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diff --git a/26495.txt b/26495.txt new file mode 100644 index 0000000..12bec08 --- /dev/null +++ b/26495.txt @@ -0,0 +1,17546 @@ +The Project Gutenberg EBook of A System Of Logic, Ratiocinative And +Inductive (Vol. 1 of 2) by John Stuart Mill + + + +This eBook is for the use of anyone anywhere at no cost and with almost no +restrictions whatsoever. You may copy it, give it away or re-use it under +the terms of the Project Gutenberg License included with this eBook or +online at http://www.gutenberg.org/license + + + +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: US-ASCII + + +***START OF THE PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE (VOL. 1 OF 2)*** + + + + + + A SYSTEM OF LOGIC, + + RATIOCINATIVE AND INDUCTIVE, + + BEING A CONNECTED VIEW OF THE + + PRINCIPLES OF EVIDENCE, + + AND THE + + METHODS OF SCIENTIFIC INVESTIGATION. + + by + + JOHN STUART MILL. + + In Two Volumes. + + Vol. I. + + Third Edition. + + London: + + John Parker, West Strand. + + M DCCC LI. + + + + + +CONTENTS + + +PREFACE TO THE FIRST EDITION. +PREFACE TO THE THIRD EDITION. +INTRODUCTION. +BOOK I. OF NAMES AND PROPOSITIONS. + CHAPTER I. OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE. + CHAPTER II. OF NAMES. + CHAPTER III. OF THE THINGS DENOTED BY NAMES. + I. Feelings, or States of Consciousness. + II. Substances. + III. Attributes: and, first, Qualities. + IV. Relations. + V. Quantity. + VI. Attributes Concluded. + VII. General Results. + CHAPTER IV. OF PROPOSITIONS. + CHAPTER V. OF THE IMPORT OF PROPOSITIONS. + CHAPTER VI. OF PROPOSITIONS MERELY VERBAL. + CHAPTER VII. OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES. + CHAPTER VIII. OF DEFINITION. +BOOK II. OF REASONING. + CHAPTER I. OF INFERENCE, OR REASONING, IN GENERAL. + CHAPTER II. OF RATIOCINATION, OR SYLLOGISM. + CHAPTER III. OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE SYLLOGISM. + CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES. + CHAPTER V. OF DEMONSTRATION, AND NECESSARY TRUTHS. + CHAPTER VI. THE SAME SUBJECT CONTINUED. +BOOK III. OF INDUCTION. + CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL. + CHAPTER II. OF INDUCTIONS IMPROPERLY SO CALLED. + CHAPTER III. OF THE GROUND OF INDUCTION. + CHAPTER IV. OF LAWS OF NATURE. + CHAPTER V. OF THE LAW OF UNIVERSAL CAUSATION. + CHAPTER VI. OF THE COMPOSITION OF CAUSES. + CHAPTER VII. OF OBSERVATION AND EXPERIMENT. + CHAPTER VIII. OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY. + CHAPTER IX. MISCELLANEOUS EXAMPLES OF THE FOUR METHODS. + CHAPTER X. OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS. + CHAPTER XI. OF THE DEDUCTIVE METHOD. + CHAPTER XII. OF THE EXPLANATION OF LAWS OF NATURE. + CHAPTER XIII. MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF + NATURE. +Footnotes + + + + + + +PREFACE TO THE FIRST EDITION. + + +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. + +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 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. + +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. + +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 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. + +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 _Edinburgh Review_) have not scrupled to pronounce it +impossible.(1) 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. + +Whatever may be the value of what the author 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 +_History of the Inductive Sciences_, the corresponding portion of this +work would probably not have been written. + +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. + + + + + +PREFACE TO THE THIRD EDITION. + + +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. + +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. + +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 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. + +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. + + + + + +INTRODUCTION. + + +§ 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. + +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 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. + +§ 2. Logic has often been called the Art of Reasoning. A writer(2) 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 be _done_, it is often +requisite to _know_ the nature and properties of many things. + +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. + +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. + +§ 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 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. + +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 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. + +§ 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. + +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. + +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 the number of the +primitive data, or of the conclusions which can be drawn from these. + +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. + +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. + +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, 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.(3) + +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 +_in_ 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 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 a priori 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. + +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. + +§ 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 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. + +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. + +It is in this sense that logic is, what Bacon so expressively called it, +_ars artium_; 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 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. + +§ 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. + +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 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. + +§ 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. + +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 _pari __ passu_ 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. + +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. + +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 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. + +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. + +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 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. + + + + + +BOOK I. OF NAMES AND PROPOSITIONS. + + +"La scolastique, qui produisit dans la logique, comme dans la morale, et +dans une partie de la metaphysique, une subtilite, une precision d'idees, +dont l'habitude inconnue aux anciens, a contribue plus qu'on ne croit au +progres de la bonne philosophie."--CONDORCET, _Vie de Turgot_. + + + + +CHAPTER I. OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE. + + +§ 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. + +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. + +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 +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. + +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. + +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. + +§ 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, 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. + +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, _discourse_, _in +which something is affirmed or denied of something_. Thus, in the +proposition, Gold is yellow, the quality _yellow_ is affirmed of the +substance _gold_. In the proposition, Franklin was not born in England, +the fact expressed by the words _born in England_ is denied of the man +Franklin. + +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 +_round_, which denotes the quality affirmed, or (as the phrase is) +predicated: _the earth_, words denoting the object which that quality is +affirmed of, compose the Subject; the word _is_, which serves as the +connecting mark between the subject and predicate, to show that one of +them is affirmed of the other, is called the Copula. + +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, _one_ object is not sufficient; the simplest act of belief +supposes, and has something to do with, _two_ objects: two names, to say +the least; and (since the names must be names of something) two _nameable +things_. A large class of thinkers would cut the matter short by saying, +two _ideas_. 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 _two_ 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. + +I may say, for instance, "the sun." 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, "the sun exists." 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 involved in the +first; for the sun may be conceived as no longer existing. "The sun" does +not convey all the meaning that is conveyed by "the sun exists:" "my +father" does not include all the meaning of "my father exists," for he may +be dead; "a round square" does not include the meaning of "a round square +exists," for it does not and cannot exist. When I say, "the sun," "my +father," or a "round square," 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, "the sun exists," "my father exists," or "a round square exists," 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. + +§ 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. + +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 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 _catalogue raisonne_ as the notions which are in the minds of all +mankind? + +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. + + + + +CHAPTER II. OF NAMES. + + +§ 1. "A name," says Hobbes,(4) "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(5) before in his mind." 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. + +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. "But seeing," he +continues, "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 _stone_ 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." + +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 calling the word _sun_ 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, "the sun is the cause of day," 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 _name_ 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. + +But the question now arises, of what things? and to answer this it is +necessary to take into consideration the different kinds of names. + +§ 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 _of_, _to_, _truly_, _often_; the +inflected cases of nouns substantive, as _me_, _him_, _John's_;(6) and +even adjectives, as _large_, _heavy_. 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, 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 _suppositio materialis_ 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 _body_ +fell, A truly _important fact_ was asserted, A _member_ of _parliament_ +was in the room. + +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 _round_, and _a +round object_, 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. + +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 +{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON WITH VARIA~}{~GREEK SMALL LETTER NU~}, with, and {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER OMEGA~}, to predicate, because it was only _with_ some +other 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 _mixed_ 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. + +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, +"the place which the wisdom or policy of antiquity had destined for the +residence of the Abyssinian princes," 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 "John Nokes, who was the mayor of +the town," 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, "died yesterday." Suppose, however, that the words had been, +John Nokes _and_ 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. + +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 the words they are composed of, +but according to their signification. + +§ 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, _this stone_: "this" and "stone" 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. + +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 +_general_ propositions; to affirm or deny any predicate of an indefinite +number of things at once. The distinction, therefore, between _general_ +names, and _individual_ or _singular_ names, is fundamental; and may be +considered as the first grand division of names. + +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. + +Thus, _man_ is capable of being truly affirmed of John, Peter, George, +Mary, and other persons without assignable 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 _John_ 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 _sense_ at all, +consequently not in the same sense. "The present queen of England" 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. + +It is not unusual, by way of explaining what is meant by a general name, +to say that it is the name of a _class_. 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 _class_: "A class is the indefinite multitude of individuals +denoted by a general name." + +It is necessary to distinguish _general_ from _collective_ names. A +general name is one which can be predicated of _each_ individual of a +multitude; a collective name cannot be predicated of each separately, but +only of all taken together. "The 76th regiment of foot," 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. + +"The 76th regiment" is a collective name, but not a general one: "a +regiment" is both a collective and a general name. General with respect to +all individual regiments, of each of which separately it can be affirmed; +collective with respect to the individual soldiers, of whom any regiment +is composed. + +§ 4. The second general division of names is into _concrete_ and +_abstract_. 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, +_John_, _the sea_, _this table_, are names of things. _White_, 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. _Old_ is a name of +things; _old age_ is a name of one of their attributes. + +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 "abstract name" 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 +_general name_, the exact equivalent of which exists in all languages I am +acquainted with, was already available for the purpose to which _abstract_ +has been misappropriated, while the misappropriation leaves that important +class of words, the names of attributes, without 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 _abstract_, then, I shall always mean the opposite of +_concrete_: by an abstract name, the name of an attribute; by a concrete +name, the name of an object. + +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 _colour_, 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 _attribute_ 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. + +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 _white_, for +example, is as much the name of the colour, as _whiteness_ 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 +colour. The reverse is the case with the word whiteness; what we affirm to +_be_ 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 _imply_ an +attribute of some sort; but they are not names of the attribute; it has +its own proper abstract name. + +§ 5. This leads to the consideration of a third great division of names, +into _connotative_ and _non-connotative_, the latter sometimes, but +improperly, called _absolute_. 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. + +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 _white_, _long_, +_virtuous_, 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, _connotes_,(7) the attribute _whiteness_. The word white is +not predicated of the attribute, but of the subjects, snow, &c.; but when +we predicate 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. + +All concrete general names are connotative. The word _man_, 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 _man_, +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 _directly_, the attributes _indirectly_; it +_denotes_ the subjects, and implies, or involves, or indicates, or as we +shall say henceforth, _connotes_, the attributes. It is a connotative +name. + +Connotative names have hence been also called _denominative_, 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.(8) + +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 _fault_; equivalent to _bad_ or _hurtful quality_. 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. + +In regard to those concrete names which are not general but individual, a +distinction must be made. + +Proper names are not connotative: they denote the individuals 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 Caesar, 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. + +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. "The sun" is a name of this +description; "God," 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 _in fact_ 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, "the _only_ son of John +Stiles;" "the _first_ emperor of Rome." 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. "The father of Socrates," is an example of the one kind (since +Socrates could not have had two fathers); "the author of the Iliad," "the +murderer of Henri Quatre," 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 +_the_ implies that, in fact, this was not the case. What is here done by +the word _the_, is done in other cases by the context: thus, "Caesar's +army" is an individual name, if it appears from the context that the army +meant is that which Caesar commanded in a particular battle. The still more +general expressions, "the Roman army," or "the Christian army," 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 _general_ 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: "the present prime minister of +England." Prime Minister of England is a general name; the attributes +which it connotes may be possessed 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 _present_, 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. + +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 _denote_, +but in what they _connote_. The only names of objects which connote +nothing are _proper_ names; and these have, strictly speaking, no +signification. + +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. + +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 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. + +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, "built of +marble." 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. + +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 predicable +of, or in other words _denotes_, 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. + +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 _man_, 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 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. + +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 _man_, or _white_, 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 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 _proprio motu_. 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.(9) Even scientific +writers have aided in this perversion of general language from its +purpose; sometimes because, 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. + +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. + +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 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. + +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 _post_, for example, or the word _box_, 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.(10) + +§ 6. The fourth principal division of names, is into _positive_ and +_negative_. Positive, as _man_, _tree_, _good_; negative, as _not-many_, +_not-tree_, _not-good_. 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, _not-white_ 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. + +Names which are positive in form are often negative in reality, and others +are really positive though their form is negative. The word +_inconvenient_, 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 _unpleasant_, notwithstanding its +negative form, does not connote the mere absence of pleasantness, but a +less degree of what is signified by the word _painful_, which, it is +hardly necessary to say, is positive. _Idle_, on the other hand, is a word +which, though positive in form, expresses nothing but what would be +signified either by the phrase _not working_, or by the phrase _not +disposed to work_; and _sober_, either by _not drunk_ or by _not drunken_. + +There is a class of names called _privative_. 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 _blind_, which is not equivalent to +_not seeing_, or to _not capable of seeing_, 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. + +§ 7. The fifth leading division of names is into _relative_ and +_absolute_, or let us rather say, _relative_ and _non-relative_; 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 _civil_ in the language of jurisprudence, which stands for the +opposite of criminal, the opposite of ecclesiastical, the opposite of +military, the opposite of political, in short, the opposite of any +positive word which wants a negative. + +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 _correlative_ 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. + +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 +_like_ has its abstract _likeness_; 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? + +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, 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. + +It is obvious, in fact, that if we take any two correlative names, +_father_ and _son_, for instance, although the objects _de_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 _attribute_; 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 +_constitute_ the relation; the schoolmen called it the foundation of the +relation, _fundamentum relationis_. + +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. _Father_ connotes the fact, regarded as constituting an +attribute of A: _son_ 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 are +concerned, an attribute grounded on that fact may be ascribed to either of +these individuals. + +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;(11) but those of its attributes which +are expressed by relative names, would on that supposition be swept away. + +§ 8. Names have been further distinguished into _univocal_ and +_aequivocal_: 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 _in the same sense_; +but it is aequivocal, or applied aequivocally, 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 aequivocal or ambiguous word is +not one name, but two names, accidentally coinciding in sound. _File_ +standing for an iron instrument, and _file_ standing for a line of +soldiers, have no more title to be considered one word, because written +alike, than _grease_ and _Greece_ have, because they are pronounced alike. +They are one sound, appropriated to form two different words. + +An intermediate case is that of a name used _analogically_ 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. + + + + +CHAPTER III. OF THE THINGS DENOTED BY NAMES. + + +§ 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. + +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 _summa genera_, _i.e._ 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:-- + + {~GREEK CAPITAL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~}, Substantia. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER OMICRON WITH VARIA~}{~GREEK SMALL LETTER NU~}, Quantitas. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER NU~}, Qualitas. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}, Relatio. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER NU~}, Actio. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER ALPHA WITH OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}, Passio. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}, Ubi. + {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}, Quando. + {~GREEK CAPITAL LETTER KAPPA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER THETA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~}, Situs. + {~GREEK CAPITAL LETTER EPSILON~}{~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}, Habitus. + +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 _rationale_ 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 _summum genus_ 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, and +the like? Probably all these would have been placed by the Aristotelian +school in the categories of _actio_ and _passio_; 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. + +§ 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 _object_, or of a _thing_, we are almost always +supposed to mean a substance. There seems a kind of contradiction in using +such an expression as that one _thing_ 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 _being_: originally the present +participle of a verb which in one of its meanings is exactly equivalent to +the verb _exist_; and therefore suitable, even by its grammatical +formation, to be the concrete of the abstract _existence_. But this word, +strange as the fact may appear, is still more completely spoiled for the +purpose which it seemed expressly made for, than the word Thing. _Being_ +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. + +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 _essence_, born at the same time and of the same parents, +scarcely underwent a more complete transformation when, from being the +abstract of the verb _to be_, 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 _entity_, you are indeed somewhat less strongly +suspected of believing it to be a substance than if you called it a +_being_; 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 _separate_ 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. + +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 which brings the +meaning home to the mind, as it were by a flash. + +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. + +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. + + + +I. Feelings, or States of Consciousness. + + +§ 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 _feels_, 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 sensations +of a single sense, that of touch, needs not be more particularly adverted +to. + +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. + +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 _white_. We have a name for the quality in those objects, to +which we ascribe the sensation; the name _whiteness_. 