m^- THE LIBRARY OF THE UNIVERSITY OF CALIFORNIA GIFT OF (MrJ Emmet P. X. Sheehan ■^ "^ IVV/l V*-*. 1 ^ V.I SYSTEM OF LOGIC, RATIOGIIATIVE AND INDUCTIVE; :1NG A CONNECTED VIEW OF THE PRINCIPLES OF EVIDENCE AND THE METHODS OF SCIENTIFIC INVESTIGATION. BY JOHN STUART MILL NEW-YORK: HARPER & BROTHERS, PUBLISHERS, 82 CLIFF STREET. 18 4 6. ig^i; PREFACE. This book makes no pretence of giving to the world a new theory of our 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 pre- sumption 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 im- provement which remains to be effected in methods of philoso- phizing (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 con- tempt 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 eri'oneous : and the view which he has suggested of the nature and functions of the Syllogism may, perhaps, afford the means of IV PREFACE. 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 con- fused appz'ehension of the import of the different classes of Words and Assertions, will not regai'd 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. The author has endeavored to combat their theory in the manner in which Diogenes confuted the skeptical reasonings against the possibility of motion ; remembering that Diogenes' argument would have been equally conclusive, although his individual perambula- tions 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 trea- tises, 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 endeavored to do full justice in the body of the work. But as with one of these writers, Mr. 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 Induc- tive Sciences, the corresponding portion of this work would probably not have been written. PREFACE. V 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 irrevo- cably acquired and universally assented to, can be made instru- mental to the gradual formation of a similar body of received doctrine in moral and political science. While the views promulgated in these volumes still await the verdict of competent judges, it would have been useless to attempt to make the exposition of them so elementary, as to be suited to readers wholly unacquainted with the subject. It can scarcely be hoped that the Second Book will be throughout intelligible to any one who has not gone carefully through some one of the common treatises on Logic ; among which that of Archbishop Whately is, on every account, to be preferred. And the Third Book presup- poses some degree of acquaintance with the most general truths of mathematics, as well as of the principal branches of physical science, and with the evidence on which those doctrines rest. Among books professedly treating of the mental phenomena, a previous familiarity with the earlier portion of Dr. Brown's Lec- tures, or with his treatise on Cause and Effect, would, though not indispensable, be advantageous ; that philosopher having, in the author's judgment, taken a more correct view than any other English writer on the subject of the ultimate intellectual laws of scientific inquiry; while his unusual powers of popularly stating ond felicitously illustrating whatever he understood, render his works the best preparation which can be suggested, for speculations sim- ilar to those contained in this Treatise. CONTENTS. INTRODUCTION. ''"s« ^ 1 . A definition at the commencement of a subject must be provisional . 1 2. Is logic the art and science of rea- soning ? 2 3. Or the art and science of the pursuit of truth? ib. 4. Logic is concerned with inferences, not with intuitive truths . . 3 5. Relation of logic to the other sci- ences 5 6. Its utility, how shown ... 6 7. Definition of logic stated and illus- trated ~ BOOK I. OF NAMES AND PROPOSITIONS. CHAPTER I. Of the necessity of commencing with an Anaylsis of Language. j ^ 1. Theory of names, why a necessary part of logic 11 2. First step in the analysis of Propo- sitions 12 3. Names must be studied before Things 13 CHAPTER II. Of Names, (f 1. Names are names of things, not of our ideas 15 2. Words which are not names, but parts of names 3. General and Singular names . 4. Concrete and Abstract . 5. Connotative and Non-connotative 6. Positive and Negative . 7. Relative and Absolute . 8. Univocal and ^Equivocal CHAPTER III. Of the Things denoted by Names, i) 1. Necessity of an enumeration of Namable Things. The Categories of Aristotle 2. Ambiguity of the most general names 3. Feelings, or states of consciousness 4. Feelings must be distinguished from their physical antecedents. Perceptions, what 5. "Volitions, and Actions, what . 6. Substance and Attribute Pago ^ 7. Body 38 8. Mind 41 9. Qualities 42 10. Relations 44 11. Resemblance 46 12. Quantity 43 13. All attributes of bodies are grounded upon states of consciousness . 49 14. So also all attributes of mind . 50 15. Recapitulation . . . .51 CHAPTER IV. Of Propositions. () 1. Nature and office of the copula . 52 2. Affirmative and Negative proposi- tions 54 3. Simple and Complex . , .55 4. Universal, Particular, and Singular 57 CHAPTER V. Of the Import of Propositions. § 1. Doctrine that a proposition is the expression of a relation between two ideas 59 2. Doctrine that it is the expression of a relation between the meanings of two names . . . .01 3. Doctrine that it consists in referring something to, or excluding some- thing from, a class . . .63 4. What it really is . . . .66 5. It asserts (or denies) a sequence, a coexistence, a simple existence, a causation 67 6. — or a resemblance . . . .69 7. Propositions of which the terms are abstract 71 CHAPTER VI. Of Propositions merely Verbal. (J 1. Essential and Accidental proposi- tions 73 2. All essential propositions are identi- cal propositions . . . .74 3. Individuals have no essences . . 77 4. Real propositions, how distinguished from verbal T8 5. Two modes of representing the im- port of a Real proposition . . 79 CHAPTER VII. Of the Nature of Classification, and the Five Predicables. ij 1. Classification, how connected with Naming 80 CONTENTS. Vll Page § 2. The Predicables, what ... 81 3. Genus and Species .... ib. 4. Kinds have a real existence in nature 83 5. Differentia 8C G. Differentiae for general purposes, acd differentise for special or technical purposes 88 7. Proprium 89 8. Accidens 90 CHAPTER VIII. Of Definition. •^ 1. Definition, why treated of in this place 91 2. A definition, what . . . . (6. 3. Every name can be defined, whose meaning is susceptible of analysis 92 4. Complete, how distinguished from incomplete definitions . . .94 5. — and from descriptions . . .95 G. What are called definitions of Things are definitions of Names with an imphed assumption of the e.xistence of Things corresponding to them . 98 7. — even when such things do not in reality exist 101 8. Definitions, though of tiames only, must be grounded on knowledge of the corresponding Things . 103 BOOK II. OF REASONING. CHAPTER J. Of Inference, or Reasoning, in general. ^ 1. Retrospect of the preceding Book . 107 2. Inferences improperly so called . 108 3. Inferences proper, distinguished into inductions and ratiocinations .111 CHAPTER II. Of Ratiocination, or Syllogism. § 1. Analysis of the Syllogism . .112 2. The dictum de omui not the founda- tion of reasoning, but a mere iden- tical proposition . . . . IIG 3. What is the really fundamental ax- iom of Ratiocmation . . . 119 4. The other form of the axiom . . 120 CHAPTER HI. Of the Functions, and Logical Value, of the Syllogism. § 1. ]s \.\ie SyWogism a petitio priricipii ? . 122 2. Insufficiency of the common theory ih. 3. All inference is from particulars to particulars 124 4. General propositions are a record of such inferences, and the rules of the syllogism are rules for the in- terpretation of the record . . 129 5. The syllogism not the type of rea- soning, but a test of it . . . 131 6. The true type, what . . .134 7. Relation between Induction and De- duction 136 CHAPTER IV. Of Trains of Reasoning, and Deductive Sciences. § 1. For what purpose trains of reasoning exist 137 Pago 'J 2. A tram of reasoning is a series of inductive inferences . . 138 3. — from particulars to particulars through marks of marks . . 139 4. Why there are deductive sciences . 141 5. — and why other sciences still re- mam experimental . . . 144 G. Experimental sciences may become deductive by the progress of experi- ment 145 7. In what manner this usually takes place 14G CHAPTER V. Of Demonstration, and Necessary Truths. ^ 1. The theorems of geometry arc only necessary truths in the sense of necessarily following from hypoth- eses 148 2. Those hypotheses are real facts with some of their circumstances omit- ted 150 3. Some of the first principles of geom- etry are axioms, and these are not hypothetical 151 4. — but are experimental truths . . 152 5. An objection answered . . . 154 6. Mr. Vvhewell's opinions on axioms examined 155 CHAPTER VI. The same Subject continued. ^ 1. All deductive sciences are inductive 162 2. The propositions of the science of number are not verbal, but gener- alizations from experience , . 164 3. In what sense hypothetical . . 168 4. The characteristic property of dem- onstrative science is to be hypo- thetical 169 5. Definition of demonstrative evidence and of logical necessity . . .170 BOOK III. OF INDUCTION. CHAPTER I. Preliminary Observations on Induction in general, § 1. Importance of an Inductive Logic . 171 2. The logic of science is also that of business and life .... 172 CHAPTER II. Of Inductions improperly so called. § 1. Inductions distinguished from verbal transformations .... 174 2. — from inductions, falsely so called, in mathematics .... 175 3. —and from descriptions . . . 177 4. Examination of I\lr. Whewell's the- ory of induction .... 178 CHAPTER III. On the Ground of Induction. 5 1. Axiomofthe uniformity of the course of nature 183 2. Not true in every sense. Induction per enumerationem simplicem . .180 3. Tne question of Inductive Logic stated 187 VUl CHAPTER IV. Of Laws of Nature. (l 1. The general regularity in nature is a tissue of partial regularities, call- ed laws 189 2. Scientific induction must be ground- ed upon previous spontaneous in- ductions 191 3. Are there any inductions fitted to be a test of all others ? . . .192 CHAPTER V. Of the Law of Universal Caxisation. ^ 1. Theuniversallawof successive phe- nomena is the Law of Causation . 194 2. — i. e. the law that every consequent has an invariable antecedent . 196 3. The cause of a phenomenon is the assemblage of its conditions . . 