducing it to a surmise <span class="tei tei-q">“that if we could +conceive the composition of bodies distinctly, we might be able to see that it is +necessary that the modes of their composition should be definite.”</span> The passage in the +text asserts that we already see, or may and ought to see, this necessity; giving as the +reason, that no other mode of combination is conceivable. That Dr. Whewell should +ever have made this statement, is enough for the purposes of my illustration. +To what he now says I have nothing to object. Undoubtedly, if we understood +the ultimate molecular composition of bodies, we might find that their combining +with one another in definite proportions is, in the present order of nature, a +<em class="tei tei-emph"><span style="font-style: italic">necessary consequence</span></em> of that molecular composition; and has thus the only +kind of necessity of which, in my view of the subject, any law of nature is susceptible. +But in that case, the doctrine would be taken out of the class of axioms altogether. +It would be no longer an ultimate principle, but a mere derivative law; +regarded as necessary, not because self-evident, but because demonstrable.</dd><dt class="tei tei-notelabel"><a id="note_52" name="note_52" href="#noteref_52">52.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">The <span class="tei tei-hi"><span style="font-style: italic">Quarterly Review</span></span> for +June 1841, contains an article of great ability on Dr. Whewell's two great works, the +writer of which maintains, on the subject of axioms, the doctrine advanced in the text, +that they are generalizations from +experience, and supports that opinion by a line of argument strikingly coinciding +with mine. When I state that the whole of the present chapter was +written before I had seen the article, (the greater part, indeed, before it was +published,) it is not my object to occupy the reader's attention with a matter +so unimportant as the degree of originality which may or may not belong to +any portion of my own speculations, but to obtain for an opinion which is +opposed to reigning doctrines, the recommendation derived from a striking +concurrence of sentiment between two inquirers entirely independent of one +another. I embrace the opportunity of citing from a writer of the extensive +acquirements in physical and metaphysical knowledge and the capacity of systematic +thought which the article evinces, passages so remarkably in unison +with my own views as the following:— +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“The truths of geometry are summed up and embodied in its definitions +and axioms.... Let us turn to the axioms, and what do we find? A string +of propositions concerning magnitude in the abstract, which are equally true of +space, time, force, number, and every other magnitude susceptible of aggregation +and subdivision. Such propositions, where they are not mere definitions, +as some of them are, carry their inductive origin on the face of their enunciation.... +Those which declare that two straight lines cannot inclose a space, +and that two straight lines which cut one another cannot both be parallel to a +third, are in reality the only ones which express characteristic properties of +space, and these it will be worth while to consider more nearly. Now the only +clear notion we can form of straightness is uniformity of direction, for space in +its ultimate analysis is nothing but an assemblage of distances and directions. +And (not to dwell on the notion of continued contemplation, <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span>, +mental experience, as included in the very idea of uniformity; nor on that of transfer of +the contemplating being from point to point, and of experience, during such +transfer, of the homogeneity of the interval passed over) we cannot even propose +the proposition in an intelligible form, to any one whose experience ever +since he was born has not assured him of the fact. The unity of direction, or +that we cannot march from a given point by more than one path direct to the +same object, is matter of practical experience long before it can by possibility +become matter of abstract thought. <em class="tei tei-emph"><span style="font-style: italic">We cannot attempt mentally to exemplify the +conditions of the assertion in an imaginary case opposed to it, without violating our +habitual recollection of this experience, and defacing our mental picture of space as +grounded on it.</span></em> What but experience, we may ask, can possibly assure us of the +homogeneity of the parts of distance, time, force, and measurable aggregates in +general, on which the truth of the other axioms depends? As regards the +latter axiom, after what has been said it must be clear that the very same course +of remarks equally applies to its case, and that its truth is quite as much forced +on the mind as that of the former by daily and hourly experience ... <em class="tei tei-emph"><span style="font-style: italic">including +always, be it observed, in our notion of experience, that which is gained by +contemplation of the inward picture which the mind forms to itself in any proposed case, +or which it arbitrarily selects as an example—such picture, in virtue of the +extreme simplicity of these primary relations, being called up by the imagination with as +much vividness and clearness as could be done by any external impression, which is +the only meaning we can attach to the word intuition, as applied to such +relations.</span></em>”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +And again, of the axioms of mechanics:—<span class="tei tei-q">“As we admit no such propositions, +other than as truths inductively collected from observation, even in +geometry itself, it can hardly be expected that, in a science of obviously contingent +relations, we should acquiesce in a contrary view. Let us take one of +these axioms and examine its evidence: for instance, that equal forces perpendicularly +applied at the opposite ends of equal arms of a straight lever will +balance each other. What but experience, we may ask, in the first place, can +possibly inform us that a force so applied will have any tendency to turn the +lever on its centre at all? or that force can be so transmitted along a rigid line +perpendicular to its direction, as to act elsewhere in space than along its own +line of action? Surely this is so far from being self-evident that it has even a +paradoxical appearance, which is only to be removed by giving our lever thickness, +material composition, and molecular powers. Again we conclude, that the +two forces, being equal and applied under precisely similar circumstances, must, +if they exert any effort at all to turn the lever, exert equal and opposite efforts: +but what <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> reasoning can +possibly assure us that they <em class="tei tei-emph"><span style="font-style: italic">do</span></em> act under precisely +similar circumstances? that points which differ in place <em class="tei tei-emph"><span style="font-style: italic">are</span></em> similarly +circumstanced as regards the exertion of force? that universal space may not +have relations to universal force—or, at all events, that the organization of the +material universe may not be such as to place that portion of space occupied by +it in such relations to the forces exerted in it, as may invalidate the absolute +similarity of circumstances assumed? Or we may argue, what have we to do +with the notion of angular movement in the lever at all? The case is one of +rest, and of quiescent destruction of force by force. Now how is this destruction +effected? Assuredly by the counter-pressure which supports the fulcrum. +But would not this destruction equally arise, and by the same amount of counteracting +force, if each force simply pressed its own half of the lever against the +fulcrum? And what can assure us that it is not so, except removal of one or +other force, and consequent tilting of the lever? The other fundamental axiom +of statics, that the pressure on the point of support is the sum of the weights ... +is merely a scientific transformation and more refined mode of stating +a coarse and obvious result of universal experience, viz. that the weight of a +rigid body is the same, handle it or suspend it in what position or by what +point we will, and that whatever sustains it sustains its total weight. Assuredly, +as Mr. Whewell justly remarks, <span class="tei tei-q">‘No one probably ever made a trial for the +purpose of showing that the pressure on the support is equal to the sum of the +weights’</span> ... But it is precisely because in every action of his life from +earliest infancy he has been continually making the trial, and seeing it made +by every other living being about him, that he never dreams of staking its +result on one additional attempt made with scientific accuracy. This would +be as if a man should resolve to decide by experiment whether his eyes were +useful for the purpose of seeing, by hermetically sealing himself up for half an +hour in a metal case.