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 _does_, might very +well be _conceived_ 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 _perceptible_ 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, +_colour_ 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 _properties_. + +§ 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 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. + +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 _act_ 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. + +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 may be +legitimate or the reverse. Far less do I mean (as Dr. Whewell seems to +suppose must be meant in an analogous case(12)) to indicate that as they +are "_merely_ states of mind," 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 _perceive_, the meaning of these words is, that receiving +the sensations, I intuitively _believe_ 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. + +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 _acts_ of the mind and +its merely passive _states_; 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 +facts with which they may be connected, either as effects or as causes. + +§ 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 _volitions_, 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 +_actions_ 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. + +§ 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. + + + +II. Substances. + + +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 _of_ something: +colour, for example, must be the colour _of_ something; goodness must be +the goodness _of_ 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 _of_ after its name. +A stone is not the stone _of_ anything; the moon is not the moon _of_ +anything, but simply the moon. Unless, indeed, the name which we choose to +give to the substance be a relative name; if so, it must be followed +either by _of_ 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 _something_ might be +destroyed, and the substance might still subsist. Thus, a father must be +the father _of_ 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. + +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 _of_ something, it seems highly necessary to +understand what is meant by _of_: 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. + +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. + +§ 7. A Body, according to the received doctrine of modern metaphysicians, +may be defined the external cause 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. + +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. + +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 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. + +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 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. + +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 _substratum_; and its attributes (as they expressed +themselves) _inhered_, literally _stuck_, 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. + +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 _all we know_ +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 "Things in themselves," 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 (_Noumenon_) to denote what the +thing is in itself, as contrasted with the _representation_ 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.(13) There is not the slightest reason for 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?(14) 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 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. + +§ 8. Body having now been defined the external cause, and (according to +the more reasonable opinion) the _hidden_ 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 "thread of consciousness;" 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 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. + +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 _subject_ (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. + + + +III. Attributes: and, first, Qualities. + + +§ 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. + +Attributes are usually distributed under the three heads of Quality, +Quantity, and Relation. We shall come to the two latter presently: in the +first place we shall confine ourselves to the former. + +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. + +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 _know_ +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 _ground_ 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 _power_ inherent in +it; something _in virtue_ 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. + +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 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 _quality_ +and _sensation_ 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 _per se_ 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 Moliere +so happily ridiculed when he made one of his pedantic physicians account +for the fact that "l'opium endormit," by the maxim "parcequ'il a une vertu +soporifique." + +It is evident that when the physician stated that opium had "une vertu +soporifique," he did not account for, but merely asserted over again, the +fact that it _endormit_. 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, 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 _power_ of +producing it. + +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 _grounded_ 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 _foundation_ 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. + + + +IV. Relations. + + +§ 10. The _qualities_ 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 Relation, the foundation of the attribute must be +something in which other objects are concerned besides itself and the +percipient. + +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. + +What, then, is the character which is possessed in common by states of +circumstances so heterogeneous and discordant as these: one thing _like_ +another; one thing _unlike_ another; one thing _near_ another; one thing +_far from_ another; one thing _before_, _after_, _along with_ another; one +thing _greater_, _equal_, _less_, than another; one thing the _cause_ of +another, the _effect_ of another; one person the _master_, _servant_, +_child_, _parent_, _debtor_, _creditor_, _sovereign_, _subject_, +_attorney_, _client_, of another, and so on? + +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 _fact_ 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 _fundamentum +relationis_. Thus in the relation of greater and less between two +magnitudes, the _fundamentum relationis_ 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 _fundamentum relationis_ 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 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. + +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 _fundamentum relationis_ +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 external +objects nor the minds making their existence known otherwise than by the +states of consciousness. + +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. + +§ 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 _like_; the last two +_unlike_. What is the fact or phenomenon constituting the _fundamentum_ 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 _after_ +having the two sensations of colour, or whether (like the feeling of their +succession) it is involved 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 _sui generis_. They are attributes grounded on +facts, that is, on states of consciousness, but on states which are +peculiar, unresolvable, and inexplicable. + +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. + +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, +resemble each other. We may also say that two relations are alike. The +fact of resemblance between relations is sometimes called _analogy_, +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 _fundamentum relationis_. + +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 _fundamenta +relationis_, 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. + +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; 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 _same_ sensation +or emotion to-day that it did yesterday, or the _same_ which it gives to +some other person. This is evidently an incorrect application of the word +_same_; 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 _same_ disease; that two persons hold the +_same_ 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. + +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 _quantity_. 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. + + + +V. Quantity. + + +§ 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 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. + + + +VI. Attributes Concluded. + + +§ 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 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. + +§ 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, _mutatis mutandis_, 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. + +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 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. + +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. + + + +VII. General Results. + + +§ 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. + +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 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. + +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. + +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, 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. + +As the result, therefore, of our analysis, we obtain the following as an +enumeration and classification of all Nameable Things:-- + +1st. Feelings, or States of Consciousness. + +2nd. The Minds which experience those feelings. + +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. + +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. + +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. + +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. + +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, 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. + + + + +CHAPTER IV. OF PROPOSITIONS. + + +§ 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. + +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 +_inflection_; as when we say, Fire burns; the change of the second word +from _burn_ to _burns_ showing that we mean to affirm the predicate burn +of the subject fire. But this function is more commonly fulfilled by the +word _is_, when an affirmation is intended, _is not_, when a negation; or +by some other part of the verb _to be_. The word which thus serves the +purpose of a sign of predication is called, as we formerly observed, the +_copula_. 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. + +It is apt to be supposed that the copula is something more than a mere +sign of predication; that it also signifies _existence_. In the +proposition, Socrates is just, it may seem to be implied not only that the +quality _just_ can be affirmed of Socrates, but moreover that Socrates +_is_, that is to say, exists. This, however, only shows that there is an +ambiguity in the word _is_; 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. + +Many volumes might be filled with the frivolous speculations concerning +the nature of Being, ({~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~} {~GREEK SMALL LETTER OMICRON WITH PSILI AND OXIA~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~}, Ens, Entitas, Essentia, and the like,) +which have arisen from overlooking this double meaning of the words _to +be_; from supposing that when it signifies _to exist_, and when it +signifies to _be_ some specified thing, as to _be_ a man, to _be_ +Socrates, to _be_ seen or spoken of, to _be_ a phantom, even to _be_ 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, 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(15) +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. + +We shall now briefly review the principal distinctions which exist among +propositions, and the technical terms most commonly in use to express +those distinctions. + +§ 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 _affirmed_ of the subject; as, Caesar is dead. A negative +proposition is that in which the predicate is _denied_ of the subject; as, +Caesar is not dead. The copula, in this last species of proposition, +consists of the words _is not_, which are the sign of negation; _is_ being +the sign of affirmation. + +Some logicians, among whom may be mentioned Hobbes, state this distinction +differently; they recognise only one form of copula, _is_, and attach the +negative sign to the predicate. "Caesar is dead," and "Caesar is not dead," +according to these writers, are propositions agreeing not in the subject +and predicate, but in the subject only. They do not consider "dead," but +"not dead," 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 _absence_ 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 _is_, but that something is _not_; 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 Caesar'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. + +A remark of a similar nature may be applied to most of those distinctions +among propositions which are said to have reference to their _modality_; +as, difference of tense or time; the sun _did_ rise, the sun _is_ rising, +the sun _will_ 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 _an object having +risen_, The sun is _an object now rising_, The sun is _an object to rise +hereafter_. 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 _sun's_ 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, Caesar _may_ be dead; Caesar is _perhaps_ dead; it +is _possible_ that Caesar 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 "Caesar may be dead" means "I am not +sure that Caesar is alive." + +§ 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. + +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: Caesar is dead, and Brutus is alive: or even this, Caesar is dead, +_but_ 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 _and_ and +_but_ 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, Caesar is dead and Brutus is alive, are equivalent to +these: Caesar is dead; Brutus is alive; it is desired that the two +preceding propositions should be thought of together. If the words were, +Caesar is dead _but_ Brutus is alive, the sense would be equivalent to the +same three propositions together with a fourth; "between the two preceding +propositions there exists a contrast:" viz., either between the two facts +themselves, or between the feelings with which it is desired that they +should be regarded. + +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, "Peter and James +preached at Jerusalem and in Galilee," which contains four propositions: +Peter preached at Jerusalem, Peter preached in Galilee, James preached at +Jerusalem, James preached in Galilee. + +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 example of this is, when the simple propositions are +connected by the particle _or_; as, Either A is B _or_ C is D; or by the +particle _if_; as, A is B _if_ C is D. In the former case, the proposition +is called _disjunctive_, in the latter _conditional_: the name +_hypothetical_ 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. "Either A is B or C is D," means, "if A is not B, C is +D; and if C is not D, A is B." 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 _categorical_. + +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? +"The Koran" is not the subject of it, nor is "Mahomet:" for nothing is +affirmed or denied either of the Koran or of Mahomet. The real subject of +the predication is the entire proposition, "Mahomet is the prophet of +God;" and the affirmation is, that this is a legitimate inference from the +proposition, "The Koran comes from God." 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 to propositions; of this form--"an inference from so and so." A +fresh instance is here afforded of the remark, that all particles are +abbreviations; since "_If_ A is B, C is D," is found to be an abbreviation +of the following: "The proposition C is D, is a legitimate inference from +the proposition A is B." + +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 +_the proposition_, "the whole is greater than its part;" _the +proposition_, "the Holy Ghost proceeds from the Father alone;" _the +proposition_, "kings have a divine right;" _the proposition_, "the Pope is +infallible." + +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. + +§ 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: + +_All men_ are mortal-- Universal. +_Some men_ are mortal-- Particular. +_Man_ is mortal-- Indefinite. +_Julius Caesar_ is mortal-- Singular. + +The proposition is Singular, when the subject is an individual name. The +individual name needs not be a proper name. "The Founder of Christianity +was crucified," is as much a singular proposition as "Christ was +crucified." + +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 _all_ 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 "some men are +wise," "some men are not wise," are particular propositions; the predicate +_wise_ 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, "all _properly instructed_ men are wise." There +are other forms of particular propositions: as, "_Most_ men are +imperfectly educated:" it being immaterial how large a portion of the +subject the predicate is asserted of, as long as it is left uncertain how +that portion is to be distinguished from the rest. + +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 _doubtful_ 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 "Man is mortal," 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, "Wine is good," it is understood with +equal readiness, though for somewhat different reasons, that the assertion +is not intended to be universal, but particular. + +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 _distributed_, 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. + +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. + +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. + + + + +CHAPTER V. OF THE IMPORT OF PROPOSITIONS. + + +§ 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. + +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. + +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 _idea_ 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 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. + +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 +of the ground, and of a spade, and of all the other things I am operating +upon, and unless I put those ideas together.(16) 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. + +The notion that what is of primary importance to the logician in a +proposition, is the relation between the two _ideas_ corresponding to the +subject and predicate, (instead of the relation between the two +_phenomena_ 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, 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. + +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? + +§ 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 _living being_ is a name of everything of which _man_ is a +name. All men are six feet high, is not true, because _six feet high_ is +not a name of everything (though it is of some things) of which _man_ is a +name. + +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. + +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 proposition a proposition, conveys no +more than this scanty amount of meaning, that same collocation combined +with other circumstances, that _form_ combined with other _matter_, does +convey more, and much more. + +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 _connotation_ +of words; and sought for their meaning exclusively in what they _denote_: +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. + +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 _denote_, or in +the language of Hobbes, (language so far correct,) are names of. + +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, 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 _happen_ to fit the same person because of a +certain _fact_, 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 _connotation_ of the names. + +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 _mortal_, 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 _man_ are always +accompanied by the attribute connoted by _mortal_, it will follow as a +consequence, that the class _man_ will be wholly included in the class +_mortal_, and that _mortal_ will be a name of all things of which _man_ 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 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 "called by the +name," 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. + +§ 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 _class_, _i.e._, +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. +"Plato is a philosopher," 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 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 _is_ 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. + +How widely these views of predication have prevailed, is evident from +this, that they are the basis of the celebrated _dictum de omni et nullo_. +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. + +This theory appears to me a signal example of a logical error very often +committed in logic, that of {~GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}, 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 is, I conceive, founded on a latent misconception of the +nature of classification. + +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 _toties quoties_ 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. + +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. + +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 _meaning_ 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, 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. + +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. + +Although, however, Hobbes' theory of Predication, according to the +well-known remark of Leibnitz, and the avowal of Hobbes himself,(17) +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 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;(18) 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. "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 upon our senses, but by most men they are +called _accidents_."(19) 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 _because_ 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. + +§ 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: "The +summit of Chimborazo is white." The word white connotes an attribute which +is possessed by the individual object designated by the words, "summit of +Chimborazo," 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. + +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: "All men are mortal." 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 _individually_ 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: 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 _constantly accompany_ the former set. Whatever has the +attributes of man has the attribute of mortality; mortality constantly +accompanies the attributes of man. + +If it be remembered that every attribute is _grounded_ on some fact or +phenomenon, either of outward sense or of inward consciousness, and that +to _possess_ 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 _when_; for +the connotation of the word _mortal_ goes no farther than to the +occurrence of the phenomenon at some time or other, leaving the precise +time undecided. + +§ 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. +"Worthy of honour" 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, honour, would be followed in our minds +by another inward feeling, approval. + +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 _conjunction_, in short, so that +where the one is found, we may calculate on finding both. + +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, _mutatis mutandis_, 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 _noumenon_ Socrates, was existing, and doing or 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. + +§ 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 _fundamentum_, 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 _equal_ 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 +_followed_ 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. + +It is sometimes said that all propositions whatever, of which the +predicate is a general name, do, in point of fact, 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. + +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 _metal_, or the class _man_, 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. + +But we remarked some time ago, (and the reasons of the remark will be more +fully entered into in a subsequent Book,(20)) that there is sometimes a +convenience in extending 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 _either_ 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 _considered_, or _may be ranked_, 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. + +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 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 _likeness_ 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. + +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. + +§ 7. In the foregoing inquiry into the import of Propositions, we have +thought it necessary to analyse _directly_ 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; 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. + +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. + +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 _fundamenta_ 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,--"Thoughtlessness is dangerous." +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 the predicate as +well as the subject are abstract names: "Whiteness is a colour;" or "The +colour of snow is a whiteness." 