197 4. The distinction of agent and patient illusory 201 5. The cause is not the invariable ante- cedent, Ijut the unconditional invari- able antecedent .... 202 6. Can a cause be simultaneous with its effect ? 204 7. Idea of a Permanent Cause, or ori- ginal natural agent . . . 206 8. Uniformities of coexistence between effects of different permanent causes, are not laws . . . 208 9. M. Comte's objections to the word cause 209 CHAPTER VI. Of ihe Compositimi of Causes. ij 1. Two modes of the conjunct action of causes, the arechanical and the chemical 210 2. The composition of causes the gen- eral rule ; the other case excep- tional 212 3. Are effects proportional to their causes? 214 CHAPTER Vn. Of Observation and Experiment. ^ 1. The first step of inductive inquiry is a mental analysis of complex phe- nomena into their elements . . 216 2. The next is an actual separation of those elements .... 217 3. Advantages of experiment over ob- servation 218 4. Advantages of observation over ex- periment 220 CHAPTER VIII. Of the Four Methods of Experimental Inqxary. (j 1. Method of Agreement . . . 222 2. Method of Difference . . .224 3. Mutual relation of these two meth- ods 225 4. Joint Method of Agreement and Dif- ference 227 5. Method of Residues . . .229 6. Method of Concomitant Variations . 230 7. Limitations of this last method . 234 Page CHAPTER IX. Miscellaneous Examples of the Fowr Methods. (} 1. Liebig's theory of metallic poisons . 237 2. — how far a perfect example . . 239 3. Theory of induced electricity . . 240 4. Dr. Wells' theory of dew . . .242 5. Examples ofthe Method of Residues 247 CHAPTER X. Of Plurality of Causes ; and of the Intermixture of Effects. () 1. One effect may have several causes 250 2. — which is the source of a character- istic imperfection of the Method of Agreement 251 3. Plurahty of Causes, how ascertained 253 4. Concurrence of causes which do not compound their effects . . . 254 5. Difiiculties of the investigation, when causes compound their ef- fects 256 0. Three modes of investigating the laws of complex effects . . 259 7. The method of simple observation inapplicable 260 8. The purely experimental method in- applicable 261 CHAPTER XL Of the Deductive Method. ^ 1. First stage ; ascertainment of ttie laws of the separate causes by di- rect induction .... 264 2. Second stage ; ratiocination from the simple laws to the complex cases 267 3. Third stage ; verification by specific experience . . . . . 268 CHAPTER XII. Of the Explanation of Laws of Nature. 9 1. Explanation defined . . . 271 2. First mode of explanation, by resolv- ing the law of a complex effect into the laws of the concurrent causes and the fact of their coexistence . ib. 3. Second mode; by the detection of an intermediate link in the sequence . 272 4. Laws are always resolved into laws more general than themselves . ib. 5. Third mode ; the subsumption of less general laws under a more general one . . . . 274 6. What the explanation of a law of nature amounts to . . . . 276 CHAPTER Xni. Miscellaneous Examples of the Explanation of Laws of Nature, (j 1. Liebig's theory' of the contagious- ness of chemical action . .277 2. His theory of respiration . . . 280 3. Other speculations of Liebig . • 282 4. Examples of following newly-dis- covered laws into their complex manifestations .... 283 5. Examples of empirical generaliza- tions, afterwards confirmed and explained deductively . . . 284 6. Example from mental science . . 285 CONTENTS. ^ 7. The dctluctive method henceforth the main instrument of scientilic iniiuir>' 286 CHAPTER XIV. Of the Limits to the Explanation of Laws of Aature ; and of Hypotheses. ^ 1. Can all the sequences in nature be resolvable into one law ? 2. Ultimate laws cannot be less numer ous than the distinguishable feel ings of our nature .... 287 3. Ill what sense ultimate facts can be explained 289 •1. The proper use of scientific liypoth eses 290 5. Their indispensableness . . . 294 ti. Legitimate, how distinguished from illegitimate hypotheses 7. Some inquuies apparently hypothet ical are really ijiductive CHAPTER XV. Of Progressive Effects ; and of the Continued Action of Causes. <;> 1. How a progressive effect results from the simple continuance of the cause 300 2. — and from the progressiveness of the cause 302 3. Derivative laws generated from a single ultimate law . . . 301 CHAPTER XVI. Of Empirical Laws. § 1. Definition of an empirical law . 305 2. Derivative laws commonly depend upon collocations .... 306 3. The collocations of the permanent causes are not reducible to any law 307 ■i And hence empirical laws cannot be relied upon beyond the limits of actual experience .... ib. 5. Generalizations which rest only on the Method of Agreement can only be received as empirical laws . 308 C. Signs from which an observed uni- formity of sequence may be pre- sumed to be resolvable . . . 309 7. Most, if not all, cases of sequence from very complex antecedents, are resolvable . . . .311 3. Two kinds of empirical laws . . 312 CHAPTER XVII. Of Chance, and its Elimination. % 1. The proof of empirical laws depends on the theon,' of chance . . 312 2. Chance defined and characterized .313 3. The elimination of chance . . 316 4. Discovery of a residual phenomena by eliminating chance . . .317 5. The doctrine of chances . . . 318 CHAPTER XVJII. Of the Calculation of Chances. riori 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 knowl- edge 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. So far forth as belief professes to be founded upon proof, the office of logic is to supply a test for ascer- taining whether or not the bfilief is well grounded. With the claims which any proposition has to belief on its own intrinsic evidence, that is, without evidence in the proper sense of the word, logic has nothing to do, § 5. As the far greatest portion of our knowledge, whether of gen- eral truths or of particular facts, is avowedly matter of inference, nearly the whole, not only of science, but of human conduct, is amen- able to the authority of logic. To draw inferences has been said to be the great business of life. Every one has daily, hourly, and moment- ary need of ascertaining facts which he has not directly observed ; not from any general pur|iose 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 com- mander, of the navigator, of the physician, of the agriculturist, is merely 6 INTRODUCTION. to judge of evidence, and to act accordingly. They all have to ascer- tain certain facts, in order that they may afterwards apply certain rules, either devised by themselves, or prescribed for their gmdance 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. Our definition of logic, therefore, will be in danger of including the whole field of knowledge, unless we qualify it by some further limitation, showing distinctly where the domain of the other arts and sciences, and of common prudence ends, and that of logic begins. The distinction is, that the science or knowledge of the particular subject-matter fmiiishes the evidence, while logic furnishes the prin- cij)les and rules of the estimation of evidence. Logic does not pre- tend to teach the surgeon what are the symptoms which indicate a violent death. This he must learn fi-om his own experience and obser- vation, or from that of others, his predecessors in his peculiar science. 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. Logic alone can never show that the fact A proves the fact B ; but it can point 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 any given case, belongs, exclusively, to the particular art or science, or to ovir knowl- edge of the particular subject. It is in this sense that logic is, what Bacon so expressively calls it, ars artmm ; 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 what- ever 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 infer- ences, of drawing conclusions which are not gi'ounded in the realities of things. Wliatever has at any time been concluded justly, whatever knowledge has been acquired otherwise than by immediate intuition, depended upon the observance of the laws which it is the province of logic to investigate. If the conclusions are just, and the knowledge sound, those laws have actually been observed. § 6. "We need not, therefore, seek any further 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 conforms in every instance in which it judges 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 imdoubtedly be brought to a certain, not inconsider- able, stage of advancement, without the application of any other logic to it than what all persons, who are said to have a sound understand- DEFINITION AND PUOVINCE OF LOGIC. 7 ing, acquire empirically in the course of their studies. Men judged of evidence, and often very coiTectly, before logic was a science, or they nevei' 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 mechan- ics, and to what thinlcers can do without principles of logic. And the limits, in the two cases, are of the same kind. The extent of what man can do without understanding the theoiy of what he is doing, is in all cases much the same : he can do whatever is very easy; what requires only time, and patient industry. But in the progress of science fi-om its easiest to its more difficult problems, every gi-eat step in advance has had either as its precursor or as its accompaniment and necessary condition, a coiTosponding 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 understand- ing which are subservient to the estimation of evidence : both the process itself of proceeding from known truths to unknown, and all intellectual operations 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 fi'om them perma- nent and readily accessible in the memory, but for so marshaling 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 eiTor whether it be sufficient. The analysis of the instruments we employ in the investigation of truth, is part of the analysis of the investigation itself; since no art is complete, unless another art, that of constructing the tools and fitting them for the purposes of the art, is embodied in it. Our object, therefore, 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 operation^ in qne-stion into their ultimate elements. It is enough if the analysis as far as it goes is coiTect, and if it goes far enough for the practical purposes- of logic considered as an art. The separation of a complicated phenomenon into its compo- nent 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 8 INTRODUCTION. analytical cliemlsti-y are not the less valuable, though it should be dis- covered that all which we novs^ call simple substances are really com- pounds. 