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +On the <span class="tei tei-q">“paradox of universal propositions obtained by experience,”</span> the +same writer says: <span class="tei tei-q">“If there be necessary and universal truths expressible in +propositions of axiomatic simplicity and obviousness, and having for their subject-matter +the elements of all our experience and all our knowledge, surely +these are the truths which, if experience suggest to us any truths at all, it +ought to suggest most readily, clearly, and unceasingly. If it were a truth, +universal and necessary, that a net is spread over the whole surface of every +planetary globe, we should not travel far on our own without getting entangled +in its meshes, and making the necessity of some means of extrication an axiom +of locomotion.... There is, therefore, nothing paradoxical, but the reverse, +in our being led by observation to a recognition of such truths, as <em class="tei tei-emph"><span style="font-style: italic">general</span></em> +propositions, coextensive at least with all human experience. That they pervade +all the objects of experience, must ensure their continual suggestion <em class="tei tei-emph"><span style="font-style: italic">by</span></em> +experience; that they are true, must ensure that consistency of suggestion, that +iteration of uncontradicted assertion, which commands implicit assent, and +removes all occasion of exception; that they are simple, and admit of no +misunderstanding, must secure their admission by every mind.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“A truth, necessary and universal, relative to any object of our knowledge, +must verify itself in every instance where that object is before our contemplation, +and if at the same time it be simple and intelligible, its verification must +be obvious. <em class="tei tei-emph"><span style="font-style: italic">The sentiment of such a truth cannot, therefore, but be present to our +minds whenever that object is contemplated, and must therefore make a part of the +mental picture or idea of that object which we may on any occasion summon before +our imagination.... All propositions, therefore, become not only untrue but +inconceivable</span></em>, if ... axioms be violated in their enunciation.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Another high authority (if indeed it be another authority) may be cited +in favour of the doctrine that axioms rest on the evidence of induction. +<span class="tei tei-q">“The axioms of geometry themselves may be regarded as in some sort an +appeal to experience, not corporeal, but mental. When we say, the whole is +greater than its part, we announce a general fact, which rests, it is true, on our +ideas of whole and part; but, in abstracting these notions, we begin by considering +them as subsisting in space, and time, and body, and again, in linear, +and superficial, and solid space. Again, when we say, the equals of equals are +equal, we mentally make comparisons, in equal spaces, equal times, &c., so that +these axioms, however self-evident, are still general propositions so far of the +inductive kind, that, independently of experience, they would not present themselves +to the mind. The only difference between these and axioms obtained +from extensive induction is this, that, in raising the axioms of geometry, the +instances offer themselves spontaneously, and without the trouble of search, +and are few and simple; in raising those of nature, they are infinitely numerous, +complicated, and remote, so that the most diligent research and the utmost +acuteness are required to unravel their web and place their meaning in +evidence.”</span>—<span class="tei tei-hi"><span style="font-variant: small-caps">Sir J. Herschel</span></span>'s +<span class="tei tei-hi"><span style="font-style: italic">Discourse on the Study of Natural Philosophy</span></span>, pp. 95, 96. +</p></dd><dt class="tei tei-notelabel"><a id="note_53" name="note_53" href="#noteref_53">53.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Dr. Whewell thinks it improper to +apply the term Induction to any operation not terminating in the establishment of a +general truth. Induction, he says (in p. 15 of his pamphlet) <span class="tei tei-q">“is not the same thing +as experience and observation. Induction is experience or observation +<em class="tei tei-emph"><span style="font-style: italic">consciously</span></em> looked at in a <em class="tei tei-emph"><span style="font-style: italic">general</span></em> form. This consciousness +and generality are necessary parts of that knowledge which is science.”</span> And he +objects (p. 8) to the mode in which the word Induction is employed in this work, as an +undue extension of that term <span class="tei tei-q">“not only to the cases in which the general induction is +consciously applied to a particular instance, but to the cases in which the particular +instance is dealt with by means of experience in that rude sense in which experience can +be asserted of brutes, and in which of course we can in no way imagine that the +law is possessed or understood as a general proposition.”</span> This use of the term +he deems a <span class="tei tei-q">“confusion of knowledge with practical tendencies.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +I disclaim, as strongly as Dr. Whewell can do, the application of such terms +as induction, inference, or reasoning, to operations performed by mere instinct, +that is, from an animal impulse, without the exertion of any intelligence. But +I perceive no ground for confining the use of those terms to cases in which +the inference is drawn in the forms and with the precautions required by +scientific propriety. To the idea of Science, an express recognition and distinct +apprehension of general laws as such, is essential: but nine-tenths of the +conclusions drawn from experience in the course of practical life, are drawn +without any such recognition: they are direct inferences from known cases, to +a case supposed to be similar. I have endeavoured to shew that this is not +only as legitimate an operation, but substantially the same operation, as that +of ascending from known cases to a general proposition; (except that the +latter process has one great security for correctness which the former does not +possess). In Science, the inference must necessarily pass through the intermediate +stage of a general proposition, because Science wants its conclusions +for record, and not for instantaneous use. But the inferences drawn for the +guidance of practical affairs, by persons who would often be quite incapable of +expressing in unexceptionable terms the corresponding generalizations, may +and frequently do exhibit intellectual powers quite equal to any which have +ever been displayed in Science: and if these inferences are not inductive, what +are they? The limitation imposed on the term by Dr. Whewell seems perfectly +arbitrary; neither justified by any fundamental distinction between what +he includes and what he desires to exclude, nor sanctioned by usage, at least +from the time of Reid and Stewart, the principal legislators (as far as the +English language is concerned) of modern metaphysical terminology. +</p></dd><dt class="tei tei-notelabel"><a id="note_54" name="note_54" href="#noteref_54">54.</a></dt><dd class="tei tei-notetext">Suprà, p. <a href="#Pg214" class="tei tei-ref">214</a>.</dd><dt class="tei tei-notelabel"><a id="note_55" name="note_55" href="#noteref_55">55.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. Ind. Sc.</span></span> ii. 213, +214.</dd><dt class="tei tei-notelabel"><a id="note_56" name="note_56" href="#noteref_56">56.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Ibid.</span></span></dd><dt class="tei tei-notelabel"><a id="note_57" name="note_57" href="#noteref_57">57.