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. "Prudence is a virtue:" +this may be rendered, "All prudent persons, _in so far as_ prudent, are +virtuous:" "Courage is deserving of honour," thus, "All courageous persons +are deserving of honour _in so far_ as they are courageous;" which is +equivalent to this--"All courageous persons deserve an addition to the +honour, or a diminution of the disgrace, which would attach to them on +other grounds." + +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:--"Prudence is a virtue." Let us substitute for the word virtue +an equivalent but more definite expression, such as "a mental quality +beneficial to society," or "a mental quality pleasing to God," 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 _subjects_ of the attribute, and +prudential conduct, which may be called the _foundation_ 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 _persons_? +No; except _in so far_ 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 _conduct_, 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 _so far as_ +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, +"Prudence is a virtue," is an universal proposition. What is it, then, +upon which the proposition affirms the effects in question to be +universally consequent? Upon that _in_ 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. + +And as these five are the only things which can be affirmed, so are they +the only things which can be denied. "No horses are web-footed" 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. "Some birds are web-footed," affirms that, with the attributes +connoted by _bird_, the phenomenon web-feet is sometimes coexistent: "Some +birds are not web-footed," 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. + + + + +CHAPTER VI. OF PROPOSITIONS MERELY VERBAL. + + +§ 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. + +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, 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. + +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 _essential_, and what were called _accidental_, +propositions, and between essential and accidental properties or +attributes. + +§ 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 _essence_ 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 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 _substantiae secundae_ or general substances, +and _substantial forms_, 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 _man_ cannot be conceived without +rationality. But though _man_ 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 _thing_, 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. + +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 _Isagoge_, 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 +{~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}: but by altering any property which was of its essence, you made +it _another thing_, {~GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}.(21) To a modern it is obvious that between the +change which only makes a thing different, and the change which makes it +_another thing_, 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 {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}: melt it, and it +becomes {~GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}, another thing, namely, water. Now it is really the same +thing, _i.e._ 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 _another thing_; 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 _general +substance_, called _Ice in general_, which substance, together with all +the properties that belonged to it, _inhered_ 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.(22) + +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 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 _man_, for the meaning +of the word includes all this: and, that every _man_ 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. + +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 _exists_ 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, 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. + +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. + +§ 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 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; _i.e._ 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 Caesar +is a rational being. This followed very naturally if genera and species +were to be considered as entities, distinct from, but _inhering_ in, the +individuals composing them. If _man_ was a substance inhering in each +individual man, the _essence_ of man (whatever that might mean) was +naturally supposed to accompany it; to inhere in John Thompson, and to +form the _common essence_ of Thompson and Julius Caesar. 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? + +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 Third Book.(23) 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. + +§ 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 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. + +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 _essence_ +of the species: _Omne corpus est substantia_, _Omne animal est corpus_, +_Omnis homo est corpus_, _Omnis homo est animal_, _Omnis homo est +rationalis_, 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. + +§ 5. With respect to propositions which do convey information--which 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. + +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 _evidence of_, are a _mark_ +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. + +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. + +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, 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 _mark_ or _evidence_ 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. + + + + +CHAPTER VII. OF THE NATURE OF CLASSIFICATION, AND THE FIVE PREDICABLES. + + +§ 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, _ipso facto_, 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. + +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 +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, +_Plantigrades_, _Digitigrades_, &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. + +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 forbear to treat here, without leaving the theory of general names, +and of their employment in predication, mutilated and formless. + +§ 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:-- + +A _genus_ of the thing ({~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER FINAL SIGMA~}). +A _species_ ({~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER FINAL SIGMA~}). +A _differentia_ ({~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER PHI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}). +A _proprium_ ({~GREEK SMALL LETTER IOTA WITH PSILI~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER NU~}). +An _accidens_ ({~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER FINAL SIGMA~}). + +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 differentiae; but the same name is referred to +one or another Predicable, according to the subject of which it is +predicated on the particular occasion. _Animal_, for instance, is a genus +with respect to man, or John; a species with respect to Substance, or +Being. _Rectangular_ is one of the Differentiae 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 _de_notes, and on the place +which, in some given classification, that class occupies relatively to the +particular subject. + +§ 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. _Biped_, or +_two-footed animal_, may also be considered a genus, of which man and bird +are two species. _Taste_ is a genus, of which sweet taste, sour taste, +salt taste, &c. are species. _Virtue_ is a genus; justice, prudence, +courage, fortitude, generosity, &c. are its species. + +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. + +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. 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 _name_ mortal; and by +predicating the name, we may be said, in an intelligible sense, to +predicate what the name expresses, the _attribute_ mortality; but in no +allowable sense of the word predication do we predicate of man the _class_ +mortal. We predicate of him the fact of _belonging_ to the class. + +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: _biped_ +would not have been admitted to be a genus with reference to man, but a +_proprium_ or _accidens_ only. It was requisite, according to their +theory, that genus and species should be of the _essence_ of the subject. +_Animal_ was of the essence of man; _biped_ was not. And in every +classification they considered some one class as the lowest or _infima_ +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. + +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 essence of the +class to which that individual was most familiarly referred. + +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 _in kind_ (_genere_ +or _specie_), 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 _kinds_, 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. + +§ 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. + +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, 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. + +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 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. + +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 _accidents_ 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 _kind_, and spoke of it as being an _essential_ difference, +which is also one of the usual meanings of that vague expression at the +present day. + +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 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. + +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, _account for_ 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 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. + +When the _infima species_, 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 +_flat-nosed_; 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. + +We are now able to fix the logical meaning of these 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 Praedicabilis 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. + +§ 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 _essence_ of the +subject. + +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 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, _i.e._, 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 _infima species_, to be the essence of the +individual too; for it was their maxim, that the species contained the +"whole essence" 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. + +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. + +From the fact that the genus includes the species, in other words +_de_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. + +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 _existing_ things, although by so doing they might not exhaust the +connotation of the name. + +§ 6. And here, to prevent the notion of differentia from being restricted +within too narrow limits, it is necessary 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. + +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; _a fortiori_ must we be warranted, when our genera +and species _are_ real genera and species, in marking the distinction +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 "four incisors in each jaw, tusks +solitary, and erect posture." 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 Linnaean system it connotes the number of incisor and canine teeth, +but does not connote rationality nor any particular form. The word _man_ +has, therefore, two different meanings; although not commonly considered +as ambiguous, because it happens in both cases to _de_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 Linnaeus'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, who adhere to the Linnaean 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. + +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 "the colour produced by the mixture of all the simple rays;" 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.(24) + +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. + +§ 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. + +In the Aristotelian phraseology, Genus and Differentia are of the +_essence_ 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 Accidens, on the other hand, form no part of the +essence, but are predicated of the species only _accidentally_. 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 _accidentally_, +indeed, but _necessarily_; 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; _e.g._ 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. + +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. + +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 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 _demonstration_. 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 _causation_. 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 +_necessarily_; that is to say, it _cannot but_ follow, consistently with +some law which we regard as a part of the constitution either of our +thinking faculty or of the universe. + +§ 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 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. + +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. _A fortiori_ 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. + + + + +CHAPTER VIII. OF DEFINITION. + + +§ 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. + +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. + +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 "John Thomson" to say he is "the son of General Thomson;" for the name +John Thomson does not express this. Neither is it any definition of "John +Thomson" to say he is "the man now crossing the street." These +propositions may serve to make known who is the particular man to whom the +name belongs; 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. + +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: "Man" (or whatsover the word may be) "is a name connoting such and +such attributes," or "is a name which, when predicated of anything, +signifies the possession of such and such attributes by that thing." 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. + +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, "Man is a human being," 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 _animal_, shaped so and so. + +The definition of a name, according to this view of it, is the sum total +of all the _essential_ 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 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 _analysis_. 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. + +§ 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, +"white," which connotes nothing but whiteness; "rational," 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: "White is +a name connoting the attribute whiteness." 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 _white_, it is obvious +that in the case of _rational_ some further explanation may be given of +its meaning than is contained in the proposition, "Rational is that which +possesses the attribute of reason;" 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. + +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 _fault_ may be defined, "a quality productive of evil or +inconvenience." Sometimes, again, the attribute to be defined is not one +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 _a human being_ be this, "a being, corporeal, animated, +rational, and shaped so and so," the definition of _humanity_ will be, +corporeity and animal life, combined with rationality, and with such and +such a shape. + +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. + +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 (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 _sensation of white_ 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. + +§ 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. + +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 _de_notes; although not embracing the whole, and +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. + +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 "man;" 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. + +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 _per genus +et differentiam_. 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 _per genus et +differentias_, rather than _differentiam_. It would include, with the name +of the superior genus, not merely _some_ attribute which distinguishes the +species intended to be defined from all other species of the same genus, +but _all_ 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 +differentiae, is not tenable. It was early remarked by logicians, that the +_summum genus_ 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. + +§ 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 _essence_ 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. + +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, should be _convertible_ 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. + +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, "Man is a +mammiferous animal having two hands," which is the scientific definition +of man considered as one of the species in Cuvier's distribution of the +animal kingdom. + +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 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. + +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 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 _differentiae_ +which form the fixed connotation of the word Acid, as a term of chemical +science. + +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 differentiae 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. + +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 +differentiae for defining its name. + +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 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 _per genus et +differentiam_, 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. + +§ 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. + +This opinion was held by the ancient philosophers, and by their followers, +with the exception of the Nominalists; 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 _Logic_.(25) In a review of that work published by me +in the _Westminster Review_ 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. + +"The distinction between nominal and real definitions, 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 +'explain and unfold the nature of the thing.' 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. 'A +centaur is an animal with the upper parts of a man and the lower parts of +a horse,' and 'A triangle is a rectilineal figure with three sides,' are, +in form, expressions precisely similar; although in the former it is not +implied that any _thing_, conformable to the term, really exists, while in +the latter it is; as may be seen by substituting, in both definitions, the +word _means_ for _is_. In the first expression, 'A centaur means an +animal,' &c., the sense would remain unchanged: in the second 'A triangle +means,' &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. + +"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 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, 'There may exist +a figure, bounded by three straight lines:' the other, 'And this figure +may be termed a triangle.' 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." + +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. + +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 "unfolding the nature of the thing," 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 to affirm as broadly as any of his +predecessors, that the {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~}, _principia_, 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. + +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? + +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. "A figure may exist, +having all the points in the line which bounds it equally distant from a +single point within it:" "Any figure possessing this property is called a +circle." 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. "About the centre A, describe the +circle BCD." Here is an assumption, that a figure, such as the definition +expresses, _may_ 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, "Through +the point B, draw a line returning into itself, of which every point shall +be at an equal distance from the point A." 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. "Since B C D is a +circle, the radius B A is equal to the radius C A." 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. + +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: + +A dragon is a serpent breathing flame. + +This proposition, considered only as a definition, is indisputably +correct. A dragon _is_ a serpent breathing flame: the word _means_ that. +The tacit assumption, indeed, (if there were any such understood +assertion,) of the existence of an object with properties corresponding to +the definition, would, in the present instance, be false. Out of this +definition we may carve the premisses of the following syllogism: + +A dragon is a thing which breathes flame: +A dragon is a serpent: + +From which the conclusion is, + +Therefore some serpent or serpents breathe flame:-- + +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-- + +A dragon is a _really existing_ thing which breathes flame: +A dragon is a _really existing_ serpent: + +which implied premisses being false, the falsity of the conclusion +presents no absurdity. + +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 +_means_ for _is_. We then have-- + +Dragon is _a word meaning_ a thing which breathes flame: +Dragon is _a word meaning_ a serpent: + +From which the conclusion is, + +Some _word or words which mean_ a serpent, also mean a thing which + breathes flame: + +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. + +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-- + +The _idea of_ a dragon is _an idea of_ a thing which breathes flame: +The _idea of_ a dragon is _an idea of_ a serpent: + +Therefore, there is _an idea of_ a serpent, which is _an idea of_ a thing +breathing flame. + +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.(26) + +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. 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. + +§ 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 _exactly_ +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 _more_ 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, "A circle is a plane figure +bounded by a line all the points of which are at an equal distance from a +given point within it," was considered by them, not as an assertion that +any real circle has that property, (which would not be exactly true,) but +that we _conceive_ a circle as having it; that our abstract idea of a +circle is an idea of a figure with its radii exactly equal. + +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. + +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, _attend_ 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 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 +_Philosophy of the Inductive Sciences_: 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. + +§ 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, "What is rhetoric?" the +topic of the Gorgias, or "What is justice?" that of the Republic. Such, +also, is the question scornfully asked by Pilate, "What is truth?" and the +fundamental question with speculative moralists in all ages, "What is +virtue?" + +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. + +Although the meaning of every concrete general name resides in the +attributes which it connotes, the objects were 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 _white_, 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. + +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 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 _just_ or _unjust_ of any action, _noble_ or _mean_ of +any sentiment, expression, or demeanour, _statesman_ or _charlatan_ 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. + +Language, as Sir James Mackintosh used to say of governments, "is not +made, but grows." A name is not imposed at once and by previous purpose +upon a _class_ 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 "is not made, but grows." 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. + +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. + +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 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.(27) + +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 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. + +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 _differentiae_ as lead to the greatest +number of interesting _propria_. 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. + + + + + +BOOK II. OF REASONING. + + +{~GREEK CAPITAL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER ETA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER ETA~}, {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}, {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMEGA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~} +{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER ALPHA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER FINAL SIGMA~}; {~GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON WITH VARIA~} {~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER XI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER FINAL SIGMA~}. {~GREEK CAPITAL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}{~GREEK SMALL LETTER RHO~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH VARIA~} +{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~} {~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER ETA WITH DASIA AND VARIA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER XI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER FINAL SIGMA~}, {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER THETA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER ALPHA WITH PERISPOMENI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PSILI~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~}{~GREEK SMALL LETTER NU~} +{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER NU~}. {~GREEK CAPITAL LETTER ETA WITH DASIA~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}{~GREEK SMALL LETTER RHO~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER XI~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~}, {~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~}; {~GREEK SMALL LETTER OMICRON WITH DASIA~} {~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON WITH VARIA~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~} +{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER ALPHA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~}, {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER XI~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~}. + +ARIST. _Analyt. Prior._ 1. i. cap. 4. + + + + +CHAPTER I. OF INFERENCE, OR REASONING, IN GENERAL. + + +§ 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. + +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, 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. + +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. + +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 +_follow_. 