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 analyze 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 perfonnance of those processes. The reason for thus hmit- ing 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 om* muscles were vitiated by local weakness, or other physical defect, a knowledge of their anatomy might be very necessaiy for effecting a cvire. 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 analyze the bodily motions, so far as is necessary for distinguishing those which ought to be performed fi-om those which ought not. To a similar extent, and no further, it is necessaiy that the logician should analyze the mental processes with which Logic is concerned. Any ulterior and minuter analysis must be left to transcendental 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 gi'ound 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 philosophers will no doubt occasion- ally be controverted, since all of them were logicians as well as meta- physicians ; but the field on which their great battles have been fought, lies beyond the boundaries of our science ; and the views which will be here promulgated, may, I believe, be held in conjunction with the principal conclusions of any one of their systems of philosophy. It cannot, indeed, be pretended that logical principles can be alto- gether iiTelevant to those more abstruse discussions ; nor is it possible but that the view we are led to take of the problem which logic pro- poses, must have a tendency favorable to the adoption of some one opinion on these controverted subjects rather than another. Logic, although differing from the higher metaphysics like the other half of a great whole (the one being the science of the appreciation of evidence, the other having for its main object to determine what are the propo- sitions for the establishment of which evidence is not required), yet when viewed under another of its aspects, stands in the same relation to this, its sister science, as it does to all the other sciences. For metaphysics, in endeavoring to solve its own peculiar problem, must employ means, the validity ofwhich 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 speak- ing, of our memory ; and so far is not amenable to logic. But where- DEFINITION AND PROVINCE OF LOGIC. [f ever this method is insufRcient 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-gi'ounded, or what other inferences would be so. This influence, however, of logic over the questions which have divided philosophers in the higher regions of metaphysics, is indirect and remote ; and I can conscientiously affirm, that no one proposition laid do-\vn 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. B BOOK I. OF NAMES AND PROPOSITIONS. " La scolastique, qui produisit dans la logique, comme dans la morale, et dans une partie de la mctaphysique, une subtilitc, une precision d'idees, dont I'habitude inconnue aux an- ciens, a contribue plus qu'on nacroit au progrtis de la bonne philosoplrie."— Condorcet, Vie de Turcot. CHAPTER I. OF THE NECESSITY OF COMMENCING WITH AN ANALYSIS OF LANGUAGE. § 1. It is SO much the estabhshed practice of wi-iters 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, per- haps, scarcely be required from me, in merely following the common usage, to be as particular in assigning my reasons, as it is usually ex- pected that those should be who deviate from it. The practice, indeed, is recommended by considerations far too ob- vious to require a formal justification. Logic is a portion of the Art of Thinking : Language is evidently, and by the admission of all phi- losophers, one of the principal instruments or helps of thought ; and any imperfection in the instrument, or in the mode of employino- it, is confessedly liable, still more than in almost any other art, to confuse and impede the process, and desti'oy all gi-ound 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 phi- losophizing, would be as if some one should attempt to make himself an astronomical observer, having never learned to adjust the focal dis- tance 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 all 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 imder almost a necessity of reasoning or infen-ing incon-ectly. 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 neces- sary preliminary to the science of logic. But there is another reason, of a still more fundamental nature, why 12 NAMES AND PROPOSITIONS. the import of words should be the earliest subject of the logician's con- sideration : because without it he cannot examine into the import of Propositions. Now this is a subject which stands on the very thresh- hold 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 the universe presents to our inquiring faculties, some are soluble by direct consciousness, others only by means of evidence. Logic is concerned with these last. The solution, by means of evidence, of questions respecting the universe and the things contained in it, is the pm'pose of logic. But before inquiring into the mode of resolving questions, it is necessary to inquire, what are the questions which present themselves 1 what questions are con- ceivable I what inquiries are there, to which men 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 wnich 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 eiTor lie in propositions. What, by a convenient misapplication of an abstract term, we call a Truth, is simply a True Proposition ; and eiTors 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'be- ing 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 propo- sitions ; a sufficient scrutiny of Propositions and of their varieties will apprise us what questions mankind have actually asked themselves, and what, in the nature of answers to those cjuestions, they have actu- ally thought they had gi'ounds to believe. Now the first glance at a proposition shows that it is fomied by put- ting 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 prop- osition, Gold is yellow, the quality yellow is affirmed of the substance gold. In the proposition, Franklin was not bom in England, the fact expressed by the words born in England is denied of the man Franklin. Every p'roposition consists of three parts: the Subject, the Predi- cate, 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 ena- bling 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 NECESSITY OF AN ANALYSIS OP NAMES. 13 (as the phrase is) predicated : the eartJi, words denoting the object which that quaUty is affirmed of, compose the Subject; the word is, which serves as the connecting mark between the subject and predi- cate, 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 be- lief 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 namcable 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 in- stance, 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 coiTect 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 itseH", 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 dis- believe. Now, however, let me make, of all possible assertions respect- ing 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 some- thing 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 affiarded me ; but if I say, " the sun exists," " my father exists," or " a rovmd square exists," I call for be- lief; and should, in the first of the three instances i^ect with it ; hi 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 sur- vey of language. If we attempt to proceed further in the same path. 14 NAMES AND PROPOSITIONS, that is, to analyze 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 afiiiTQS 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 upon what they are names of; since it is with refer-ence to that, and not to the mere names them- selveSj that we make the affinnation 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 oc- cupy the preHminary 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 gi'oundless 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 fortu- nately no one has it in his power to follow) is in reality an exhortation to discard the whole fi-uits of the labors of his predecessors, and de- mean 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, aft:er subtracting all which he has acquired by- means of the w^ords of other people ] Even after he has leanit as much as men usually do learn from others, mil the notions of things contained in his indi\"idual mind afford as sufficient a basis for a cata- logue raisonnee as the notions wliich are in the minds of all man- kind? In any enumeration and classification of Things, which does not set out from their names, no varieties of things will of course be compre- hended but those recognized by the particular inquirer ; and it "will still remain for him to establish, by a subsequent examination of names, that his 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 recognized, not by a single inquirer of perhaps hmited views, but by the collective intelligence of mankind. 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 recognizing the distinctions made by ordinaiy language. If some of these appear, on a close examination, not to be fundamental, our enumeration of the different kinds of realities may be abridged accord- ingly. But to impose upon the facts in the first instance the yoke of a theory, while the grounds of the theory are resei"A-ed for discussion in a subsequent stage,js evidently not a course which a logician can rea- sonably adopt. CHAPTER 11. OF NAMES. § 1. "A NAME, says Hobbes,* " is a word taken at pleasure to serve for a mark, wliicli may raise in our mind a thought Uke to some thought we had before, and which being pronounced to others, may be to them a sign of what thought the speaker hadf before iji his mind." This simple definition of a name, as a word (or set of words) serving the double pui-pose, of a mark to recall to ourselves the likeness of a foiTQer thought, and a sign to make it known to others, appears unex- ceptionable. 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 philosophers, 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 them- selves ; 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 adher- ing 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 ; but that the physical object, the sun itself, is the cause fi'om which the outward phenomenon, day, follows as an effect. 