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Phil. +Ind. Sc.</span></span> ii. p. 173.</dd><dt class="tei tei-notelabel"><a id="note_58" name="note_58" href="#noteref_58">58.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Cours +de Philosophie Positive</span></span>, vol. ii, p. 202.</dd><dt class="tei tei-notelabel"><a id="note_59" name="note_59" href="#noteref_59">59.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Dr. +Whewell, in his reply, contests the distinction here drawn, and maintains, +that not only different descriptions, but different explanations of a +phenomenon, may all be true. Of the three theories respecting the motions +of the heavenly bodies, he says (p. 25): <span class="tei tei-q">“Undoubtedly all these explanations +may be true and consistent with each other, and would be so if each had been +followed out so as to shew in what manner it could be made consistent with +the facts. And this was, in reality, in a great measure done. The doctrine +that the heavenly bodies were moved by vortices was successively modified, +so that it came to coincide in its results with the doctrine of an inverse-quadratic +centripetal force.... When this point was reached, the vortex +was merely a machinery, well or ill devised, for producing such a centripetal +force, and therefore did not contradict the doctrine of a centripetal +force. Newton himself does not appear to have been averse to explaining +gravity by impulse. So little is it true that if one theory be true the other +must be false. The attempt to explain gravity by the impulse of streams of +particles flowing through the universe in all directions, which I have mentioned +in the <span class="tei tei-hi"><span style="font-style: italic">Philosophy</span></span>, is so far from being inconsistent with the +Newtonian theory, that it is founded entirely upon it. And even with regard to the +doctrine, that the heavenly bodies move by an inherent virtue; if this doctrine had been +maintained in any such way that it was brought to agree with the facts, the +inherent virtue must have had its laws determined; and then it would have +been found that the virtue had a reference to the central body; and so, the +<span class="tei tei-q">‘inherent virtue’</span> must have coincided in its effect with the Newtonian force; +and then, the two explanations would agree, except so far as the word <span class="tei tei-q">‘inherent’</span> +was concerned. And if such a part of an earlier theory as this word +<em class="tei tei-emph"><span style="font-style: italic">inherent</span></em> indicates, is found to be untenable, it is of course rejected in +the transition to later and more exact theories, in Inductions of this kind, as well +as in what Mr. Mill calls Descriptions. There is, therefore, still no validity +discoverable in the distinction which Mr. Mill attempts to draw between descriptions +like Kepler's law of elliptical orbits, and other examples of induction.”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If the doctrine of vortices had meant, not that vortices existed, but only +that the planets moved <em class="tei tei-emph"><span style="font-style: italic">in the same manner</span></em> as if they had been whirled by +vortices; if the hypothesis had been merely a mode of representing the facts, +not an attempt to account for them; if, in short, it had been only a Description; +it would, no doubt, have been reconcileable with the Newtonian theory. The +vortices, however, were not a mere aid to conceiving the motions of the planets, +but a supposed physical agent, actively impelling them; a material fact, which +might be true or not true, but could not be both true and not true. According +to Descartes' theory it was true, according to Newton's it was not true. Dr. +Whewell probably means that since the phrases, centripetal and projectile +force, do not declare the nature but only the direction of the forces, the Newtonian +theory does not absolutely contradict any hypothesis which may be framed respecting the +mode of their production. The Newtonian theory, regarded as a mere +<em class="tei tei-emph"><span style="font-style: italic">description</span></em> of the planetary motions, does not; but the Newtonian theory +as an <em class="tei tei-emph"><span style="font-style: italic">explanation</span></em> of them does. For in what does the explanation +consist? In ascribing those motions to a general law which obtains between +all particles of matter, and in identifying this with the law by which bodies +fall to the ground; a kind of motion which the vortices did not, and as it was +rectilineal, could not, explain. The one explanation, therefore, absolutely +excludes the other. Either the planets are not moved by vortices, or they do +not move by the law by which heavy bodies fall. It is impossible that both +opinions can be true. As well might it be said that there is no contradiction +between the assertions, that a man died because somebody killed him, and that +he died a natural death. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +So, again, the theory that the planets move by a virtue inherent in their +celestial nature, is incompatible with either of the two others; either that of +their being moved by vortices, or that which regards them as moving by a +property which they have in common with the earth and all terrestrial bodies. +Dr. Whewell says, that the theory of an inherent virtue agrees with Newton's +when the word inherent is left out, which of course it would be (he says) if +<span class="tei tei-q">“found to be untenable.”</span> But leave that out, and where is the theory? The +word inherent <em class="tei tei-emph"><span style="font-style: italic">is</span></em> the theory. When that is omitted, there remains nothing +except that the heavenly bodies move by <span class="tei tei-q">“a virtue,”</span> <span class="tei tei-hi"><span style="font-style: italic">i.e.</span></span> by +a power of some sort. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If Dr. Whewell is not yet satisfied, any other subject will serve equally +well to test his doctrine. He will hardly say that there is no contradiction +between the emission theory and the undulatory theory of light; or that there +can be both one and two electricities; or that the hypothesis of the production +of the higher organic forms by development from the lower, and the supposition +of separate and successive acts of creation, are quite reconcileable; or +that the theory that volcanoes are fed from a central fire, and the doctrines +which ascribe them to chemical action at a comparatively small depth below +the earth's surface, are consistent with one another, and all true as far as +they go. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If different explanations of the same fact cannot both be true, still less, +surely, can different predictions. Dr. Whewell quarrels (on what ground it is +not necessary to consider) with the example I had chosen on this point, and +thinks an objection to an illustration a sufficient answer to a theory. Examples +not liable to his objection are easily found, if the proposition that conflicting +predictions cannot both be true, can be made clearer by any examples. Suppose +the phenomenon to be a newly-discovered comet, and that one astronomer predicts +its return once in every 300 years—another, once in every 400: can they +both be right? When Columbus predicted that by sailing constantly westward he +should in time return to the point from which he set out, while others asserted +that he could never do so except by turning back, were both he and his opponents +true prophets? Were the predictions which foretold the wonders of +railways and steamships, and those which averred that the Atlantic could never +be crossed by steam navigation, nor a railway train propelled ten miles an hour, +both (in Dr. Whewell's words) <span class="tei tei-q">“true, and consistent with one another”</span>? +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Dr. Whewell sees no distinction between holding contradictory opinions on +a question of fact, and merely employing different analogies to facilitate the +conception of the same fact. The case of different Inductions belongs to the +former class, that of different Descriptions to the latter. +</p></dd><dt class="tei tei-notelabel"><a id="note_60" name="note_60" href="#noteref_60">60.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Of Induction</span></span>, p. +33.