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 _inferred_. 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 _reason_, 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. + +§ 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 aequipollency 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. + +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. + +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 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. + +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 _per +accidens_. 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 _is not_ B, is +first changed into a proposition aequipollent with it, Some A _is_ "a thing +which is not B"; 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, _simple_ conversion. + +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 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 "lawful sovereign," and the attributes +connoted by the term "tyrant," 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 "great general," +and those connoted by "rash," 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 "quadruped" and those +connoted by "warm-blooded" 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 _all_ warm-blooded +creatures are quadrupeds, or, in other words, that the attributes connoted +by "warm-blooded" never exist without those connoted by "quadruped," 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 creature +are present, is to say that when the latter are absent the former are +absent. + +In a manual for young students, it would be proper to dwell at greater +length on the conversion and aequipollency 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 _vice +versa_(28); 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 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 _general_ 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. + +§ 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. + +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. + +It is necessary to observe, that the expressions, reasoning 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 _less general_ than itself, and Ratiocination is inferring a +proposition from propositions _equally_ or _more_ 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. + +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. + +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. + +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. + + + + +CHAPTER II. OF RATIOCINATION, OR SYLLOGISM. + + +§ 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, _memoriae +causa_, 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. + +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. + +Syllogisms are divided by some logicians into three _figures_, 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 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. + +Each figure is divided into _modes_, according to what are called the +_quantity_ and _quality_ 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. + +FIRST FIGURE. + +All B is C No B is C All B is C No B is C +All A is B All A is B Some A is B Some A is B +therefore therefore therefore therefore +All A is C No A is C Some A is C Some A is not C + +SECOND FIGURE. + +No C is B All C is B No C is B All C is B +All A is B No A is B Some A is B Some A is not B +therefore therefore therefore therefore +No A is C No A is C Some A is not C Some A is not C + +THIRD FIGURE. + +All B is C No B is C Some B is C All B is C Some B is No B is C + not C +All B is A All B is A All B is A Some B is A All B is A Some B is A +therefore therefore therefore therefore therefore therefore +Some A is C Some A is Some A is C Some A is C Some A is Some A is + not C not C not C + +FOURTH FIGURE. + +All C is B All C is B Some C is B No C is B No C is B +All B is A No B is A All B is A All B is A Some B is A +therefore therefore therefore therefore therefore +Some A is C Some A is Some A is C Some A is Some A is + not C not C not C + +In these exemplars, or blank forms of making syllogisms, no place is +assigned to _singular_ 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-- + +All men are mortal, All men are mortal, +All kings are men, Socrates is a man, +therefore therefore +All kings are mortal, Socrates is mortal, + +are arguments precisely similar, and are both ranked in the first mode of +the first figure. + +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 _mode_, (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 _Elements of Logic_, where he will find stated with +philosophical precision, and explained with remarkable perspicuity, the +whole of the common doctrine of the syllogism. + +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. + +Although a syllogism framed according to any of these formulae 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 +_reduction_ of syllogisms. It is done by the _conversion_ of one or other, +or both, of the premisses. Thus an argument in the first mode of the +second figure, as-- + +No C is B +All A is B +therefore +No A is C, + +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:-- + +No B is C +All A is B +therefore +No A is C, + +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:-- + +All B is C +All B is A +therefore +Some A is C, + +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 _per accidens_, 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:-- + +All B is C +Some A is B, +from which it obviously follows, that +Some A is C. + +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, 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:-- + +Every B is C No B is C +All A is B, All A is B, +Some A is B, Some A is B, +therefore therefore +All A is C. No A is C. +Some A is C. Some A is not C. + +Or if more significant symbols are preferred:-- + +To prove an affirmative, the argument must admit of being stated in this +form:-- + +All animals are mortal; +All men/Some men/Socrates are animals; +therefore +All men/Some men/Socrates are mortal. + +To prove a negative, the argument must be capable of being expressed in +this form:-- + +No one who is capable of self-control is necessarily vicious; +All negroes/Some negroes/Mr. A's negro are capable of self-control; +therefore +No negroes are/Some negroes are not/Mr. A's negro is not necessarily +vicious. + +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 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, + +Aristides was virtuous, +Aristides was a pagan, +therefore +Some pagan was virtuous, + +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-- + +Aristides was virtuous, +Some pagan was Aristides, +therefore +Some pagan was virtuous. + +A German philosopher, Lambert, whose _Neues Organon_ (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.(29) The 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 scientific importance, those in which the conclusion is an +universal affirmative, such conclusions being susceptible of proof in the +first figure alone. + +§ 2. On examining, then, these two general formulae, 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 _general_ 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. + +The other premiss is always affirmative, and asserts that something (which +may be either an individual, a class, or 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. + +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 _dictum de omni et nullo_. + +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 _dictum de omni_ 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 _substantia secunda_ formed part of the properties of +each of the individual substances called by the same name; that the +properties of Man, for example, were properties of all men; was a +proposition of real significance when man did not _mean_ 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 _per se_, 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 +_is_ nothing but the objects contained in it: and the _dictum de omni_ +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 _dictum de omni_ is on a par with another truth, +which in its time was also reckoned of great importance, "Whatever is, +is;" and not to be compared in point of significance to the cognate +aphorism, "It is impossible for the same thing to be and not to be;" 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 _dictum +de omni_, 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 _class_. + +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 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 _dictum de omni_ 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 _une langue bien faite_: 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 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 _remember_ and to +_communicate_ 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. + +§ 3. Those who considered the _dictum de omni_ 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 +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. + +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, + +All men are mortal, +Socrates is a man, +therefore +Socrates is mortal, + +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 "man" 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 + +All men are mortal, +All kings are men, +therefore +All kings are mortal, + +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. + +If the major premiss were negative, as, No men are omnipotent, it would +assert, not that the attributes connoted by "man" never exist without, but +that they never exist with, those connoted by "omnipotent:" 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. + +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 _dictum de omni et nullo_, 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. + +§ 4. It remains to translate this exposition of the syllogism from the one +into the other of the two languages in which we formerly remarked(30) 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:-- + +Attribute A is a mark of attribute B, +A given object has the mark A, +therefore +The given object has the attribute B. + +Referred to this type, the arguments which we have lately cited as +specimens of the syllogism, will express themselves in the following +manner:-- + +The attributes of man are a mark of the attribute mortality, +Socrates has the attributes of man, +therefore +Socrates has the attribute mortality. + +And again, + +The attributes of man are a mark of the attribute mortality, +The attributes of a king are a mark of the attributes of man, +therefore +The attributes of a king are a mark of the attribute mortality. + +And lastly, + +The attributes of man are a mark of the _absence_ of the attribute +omnipotence, +The attributes of a king are a mark of the attributes of man, +therefore +The attributes of a king are a mark of the absence of the attribute +signified by the word omnipotent, (or, are _evidence_ of the absence of +that attribute.) + +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. + + + + +CHAPTER III. OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE SYLLOGISM. + + +§ 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. + +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, have been led to impute uselessness +and frivolity to the syllogistic theory itself, on the ground of the +_petitio principii_ 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. + +§ 2. It must be granted that in every syllogism, considered as an argument +to prove the conclusion, there is a _petitio principii_. When we say, + +All men are mortal +Socrates is a man +therefore +Socrates is mortal; + +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 _aliunde_; 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. + +This doctrine appears to me irrefragable; and if logicians, 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 _bona fide_ 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:-- + +All men are mortal +The Duke of Wellington is a man +therefore +The Duke of Wellington is mortal. + +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 _by implication_ in the premisses, and being +directly asserted in them. When Archbishop Whately, for example, says,(31) +that the object of reasoning is "merely to expand and unfold 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," he does not, I think, meet the real +difficulty requiring to be explained, namely, how it happens that a +science, like geometry, _can_ be all "wrapt up" 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?(32) + +§ 3. From this difficulty there appears to be but one issue. The +proposition that the Duke of Wellington is 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. + +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. + +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 +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. + +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 _inference_ +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. + +Archbishop Whately has contended that syllogising, or reasoning from +generals to particulars, is not, agreeably to the vulgar idea, a peculiar +_mode_ of reasoning, but the philosophical analysis of _the_ 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 "high priori road," by the arbitrary fiat of +logicians. I cannot perceive why it should be impossible to journey from +one place to another unless we "march up a hill, and then march down +again." 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. + +Not only _may_ 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. + +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, 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. + +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. + +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 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 _in +fact_ 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. + +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 "things which are equal to the same thing are equal +to one another." 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 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 kind, some of which _when generalized_ 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 +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. + +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. + +§ 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 formulae for making more: The major premiss of a syllogism, +consequently, is a formula of this description: and the conclusion is not +an inference drawn _from_ the formula, but an inference drawn _according_ +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, 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. + +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 _are_ anything, but +that all men _shall_ do something. + +In both these cases the generalities are the original data, 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. + +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,) +concerning the inferences which that former experience would warrant. + +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 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. + +§ 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. + +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, 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. + +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 _reductio ad +impossibile_. + +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. + +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. + +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 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. + +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 _must_ reason, but +it is a form in which we _may_ 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. + +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 in a commodious +and immediately available shape by means of general language. + +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. + +The use of the syllogism is in truth no other than the use of general +propositions in reasoning. We _can_ 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 formulae 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 formulae; +and the rules of syllogism are a system of securities for the correctness +of the application. + +§ 6. To complete the series of considerations connected with the +philosophical character of the syllogism, it is requisite 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. + +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 _petitio principii_ 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. 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. + +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 "mortal" were involved in the +meaning of "man;" 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 _previously perceiving_ 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 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. + +In the argument, then, which proves that Socrates is mortal, one +indispensable part of the premisses will be as follows: "My father, and my +father's father, A, B, C, and an indefinite number of other persons, were +mortal;" which is only an expression in different words of the observed +fact that they have died. This is the major premiss, divested of the +_petitio principii_, and cut down to as much as is really known by direct +evidence. + +In order to connect this proposition with the conclusion, Socrates is +mortal, the additional link necessary is such a proposition as the +following: "Socrates resembles my father, and my father's father, and the +other individuals specified." 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. + +§ 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 _bona fide_ +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. + +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 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. + +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. + + + +NOTE SUPPLEMENTARY TO THE PRECEDING CHAPTER. + + + This theory of the syllogism, (which has received the important + adhesion of Dr. Whewell,(33)) has been controverted by a writer in + the "British Quarterly Review."(34) 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. + + + The reviewer denies that there is a _petitio principii_ 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 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.(35) That he had reflected very little on + the point when he wrote his remarks, is shown by his oversight + respecting the _dictum de omni et nullo_. He acknowledges that + this maxim as commonly expressed,--"Whatever is true of a class, is + true of everything included in the class," is a mere identical + proposition, since the class _is_ nothing but the things included + in it. But he thinks this defect would be cured by wording the + maxim thus,--"Whatever is true of a class, is true of everything + which _can be shown_ to be a member of the class:" as if a thing + could "be shown" 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 "can be shown" to be included in it are a part of + these; it is the sum of them too, and the _dictum_ 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 _is not_ 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. + + + The reviewer says that if the major premiss included the + conclusion, "we should be able to affirm the conclusion without + the intervention of the minor premiss; but every one sees that + that is impossible." 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 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 _interpreted_ to us. But according to + the reviewer's theory, it is our having _made_ 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. + + + The reviewer comes much nearer to the gist of the question, when + he objects that the formula in which the major is left out--"A, B, + C, &c., were mortal, therefore the Duke of Wellington is mortal," + 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 _sufficient evidence_ of what is true of the + Duke of Wellington. This recognition of the sufficiency of the + induction he calls an "inference," and says, that its result must + be interpolated between the cases A, B, C, and the case of the + Duke of Wellington; and that "our final conclusion is from what is + thus interpolated, and not directly from the individual facts that + A, B, C, &c. were mortal." 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 _desirable_ 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 _from_ the + general one.(36) 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 instances, there + is ground for a _general_ 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. + + + 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 _petitio + principii_ in this syllogism, "Every poet is a man of genius, A B + is not a man of genius, therefore A B is not a poet." It is true + that in a syllogism of this particular type, the _petitio + principii_ is disguised. A B is not included in the terms, every + poet. But the proposition, "every poet is a man of genius" (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 "men of genius," + 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 aequipollent with "No one who is not a man + of genius is a poet," and in this the _petitio principii_, as + regards A B, is no longer implied, but express, as in an ordinary + syllogism of the first figure. + + + Another critic has endeavoured to get rid of the _petitio + principii_ in the syllogism by substituting for the common form of + expression, the following form--All _known_ 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 _known_ 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. + + + + +CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES. + + +§ 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. + +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 "Socrates is a man," 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. + +§ 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, 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. + +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 other particulars which are not, +as in the simple case, _seen_ to resemble them in the material points, but +_inferred_ 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. + +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 _a priori_, 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 _does_ the government in question +thus resemble them? This may be debated _pro_ and _con_ 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 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. + +§ 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 +formulae for inferring particulars from particulars. 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 _them_. 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. + +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 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. + +In the more complex branches of knowledge, the deductions seldom consist, +as in the examples hitherto exhibited, of a single chain, _a_ a mark of +_b_, _b_ of _c_, _c_ of _d_, therefore _a_ a mark of _d_. They consist (to +carry on the same metaphor) of several chains united at the extremity, as +thus: _a_ a mark of _d_, _b_ of _e_, _c_ of _f_, _d e f_ of _n_, therefore +_a b c_ a mark of _n_. 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 are abundant, as in all +propositions where the hypothesis includes numerous conditions: "_If_ a +circle be taken, and _if_ within that circle a point be taken, not the +centre, and _if_ straight lines be drawn from that point to the +circumference, then," &c. + +§ 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. + +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 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 formulae:--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 formulae 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 formulae. The angles at the base of an isosceles +triangle do not obviously come within any of these. The formulae 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 formulae, 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, "The differences +of equal things are equal." 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 formulae. 