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 infonnation. 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 * Compulation or Losic, chap. ii. + In the original, " had, or had not." These last words, as involving a subtlety foreign to our present purpose, I have forborne to quote. 16 NAMES AND PROPOSITIONS. of names. Among such are reckoned particles, as of, to, truly ^ often ; the inflected cases of nouns substantive, as 77ie, Mm, John's ;* and even adjectives, as large, heavy. These words do not express things oi 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 wi-itten characters. This employment of a word to denote the mere letters and syllables of which it is composed, was tenned 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 hody fell, A tiaily impor- tant fact was asserted, A memher o^ parliament was in the room. An adjective, however, is capable of standing by itself as the predi- cate of a proposition ; as when we say. Snow is white ; and occasion- ally even as the subject, for we may say, "White is an agreeable color. The adjective is often said to be so used by a gi'ammatical ellipsis : Snow is white, instead of. Snow is a white object ; White is an agree- able color, instead of, A w^hite color, or. The color of white, is agi-eeable. The Greeks and Romans were permitted, by the rules of their lan- guage, 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 dis- tinction, however, is rather grammatical than logical. Since there is no difference of meaning between round and a round ohject, 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 con- sidered 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 SjTicategore- matic terms: from ovv, with, and Karrf/opEO), 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 pi-edicate of a pro- position, without being accompanied by any other word, was termed by the same authorities a Categorematic tenn. 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, Categore- matic. ' It belongs to the class of what have been called many-worded names. * It would, perhaps, be more correct to say that inflected cases are names and something more ; and that this addition prevents th.em from being used as the subjects of propositions. But the purposes of our inquiry do not demand that we should enter with scrupulous accu- racy into similar minutiK. NAMES. " 17 For, as one word is frequently not a name, but only part of a name, so a number of wortls often compose one single name, and no more. Thus, in the opening of the Faradi/ic Lost, these lines — the fruit Of that forbidckMi tree, whose mortal taste Brought death iiito ihe vvorki, and all our woe, With loss of Eden, til^ one greater Mail Restore us, and regain the bhssful seat, — form in tlie estimation of the logician only one name j-one C.ategOre- matic term. A mode of determining whether any set of Words makes only one name, or more than one, is by predicating something of it, apd' obsei'ving 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 diat 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 yestei'day." Suppose, however, that the words had been, John Nakes, aiicl 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 mg-ke two assertions ; one, that John Nokes died yesterday ; the other, that the mayor of the tovra died yesterday. It being needless to illusti-ate, 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 com- posed of, but according to theii- 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 distin- guishing names ; there is a name for every person, and for every re- markable place. Other object36, of which we haA^e not occasion to speak so frequently, we <3o not designate by a naine of their own ; but when the necessity arises for naming them, we do so by putting to- gether several words, each of which, by itself, miglit be and is used for an indefinite number of other objects ; as when I say, this stone: "this" and " stene" being, each of them, names that may be used of many other objects besides the particular one meant, although the only ob- ject 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 oidy served, by mutually limiting each other, to aiibrd a designation for such individual objects as have no names of their own ; they could only be ranked among contrivances for economizing the tise of language. But it is evident that this is not their solo function. It is by their means that we are enabled to assert general propositions ; to affinn or deny any predicate of an indefinite number of things at once. The disthiction, therefore, between general names, and individiuil or singular names, is funda- mental ; and may be considered as the first gi'and division of names. C 18 NAMES AND PROPOSITIONS. A genei'al name is familiarly defined, a name which is capable of being truly affirmed, in the same sensfe, of each of an indefinite number of things. An individual or singular naine is a name which is only ca- pable of being truly affinned, in the same sense, of one thing. Thus, man is capable of being truly affirmed of John, Peter, George, and other persons without assignable limits : 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 cj^ualities. But Jo7m. is only capable of being truly af- , firmed of one single persen, at least in the same sense. For although there are many persons who bear that name, it is not confeiTed ujjon them to indicate any qualities, or anything which belongs to them in common ; and cannot be said to be affinned of them in any sense at all, consequently not in the same sense. ",The present king of England" is also an individual name. For, that there never can he 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 conve- nieilt mode of expression for some purposes, is objectionable as a defi- nition, since it explains tlifi 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 in- dividuals denoted by a general name." It is necessary to distinguish general from collective names. A gen- eral name is one which can be predicated of cacli individual of a mul- titude ; . a collective name cannot be predicated of each separately, but only of all taken together. " The 76th regiment of foot," winch is a collective name, is not a general bvit 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 can- not say, Jones is the 76th regiment, and Thompson is the 76th regi- ment, aixl Sn;iith is the 76th regiment. We can only say, Jones, and Thompson,^ and Staith, and Brown, and so forth, (enumerating all the sol^liers,) Hre the 76th regiment. *' The 76th regiment" is a collective name, but not a general one : "a regimen,t" is both a collective and a general name. General with respect to all individual regiments, of each of which separately it can oe 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 ah- stract. A concrete name is a name which stands for a thing ; an ab- stract name is a name which stands for an attribute of a thing. Thus, Jolm, the sea; this table, are ijames of things. White, also, is a name of a thing, or rather of things. AVliiteness, agdn, is the name of a quality or atti'ibute 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 otie of their attributes. I have used the words concrete and abstract in the sense annexed to them by the schoolmen, who, notwiths=tanding the impci-fections of their philosophy, were unrivalled in the construction of technical language. NAMES. 19 and wHose clofinitions/ in logic at least, thongli tlioy never went more than a little way into the subject, have seldom, I think, been altered but to be spoiled. A practice, however, lias gi'own up in more mod- em times, which, if not introduced by Locke, has gained cun-ency 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 contining it to the names of atti'ibutes. The metaphysicians of the Condillac school — Whose ad- miration of Locke, passing over the profoundest speculations of that ti'uly original genius, usually fastens with peculiar eagerness upon his weakest points — ^liave gone on imitating him in this abuse oflanguage, 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 exprcssioir general nanie, the exact equivalent of which exists in all languages I am acquainted with, was already available for the purpose to which abstract has .ibeen misap- propriated, while the misappropriation leaves that important class of words, the names of attributes, without any compact distinctive appel- lation. The old acceptation, however, has nt3t gone so completely out of use, as to deprive those who still adhere to it of all chance of being miderstood. By abstract, then, I shall always mean the opposite of concrete : by an abstract name, the name of an attribute ; by a con- crete name, the name of an object. Do abstract names belong to the class of general, or to that of sin- gular names ? Some of them are certainly general. I mean those which are names not of one single and definite attribute, but of ^ class of attributes. Such is the word color, 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 xespect of the various degrees of weight. Such also is the word attribute itself, the common name of all particular attributes. But when only one at- tribute, neither variable in degree nor in kind, is designated b.Y the name; as. visibleness ; tangibleness ; equality; squareness; milkwhite- ness ; then the name can hardly be considered general ; for though it denotes an attribute of many different objects, the attribute itself is al- ways 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 ajrart. It may be objected to our definition of an abstract name^ that not only the names which we have called abstract, biit adjectives, which We have placed in the concrete class, are names of attributr instance, although the objects <^enoted 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 fatlier 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, v<^hich 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 ditfcrent words. The two propositions are exactly equiv- alent : neither of them asserts more or asserts less than the otlier. The paternity of A and the filiation of B are not two facts, but two mode^ of expressing the same fact. That fact, when analyzed, consists of a series of physical events or phenometia, in whicli both A and B are parties concerned, and fi-om 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 relatioh ; the school- men called it the foundation of the x^dX\oxy, 