</dd><dt class="tei tei-notelabel"><a id="note_61" name="note_61" href="#noteref_61">61.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">But though it is a +condition of the validity of every induction that there be uniformity in the course of +nature, it is not a necessary condition that the uniformity should pervade all nature. It +is enough that it pervades the particular class of phenomena to which the induction +relates. An induction concerning the motions of the planets, or the properties of the +magnet, would not be vitiated though we were to suppose that wind and weather are the +sport of chance, provided it be assumed that astronomical and magnetic phenomena are +under the dominion of general laws. Otherwise the early experience of mankind +would have rested on a very weak foundation; for in the infancy of +science it could not be said to be known that <em class="tei tei-emph"><span style="font-style: italic">all</span></em> phenomena are regular in +their course. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Neither would it be correct to say that every induction by which we infer +any truth, implies the general fact of uniformity <em class="tei tei-emph"><span style="font-style: italic">as foreknown</span></em>, even in +reference to the kind of phenomena concerned. It implies, <em class="tei tei-emph"><span style="font-style: italic">either</span></em> that this +general fact is already known, <em class="tei tei-emph"><span style="font-style: italic">or</span></em> that we may now know it: as the +conclusion, The Duke of Wellington is mortal, drawn from the instances A, B, and C, +implies either that we have already concluded all men to be mortal, or that we are now +entitled to do so from the same evidence. A vast amount of confusion and +paralogism respecting the grounds of Induction would be dispelled by keeping +in view these simple considerations. +</p></dd><dt class="tei tei-notelabel"><a id="note_62" name="note_62" href="#noteref_62">62.</a></dt><dd class="tei tei-notetext">Infra, +chap. xxi.</dd><dt class="tei tei-notelabel"><a id="note_63" name="note_63" href="#noteref_63">63.</a></dt><dd class="tei tei-notetext">Infra, chap. xxi, +xxii.</dd><dt class="tei tei-notelabel"><a id="note_64" name="note_64" href="#noteref_64">64.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Dr. Whewell (<span class="tei tei-hi"><span style="font-style: italic">Of Induction</span></span>, p. +16) will not allow these and similar erroneous opinions to be called inductions; +inasmuch as such superstitious fancies <span class="tei tei-q">“were not collected from the facts by seeking a +law of their occurrence, but were suggested by an imagination of the anger of superior +powers, shown by such deviations from the ordinary course of nature.”</span> I conceive the +question to be, not in what manner these notions were at first suggested, but by what +evidence they have, from time to time, been supposed to be substantiated. If +the believers in these erroneous opinions had been put on their defence, they +would have referred to experience; to the comet which preceded the assassination +of Julius Cæsar, or to oracles and other prophecies known to have been +fulfilled. It is by such appeals to facts that all analogous superstitions, even +in our day, attempt to justify themselves; the supposed evidence of experience +is what really gives them their hold on the mind. I quite admit that the influence +of such coincidences would not be what it is, if strength were not lent +to it by an antecedent presumption; but this is not peculiar to such cases; preconceived +notions of probability form part of the explanation of many other +cases of belief on insufficient evidence. The <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> prejudice does not prevent +the erroneous opinion from being sincerely regarded as a legitimate conclusion +from experience; but is, on the contrary, the very thing which predisposes the +mind to that interpretation of experience. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Thus much in defence of the sort of examples objected to. But it would +be easy to produce instances, equally adapted to the purpose, and in which no +antecedent prejudice is at all concerned. <span class="tei tei-q">“For many ages,”</span> says Archbishop +Whately, <span class="tei tei-q">“all farmers and gardeners were firmly convinced—and convinced +of their knowing it by experience—that the crops would never turn out good +unless the seed were sown during the increase of the moon.”</span> This was induction, +but bad induction: just as a vicious syllogism is reasoning, but bad +reasoning.</p></dd><dt class="tei tei-notelabel"><a id="note_65" name="note_65" href="#noteref_65">65.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">The assertion, that any and every one of the +conditions of a phenomenon may be and is, on some occasions and for some purposes, spoken +of as the cause, has been disputed by an intelligent reviewer of this work, +(<span class="tei tei-hi"><span style="font-style: italic">Prospective Review</span></span> for February 1850,) who maintains that <span class="tei tei-q">“we +always apply the word cause rather to that element in the antecedents which exercises +<em class="tei tei-emph"><span style="font-style: italic">force</span></em>, and which would <em class="tei tei-emph"><span style="font-style: italic">tend</span></em> at all times to produce the same or +a similar effect to that which, under certain conditions, it would actually produce.”</span> +And he says, that <span class="tei tei-q">“every one would feel”</span> the expression, that the cause of a +surprise was the sentinel's being off his post, to be incorrect; but that <span class="tei tei-q">“the +allurement or force which <em class="tei tei-emph"><span style="font-style: italic">drew</span></em> him off his post, might be so called, because +in doing so it removed a resisting power which would have prevented the surprise.”</span> I +cannot think that it would be wrong to say, that the event took place because the +sentinel was absent, and yet right to say that it took place because he was bribed to be +absent. Since the only direct effect of the bribe was his absence, the bribe could be +called the remote cause of the surprise, only on the supposition that the absence was +the proximate cause; nor does it seem to me that any one, who had not a theory +to support, would use the one expression and reject the other. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The reviewer observes, that when a person dies of poison, his possession +of bodily organs is a necessary condition, but that no one would ever speak of +it as the cause. I admit the fact; but I believe the reason to be, that the occasion +could never arise for so speaking of it; for when in the inaccuracy of common +discourse we are led to speak of some one condition of a phenomenon as +its cause, the condition so spoken of is always one which it is at least possible +that the hearer may require to be informed of. The possession of bodily organs +is a known condition, and to give that as the answer, when asked the cause of +a person's death, would not supply the information sought. Once conceive +that a doubt could exist as to his having bodily organs, or that he were to be +compared with some being who had them not, and cases may be imagined in +which it might be said that his possession of them was the cause of his death. +If Faust and Mephistopheles together took poison, it might be said that Faust +died because he was a human being, and had a body, while Mephistopheles +survived because he was a spirit. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +It is for the same reason, that no one (as the reviewer remarks) <span class="tei tei-q">“calls the +cause of a leap, the muscles or sinews of the body, though they are necessary +conditions; nor the cause of a self-sacrifice, the knowledge which was necessary +for it; nor the cause of writing a book, that a man has time for it, which +is a necessary condition.”