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 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. + +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.) + +FIRST FORMULA. _The sums of equals are equal._ + +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. + +SECOND FORMULA. _Equal straight lines being applied to one another +coincide_. + +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. + +THIRD FORMULA. _Straight lines, having their extremities coincident, +coincide_. + +B E and C D have been brought within this formula by the preceding +induction; they will, therefore, coincide. + +FOURTH FORMULA. _Angles, having their sides coincident, coincide_. + +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. + +FIFTH FORMULA. _Things which coincide are equal_. + +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, _mutatis mutandis_, to the angles E B C, D C B, these also are +brought within the fifth formula. And, finally, + +SIXTH FORMULA. _The differences of equals are equal_. + +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. + +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 involved in all geometry are comprised in +those simple ones, the formulae 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. + +§ 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, 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. + +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, _a_ a +mark of _b_, or _a_ and _b_ marks of one another, _c_ a mark of _d_, or +_c_ and _d_ marks of one another, without anything to connect _a_ or _b_ +with _c_ or _d_; 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 +kind: _a_ a mark of _b_, _b_ a mark of _c_, _c_ of _d_, _d_ of _e_, &c. In +these sciences we can mount the ladder from _a_ to _e_ by a process of +ratiocination; we can conclude that _a_ is a mark of _e_, and that every +object which has the mark _a_ has the property _e_, although, perhaps, we +never were able to observe _a_ and _e_ together, and although even _d_, +our only direct mark of _e_, may be not perceptible in those objects, but +only inferrible. Or varying the first metaphor, we may be said to get from +_a_ to _e_ underground: the marks _b_, _c_, _d_, which indicate the route, +must all be possessed somewhere by the objects concerning which we are +inquiring; but they are below the surface: _a_ is the only mark that is +visible, and by it we are able to trace in succession all the rest. + +§ 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, _a_ a mark of +_b_, _c_ a mark of _d_, _e_ a mark of _f_, 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; _b_, for example, may be +ascertained to be a mark of _c_, which enables us thenceforth to prove +deductively that _a_ is a mark of _c_. Or, as sometimes happens, some +comprehensive induction may raise an arch high in the air, which bridges +over hosts of them at once: _b_, _d_, _f_, 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. + +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. + +§ 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. + +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. + +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 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. + +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. + +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 _vice versa_, 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. + + + + +CHAPTER V. OF DEMONSTRATION, AND NECESSARY TRUTHS. + + +§ 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? + +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 +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 _a priori_ +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 _minimum visibile_, 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 _attending_ +to a part only of that perception or conception, instead of the whole. But +we cannot _conceive_ a line without breadth; we 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. + +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, _as_ 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 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. + +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 _suppose_ 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, _on condition_ that those hypotheses are +true. + +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 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. + +§ 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 _Mechanical Euclid_, and in his more recent +elaborate work on the _Philosophy of the Inductive Sciences_; in which +last he also replies to an article in the _Edinburgh Review_, (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 _arbitrary_ +hypotheses; that we should not be at liberty to substitute other +hypotheses for them; that not only "a definition, to be admissible, must +necessarily refer to and agree with some conception which we can +distinctly frame in our thoughts," but that the straight lines, for +instance, which we define, must be "those by which angles are contained, +those by which triangles are bounded, those of which parallelism may be +predicated, and the like."(37) 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 _would_ 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 will always express, under known liability to correction, +actual truth. + +§ 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, "Equal magnitudes are those which +may be so applied to one another as to coincide;" 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: "Two +straight lines which intersect each other cannot both of them be parallel +to a third straight line."(38) + +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. + +§ 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 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. + +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. + +It is not necessary to show that the truths which we call axioms are +originally _suggested_ 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 _proves_ the axiom; but that its truth is +perceived _a priori_, 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. + +They cannot, however, but allow that the truth of the axiom, Two straight +lines cannot inclose a space, even if evident independently of experience, +is also evident from experience. Whether the axiom _needs_ confirmation or +not, it _receives_ 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 _a priori_ 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. + +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 _a +priori_ theory are obliged to have recourse to other arguments. These are +reducible to two, which I shall endeavour to state as clearly and as +forcibly as possible. + +§ 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 +"imaginary looking;"(39) 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. + +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 _cannot_ +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. + +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 +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. + +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, "a bent line," not by the expression, "a straight +line."(40) + +§ 6. The first of the two arguments in support of the theory that axioms +are _a priori_ 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 _must_ be white. "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 +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." Besides, axioms are not only universal, they are also +necessary. Now "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 _must_ 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."(41) And Dr. Whewell adds, "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."(42) + +In the following passage, we are told what the distinction is, the +non-recognition of which incurs this denunciation. "Necessary truths are +those in which we not only learn that the proposition _is_ true, but see +that it _must be_ 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."(43) + +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. + +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. + +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, 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.(44) +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 seemed to +them so great an absurdity.(45) 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 _some_ 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 _attracting_ the earth without any +intervening fluid, they cannot yet conceive the sun _illuminating_ the +earth without some such medium. + +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 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. + +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 _could_ 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 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. + +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 +_Philosophy of the Inductive Sciences_ 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. "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 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. _The very essence of these triumphs is, that they lead us to +regard the views we reject as not only false but inconceivable._"(46) + +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 +_right_ in 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. + +With respect to the laws of motion, Dr. Whewell says: "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."(47) +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 "a demonstrable necessity, compelling them to be such as +they are and no other;" and he himself, though not venturing "absolutely +to pronounce" that _all_ these laws "can be rigorously traced to an +absolute necessity in the nature of things,"(48) does actually think in +that manner of the law just mentioned; of which he says: "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."(49) 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? + +The other instance which I shall quote is a truly astonishing one, and may +be called the _reductio ad absurdum_ of the theory of inconceivableness. +Speaking of the laws of chemical composition, Dr. Whewell says:(50) "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. _For how, in fact, can we conceive +combinations, otherwise than as definite in kind and quality?_ 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. 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 _we cannot conceive a world +in which this should not be the case_, 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."(51) + +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.(52) + + + + +CHAPTER VI. THE SAME SUBJECT CONTINUED. + + +§ 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. + +While the axioms of demonstrative sciences thus appeared to be +experimental truths, the definitions, as they are 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. + +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. + +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 _a priori_, 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 _a priori_ philosophers on one side; and on the +other, a theory the most opposite to theirs, which was at one time very +generally received, and is still far from being altogether exploded among +metaphysicians. + +§ 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. + +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 imagination as lines, +intersecting other lines, forming an angle with one another, and the like; +but not so _a_ and _b_. These may represent lines or any other magnitudes, +but those magnitudes are never thought of; nothing is realized in our +imagination but _a_ and _b_. 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 +_experimentum crucis_ on the nature of reasoning itself. + +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. _Ten_ 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 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 _a_ +or _x_, and apply to it, without danger of error, every algebraical +formula in the books. The proposition, 2(_a_ + _b_) = 2_a_ + 2_b_, 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 _a_, picture to ourselves all things whatever, but only some one +thing; why not, then, the letter itself? The mere written characters, _a_, +_b_, _x_, _y_, _z_, 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 _a_, _b_, and _x_ 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 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. + +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 "Two +pebbles and one pebble are equal to three pebbles," 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 "objects are themselves" 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. + +This, however, though it looks so plausible, will not bear examination. +The expression "two pebbles and one pebble," and the expression, "three +pebbles," 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 +_de_note the same things, their _con_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 +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 _mind_ 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. + +We may, if we please, call the proposition "Three is two and one," 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, "A circle is a figure bounded by a line which has all its +points equally distant from a point within it," 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, "Three is two +and one," 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. + +The Science of Number is thus no exception to the conclusion 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. + +§ 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 _reductio +ad absurdum_. + +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. + +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 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 _number_ 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. + +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. + +§ 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. + +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--_a_ is a mark of _b_, _b_ of _c_, _c_ of _d_, therefore _a_ +is a mark of _d_, which last may be a truth inaccessible to direct +observation. In like manner it is allowable to say, _Suppose_ that _a_ +were a mark of _b_, _b_ of _c_, and _c_ of _d_, _a_ would be a mark of +_d_, 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 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 _reductio ad absurdum_. In such cases, the reasoning is +as follows: _a_ is a mark of _b_, and _b_ of _c_; now if _c_ were also a +mark of _d_, _a_ would be a mark of _d_; but _d_ is known to be a mark of +the absence of _a_; consequently _a_ would be a mark of its own absence, +which is a contradiction; therefore _c_ is not a mark of _d_. + +§ 5. It has even been held by some writers, that all ratiocination rests +in the last resort on a _reductio ad absurdum_; 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 _reductio ad absurdum_, +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 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. + +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. + +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. + +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. + + + + + +BOOK III. OF INDUCTION. + + + "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."--D. STEWART, + _Elements of the Philosophy of the Human Mind_, vol. ii. chap. iv. + sect. 1. + + + + +CHAPTER I. PRELIMINARY OBSERVATIONS ON INDUCTION IN GENERAL. + + +§ 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 on the subject, +nor regarded the mode in which they arrived at their conclusions as +deserving of study, independently of the conclusions themselves. + +§ 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. + +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. + +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 principles of induction will afford him no +assistance. It lies not in _making_ his inductions but in the _selection_ +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. + +But when he _has_ 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 formulae 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 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. + +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 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. + +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 _is_ 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.(53) + +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. + + + + +CHAPTER II. OF INDUCTIONS IMPROPERLY SO CALLED. + + +§ 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. + +This definition excludes from the meaning of the term Induction, various +logical operations, to which it is not unusual to apply that name. + +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, "This and +that A are B, therefore every A is B,"--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 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. "All +men are mortal" 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. + +§ 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, 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(54)) 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. + +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 _law_ 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 _a priori_ 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. + +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 _per saltum_ 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 _a priori_ 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. + +§ 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 question +is that of confounding a mere description of a set of observed phenomena, +with an induction from them. + +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. + +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. + +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 +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. + +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 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. + +§ 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.(55) 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. + +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. "The +particular facts," says he,(56) "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 there, but they will not hang together till some one +provides the string." + +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 _of_ 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. + +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 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 "who should establish a precise, tenable, +and consistent conception of life."(57) Such a conception _can_ 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. + +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 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. + +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 "conception" 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. + +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. + +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 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 from being entirely false, that +they are even now habitually employed by astronomers when only a rough +approximation to correctness is required. "L'astronomie moderne, en +detruisant sans retour les hypotheses primitives, envisagees comme lois +reelles du monde, a soigneusement maintenu leur valeur positive et +permanente, la propriete de representer commodement les phenomenes quand +il s'agit d'une premiere ebauche. Nos ressources a cet egard sont meme +bien plus etendues, precisement a cause que nous ne nous faisons aucune +illusion sur la realite des hypotheses; ce qui nous permet d'employer sans +scrupule, en chaque cas, celle que nous jugeons la plus avantageuse."(58) + +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. + +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, +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.(59) + +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. + +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, 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. + +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. + +§ 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. + +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, 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. + +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 _subject_ +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 _merely_; it was the sum of the observations _seen under a +new point of view_.(60) But it was not the sum of _more_ 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. + +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 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. + +The mental operation which extracts from a number of detached observations +certain general characters in which 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. + +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. + + + + +CHAPTER III. OF THE GROUND OF INDUCTION. + + +§ 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 _resemble_ the former, in what are regarded as the material +circumstances. + +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 _what_ description. + +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, 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 "our +intuitive conviction that the future will resemble the past." 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, _as_ 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. + +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 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. + +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, "John, Peter, &c., are mortal, therefore +all mankind are mortal," 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 +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.(61) + +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 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.(62) 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. + +§ 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. + +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 +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. + +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 "Inductio per enumerationem simplicem, ubi non +reperitur instantia contradictoria." 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 _interrogating_ nature (to use Bacon's +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. + +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.(63) 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. + +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 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 _inductio per enumerationem simplicem_ 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, +_mera palpatio_. + +§ 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. + +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 "men whose heads do grow beneath their shoulders," +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 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. + +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. + +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. + + + + +CHAPTER IV. OF LAWS OF NATURE. + + +§ 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. + +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 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 _cases_ of the +three first; virtually included in them; said, therefore, to _result_ from +them: whoever affirms those three has already affirmed all the rest. + +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 _case_ 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 _deduce_ 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 +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, _verification_ by specific experience +would still be desirable, and might possibly be indispensable. + +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 _laws_, 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 _law_; as +when, in mathematics, we speak of the law of decrease of the successive +terms of a converging series. But the expression, _law of nature_, has +generally been employed with a sort of tacit reference to the original +sense of the word _law_, 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? + +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 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. + +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, _means_ 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 _a_ 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. + +§ 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. + +Let us revert, for instance, to one of our former illustrations, 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. + +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. + +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 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. + +§ 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. + +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 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:(64) 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. + +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. + +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. + +There are such certain and universal inductions; and it is because there +are such, that a Logic of Induction is possible. + + + + +CHAPTER V. OF THE LAW OF UNIVERSAL CAUSATION. + + +§ 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. + +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. + +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 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. + +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. + +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, 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. + +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 peculiarity, that of never being, in any instance +whatever, defeated or suspended by any change of circumstances. + +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. + +This generalization may appear to some minds not to amount to much, since +after all it asserts only this: "it is a law, that every event depends on +some law." 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. + +§ 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. + +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 _efficient_, but _physical_ 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 _produces_, 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 "Things in themselves." + +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; 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. + +§ 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, 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 _conditions_ 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 _events_ +(that is, instantaneous changes, or successions of instantaneous changes) +but _states_, 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 _exist_ immediately previous, though not that they should all _begin_ +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 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. + +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. + +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 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 +_material_ cause, _causa materialis_. 