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 for- mer or in the latter aspect, it is connoted by the one or the other of the two con'elative names. Father connotes the fact, regarded as consti- tuting 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 hght. And all that appears necessary to account for the exist- ence of relative names, is, that whenever there is a fact, in which two ' individuals are alike concerned, an attribute gi'ounded 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 im.plies in its signification the existence of another object, also derivdng a denomination from the same fact which is thegi'ound 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 eanaot be explained but by mentioning another. Or we may state it thus : — when the name cannot be employed in dis- course, 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. We may take our choice among these definitions. Thoy are all, at bottom, equivalent, being modes of variously expressing this one dis- tinctive circumstance — that every other attribute of an object might, without any contradiction, be conceived still to exist if all objects- be- sides that one were annihilated ;* but those of its attributes whidi aj-e expressed by relative names would on that supposition be swept away. * Or rather all objects, except itself and the percipient mind ; for, as we shall S' after, to ascribe any attribute to an object necessarily implies a mind to perceive it see here- 30 NAMES AND PROPOSITIONS. § S. Names liave been further distinguished into lodvocal and cpquiv- ocal : these, however, are not two kinds of names, but two different modes of employing names. A name is univocal, or appHed, imivo- cally, with respect to all things of which it can be precicated in the same sense; but it is Eequivocal, or applied gequivocally, as rfespects those things of which it is predicated in different senses. It is scai'cely necessary to giye instances of a fact so familiar as the double meaning of a word. In reality, a§ has, been already observed, an aequivocal or ambiguous word is not one name, but two names, accidentally coinci- ding in, sound. File standing for an iron instrument, and Jile standing for a line of soldiers, have no more title to be considered one word, because ^vTitten alike, than grease and Greece have, because they are pronounced alike. They are one sound, appropriated to form two dif- ferent words. An intermediate case is that of a name used analogically or meta- phorically ; that is, a name which is predicated of two things, not univocally, or exactly in the same signification, bvit in significations somewhat similar, and which being derived one fx-om the other, one of them may be considered the jarimary, and the other a secondary .sig- nification. 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 am- biguity. And one of the commonest forms of fallacious reasoning arising from ambiguity, is that of arguing fit'om a metaphorical expres- sion as if it were literal ; that is, as if a word, when applied metaphor- ically, 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 commeticement 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, Avhich must be a Proposition or Assertion ; since nothing but a Proposition can be tin object of belief, or therefore of proof. A Proposition is, discourse which affinns 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, Ave knew what all Names signify, we should know everything which is capable either of being made a subject of affimiation or denial, or of being itself affinned or denied of a subject. We have accordingly, in the preceding chapter, reviewed the various kinds of Names, in oz'der to ascertain what is sig- THINGS DENOTED BY NAMES. 31 nified by each of them. And we have now canied this survey fai' enough to be able to take an account of its I'eSults, 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 ancieht 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 emnncration by the summa genera, i. e. the most extensive classes into wIiIcIk things could be distributed ; which, therefore, were so many highest Predicates, one or other of which was supposed capable of being affiiTned with triith of every nameable thing whatsoever. The following are the classes into which, according to this school of philosophy. Things in general might be re- duced : — 'Ovaia, Substantia. Uoaov, Quantitas. Uoiov, Qualitas. Upog Ti, Relatio. IIoLelv, Actio. IlaaxEtv, Passio. Ugv, Ubi. Uors, Quando. Keladai, Situs. Exscv, 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 lan- guage of familiar life, with little or no attempt to penetrate, by philo- sophic 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 lo- cal situation from that category. The same observation applies to the categories Quando (or position in time) and Ubi (or position in space) ; wlxile the' distinction between' tlie latter and Situs is merely veilsal. The incongruity of erecting into a sujnimim genus the class which forms the tenth category is manifest. On the other hand, the enumeration take.? no notice of anything besides substances and atti-ibutes. In what category are we to place sensatipns, or any other feelings, and states of mind ; as hope, joy, fear j sound, smell, taste ; pain," ple,asure ; thought, judgment, conception, and the like 1 Probably all- these would have been placed by the Aristotelian school' in the categories of actio and 2^(iss/o ; 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 j but the things themselves, the feelings Or states '32 NAMES AND PROPOSITIONS. 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 recommeticing, 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 Classifica- tion of Things would, I believe, prepare most i-eaders for an enumer- ation 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 endeavot 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 heing : 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 ex- istence. But this word, str-ange as the fact may appear, is still more com- pletely 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 fi-om a slight taint of a second ambigu- ity ; 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 attiibutes. The soul is called a Being ; God and angels are called Beings ; but if we were to say, extension, color, wisdom, virtue are beings, we should perhaj^s 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 witli 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 absti^act name, in which class its grammatical foiTU 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 con- crete name. The kindred word essence, born at the same time, and of the same parents, scarcely underwent a more complete transfoi'mation THINGS DENOTED BY NAMES. 33 when, from being the abstract of the verb to he, it came to denote some- thing sufficiently concrete to be inclosed in a glass bottle. The word Entity, since it settled down into a c<»ncrete name, has retained its universality of signification somewhat less unimpaired than any of the names before mentioned. Yet the same gi'adual 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 So a substance; which condition being precisely what constitutes an atti'ibute, attributes are gradually shut out, aTid along with tlann feelings, which, in ninety-nine cases out of a hundred, havt? no other name than that of the attribute which is grounded upon them. Strange that when the greatest em- ban-assment felt by all who have any considerable number of thoughts to express, is to find a sufficient variety of words fitted to express them, there should be no practice to which even philosophers are more ad- dicted 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 imderstand 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 endeavor so to employ them as in no case to leave his meaning doubtful or obscure. No one of the above terms being altogether ambiguous, 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 a misunderstanding of my meaning ; 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 sig- nified by a known word in some one or other of its senses: unless authors had an unlimited license 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 wi'iter, 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 affi^rd an example of that, to facilitate which is among the most impoitaiit uses of logic. Philosophical language will for a long time, and popular language pcrhajjs always, 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 E 34 NAMES AND PROPOSITIONS. 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 naiTower resti'iction, to the emotional alone : as distinguished from what are conceived as belonging to the percipient, or 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 gi'eater 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 particulai'ly 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 con- scious of when we are said to think ; from the consciousness we have when we think of a red color wdthout 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 therri. 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-moiTow. 