</span> These conditions (besides that they are antecedent +<em class="tei tei-emph"><span style="font-style: italic">states</span></em>, and not proximate antecedent <em class="tei tei-emph"><span style="font-style: italic">events</span></em>, and are therefore +never the conditions in closest apparent proximity to the effect) are all of them so +obviously implied, that it is hardly possible there should exist that necessity for +insisting on them, which alone gives occasion for speaking of a single condition as if it +were the cause. Wherever this necessity exists in regard to some one condition, +and does not exist in regard to any other, I conceive that it is consistent +with usage, when scientific accuracy is not aimed at, to apply the name cause +to that one condition. If the only condition which can be supposed to be unknown +is a negative condition, the negative condition may be spoken of as the +cause. It might be said that a person died for want of medical advice: though +this would not be likely to be said, unless the person was already understood to +be ill; and in order to indicate that this negative circumstance was what made +the illness fatal, and not the weakness of his constitution, or the original virulence +of the disease. It might be said that a person was drowned because he +could not swim; the positive condition, namely that he fell into the water, +being already implied in the word drowned. And here let me remark, that +his falling into the water is in this case the only positive condition: all the +conditions not expressly or virtually included in this (as that he could not +swim, that nobody helped him, and so forth) are negative. Yet, if it were +simply said that the cause of a man's death was falling into the water, there +would be quite as great a sense of impropriety in the expression, as there +would be if it were said that the cause was his inability to swim; because, +though the one condition is positive and the other negative, it would be felt +that neither of them was sufficient, without the other, to produce death. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +With regard to the assertion that nothing is termed the cause, except the +element which exerts active force; I waive the question as to the meaning of +active force, and accepting the phrase in its popular sense, I revert to a former +example, and I ask, would it be more agreeable to custom to say that a man +fell because his foot slipped in climbing a ladder, or that he fell because of his +weight—for his weight, and not the motion of his foot, was the active force +which determined his fall. If a person walking out in a frosty day, stumbled +and fell, it might be said that he stumbled because the ground was slippery, +or because he was not sufficiently careful; but few people, I suppose, would +say that he stumbled because he walked. Yet the only active force concerned +was that which he exerted in walking: the others were mere negative conditions; +but they happened to be the only ones which there could be any +necessity to state; for he walked, most likely, in exactly his usual manner, and +the negative conditions made all the difference. Again, if a person were +asked why the army of Xerxes defeated that of Leonidas, he would probably +say, because they were a thousand times the number; but I do not think he +would say, it was because they fought; although that was the element of +active force. The reviewer adds, <span class="tei tei-q">“there are some conditions absolutely +passive, and yet absolutely necessary to physical phenomena, viz., the relations +of space and time; and to these no one ever applies the word cause without +being immediately arrested by those who hear him.”</span> Even from this statement +I am compelled to dissent. Few persons would feel it incongruous to +say (for example) that a secret became known because it was spoken of when +A. B. was within hearing; which is a condition of space; or that the cause +why one of two particular trees is taller than the other, is that it has been +longer planted; which is a condition of time. +</p></dd><dt class="tei tei-notelabel"><a id="note_66" name="note_66" href="#noteref_66">66.</a></dt><dd class="tei tei-notetext">There are a few exceptions; for there are +some properties of objects which seem to be purely preventive; as the property of opaque +bodies, by which they intercept the passage of light. This, as far as we are able to +understand it, appears an instance not of one cause counteracting another by the same law +whereby it produces its own effects, but of an agency which manifests itself in +no other way than in defeating the effects of another agency. If we knew on +what other relations to light, or on what peculiarities of structure, opacity +depends, we might find that this is only an apparent, not a real, exception to +the general proposition in the text. In any case it needs not affect the practical +application. The formula which includes all the negative conditions of an +effect in the single one of the absence of counteracting causes, is not violated by +such cases as this; though, if all counteracting agencies were of this description, +there would be no purpose served by employing the formula, since we +should still have to enumerate specially the negative conditions of each phenomenon, +instead of regarding them as implicitly contained in the positive laws +of the various other agencies in nature.</dd><dt class="tei tei-notelabel"><a id="note_67" name="note_67" href="#noteref_67">67.</a></dt><dd class="tei tei-notetext">I use the words <span class="tei tei-q">“straight +line”</span> for brevity and simplicity. In reality the line in question is not exactly +straight, for, from the effect of refraction, we actually see the sun for a short +interval during which the opaque mass of the earth is interposed in a direct line between +the sun and our eyes; thus realizing, though but to a limited extent, the coveted +desideratum of seeing round a corner.</dd><dt class="tei tei-notelabel"><a id="note_68" name="note_68" href="#noteref_68">68.</a></dt><dd class="tei tei-notetext">The reviewer of Dr. Whewell in the +<span class="tei tei-hi"><span style="font-style: italic">Quarterly Review</span></span>.</dd><dt class="tei tei-notelabel"><a id="note_69" name="note_69" href="#noteref_69">69.</a></dt><dd class="tei tei-notetext">To the universality which mankind are +agreed in ascribing to the Law of Causation, there is one claim of exception, one +disputed case, that of the Human Will; the determinations of which, a large class of +metaphysicians are not willing to regard as following the causes called motives, +according to as strict laws as those which they suppose to exist in the world of mere +matter. This controverted point will undergo a special examination when we come to +treat particularly of the Logic of the Moral Sciences, (Book vi. ch. 2). In +the meantime I may remark that these metaphysicians, who, it must be +observed, ground the main part of their objection on the supposed repugnance +of the doctrine in question to our consciousness, seem to me to mistake the +fact which consciousness testifies against. What is really in contradiction to +consciousness, they would, I think, on strict self-examination, find to be, the +application to human actions and volitions of the ideas involved in the common +use of the term Necessity; which I agree with them in objecting to. But +if they would consider that by saying that a person's actions <em class="tei tei-emph"><span style="font-style: italic">necessarily</span></em> +follow from his character, all that is really meant (for no more is meant +in any case whatever of causation) is that he invariably <em class="tei tei-emph"><span style="font-style: italic">does</span></em> act in +conformity to his character, and that any one who thoroughly knew his character +could certainly predict how he would act in any supposable case; they probably +would not find this doctrine either contrary to their experience or +revolting to their feelings. And no more than this is contended for by any +one but an Asiatic fatalist.</dd><dt class="tei tei-notelabel"><a id="note_70" name="note_70" href="#noteref_70">70.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Unless we are +to consider as such the following statement, by one of the +writers quoted in the text: <span class="tei tei-q">“In the case of mental exertion, the result to be +accomplished is <em class="tei tei-emph"><span style="font-style: italic">preconsidered</span></em> or meditated, and is therefore known +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span>, +or before experience.”