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 _towards_ 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 _within the sphere_ 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. + +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 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 _positive_ 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. + +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 _event_, rather than with +any of the antecedent _states_, 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 _force_ exerted by the earth, or an +_attraction_ 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, 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.(65) + +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 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 which they produce their own,(66) 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. + +§ 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 _agent_ and a _patient_. 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 _acted upon_, and which is 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 "the stone itself," 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 _weight_ or _gravitation_ of the stone. + +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 _states_ 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 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 +the effect; nor by including even these would there be incurred any but a +merely verbal inconsistency. + +§ 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. + +When we define the cause of anything (in the only sense in which the +present inquiry has any concern with causes) to be "the antecedent which +it invariably follows," we do not use this phrase as exactly synonymous +with "the antecedent which it invariably _has_ followed in our past +experience." 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 _has_ been followed by +the consequent, but that, as long as the present constitution of things +endures, it always _will_ 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 _provided_ 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 being no opaque medium in +a straight line(67) 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 _unconditionalness_. That which is necessary, that +which _must_ 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. + +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. + +We may define, therefore, the cause of a phenomenon, to be the antecedent, +or the concurrence of antecedents, on which it is invariably and +_unconditionally_ 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 +"unconditionally," we must say, "subject to no other than negative +conditions." + +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. + +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 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 _can_ +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. + +§ 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. _Cessante causa +cessat et effectus_, 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 _coup de soleil_ 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 +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. + +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. + +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 from whom I have quoted,(68)) 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. + +§ 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, 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. + +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 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 +_origin_ 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. + +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 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. + +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.(69) And if any particular state of the entire universe +could ever recur a second time, all subsequent states would return too, +and history would, like a circulating decimal of many figures, +periodically repeat itself:-- + +Jam redit et virgo, redeunt Saturnia regna.... +Alter erit tum Tiphys, et altera quae vehat Argo +Delectos heroas; erunt quoque altera bella, +Atque iterum ad Troiam magnus mittetur Achilles. + +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 _a priori_ 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. + +§ 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, 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. + +§ 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. + +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, "of force exerted, of power in +action, which is necessarily causal, or causative." This feeling of energy +or force, inherent in an act of will, is knowledge _a priori_; assurance, +prior to experience, that we have the power of causing effects. Volition, +therefore, 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 _sole_ Efficient Cause of all phenomena. "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." "The word _action_ itself," says another +writer of the same school, "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." 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. + +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. + +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, 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 _a priori_ 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 "consciousness of effort:" 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. + +Those against whom I am contending have never produced, and do not pretend +to produce, any positive evidence(70) 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, "inconceivable" 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 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. + +"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. + +"Our first thoughts seem to be, that the objects in which we perceive such +motion have understanding and active power as we have. 'Savages,' says the +Abbe Raynal, 'wherever they see motion which they cannot account for, +there they suppose a soul.' 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." + +"The Abbe Raynal's observation is sufficiently confirmed, both from fact, +and from the structure of all languages. + +"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. + +"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 Abbe Raynal's observation, +savages suppose a soul. + +"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. It was therefore proper and natural to express their motions +and changes by active verbs. + +"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. + +"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. + +"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."(71) + +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 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. + +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 _not_ conceivable, or +that the action of mind upon matter _was_. 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. + +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. "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 _per se_ carry some presumption to their own +mind.... They wanted to see some _reason_ why the physical antecedent +should produce this particular consequent, and their only attempts were in +directions where they could find such reasons."(72) 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 _previous to trial_ 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 _he_ 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, 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. + +It was not the Greeks alone, who "wanted to see some reason why the +physical antecedent should produce this particular consequent," some +connexion "which would _per se_ carry some presumption to their own mind." +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 _per se_ 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 _better_ for the phenomena of nature +than a mere reference to divine volition.(73) + +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 _a priori_, 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 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 _qua_ mind, or _qua_ endowed with volition, but _qua_ +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 _deus ex machina_ 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. + +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 {~GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER UPSILON~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER KAPPA~} {~GREEK SMALL LETTER ALPHA WITH PSILI AND VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER TAU~}{~GREEK KORONIS~} {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER ETA~} +{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}. 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 _per se_ 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; 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. + +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 _per se_ 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. + +I am unwilling to leave the subject without adverting to the additional +fallacy contained in the corollary from this 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 _is_ 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 +_can_ 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 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.(74) + + + + +CHAPTER VI. OF THE COMPOSITION OF CAUSES. + + +§ 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. + +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 _a priori_, 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 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 _both_ 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. + +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 from any new combination, until we have tried the specific +experiment. + +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. + +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 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,(75) 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. + +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. + +§ 2. This difference between the case in which the 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. + +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 +they might be termed, _heteropathic_ 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 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. + +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 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. + +§ 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 _kind_ 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 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. + +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. + +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. + + + + +CHAPTER VII. OF OBSERVATION AND EXPERIMENT. + + +§ 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. + +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 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 _kind_ 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. + +The extent and minuteness of observation which may be requisite, and the +degree of decomposition to which it may be 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. + +§ 2. The different antecedents and consequents being, then, supposed to +be, so far as the case requires, ascertained 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 (_a posteriori_ 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 _varying the circumstances_. 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. + +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 _find_ an instance in nature, suited to our +purposes, or, by an artificial arrangement of circumstances, _make_ 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. + +§ 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 _sort_ 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 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. + +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. + +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. + +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, 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. + +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. + +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 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. + +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. + +§ 4. If what is called pure observation is at so great a disadvantage, +compared with artificial experimentation, in one department of the direct +exploration of phenomena, there is another branch in which the advantage +is all on the side of the former. + +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. + +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 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. + +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. + +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 complete; that +antecedent is the cause of that consequent.(76) But we have then added the +evidence of experiment to that of simple observation. Until we had done +so, we had only proved _invariable_ antecedence, but not _unconditional_ +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. + +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 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. + +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. + + + + +CHAPTER VIII. OF THE FOUR METHODS OF EXPERIMENTAL INQUIRY. + + +§ 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. + +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. + +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 _a_ +_b_ _c_; and suppose that A is next tried with D and E, but without B and +C, and that the effect is _a_ _d_ _e_. Then we may reason thus: _b_ and +_c_ are not effects of A, for they were not produced by it in the second +experiment; nor are _d_ and _e_, 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 _a_. +The phenomenon _a_ 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. + +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. + +In a similar manner we may inquire into the cause of a given effect. Let +_a_ 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 _a_ in two different combinations, _a_ _b_ +_c_, and _a_ _d_ _e_; 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 _a_ by a law of causation. +B and C, we may say, cannot be causes of _a_, 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 _a_ in both instances. + +For example, let the effect _a_ 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 of solution. We +conclude, therefore, that the solidification of a substance from a liquid +state is an invariable antecedent of its crystallization. + +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 _a_ 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. + +But if we cannot artificially produce the phenomenon A, the conclusion +that it is the cause of _a_ remains subject to very considerable doubt. +Though an invariable, it may not be the unconditional antecedent of _a_, +but may precede it as day precedes night or night day. This uncertainty +arises from the impossibility of assuring ourselves that A is the _only_ +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 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. + +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, _mutatis +mutandis_, 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:-- + +FIRST CANON. + +_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._ + +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. + +§ 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 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 _a b c_, and the effect of B C, _b c_, it is +evident that the effect of A is _a_. So again, if we begin at the other +end, and desire to investigate the cause of an effect _a_, we must select +an instance, as _a b c_, 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, _b c_, occur without _a_. If the antecedents, +in that instance, are B C, we know that the cause of _a_ must be A: either +A alone, or A in conjunction with some of the other circumstances present. + +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. + +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:-- + +SECOND CANON. + +_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_. + +§ 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 _elimination._ 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 _not_ be +eliminated, _is_ connected with the phenomenon by a law. + +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. + +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 _a b c_ and _b c_. 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 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 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. + +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 _all_ 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 _a_, +then _a_ is an invariable consequent of A. If _a_ _b_ _c_, _a_ _d_ _e_, +_a_ _f_ _g_, all number A among their antecedents, then A is connected as +an antecedent, by some invariable law, with _a_. 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, _a_, +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. + +It thus appears to be by the Method of Difference alone 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 _a_); 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. + +§ 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 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. + +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 _a_; we may yet be able, by a double employment of the +Method of Agreement, to discover in what the instances which contain A or +_a_, differ from those which do not. + +If we compare various instances in which _a_ 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 _a_. 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, _a_ 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 previously examined a variety of instances in which _a_ +occurred, and found them to agree in containing A, so we now observe a +variety of instances in which _a_ 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 _a_, which was +before established between their presence. As, then, it had been shown +that whenever A is present _a_ is present, so it being now shown that when +A is taken away _a_ is removed along with it, we have by the one +proposition A B C, _a b c_, by the other B C, _b c_, the positive and +negative instances which the Method of Difference requires. + +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 _a_ agree in no antecedent whatever but A, or that the +instances negative of _a_ 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:-- + +THIRD CANON. + +_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._ + +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. + +§ 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. + +Suppose, as before, that we have the antecedents A B C, followed by the +consequents _a b c_, 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 _a_, and that the effect of B +is _b_. Subtracting the sum of these effects from the total phenomenon, +there remains _c_, 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, _a b c_, +could have been compared with a single instance A B, _a b_, we should have +proved C to be the cause of _c_, 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. + +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 _only_ antecedent to which the +residual phenomenon _c_ 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. + +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 _c_ may be so +disguised by its intermixture with _a_ and _b_, 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:-- + +FOURTH CANON. + +_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._ + +§ 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, + +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 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. + +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. + +If, therefore, there were no other methods of experimental investigation +than these three, we should be unable to determine 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 _a_, the +other consequents _b_ and _c_ remaining the same; or, _vice versa_, if +every change in _a_ 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 _a_ 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. + +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 _position_ 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 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. + +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. + +The method by which these results were obtained, may be termed the Method +of Concomitant Variations: it is regulated by the following canon:-- + +FIFTH CANON. + +_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._ + +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. + +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. + +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 _a_, any +variation in the quantity or in the various relations of A, is uniformly +followed by a variation in the quantity or relations of _a_. To take a +familiar instance, that of gravitation. The sun causes a certain tendency +to motion in the earth; here we have cause and effect; but that tendency +is _towards_ 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. + +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. + +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 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. + +§ 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, +_a_ 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, _a_ is double; that when A is treble or quadruple, _a_ is treble +or quadruple; we may conclude that if A were a half or a third, _a_ would +be a half or a third, and finally, that if A were annihilated, _a_ would +be annihilated, and that _a_ 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 _a_ would vanish simultaneously; as for instance +if _a_ were proportional to the square of A. If, on the other hand, _a_ 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, _a_ will seem to approach not towards zero, but towards some +other limit: and when the series of variations is such as to indicate what +that limit is, if constant, or the law of its variation if variable, the +limit will exactly measure how much of _a_ is the effect of some other and +independent cause, and the remainder will be the effect of A (or of the +cause of A). + +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 _a_. 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. + +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 _inductio per enumerationem simplicem_, 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 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. + +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, +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. "The formulae," says Sir John Herschel,(77) +"which have been empirically deduced for the elasticity of steam, (till +very recently,) and those for the resistance of fluids, and other similar +subjects," when relied on beyond the limits of the observations from which +they were deduced, "have almost invariably failed to support the +theoretical structures which have been erected on them." + +In this uncertainty, the conclusion we may draw from the concomitant +variations of _a_ 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, must be _one_ of the causes which collectively determine _a_. +We may, however, feel assured that the relation which we have observed to +exist between the variations of A and _a_, 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. + +The four methods which it has now been attempted to describe, are the only +possible modes of experimental inquiry, of direct induction _a +posteriori_, 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. + +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. + + + + +CHAPTER IX. MISCELLANEOUS EXAMPLES OF THE FOUR METHODS. + + +§ 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. + +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. + +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. + +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. + +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. + +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. + +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 _a fortiori_ 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, "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." Now +when these substances are brought into contact with the tissues in any +way, they do not combine with them; they 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. + +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. + +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 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. + +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 _circumstance_, but +of a single _substance_: 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 +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. + +§ 2. Let the object be(78) to ascertain the law of what is termed +_induced_ 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. + +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, 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. + +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. + +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 of the opposite electricity in some neighbouring +body. + +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 _pari +passu_ with that of the other. + +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 for supporting the opposition +increases, a higher charge becomes possible: and to this appears to be +owing the great superiority of the Leyden jar. + +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. + +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. + +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.