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 ^vith 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 ; thougli at the present time all the objects are alik.e 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 w'hite object; nor is it less to be distinguished fi'om the attribute whiteness, which we ascribe to the object in consequence of its exci- ting 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 tvJiite- ness. But when we speak of the sensation itself, (as we have not occasion to do this often except in our philosophical speculations,) language, which adapts itself for the most part only to the common rniNGS DENOTED BY NAMES, 35 uses of life, has provided us with no single-worded or immediate desig- nation ; we nmst employ a circumlocution, and say, The sensation of white, or The sensation of whiteness; we must denominate the sensation either from the oliject, or from the attribute, by which it is excited. Yet the sensation, though it never docs, might very well be conceioed 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 a,re often conscious of these sensations in the absence of any j^cfcejftible 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 a 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, color stands for the sensations of white, red, &c., but also for the quality in the colored object. We talk of the colors 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 color blue, is a feel- ing of blue color, 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, M'hich 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 feel- ings, but in the agency which produces our feelings ; all of them when actually pi-oduced are states of mind. Besides the affection of our bodily organs from without, and the sensation thereby produced in our minds, many waiters admit a third link in the chain of phenomena, which they term a Perception, and which consists in the recognition of an cxtei-nal 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 philosophers it is by an act of the mind, similar OD NAMES AND PROPOSITIONS. to perception, except in not being preceded by any sensation, that we recognize the existence of God, of the soul, and other hyperphysical reahties. These acts of 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 Mr. Wliewell seems to suppose must be meant in an analogous case*) to indicate that as they are ^'■merely states of mind," it is supei-fluous to inquire into their distin- guishing 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 ex- ternal to itself, I can see only cases of belief; but of behef which claims to be intuitive, or independent of external evidence. \Mien 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 helieve 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 higher or transcen- dental branch of metaphysics. To the same region of speculation belongs all that can be said re- specting the distinction which the German metaphysicians and their French and English followers, (among whom Mr. Whewell is one of the inost distinguished,) 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 aAvare that with reference to the view which those writers take of the primary elements of thought and knowledge, this distinction is fimdamental. But for our 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 to be carefully distinguished from the external or physical facts with which they may be connected, either as eifects or as causes. § 5. Among active states of mind', there is, however, one species which merits particular attention, because it fonns a principal part of the connotation of some important classes of names. I mean volitions, or acts of the will. Wlien 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 pro- bable future. Take, for instance, the words Sovereign and Subject. What meaning do these words convey, but that of innumerable actions, * Philosophy of the Inductive Sciences, vol. i. p. 40. THINGS DENOTED BY NAMES. 37 done oi" to be done by the sovei-eign and the subjects, to or in regai-d to one another reciprocally I So with the words physician and patient, leader and follower, master and servant. 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 fuliilled. There arc 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 oi^e thing ; the effect produced in consequence of the ' intention is another thing ; the two together constitute the action. I form the pui-pose of instantly moving my arm ; that is a state of my mind ; my arm (not being tied nor paralytic) moves in obedience to my purpose ; that is a physical fact, consequent upon a state of mind. The intention, when followed by the fact, or, (if we prefer the expres- sion,) 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 recognizing three sub-divi- sions : 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 exem- plification. And, finally, we have found it necessary to add to these three a fourth species, commonly known by the name Volitions. With- out 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 illus- tration bestowed upon these may, so far as we are concerned, suffice for the whole genus. We shall, thei-efore, proceed to the two remain- ing 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 endeavored to define Substance and Attribute ; but their definitions are not so much attempts to dratw a distinction between the things themselves, as instructions what difference it is customary to make in the grammatical structure of the sentence, according as you are speaking of substances or of attributes. Such deSnitions are rather lessons of English, or of Greek, Latin, or Ger- man, than of mental philosophy. An attribute, say the schocjl logi- cians, must be the attribute o/" something : color, for example, nmst be the color of something ; goodness must be the goodness of something : and if this something should cease to exist, or should cease to be con- nected with the attribute, the existence of the attribute would be at an end, A substance, oft the contrary, is self-existent ; in speaking 38 NAMES AND PROPOSITIONS. about it, we need not put o/" after its name. A stone is not the stone of any thing ; the moon is not the moon of anything, but simply the moon. Unless, indeed, the name which Ave choose to give to the substance be a relative name ; if so, it must be followed either by oj", or by some other particle, implying, as that preposition does, a reference to some- thing 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 refen-ed to something besides him- self: 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 the child were annihi- lated ; 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 Avhite- ness ? 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 satisfactoiy one. If an attribute is distinguished from a sub- stance 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 atti'ibute : and we can ik) 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. Sub- stances 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 modem metaphy- sicians, 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 color, 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 contro- versy on the point ; maintaining the paradox, that we are not Avarranted in refen-ing our sensations to a cause, such as we understand by the word Body, or to any cause whatever, unless, indeed, the 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. THINGS DENOTED BY NAMES. 39 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 otlier 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 organ of touch and of our muscles ; its weight, which is also a sensation of touch and of the muscles ; its color, wliich 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 sensa- tions frequently are, and, as we learn by experience, always might be, experienced simultaneously, or in many differefit orders of succession, at our own choice : and hence, the thought of any one of them makes us think bl" the others, and the whole become mentally amalgamated into one mixed state of consciousness, which, in the language of the school of Locke and Hai'tley, is termed a Complex Idea. Now there ai-e philosophers who have argued as follows: — if we take an orange, and conceive it to be divested of its natural color 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, and imperceptil)le not only by all our senses, but by the senses of all other sentient beings, real or possible ; nothing, say these philosophers, would remain. For of what nature, they ask, could be the residuum "? and by what token could it manifest its presence 1 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 sub- stratum 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 annihilated by the fiat of Omnipotence, and let the sensations continue to occur in the same order, and how would the substratum be missed 1 By what signs should we be able to discover that its existence had terminated 1 should we not have a.s much reason to believe that it still existed, as we now have ] and if we should not then be wananted in believing it, how can we be so now? A body, therefore, according to these meta- physicians, is not anything intrinsically different from the sensations which the body is said to produce in us ; it is, in short, a set of sensa- tions joined together according to a fixed law. These ingenious speculations have at no time in the history of phi- losophy made many ])roselyt(!H ; but the controversies to which they have given rise, and the doctrines which have been developed in the 40 NAMES AND PROPOSITIONS. attempt to find a conclusive answer to them, have been fruitful of im- portant 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 stucTi, in it. To this substratum the name Matter is usually given in philosophical discussions. It was soon, however, acknowl- edged 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 ex- ternal to them : this knowledge, therefore, is as evidently intuitive as our knowledge of our sensations themselves is intuitive. And here the question merges in the fundamental problem of transcendental metaphysics ; 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 appeared to &\v subsequent thinkers to be worthy of assent ; the only point of much real importance is one upon which those meta- physicians are now very generally considered to have made out their case : viz., that all toe 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 fi-om the universe of phenomena, or of things as they appear to our senses ; and even when bringing into use the technical expression [Noumcnon) to denote what the thing is in itself, as con- trasted 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 con- stitution of our faculties ever must remain, at least in this sublunary existence, an impenetrable mystery to us.* There is not the slightest * I have much pleasure in quoting a passage in which this doctrine is laid down in the clearest and strongest terms by M. Cousm, the most distinguished living teacher of German philosophy out of Germany, whose authority on this side of the question is the more valu- able, as his philosophical views are generally those of the post-Kantian movement, repre- sented by Schelling and Hegel, whose tendencies are much more objective and ontological than those of their master, Kant. " Nous savons qu'il existe quelque chose hors de nous, parceque nous ne poavons expli- quer nos perceptions sans les rattacher a des causes distinctes de nous-m^mes ; nous savons de plus que ces causes, dont nous ne connaissons pas d'ailleurs I'essence, produisent les effets les plus variables, les plus divers, et m6me les plus contraires, selon qu'elles rencon- trent telle nature ou telle disposition du sujet. Mais savons-nous quelque chose de plus? et m6me, vu le caractfere 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, ;9 dis qu'il est absurde et enfcrme une contradiction. Nous ne savons pas ce que ces causes sont en elles-m^mes, et la raison nous defend de chercher a le connaitre : mais il est bien evident ^ THINGS DENOTED BY NAMES. 