</span>—(Bowen's <span class="tei tei-hi"><span style="font-style: italic">Lowell Lectures on the +Application of Metaphysical and Ethical Science to the Evidence of Religion</span></span>, +Boston, 1849.) This is merely saying that when we will a thing we have an idea of it. +But to have an idea of what we wish to happen, does not imply a prophetic knowledge that +it will happen. Perhaps it will be said that the <em class="tei tei-emph"><span style="font-style: italic">first time</span></em> we exerted our +will, when we had of course no experience of any of the powers residing in us, we +nevertheless must already have known that we possessed them, since we cannot +<em class="tei tei-emph"><span style="font-style: italic">will</span></em> that which we do not believe to be in our power. But the +impossibility is perhaps in the words only, and not in the facts; for we may +<em class="tei tei-emph"><span style="font-style: italic">desire</span></em> what we do not know to be in our power; and finding by experience +that our bodies move according to our <em class="tei tei-emph"><span style="font-style: italic">desire</span></em>, we may then, and only then, +pass into the more complicated mental state which is termed will. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +After all, even if we had an instinctive knowledge that our actions would +follow our will, this, as Brown remarks, would prove nothing as to the nature +of Causation. Our knowing, previous to experience, that an antecedent will be +followed by a certain consequent, would not prove the relation between them +to be anything <em class="tei tei-emph"><span style="font-style: italic">more</span></em> than antecedence and consequence. +</p></dd><dt class="tei tei-notelabel"><a id="note_71" name="note_71" href="#noteref_71">71.</a></dt><dd class="tei tei-notetext">Reid's +<span class="tei tei-hi"><span style="font-style: italic">Essays on the Active Powers</span></span>, Essay iv. ch. 3.</dd><dt class="tei tei-notelabel"><a id="note_72" name="note_72" href="#noteref_72">72.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Prospective +Review</span></span> for February 1850.</dd><dt class="tei tei-notelabel"><a id="note_73" name="note_73" href="#noteref_73">73.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Vide supra</span></span>, p. +<a href="#Pg267" class="tei tei-ref">267</a>, note.</dd><dt class="tei tei-notelabel"><a id="note_74" name="note_74" href="#noteref_74">74.</a></dt><dd class="tei tei-notetext">In combating the theory, +that Volition is the universal cause, I have +purposely abstained from one of the strongest positive arguments against it—that +volitions themselves obey causes, and even external causes, namely, the +inducements, or motives, which determine the will to act; because an objector +might say that to employ this argument would be begging the question against +the freedom of the will. Though it is not begging the question to affirm a +doctrine, referring elsewhere for the proof of it, I am unwilling without +necessity to build any part of my reasoning on a proposition which I am aware +that those opposed to me in the present discussion do not admit.</dd><dt class="tei tei-notelabel"><a id="note_75" name="note_75" href="#noteref_75">75.</a></dt><dd class="tei tei-notetext">I omit, for simplicity, to take +into account the effect, in this latter case, of +the diminution of pressure, in diminishing the flow of water through the +drain; which evidently in no way affects the truth or applicability of the +principle.</dd><dt class="tei tei-notelabel"><a id="note_76" name="note_76" href="#noteref_76">76.</a></dt><dd class="tei tei-notetext">Unless, +indeed, the consequent was generated not by the antecedent, but +by the means we employed to produce the antecedent. As, however, these +means are under our power, there is so far a probability that they are also +sufficiently within our knowledge, to enable us to judge whether that could be +the case or not.</dd><dt class="tei tei-notelabel"><a id="note_77" name="note_77" href="#noteref_77">77.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Discourse on the Study +of Natural Philosophy</span></span>, p. 179.</dd><dt class="tei tei-notelabel"><a id="note_78" name="note_78" href="#noteref_78">78.</a></dt><dd class="tei tei-notetext">For this speculation I am indebted to +Mr. Alexander Bain.</dd><dt class="tei tei-notelabel"><a id="note_79" name="note_79" href="#noteref_79">79.</a></dt><dd class="tei tei-notetext">This view of the necessary +coexistence of opposite excitements involves +a great extension of the original doctrine of two electricities. The early +theorists assumed that, when amber was rubbed, the amber was made positive +and the rubber negative to the same degree; but it never occurred to them to +suppose that the existence of the amber charge was dependent on an opposite +charge in the bodies with which the amber was contiguous, while the existence +of the negative charge on the rubber was equally dependent on a contrary +state of the surfaces that might accidentally be confronted with it; that, in +fact, in a case of electrical excitement by friction, four charges were the +minimum that could exist. But this double electrical action is essentially +implied in the explanation now universally adopted in regard to the phenomena +of the common electric machine.</dd><dt class="tei tei-notelabel"><a id="note_80" name="note_80" href="#noteref_80">80.</a></dt><dd class="tei tei-notetext">Pp. 159-162.</dd><dt class="tei tei-notelabel"><a id="note_81" name="note_81" href="#noteref_81">81.</a></dt><dd class="tei tei-notetext">Infra, book iv., chap. +ii. On Abstraction.</dd><dt class="tei tei-notelabel"><a id="note_82" name="note_82" href="#noteref_82">82.</a></dt><dd class="tei tei-notetext">I must, however, remark, that +this example, which seems to militate +against the assertion we made of the comparative inapplicability of the Method +of Difference to cases of pure observation, is really one of those exceptions +which, according to a proverbial expression, prove the general rule. For +this case, in which Nature, in her experiment, seems to have imitated the +type of the experiments made by man, she has only succeeded in producing +the likeness of man's most imperfect experiments; namely, those in which, +though he succeeds in producing the phenomenon, he does so by employing +complex means, which he is unable perfectly to analyse, and can form therefore +no sufficient judgment what portion of the effects may be due, not to the +supposed cause, but to some unknown agency of the means by which that +cause was produced. In the natural experiment which we are speaking of, +the means used was the clearing off a canopy of clouds; and we certainly do +not know sufficiently in what this process consists, or on what it depends, to +be certain <span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">à priori</span></span> +that it might not operate upon the deposition of dew independently +of any thermometric effect at the earth's surface. Even, therefore, +in a case so favourable as this to Nature's experimental talents, her experiment +is of little value except in corroboration of a conclusion already attained +through other means.</dd><dt class="tei tei-notelabel"><a id="note_83" name="note_83" href="#noteref_83">83.</a></dt><dd class="tei tei-notetext">Discourse, pp. 156-8, and +171.</dd><dt class="tei tei-notelabel"><a id="note_84" name="note_84" href="#noteref_84">84.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Outlines of Astronomy</span></span>, p. +584.</dd><dt class="tei tei-notelabel"><a id="note_85" name="note_85" href="#noteref_85">85.