(79) + +§ 3. Our third example shall be extracted from Sir John Herschel's +_Discourse on the Study of Natural Philosophy_, 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 "one of the most beautiful specimens" +which can be cited "of inductive experimental inquiry lying within a +moderate compass;" 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 "Discourse."(80) + +"Suppose _dew_ were the phenomenon proposed, whose cause we would know. In +the first place" we must determine precisely what we mean by dew: what the +fact really is, whose cause we desire to investigate. "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 _visible_ +wet is falling." This answers to a preliminary operation which will be +characterized in the ensuing book, treating of operations subsidiary to +induction.(81) The state of the question being fixed, we come to the +solution. + +"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." +Comparing these cases, we find that they all contain the phenomenon which +was proposed as the subject of investigation. Now "all these instances +agree in one point, the coldness of the object dewed, in comparison with +the air in contact with it." But there still remains the most important +case of all, that of nocturnal dew: does the same circumstance exist in +this case? "Is it a fact that the object dewed _is_ colder than the air? +Certainly not, one would at first be inclined to say; for what is to +_make_ 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 _is_ +colder than the air." + +Here then is a complete application of the Method of Agreement, +establishing the fact of an invariable connexion 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. "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, +_i.e._, where no dew is produced:" for a comparison between instances of +dew and instances of no dew, is the condition necessary to bring the +Method of Difference into play. + +"Now, first, no dew is produced on the surface of polished metals, but it +_is_ 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." 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 _one_ quality in common, +and that polished metals and the other substances on which dew is _not_ +deposited have also nothing in common but the one circumstance, of _not_ +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. + +"In the cases of polished metal and polished glass, the contrast shows +evidently that the _substance_ has much to do with the phenomenon; +therefore let the substance _alone_ be diversified as much as possible, by +exposing polished surfaces of various kinds. This done, a _scale of +intensity_ 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." 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 _caeteris paribus_ 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. + +"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 +_surface_, therefore, has a great influence. Expose, then, the _same_ +material in very diversified states as to surface," (that is, employ the +Method of Difference to ascertain concomitance of variations,) "and +another scale of intensity becomes at once apparent; those _surfaces_ +which _part with their heat_ most readily by radiation, are found to +contract dew most copiously." 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 _caeteris paribus_ 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. + +"Again, the influence ascertained to exist of _substance_ and _surface_ +leads us to consider that of _texture_: and here, again, we are presented +on trial with remarkable differences, and with a third scale of intensity, +pointing out substances 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." 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 "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;" and this last is, therefore, an +induction (from fresh instances) simply _corroborative_ of a former +induction. + +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 _not_ 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. + +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 _nothing_ +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. + +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. + +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 +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 _exceptions_ 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. + +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 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. + +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. "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 _if the clouds withdraw even for a few minutes, and +leave a clear opening, a deposition of dew presently begins_, and goes on +increasing.... Dew formed in clear intervals will often even evaporate +again when the sky becomes thickly overcast." 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.(82) + +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. + +§ 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. + +"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. + +"For example: the return of the comet predicted by Professor 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 +_residual phenomenon_, 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 _vera causa_," (an actually existing antecedent,) +"it has therefore been ascribed to such a resistance. + +"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 _verae causae_ (antecedents known to +exist) "why it _should_ 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 have been calculated _a priori_, from the laws obtained +by separate and foregone experiments." + +"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 _whole_ 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 _heat_ 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." + +"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 +Tennant. It was a happy thought of Glauber to examine what everybody else +threw away."(83) + +"Almost all the greatest discoveries in Astronomy," says the same +author,(84) "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 _caput +mortuum_ 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." + +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, 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. + +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.(85) + + + + +CHAPTER X. OF PLURALITY OF CAUSES; AND OF THE INTERMIXTURE OF EFFECTS. + + +§ 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 _a b c d e_, +the aggregate of the phenomena existing at any moment, as consisting of +dissimilar facts, _a_, _b_, _c_, _d_, and _e_, 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. + +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 _a_ 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 _a_ +and _b_, but different portions of an effect _a_. The obscurity and +difficulty of the investigation of the laws of phenomena is singularly +increased by the necessity 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. + +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. + +§ 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 _a b c_, and A D E followed by _a d e_. From these instances +it might be concluded that A is an invariable antecedent of _a_, 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 _a_ 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 _a_ in the former of the instances, the +other in the latter, A having no influence in either case. + +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 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. + +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 _b c_, and A +being added converts it into _a b c_, it is certain that in this instance +at least, A was either the cause of _a_, 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. + +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 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 _a_ 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 _a_; 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. + +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 _a_ 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 +_number_ of instances in inductive inquiry. The Plurality of Causes is the +only reason why mere 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 _mass_ 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. + +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 _a_ is, agree only in containing A, but also that the instances +in which _a_ is not, agree only in not containing A. Now, if this be so, A +must be not only the cause of _a_, but the only possible cause: for if +there were another, as for example B, then in the instances in which _a_ +is not, B must have been absent as well as A, and it would not be true +that these instances agree _only_ 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 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 +_not_ 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 _not_ transparent, agree? But we might hope much +sooner to seize some point of resemblance among the comparatively few and +definite species of objects which _are_ transparent; and this being +attained, we should quite naturally be put upon examining whether the +_absence_ of this one circumstance be not precisely the point in which all +opaque substances will be found to resemble. + +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. + +§ 3. We have thus far treated Plurality of Causes only as a possible +supposition, which, until removed, renders our 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 _all_ 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. + +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; +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. + +§ 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. + +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. + +The _effects_ of the new phenomenon, the _properties_ of water, for +instance, are as easily found by experiment as the effects of any other +cause. But to discover the _cause_ of it, that is, the particular +conjunction of agents from which it results, is often difficult enough. In +the first place, the 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. + +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. + +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 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. + +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 _as_ 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 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. + +In these cases, then, when the heteropathic effect (as we called it in a +former chapter)(86) 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. + +§ 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 _a_, _b_, +_c_, _d_, _e_, existing side by side, and continuing to be separately +discernible; they are + _a_, - _a_, 1/2 _b_, - _b_, 2 _b_, &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. + +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. 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. + +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. + +Since the laws of causes are as really fulfilled when the 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 +_tends_ 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 _tends_ 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 press +downwards with a force only equal to the difference of the two forces. + +These facts are correctly indicated by the expression _tendency_. 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 _pressure_, +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. + +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. +"What is thought to be an exception to a principle," (to quote words used +on a different occasion,) "is always some other and distinct principle +cutting into the former; some other force which impinges(87) 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 _disturbing_ force, prevails sufficiently 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. + +"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 _tend_ 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 _prevail over_ 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."(88) + +§ 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. + +The case, it is evident, is naturally susceptible of the 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 _a priori_. The other, or _a posteriori_ 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. + +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 "clothe them in +circumstances." 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. + +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 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. + +§ 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. + +When an effect results from the union of many causes, 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. + +§ 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 _a posteriori_ 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. + +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 _modi +operandi_ 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? + +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 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. + +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. + +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, by a succession of trials, that a certain +cause is _very often_ 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. + +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 _plus_ or in _minus_ 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. "How," it is asked, +"can an institution be bad, when the country has prospered under it?" "How +can such or such causes have contributed to the prosperity of one country, +when another has prospered without them?" 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 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. + +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 _a priori_ method. The more particular consideration of this +intellectual process requires a chapter to itself. + + + + +CHAPTER XI. OF THE DEDUCTIVE METHOD. + + +§ 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. + +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. + +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 +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. + +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 _were_ +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 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. + +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. + +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. + +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 the very +phenomena which it is our object to investigate: + + following life, in creatures we dissect, +We lose it, in the moment we detect. + +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. + +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 _was_ 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 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. + +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. + +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 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. + +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. + +§ 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 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. + +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 +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. + +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. + +§ 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 _a priori_ 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. + +These objections have real weight, and would be altogether 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. + +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 _accounted for_ by the laws of the causes--were +such as could not _but_ 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. + +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. + +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. + +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(89)) 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 +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. + + + + +CHAPTER XII. OF THE EXPLANATION OF LAWS OF NATURE. + + +§ 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 _explanation_ 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. + +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. + +§ 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. + +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, which tends to produce an +accelerating motion towards the sun; the real motion being a compound of +the two. + +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. + +§ 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 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. + +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. + +§ 4. It is of importance to remark, that when a sequence 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. + +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. + +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. + +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 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. + +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. + +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 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. + +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, 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. + +§ 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 _subsumption_ (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, 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. + +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 +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. + +§ 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 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. + +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 _results_ +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. + +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. + +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 _why_ for the more +extensive laws than for the partial ones. The explanation may substitute a +mystery which has become familiar, and has grown to _seem_ 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 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? + +The laws, thus explained or resolved, are sometimes said to be _accounted +for_; 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 +_causes_ 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 _case_ 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. + + + + +CHAPTER XIII. MISCELLANEOUS EXAMPLES OF THE EXPLANATION OF LAWS OF NATURE. + + +§ 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. + +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 "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." 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, "copper does not +decompose water, even when boiled in dilute sulphuric acid; but an alloy +of copper, zinc, and nickel, dissolves easily in this acid with evolution +of hydrogen gas." 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. "Now no other +explanation," he observes, "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." + +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 impossibility which we noticed and characterized in a +previous chapter.(90) 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. + +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. "A little leaven," that is, dough in a certain state of +chemical action, impresses a similar chemical action upon "the whole +lump." 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, giving out carbonic acid gas, and becoming alcohol. It is +not the elements contained in the yeast which do this. "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." 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. + +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. + +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 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 +_all_ 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. + +§ 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. + +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 +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. + +Dr. Liebig believes himself to have found the solution of this _vexata +quaestio_ in a class of chemical actions in which scarcely any less acute +and penetrating inquirer would have thought of looking for it. + +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. + +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. + +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 _vice versa_. +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 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? + +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. + +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. + +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 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.(91) + +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. + +§ 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. + +The second of the two factors (as they may be termed) 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. + +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 _not_ absorb concentrated +solutions of alkaline salts; and such solutions _do_ 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. + +§ 4. From the foregoing and similar instances, we may 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. + +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. + +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 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. + +§ 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 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. + +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.(92) Many even of 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. + +§ 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 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. + +§ 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 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. + +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 +_principia_ 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. + +These general truths will doubtless make their first appearance in the +character of hypotheses; not proved, nor 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. + +END OF VOL. I. + + + + + +BOOKS PUBLISHED BY + +John W. Parker, West Strand, London. + +Mr. J. S. Mill's Principles of Political Economy. Second Edition. 2 vols. +Octavo. 30_s._ + +Mr. J. S. Mill's Essays on some Unsettled Questions of Political Economy. +Octavo. 6_s._ 6_d._ + +Archbishop Whately's Introductory Lectures on Political Economy. Third +Edition. Octavo, 8_s._ + +Mr. Cornewall Lewis on the Influence of Authority in Matters of Opinion. +Octavo, 10_s._ 6_d._ + +Mr. E. G. Wakefield's View of the Art of Colonization. Octavo, 12_s._ + +The Evils of England, Social and Economical. 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I have elsewhere said what appeared to + me necessary in reply to his arguments (_Westminster Review, for + October 1842_.) 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. + +_ 4 Computation or Logic_, chap. ii. + + 5 In the original, "had, _or had not_." These last words, as involving + a subtlety foreign to our present purpose, I have forborne to quote. + + 6 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 minutiae. + +_ 7 Notare_ to mark; _con_notare, to mark _along with_; to mark one + thing _with_ or _in addition to_ another. + + 8 Archbishop Whately, who in the more recent editions of his _Elements + of Logic_ has aided in reviving the important distinction treated of + in the text, proposes the term "Attributive" as a substitute for + "Connotative," (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 "to + connote," it is not, I think, fitted to supply the place of the word + Connotative in scientific use. + + 9 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. _Felony_, 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. + + 10 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 _to connote_, Mr. Mill, in his _Analysis + of the Phenomena of the Human Mind_, 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 + _noting_ the attribute, and _connoting_ 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 _de_notation which would be said to be dropped, what was + previously connoted becoming the whole signification. + + 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 _to connote_. + 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 _forms_, which + word may generally, in their writings, be understood as synonymous + with _attributes_. + + Now, if the word _to connote_, 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. + + 11 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. + +_ 12 Philosophy of the Inductive Sciences_, vol. i. p. 40. + + 13 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. + + "Nous savons qu'il existe quelque chose hors de nous, parceque nous + ne pouvons expliquer nos perceptions sans les rattacher a des causes + distinctes de nous-memes; 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 meme les plus contraires, + selon qu'elles rencontrent telle nature ou telle disposition du + sujet. Mais savons-nous quelque chose de plus? et meme, vu le + caractere indetermine des causes que nous concevons dans les corps, + y a-t-il quelque chose de plus a savoir? Y a-t-il lieu de nous + enquerir si nous percevons les choses telles qu'elles sont? Non + evidemment.... Je ne dis pas que le probleme est insoluble, _je dis + qu'il est absurde et enferme une contradiction_. Nous _ne savons pas + ce que ces causes sont en elles-memes_, et la raison nous defend de + chercher a le connaitre: mais il est bien evident _a priori_, + qu'_elles ne sont pas en elles-memes ce quelles sont par rapport a + nous_, puisque la presence du sujet modifie necessairement 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 qualites et des + proprietes, mais qui ne resembleraient a rien de ce que nous + connaissons. Le feu ne manifesterait plus aucune des proprietes que + nous lui connaissons: que serait-il? C'est ce que nous ne saurons + jamais. _C'est d'ailleurs peut-etre un probleme qui ne repugne pas + seulement a la nature de notre esprit, mais a l'essence meme des + choses._ Quand meme en effet on supprimerait par la pensee tous les + sujets sentants, il faudrait encore admettre que nul corps ne + manifesterait ses proprietes autrement qu'en relation avec un sujet + quelconque, et dans ce cas _ses proprietes ne seraient encore que + relatives_: en sorte qu'il me parait fort raisonnable d'admettre que + les proprietes determinees des corps n'existent pas independamment + d'un sujet quelconque, et que quand on demande si les proprietes de + la matiere sont telles que nous les percevons, il faudrait voir + auparavant si elles sont en tant que determinees, et dans quel sens + il est vrai de dire qu'elles sont."