41 reason for believing that what wc call the sensible qualities of the ob- ject 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 is heat like the steam of boiling ^vater : why then should matter resemble our sensations 1 Why should the inmost nature of tire or water resemble the impressions made by these objects upon our senses ]* And if not on the principle of resem- blance, 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 ex- perience from it. Those, however, who still look upon Ontology as a possible science, and think, not only that bodies have an essen- tial constitution of their own, lying deeper than our perceptions, but that this essence or nature is not altogether inaccessible to human in- vestigation, cannot expect to find their refutation here. The question depends upon the nature and laws of Intuitive Knowledge, and is not within the province of logic. § S. Body having now been defined the external cause, and (accord- ing 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 concepti(m 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 myterious something which feels, and priori, qu' elles ne sont pas en elles-memes ce qu'ellcs sont par rapport a nous, puisque la presence du sujet modifie necessairement leur action. Suppriinez tout siijet sentant, il est certain que ces causes agiraient encore puisqu'elles contiriueraient 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 connaisons : que serait-il ' C'est ce que nous ne saurons jamais. C'est (Tailleurs peut-itre un probleme qui ne r'epugne pas seulement a la nature de notre esprit, mais a I'essence mirne des choses. Quand m6me en effet-on supprimcrait par la pens^e tous les sujetj sentants, il faudrait encore admettre qye 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 dcterminees des corps n'existent pas independamment d'un sujet quelconque, et que ciuand on demande si les pro- prietes 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 I8me siecle, 8me le<;on. * An attempt, indeed, has been made by Ileid 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 sensation 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 oi touch, combined with sensations of a class previously too little adverted to by metaphysi- cians, those which have their seat in our muscular frame. Whoever wishes to be more particularly acquainted with this admirable specimen of metaphysical analysis may consult the first volume of Brown's Lectures, or Mill's Analysis of the Mind. On this subject also, the authority of M. Cousin may be quoted in favor of conclusions re- jected by some of the most eminent thinkers of the school to which he belongs. M. Cousin recognizes, in opposition to Reid, the esseutial subjectivity of our conceptions of the primary qualities of matter, as extension, solidity, &c., equally with those of color, heat, and the remainder of what are called secondary qualities.— Cowrs, «t supra, 9ine leqon. F 42 NAMES AND PROPOSITIONS. thinks. It is unnecessary to give in the case of mind, as we gave in the case of matter, a particular statement of the skeptical 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 human facul- ties 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 cer- tain "thread of consciousness;" a series of feelings, that is, of sensa- tions, 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 fi-om these sensa- tions, 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 quiesence, without any thoughts at all. But what this being is, although it is myself, I have no knowledge, further than the series of its states of consciousness. As bodies mani- fest 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 con- scious. I know nothing about myself, save my capacities of feeling or being conscious (including, of course, thinking and wilhng) : and were I to learn anything new concerning myself, I cannot with my present faculties conceive this new information to be anything else, than that I have some additional capacities, before unknown to me, of feeling, thinking, or willing. Thus, then, as body is the unsentient cause to which we are nat- urally prompted to refer a certain portion of our feelings, so mind may be described as the sentient stihject (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, liiither 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 sen- sible qualities of objects, and let that example be whiteness. When we ascribe whiteness to any substance, as, for instance, snow ; when THINGS DENOTED BY NAMES. 43 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 ai'e 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 hifer that the object is present, because it gives me a certain assemblage or series of sensa- tions. 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 color 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 knaio 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 the sensation of white, is the ground on which we as- cribe to that substance the quality whiteness ; the sole proof of its pos- sessing 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 it- self; a ^.'O^i.Tr inherent in it; something ?"« 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, buf that it does so through, and by rea- son of, that power or quality. For the puiposes of logic it is not of material importance which of these views we adopt. The full discussion of the subject behmgs to the department of inquiry so often alluded to under the name of the higher 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 surround- ing circumstances. Because quality and sensation cannot be put in- discriminately one for the other, it is supposed that they cannot both signify the same thing, namely, the im])ression or feeling wth which we are affected through our senses by the presence of an object : al- though 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 ex- cites in our minds that among various other sensations or feelings. And if this be admissible as a supposition, it rests with those who con- tend for an entity y;^/- sc called a quality, to show that their opinion is preferable, or is anything in fact but a lingering remnant of the scho- lastic 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 " I'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 44 NAMES AND PROPOSITIONS. 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 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 cer- tain 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 : the constitution of things, the scheme of the universe, \vill have it so. And to this we must at last come, even after interpo- lating 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 \}(\q 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 Avith 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 upon its exciting in us the sensation of white; and, adopt- ing 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 upon 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 cori'elative 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 coiTel- ative names, and observe what all 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 for foam another ; one thing before, afoer, along with another ; one thing greater, equal, less, than another ; one thing the cause of an- THINGS DENOTED BY NAMES. 45 Other, the effect of another; one person the master, servant, child, parent, husband, wife, 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 bo one thing common to all these cases, and only one; that in each of them there exists or occurs, or has existed or occurred, some^ac^ or phenomenon, into which the two things which arc said to be related to each other, both enter as parties concerned. This fact, or phenomenon, is what the Aristotelian logicians (^lled the fundamcntum relatjonis. Thus in the relation of greater and less between two magnitudes, the funda- mentum relationis is the fact that when one of the two magnitudes is applied to the other, it more than covers it ; and cannot, by any new arrangement of parts, be entirely brought within the boundaries of the other object. In the relation of master and servant, X\\g fundamentum relationis is the fact that the one has undertaken, or is compelled, to perform certain senices for the benefit, and at the bidding, of the other. In that of husband and wife, \S\q fundamentum relationis consists of the facts that the parties are a man and a woman, that they have promised certain things with certain foniialities, and are in consequence invested by the law with certain rights, and subjected to certain duties. Exam- ples 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 propoi'tion 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 areas many con- ceivable 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 gi'ounded upon the fact that a certain sensation or sensations are produced in us by the object, so an attribute gi'ounded upon some fact into which the object enters jointly with another object, is a relation between it and that other object. But the fact in tlie latter case consists of the very same kind of elements as the fact in the former : namely, states of consciousness. In the case last cited, for example, the relation of husband and wife ; the fandamentum relationis consists entirely of thoughts, emotions, sensations, and volitions (actual or contingent), either of the parties themselves or of other parties concerned in the same scries of transactions, as, for instance, the intentions which would oe formed Ijy a judge in case a complaint were made to his tribunal of the infi-ingement of any of the legal obligations imposed by marriage; 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 (again) being but another word fOr sensa- tions, or some other feelings, occasioned cither to oneself or to some- body else. There is no part whatever of what the names expressive of the relation imply, that is not resolvable into states of consciousness ; 46 NAMES AND PROPOSITIOXS. 