</a></dt><dd class="tei tei-notetext"><p class="tei tei-p" style="margin-bottom: 1.00em">Dr. +Whewell, in his reply, expresses a very unfavourable opinion of the +utility of the Four Methods, as well as of the aptness of the examples by which +I have attempted to illustrate them. His words are these (pp. 44-6): +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +<span class="tei tei-q">“Upon these methods, the obvious thing to remark is, that they take for +granted the very thing which is most difficult to discover, the reduction of the +phenomena to formulæ such as are here presented to us. When we have any +set of complex facts offered to us; for instance, those which were offered in +the cases of discovery which I have mentioned,—the facts of the planetary +paths, of falling bodies, of refracted rays, of cosmical motions, of chemical +analysis; and when, in any of these cases, we would discover the law of +nature which governs them, or, if any one chooses so to term it, the feature in +which all the cases agree, where are we to look for our A, B, C, and +<span class="tei tei-hi"><span style="font-style: italic">a, b, c</span></span>? Nature does not present to us the cases in this +form; and how are we to reduce them to this form? You say, <em class="tei tei-emph"><span style="font-style: italic">when</span></em> we +find the combination of A B C with <span class="tei tei-hi"><span style="font-style: italic">a b c</span></span> and A B D with +<span class="tei tei-hi"><span style="font-style: italic">a b d</span></span>, then we may draw our inference. Granted; +but when and where are we to find such combinations? Even now that the +discoveries are made, who will point out to us what are the A, B, C, and +<span class="tei tei-hi"><span style="font-style: italic">a, b, c</span></span> +elements of the cases which have just been enumerated? Who will tell us +which of the methods of inquiry those historically real and successful inquiries +exemplify? Who will carry these formulæ through the history of the sciences, +as they have really grown up; and shew us that these four methods have been +operative in their formation; or that any light is thrown upon the steps of +their progress by reference to these formulæ?”</span> +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +He adds that, in this work, the methods have not been applied <span class="tei tei-q">“to a large +body of conspicuous and undoubted examples of discovery, extending along +the whole history of science,”</span> which ought to have been done in order that +the methods might be shown to possess the <span class="tei tei-q">“advantage”</span> (which he claims as +belonging to his own) of being those <span class="tei tei-q">“by which all great discoveries in science +have really been made.”</span>—(p. 66.) +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +There is a striking similarity between the objections here made against Canons +of Induction, and what was alleged, in the last century, by as able men as +Dr. Whewell, against the acknowledged Canon of Ratiocination. Those who +protested against the Aristotelian Logic said of the Syllogism, what Dr. +Whewell says of the Inductive Methods, that it <span class="tei tei-q">“takes for granted the very +thing which is most difficult to discover, the reduction of the argument to +formulæ such as are here presented to us.”</span> The grand difficulty, they said, is +to obtain your syllogism, not to judge of its correctness when obtained. On +the matter of fact, both they and Dr. Whewell are right. The greatest difficulty +in both cases is first that of obtaining the evidence, and next, of reducing it to +the form which tests its conclusiveness. But if we try so to reduce it without +knowing <em class="tei tei-emph"><span style="font-style: italic">to what</span></em>, we are not likely to make much progress. It is a more +difficult thing to solve a geometrical problem, than to judge whether a proposed +solution is correct: but if people were not able to judge of the solution when +found, they would have little chance of finding it. And it cannot be pretended +that to judge of an induction when found, is perfectly easy, is a thing for +which aids and instruments are superfluous; for erroneous inductions, false +inferences from experience, are quite as common, on some subjects much commoner, +than true ones. The business of Inductive Logic is to provide rules +and models (such as the Syllogism and its rules are for ratiocination) to which +if inductive arguments conform, those arguments are conclusive, and not +otherwise. This is what the Four Methods profess to be, and what I believe +they are universally considered to be by experimental philosophers, who had +practised all of them long before any one sought to reduce the practice to +theory. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +The assailants of the Syllogism had also anticipated Dr. Whewell in the +other branch of his argument. They said that no discoveries were ever made +by syllogism; and Dr. Whewell says, or seems to say, that none were ever +made by the four Methods of Induction. To the former objectors, Archbishop +Whately very pertinently answered, that their argument, if good at all, was +good against the reasoning process altogether; for whatever cannot be +reduced to syllogism, is not reasoning. And Dr. Whewell's argument, if good +at all, is good against all inferences from experience. In saying that no discoveries +were ever made by the four Methods, he affirms that none were ever +made by observation and experiment; for assuredly if any were, it was by one +or other of those methods. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +This difference between us accounts for the dissatisfaction which my +examples give him; for I did not select them with a view to satisfy any one who +required to be convinced that observation and experiment are modes of acquiring +knowledge: I confess that in the choice of them I thought only of illustration, +and of facilitating the <em class="tei tei-emph"><span style="font-style: italic">conception</span></em> of the Methods by concrete instances. +If it had been my object to justify the processes themselves as means of investigation, +there would have been no need to look far off, or make use of recondite +or complicated instances. As a specimen of a truth ascertained by the +Method of Agreement, I might have chosen the proposition, <span class="tei tei-q">“Dogs bark.”</span> +This dog, and that dog, and the other dog, answer to A B C, A D E, A F G. +The circumstance of being a dog, answers to A. Barking answers to +<span class="tei tei-hi"><span style="font-style: italic">a</span></span>. As +a truth made known by the Method of Difference, <span class="tei tei-q">“Fire burns”</span> might have +sufficed. Before I touch the fire I am not burnt; this is B C; I touch it, and am +burnt; this is A B C, <span class="tei tei-hi"><span style="font-style: italic">a</span></span> B C. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +Such familiar experimental processes are not regarded as inductions by +Dr. Whewell; but they are perfectly homogeneous with those by which, even +on his own shewing, the pyramid of science is supplied with its base. In vain +he attempts to escape from this truth by laying the most arbitrary restrictions +on the choice of examples admissible as instances of Induction: they must +neither be such as are still matter of discussion (p. 47), nor must any of them +be drawn from mental and social subjects (p. 53), nor from ordinary observation +and practical life (pp. 11-15). They must be taken exclusively from +the generalizations by which scientific thinkers have ascended to great and +comprehensive laws of natural phenomena. Now it is seldom possible, in these +complicated inquiries, to go much beyond the initial steps, without calling in +the instrument of Deduction, and the temporary aid of hypotheses; as I myself, +in common with Dr. Whewell, have maintained against the purely empirical +school. Since therefore such cases could not conveniently be selected to +illustrate the principles of mere observation and experiment, Dr. Whewell +takes advantage of their absence to represent the Experimental Methods as +serving no purpose in scientific investigation; forgetting that if those methods +had not supplied the first generalizations, there would have been no materials +for his own conception of Induction to work upon. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +His challenge, however, to point out which of the four methods are exemplified +in certain important cases of scientific inquiry, is easily answered. <span class="tei tei-q">“The +planetary paths,”</span> as far as they are a case of induction at all, (see, on this +point, the second chapter of the present Book) fall under the +Method of Agreement. The law of <span class="tei tei-q">“falling bodies,”</span> namely that they +describe spaces proportional to the squares of the times, was historically a +deduction from the first law of motion; but the experiments by which it was +verified, and by which it might have been discovered, were examples of the +Method of Agreement; and the apparent variation from the true law, caused +by the resistance of the air, was cleared up by experiments +<span lang="la" class="tei tei-foreign" xml:lang="la"><span style="font-style: italic">in vacuo</span></span>, constituting +an application of the Method of Difference. The law of <span class="tei tei-q">“refracted rays,”</span> +(the constancy of the ratio between the sines of incidence and of refraction for +each refracting substance) was ascertained by direct measurement, and therefore +by the Method of Agreement. The <span class="tei tei-q">“cosmical motions”</span> were determined +by highly complex processes of thought, in which Deduction was predominant, +but the Methods of Agreement and of Concomitant Variations had a large part +in establishing the empirical laws. Every case without exception of <span class="tei tei-q">“chemical +analysis”</span> constitutes a well marked example of the Method of Difference. To +any one acquainted with the subjects—to Dr. Whewell himself, there would +not be the smallest difficulty in setting out <span class="tei tei-q">“the A B C and +<span class="tei tei-hi"><span style="font-style: italic">a b c</span></span> elements”</span> of +these cases. +</p> +<p class="tei tei-p" style="margin-bottom: 1.00em"> +If discoveries are ever made by observation and experiment without +Deduction, the four methods are methods of discovery: but even if they were +not methods of discovery, it would not be the less true that they are the sole +methods of Proof; and in that character, even the results of Deduction are +amenable to them. The great generalizations which begin as Hypotheses +must end by being proved, and are in reality (as will be shown hereafter) +proved by the Four Methods. Now it is with Proof, as such, that Logic is +principally concerned. This distinction has indeed no chance of finding favour +with Dr. Whewell; for it is the peculiarity of his system not to recognise, in +cases of Induction, any necessity for proof. If, after assuming an hypothesis +and carefully collating it with facts, nothing is brought to light inconsistent +with it, that is, if experience does not <em class="tei tei-emph"><span style="font-style: italic">dis</span></em>prove it, he is content: at +least until a simpler hypothesis, equally consistent with experience, presents itself. If +this be Induction, doubtless there is no necessity for the four methods. But to +suppose that it is so, appears to me a radical misconception of the nature of +the evidence of physical truths. +</p></dd><dt class="tei tei-notelabel"><a id="note_86" name="note_86" href="#noteref_86">86.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Ante</span></span>, p. +<a href="#Pg378" class="tei tei-ref">378</a>.</dd><dt class="tei tei-notelabel"><a id="note_87" name="note_87" href="#noteref_87">87.</a></dt><dd class="tei tei-notetext">It seems hardly necessary to say that the word +<span class="tei tei-hi"><span style="font-style: italic">impinges</span></span>, as a general +term to express collision of forces, was here used by a figure of speech, and +not as expressive of any theory respecting the nature of force.</dd><dt class="tei tei-notelabel"><a id="note_88" name="note_88" href="#noteref_88">88.</a></dt><dd class="tei tei-notetext"><span class="tei tei-hi"><span style="font-style: italic">Essays on some Unsettled Questions of +Political Economy</span></span>, Essay V.</dd><dt class="tei tei-notelabel"><a id="note_89" name="note_89" href="#noteref_89">89.</a></dt><dd class="tei tei-notetext">There is no danger of confounding this acceptation +of the term with the peculiar employment of the phrase <span class="tei tei-q">“tangential force”</span> +in the theory of the planetary perturbations.</dd><dt class="tei tei-notelabel"><a id="note_90" name="note_90" href="#noteref_90">90.</a></dt><dd class="tei tei-notetext">Suprà, p. <a href="#Pg420" class="tei tei-ref">420</a>.</dd><dt class="tei tei-notelabel"><a id="note_91" name="note_91" href="#noteref_91">91.</a></dt><dd class="tei tei-notetext">As corroborating the +opinion that the protoxide of iron in the venous +blood is only partially carbonated, the fact has been suggested, that the system +shows great readiness to absorb an extra quantity of carbonic acid, as furnished +in effervescing drinks. In such cases the acid must combine with something, +and that something is not improbably the free protoxide. It would be worth +ascertaining whether the protoxide itself or its carbonate has the greatest facility +in absorbing oxygen and turning itself into hydrated peroxide in the lungs. +If the carbonate, then the beneficial effect, on the animal economy, of drinks +which give an artificial supply of carbonic acid to the system, would be, to +that extent, deductively established.</dd><dt class="tei tei-notelabel"><a id="note_92" name="note_92" href="#noteref_92">92.</a></dt><dd class="tei tei-notetext">It +was an old generalization in surgery, that tight bandaging had a tendency +to prevent or dissipate local inflammation. This sequence, being, in +the progress of physiological knowledge, resolved into more general laws, led +to the important surgical invention made by Dr. Arnott, the treatment of local +inflammation and tumours by means of an equable pressure, produced by a +bladder partially filled with air. The pressure, by keeping back the blood +from the part, prevents the inflammation, or the tumour, from being nourished; +in the case of inflammation, it removes the stimulus, which the organ is unfit +to receive: in the case of tumours, by keeping back the nutritive fluid it +causes the absorption of matter to exceed the supply, and the diseased mass is +gradually absorbed and disappears.</dd></dl> + </div> + <hr class="doublepage" /><div class="tei tei-div" style="margin-bottom: 5.00em; margin-top: 5.00em"> + <div id="pgfooter" class="tei tei-div" style="margin-bottom: 4.00em; margin-top: 4.00em"><pre class="pre tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em">***END OF THE PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE (VOL. 1 OF 2)*** +</pre><hr class="doublepage" /><div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"><a name="rightpageheader83" id="rightpageheader83"></a><a name="pgtoc84" id="pgtoc84"></a><a name="pdf85" id="pdf85"></a><h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">Credits</span></h1><table summary="This is a list." class="tei tei-list" style="margin-bottom: 1.00em; margin-top: 1.00em"><tbody><tr><th class="tei tei-label tei-label-gloss">August 31, 2008 </th></tr><tr><td class="tei tei-item"><table summary="This is a list." class="tei tei-list" style="margin-bottom: 1.00em; margin-top: 1.00em"><tbody><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item">Project Gutenberg TEI edition 1</td></tr><tr class="tei tei-labelitem"><th class="tei tei-label"></th><td class="tei tei-item"><span class="tei tei-respStmt"> + <span class="tei tei-name"> + Produced by David Clarke, David King, and the Online Distributed + Proofreading Team at <http://www.pgdp.net/>. + (This file was produced from images generously made available + by The Internet Archive/Canadian Libraries). + </span> + </span></td></tr></tbody></table></td></tr></tbody></table></div><hr class="doublepage" /><div class="tei tei-div" style="margin-bottom: 3.00em; margin-top: 3.00em"><a name="rightpageheader86" id="rightpageheader86"></a><a name="pgtoc87" id="pgtoc87"></a><a name="pdf88" id="pdf88"></a><h1 class="tei tei-head" style="text-align: left; margin-bottom: 3.46em; margin-top: 3.46em"><span style="font-size: 173%">A Word from Project Gutenberg</span></h1><p class="tei tei-p" style="margin-bottom: 1.00em">This file should be named + 26495-h.html or + 26495-h.zip.</p><p class="tei tei-p" style="margin-bottom: 1.00em">This and all associated files of various formats will be found + in: + + <a href="http://www.gutenberg.org/dirs/2/6/4/9/26495/" class="block tei tei-xref" style="margin-bottom: 1.80em; margin-left: 3.60em; margin-top: 1.80em; margin-right: 3.60em"><span style="font-size: 90%">http://www.gutenberg.org</span><span style="font-size: 90%">/dirs/2/6/4/9/26495/</span></a></p><p class="tei tei-p" style="margin-bottom: 1.00em">Updated editions will replace the previous one — the old + editions will be renamed.</p><p class="tei tei-p" style="margin-bottom: 1.00em">Creating the works from public domain print editions means that + no one owns a United States copyright in these works, so the + Foundation (and you!) can copy and distribute it in the United + States without permission and without paying copyright royalties. + Special rules, set forth in the General Terms of Use part of this + license, apply to copying and distributing Project Gutenberg™ electronic works + to protect the Project Gutenberg™ concept and trademark. 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