--_Cours d'Histoire de la + Philosophie Morale au 18me siecle_, 8me lecon. + + 14 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 + _Lectures_, or Mill's _Analysis of the Mind_. + + 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 _subjectivity_ 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.--_Cours_, ut supra, 9me lecon. + +_ 15 Analysis of the Human Mind_, i. 126 et seqq. + + 16 Dr. Whewell (_Of Induction_, p. 10) questions this statement, and + asks, "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?" I thought it had been evident that I was here speaking of + rational digging, and not of digging by instinct. + + 17 "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 _man is a living creature_, but it is for + this reason, that it pleased men to impose both these names on the + same thing."--_Computation or Logic_, ch. iii. sect. 8. + + 18 "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."--_Computation or Logic_, ch. v., sect. 1. + + 19 Ch. iii. sect. 3. + + 20 Book iv. ch. vii. + + 21 {~GREEK CAPITAL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER THETA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI AND PERISPOMENI~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER ALPHA WITH MACRON~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER ALPHA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER PHI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ALPHA WITH VARIA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER ETA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER EPSILON WITH DASIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}; {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK KORONIS~} + {~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH DASIA~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMEGA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER IOTA WITH PSILI~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER FINAL SIGMA~} (differences in the accidental + properties) {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}; {~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH DASIA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON WITH VARIA~} {~GREEK SMALL LETTER IOTA WITH PSILI~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA~} (differences in the + essential properties) {~GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}--_Isag._ cap. iii. + + 22 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. + + 23 The always acute and often profound author of _An Outline of + Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more + intelligible if, in the majority of places, we substitute 'the + knowledge of' for what he calls 'the idea of' " (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. + + 24 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. + + 25 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 "explains anything _more_ of the nature of + the thing than is implied in the name;" (including under the word + "implied," 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 _not_ be expressed by the proper definition of the + word in its ordinary employment. + + Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately, + understands by a Real Definition one which contains _less_ than the + Nominal Definition, provided only that what it contains is + sufficient for distinction. "By _real_ 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."--_Formal Logic_, 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. + + 26 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, + + A dragon is a thing which breathes flame, + A dragon is a serpent, + Therefore some serpent or serpents breathe flame, + + "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." + + 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, "Some serpent or + serpents either do or are _imagined_ to breathe flame." And to prove + this conclusion by the instance of dragons, the premisses must be, A + dragon is _imagined_ 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. + + 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, _must_ be false, (the conclusion being so,) the real + premiss cannot be the definition, which is true, but the statement + of fact, which is false. + + 27 "Few people" (I have said in another place) "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." + + 28 Contraries: + All A is B + No A is B + + Subtraries: + Some A is B + Some A is not B + + Contradictories: + All A is B + Some A is not B + + Also contradictories: + No A is B + Some A is B + + Respectively subalternate: + All A is B; No A is B + Some A is B; and Some A is not B + + 29 His conclusions are, "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." The reference of + syllogisms in the last three figures to the _dictum de omni et + nullo_ 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 _dictum_, and to which he gives the + names of _dictum de diverso_ for the second figure, _dictum de + exemplo_ for the third, and _dictum de reciproco_ for the fourth. + See part i. or _Dianoiologie_, chap. iv. § 229 _et seqq._ + + Mr. De Morgan's "Formal Logic, or the Calculus of Inference, + Necessary and Probable," (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 "most" 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 "numerically definite + propositions," and extending it to such forms as these:--"45 Xs (or + more) are each of them one of 70 Ys," or "45 Xs (or more), are no + one of them to be found among 70 Ys," 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 formulae for such inferences; creating for that purpose not + only a new technical language, but a formidable array of symbols + analogous to those of algebra. + + 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 "quantification of the predicate," + 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 "All men are mortal" is equivalent to "Every man is + _some_ mortal." But as mankind certainly will not be persuaded to + "quantify" 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 _class_ 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. + + 30 Supra, p. 129. + + 31 Logic, p. 239 (9th ed.) + + 32 It is hardly necessary to say, that I am not contending for any such + absurdity as that we _actually_ "ought to have known" 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, _knew_ that the Duke of Wellington was mortal; but I do say, + that he _asserted_ 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. + +_ 33 Of Induction_, p. 85. + + 34 For August 1846. + + 35 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. {~GREEK CAPITAL LETTER EPSILON~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA WITH OXIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} + {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ETA WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ETA WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMEGA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~}. {~GREEK SMALL LETTER ETA WITH DASIA~} {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}{~GREEK SMALL LETTER RHO~} {~GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} + {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~} {~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER EPSILON WITH PSILI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA WITH OXIA~}. {~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER DELTA~}{~GREEK KORONIS~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER KAPPA~} {~GREEK SMALL LETTER EPSILON WITH PSILI AND OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~} + {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER NU~}: {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK KORONIS~} {~GREEK SMALL LETTER ETA WITH DASIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA WITH VARIA~} + {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ALPHA WITH OXIA~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER FINAL SIGMA~} ... {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER ALPHA WITH OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER FINAL SIGMA~} + {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMEGA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~} {~GREEK SMALL LETTER CHI~}{~GREEK SMALL LETTER ALPHA WITH OXIA~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH VARIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER ZETA~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER ALPHA WITH PSILI AND OXIA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER UPSILON~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~} + {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ETA WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMEGA WITH PERISPOMENI~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER OMICRON WITH DASIA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA WITH PSILI~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA WITH PERISPOMENI~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER BETA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER IOTA WITH OXIA~}{~GREEK SMALL LETTER ZETA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER ALPHA WITH PSILI~}{~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PERISPOMENI~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER IOTA~}: {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER IOTA WITH VARIA~} + {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON WITH VARIA~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER FINAL SIGMA~}, {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~}{~GREEK SMALL LETTER DELTA~}{~GREEK KORONIS~} {~GREEK SMALL LETTER EPSILON WITH PSILI~}{~GREEK SMALL LETTER IOTA WITH OXIA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} {~GREEK SMALL LETTER ZETA~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER UPSILON WITH DASIA AND OXIA~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER ETA WITH DASIA AND VARIA~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER ETA WITH VARIA~}, {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER NU~}{~GREEK SMALL LETTER OMEGA WITH OXIA~}{~GREEK SMALL LETTER SIGMA~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER EPSILON~}{~GREEK SMALL LETTER IOTA~}{~GREEK SMALL LETTER NU~}. {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON WITH VARIA~} + {~GREEK SMALL LETTER GAMMA~}{~GREEK SMALL LETTER ALPHA WITH VARIA~}{~GREEK SMALL LETTER RHO~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER EPSILON WITH OXIA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMEGA WITH YPOGEGRAMMENI~} {~GREEK SMALL LETTER MU~}{~GREEK SMALL LETTER EPSILON WITH VARIA~}{~GREEK SMALL LETTER NU~} {~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER UPSILON WITH PSILI~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER ETA WITH PERISPOMENI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}, {~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER OMEGA WITH YPOGEGRAMMENI~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER EPSILON WITH VARIA~} {~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER ALPHA~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMEGA WITH PERISPOMENI~}{~GREEK SMALL LETTER FINAL SIGMA~} {~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER ETA~}{~GREEK SMALL LETTER PI~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER RHO~}{~GREEK SMALL LETTER KAPPA~}{~GREEK SMALL LETTER OMICRON WITH OXIA~}{~GREEK SMALL LETTER TAU~}{~GREEK SMALL LETTER IOTA~} {~GREEK SMALL LETTER DELTA~}{~GREEK SMALL LETTER ETA WITH PERISPOMENI~}{~GREEK SMALL LETTER LAMDA~}{~GREEK SMALL LETTER OMICRON~}{~GREEK SMALL LETTER NU~}. + + 36 The reviewer misunderstands me when he supposes me to say that "the + conclusion must be admitted _before_ we can admit the major + premiss." What I say is, that there must be ground for admitting it + _simultaneously_, or else the major premise is not proved. + +_ 37 Mechanical Euclid_, pp. 149 _et seqq._ + + 38 We might, it is true, insert this property into the definition of + parallel lines, framing the definition so as to require, _both_ that + when produced indefinitely they shall never meet, and _also_ 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. + + 39 Whewell's _Philosophy of the Inductive Sciences_, i. 130. + + 40 Dr. Whewell (_Of Induction_ p. 84) thinks it unreasonable to contend + that we know by experience, that our idea of a line exactly + resembles a real line. "It does not appear," he says, "how we can + compare our ideas with the realities, since we know the realities + only by our ideas." We know the realities (I conceive) by our eyes. + Dr. Whewell surely does not hold the "doctrine of perception by + means of ideas," which Reid gave himself so much trouble to refute. + + 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. + +_ 41 Phil. Ind. Sc._ i. 59-61. + + 42 Ibid. 57. + + 43 Ibid. 54, 55. + + 44 "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 _man_ to be + the mode of agitating the air which is essentially communicative of + the ideas of reason, cookery, bipedality, &c." De Morgan, _Formal + Logic_, p. 246. + + 45 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 _could not_ make a + body revolve round a distant centre, unless either by some impelling + mechanism, or by miracle:--"Tout ce qui n'est pas explicable," says + he in a letter to the Abbe Conti, "par la nature des creatures, 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 + executable par les natures des creatures. Si Dieu donnait cette loi, + par exemple, a un corps libre, de tourner a l'entour d'un certain + centre, _il faudrait ou qu'il y joignit d'autres corps qui par leur + impulsion l'obligeassent de rester toujours dans son orbite + circulaire, ou quil mit un ange a ses trousses, ou enfin il faudrait + qu'il y concourut extraordinairement_; car naturellement il + s'ecartera par la tangente."--_Works of Leibnitz_, ed. Dutens, iii. + 446. + +_ 46 Phil. Ind. Sc._ ii. 174. + +_ 47 Phil. Ind. Sc._ i., 238. + +_ 48 Phil. Ind. Sc._ i. 237. + +_ 49 Ibid._ 213. + +_ 50 Ibid._ 384, 385. + + 51 In his recent pamphlet (p. 81), Dr. Whewell greatly attenuates the + opinion here quoted, reducing it to a surmise "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." 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 + _necessary consequence_ 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. + + 52 The _Quarterly Review_ 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:-- + + "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, _i.e._, 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. _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._ 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 ... _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._" + + And again, of the axioms of mechanics:--"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 _a priori_ + reasoning can possibly assure us that they _do_ act under precisely + similar circumstances? that points which differ in place _are_ + 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, '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' ... 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." + + On the "paradox of universal propositions obtained by experience," + the same writer says: "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 _general_ + propositions, coextensive at least with all human experience. That + they pervade all the objects of experience, must ensure their + continual suggestion _by_ 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." + + "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. _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_, if ... axioms be violated + in their enunciation." + + 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. "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."--SIR J. HERSCHEL's _Discourse on the Study of Natural + Philosophy_, pp. 95, 96. + + 53 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) "is not the same thing + as experience and observation. Induction is experience or + observation _consciously_ looked at in a _general_ form. This + consciousness and generality are necessary parts of that knowledge + which is science." 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 "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." This use of the + term he deems a "confusion of knowledge with practical tendencies." + + 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. + + 54 Supra, p. 214. + +_ 55 Phil. Ind. Sc._ ii. 213, 214. + +_ 56 Ibid._ + +_ 57 Phil. Ind. Sc._ ii. p. 173. + +_ 58 Cours de Philosophie Positive_, vol. ii, p. 202. + + 59 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): + "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 _Philosophy_, 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 + 'inherent virtue' must have coincided in its effect with the + Newtonian force; and then, the two explanations would agree, except + so far as the word 'inherent' was concerned. And if such a part of + an earlier theory as this word _inherent_ 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." + + If the doctrine of vortices had meant, not that vortices existed, + but only that the planets moved _in the same manner_ 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 _description_ of the planetary motions, does not; but the + Newtonian theory as an _explanation_ 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. + + 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 + "found to be untenable." But leave that out, and where is the + theory? The word inherent _is_ the theory. When that is omitted, + there remains nothing except that the heavenly bodies move by "a + virtue," _i.e._ by a power of some sort. + + 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. + + 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) "true, and consistent with one another"? + + 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. + +_ 60 Of Induction_, p. 33. + + 61 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 _all_ phenomena are regular in their course. + + Neither would it be correct to say that every induction by which we + infer any truth, implies the general fact of uniformity _as + foreknown_, even in reference to the kind of phenomena concerned. It + implies, _either_ that this general fact is already known, _or_ 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. + + 62 Infra, chap. xxi. + + 63 Infra, chap. xxi, xxii. + + 64 Dr. Whewell (_Of Induction_, p. 16) will not allow these and similar + erroneous opinions to be called inductions; inasmuch as such + superstitious fancies "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." 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 Caesar, 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 _a priori_ 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. + + 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. "For many + ages," says Archbishop Whately, "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." This was induction, but + bad induction: just as a vicious syllogism is reasoning, but bad + reasoning. + + 65 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, (_Prospective Review_ for February 1850,) who + maintains that "we always apply the word cause rather to that + element in the antecedents which exercises _force_, and which would + _tend_ at all times to produce the same or a similar effect to that + which, under certain conditions, it would actually produce." And he + says, that "every one would feel" the expression, that the cause of + a surprise was the sentinel's being off his post, to be incorrect; + but that "the allurement or force which _drew_ him off his post, + might be so called, because in doing so it removed a resisting power + which would have prevented the surprise." 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. + + 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. + + It is for the same reason, that no one (as the reviewer remarks) + "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." These conditions (besides that they are + antecedent _states_, and not proximate antecedent _events_, 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. + + 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, "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." 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. + + 66 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. + + 67 I use the words "straight line" 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. + + 68 The reviewer of Dr. Whewell in the _Quarterly Review_. + + 69 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 _necessarily_ + follow from his character, all that is really meant (for no more is + meant in any case whatever of causation) is that he invariably + _does_ 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. + + 70 Unless we are to consider as such the following statement, by one of + the writers quoted in the text: "In the case of mental exertion, the + result to be accomplished is _preconsidered_ or meditated, and is + therefore known _a priori_, or before experience."--(Bowen's _Lowell + Lectures on the Application of Metaphysical and Ethical Science to + the Evidence of Religion_, 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 _first time_ 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 _will_ 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 _desire_ what we do not + know to be in our power; and finding by experience that our bodies + move according to our _desire_, we may then, and only then, pass + into the more complicated mental state which is termed will. + + 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 _more_ than + antecedence and consequence. + + 71 Reid's _Essays on the Active Powers_, Essay iv. ch. 3. + +_ 72 Prospective Review_ for February 1850. + +_ 73 Vide supra_, p. 267, note. + + 74 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. + + 75 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. + + 76 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. + +_ 77 Discourse on the Study of Natural Philosophy_, p. 179. + + 78 For this speculation I am indebted to Mr. Alexander Bain. + + 79 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. + + 80 Pp. 159-162. + + 81 Infra, book iv., chap. ii. On Abstraction. + + 82 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 _a + priori_ 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. + + 83 Discourse, pp. 156-8, and 171. + +_ 84 Outlines of Astronomy_, p. 584. + + 85 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): + + "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 formulae 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 _a, b, c_? Nature does not present to us the cases in + this form; and how are we to reduce them to this form? You say, + _when_ we find the combination of A B C with _a b c_ and A B D with + _a b d_, 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 _a, b, c_ + 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 formulae 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 formulae?" + + He adds that, in this work, the methods have not been applied "to a + large body of conspicuous and undoubted examples of discovery, + extending along the whole history of science," which ought to have + been done in order that the methods might be shown to possess the + "advantage" (which he claims as belonging to his own) of being those + "by which all great discoveries in science have really been + made."--(p. 66.) + + 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 "takes for granted the very thing which is most + difficult to discover, the reduction of the argument to formulae such + as are here presented to us." 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 _to what_, 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. + + 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. + + 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 + _conception_ 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, "Dogs bark." 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 _a_. As a truth made known by the + Method of Difference, "Fire burns" 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, _a_ B C. + + 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. + + His challenge, however, to point out which of the four methods are + exemplified in certain important cases of scientific inquiry, is + easily answered. "The planetary paths," 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 + "falling bodies," 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 + _in vacuo_, constituting an application of the Method of Difference. + The law of "refracted rays," (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 "cosmical motions" 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 "chemical analysis" 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 "the A B C and _a b c_ elements" of these + cases. + + 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 _dis_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. + +_ 86 Ante_, p. 378. + + 87 It seems hardly necessary to say that the word _impinges_, 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. + +_ 88 Essays on some Unsettled Questions of Political Economy_, Essay V. + + 89 There is no danger of confounding this acceptation of the term with + the peculiar employment of the phrase "tangential force" in the + theory of the planetary perturbations. + + 90 Supra, p. 420. + + 91 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. + + 92 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. + + + + + +***END OF THE PROJECT GUTENBERG EBOOK A SYSTEM OF LOGIC, RATIOCINATIVE AND INDUCTIVE (VOL. 1 OF 2)*** + + + +CREDITS + + +August 31, 2008 + + Project Gutenberg TEI edition 1 + Produced by David Clarke, David King, and the Online + Distributed Proofreading Team at <http://www.pgdp.net/>. 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