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 other- wise than by the states of consciousness. Cases of relation are not always so complicated as that 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 simultane- ous. If we say, for instance, that dawn preceded sunrise, the fact in which the two things, dawn and sunrise, wgre jointly concerned, con- sisted only of the two things themselves : no third tiling 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, suc- cession 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 analyze the matter any fmther. § 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 seUsEytions of Avhite, or one sensation of white and another of black. I call the first two sensations li/ce ; the last two unlike. ^Vliat is the fact or phenomenon constituting the funda- mentum of this relation ] The two sensations first, and then what we call a feeling of resemblance, or a feeling of want of resemblance. Let us confine ourselves to the fonner case. Resemblance is evidently a feel- ing ; a state of the consciousness of the observer. Wliether the feeling of the resemblance of the two colors be a third state of consciousness, which I have after having the two sensations of color, or whether (like the feeling of their succession) it is involved in the sensations them- selves, may be a matter of discussion. But in either ca.se, these feel- ings of resemblance, and of its opposite, dissimilarity, are parts of our nature ; and parts so far from being capable of analysis, that they are pre-supposed in every attempt to analyze 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 ai'e peculiar, unresolvable, and inexplicable. But, although likeness or unlikeness cannot be resolved into any- thing else, complex cases of likeness or unlikeness can be I'esolved into simpler ones. AVlien we say of two things whidi consist of parts, that they are like one another, the likeness of the whole does admit of analy- sis; it is compounded of likenesses between the various parts respec- tively. Of how vast a variety of resemblances of parts must that re- semblance be composed, which induces us to say that a portrait, or a landscape, is like its original. If one person mimics another with any THINGS DENOTED BY NAMES. 17 success, of how many simple likcucsst'S must the general or complex likeness be compounded: likeness in ii suocessioji of bodily i)ostures; likeness in voiee, or in the accents and intonations of the voice; like- ness in the choice of Avoids, and in the thoughts or sentiments express- ed, whether by word, countenance, or gesture. All likeness, and unlikeness of which wo have any cognizance, re- solve themselves into likeness and unlikeness between states of our own, or some other mind. AVlien we say that one body is like another, (since we know nothing of bodies but the sensations which they ex- cite,) we mi>an really that there is a resemblance between the sensa- tions excited by the two bodies, or between some portion at least of those 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 tluiX those sensa- tions, 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 Alex- ander ; resembles it so closely that they are called the same relation. The relation in which Cromwell stood to England resembles the rela- tion in which Napoleon stood to Franco, thougli 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 fundament um relationis. This resemblance may exist in all conceivable gi-adations, from perfect undistinguishableness to sometliing very slight indeed. When we say, that a thought suggested to the mind of a person of genius is like a seed cast into the gi-ound, because the former jiroduces a multi- tude 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 fundamcnta relationis, m 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 wo suppose a second pair of objects concerned in a second phenomenon, the slightest resem- blance between the two phenomena is sufficient to admit of its being said that the two relations resemble ; provided, of coiu'se, 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 mis- taken for the other : but W£ constantly use this mode of expression Avhen speaking of fijelings ; 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 sa7ne wliich it gives to some other person. This is evidently an 48 NAMES AND PROPOSITIONS. incorrect application of the word same ; for the feehng which I had yesterday is gone, never to return ; what I have to-day is another feel- ing, exactly like the fomier 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 sa7}ie disease ; that two people 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 enlight- ened 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 modem writers. Archbishop Whately stands almost alone in having drawn attention to this distinction, and to the ambiguity con- nected 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 ex- ample foniis a suitable transition to the third and last of the three heads, under Avhich, as already remarked. Attributes are commonly aiTanged. V. Quantity. § 12. Let us imagine two things, between which there is no differ- ence (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, * " Same (as well as ' One,' ' Identical,' and other words derived from them) is used fre- quently in a sense very different from its primary one, as applicable to a single object, being employed to denote great similarity. When several objects are undistinguishably alike, one single description will apply equally to any of them ; and thence they are said to be all of one and the same nature, appearance, &c., as, e. g., when we say ' this house is built of the same stone with such another,' we only mean that the stones are undistinguishable in their qual- ities; not that the one building was pulled down, and the other constructed with the ma- terials. Whereas sameness, in the primary sense, does not even necessarily imply similar- ity ; for if we say of any man, that he is greatly altered since such a time, we understand, and, indeed, imply by the very expression, that he is one person, though different in several qualities. It is worth observing, also, that Same, in the secondary- sense, admits, accord- ing to popular usage, of degrees. We speak of two things being tiearty the same, but not entirely ; personal identity does not admit of degrees. Nothing, perhaps, has contribu- ted more to the error of Realism than inattention to this ambiguity. WTien several persons are said to have One and the Sa?7ie opinion, thought, or idea, men, overlooking the true simple statement of the case, which is, that they are all thinking alike, look for something more abstruse and mystical, and imagine there must be some Otie Thing, in the primary sense, though not an individual, which is present at once in the mind of each of these persons ; and thence readily sprung Plato's Theory of Ideas, each of which was, according to him, one real, eternal object, existing entire and complete in each of the individual objects that are known by one name. . . . The Hindoos of the present day, from observing the similar symptoms which are known by the name of small-pox, and the communication of the like from one patient to another, do not merely call it (as we do) one disease, but believe (if we may credit the accounts given) that the small-pox is a goddess, who becomes incarnate in each infected patient."— l*^^c ; Appendix on Ambiguous Terms, p. 298. My references to this work are always to the first edition. THINGS DENOTED BY NAMES. 49 it is plain that tlie set of sensations is more or less difTcrent in the two cases. In Uke manner, a jrallon of water, and a gallon of Madeira, 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 Madeira is tlie same. What is the rt;al distinction between the two cases ? It is not the province oi' Logic to analyze it ; nor to decide whether it is susceptible of analysis or not. For us the following con- siderations are sufficient. It is evident that the sensations I receive from the gallon of water, and those I receive from the gallon of Madeira, 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 arc like each other, and in which the gallon and the ten gallons of water are imlike 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 upon 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, gromided, and gx-ounded exclusively, on a difference in the sensations excited by them. VI. Attributes Concluded. § 13. Thus, then, all the attrilnitcs of bodies which are classed under Quality or Quantity, are gi-oundcd upon 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 Relatiijn. They, too, are gi'ounded upon 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 recognize a somewhat different character in certain peculiar relations, tiiose of succession and simultaneity, of likeness and unlikeness. These, not being grounded on any fact or phenomenon distinct from the related G 50 NAMES AND PROPOSITIONS. objects themselves, do not admit of the same kind of ginalysis. But these relations, though not, like other relations, grounded upon 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 om- 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 ^^rtue 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 sim- plicity, 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 upon states of feel- ing 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 feel- ings. 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 exist- ence of that mind. In addition, however, to those attributes of a mind, which are grounded upon 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 inay 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 ex- presses 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 two-fold, and of the following purport : Certain feelings form habitually a part of this person's sentient existence ; and, moreover, the idea of those feel- ings 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 tliis attribute is gi-ounded upon the peculiar feeling of pleasure THINGS DENOTED BY NAMES. 51 which the statue prodiicos in our minds, and whicli is not a sensation, but an emotion. VII. General Result. § 15. Our survey of the varieties of Things whicli 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 complete. Our enumeration commenced with Feelings. These we scrupulously ropriety of expression ; than using language in conformity to a pre- vious convention. With whatever illusions even profound thinkers may have satisfied themselves when engaged in finding a general solu- tion for a metaphysical problem ; when they came to the practical ap- plication of their doctrines, they were always prepared with some means of explaining the solution away. 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 ques- tions ; that some false propositions are uttered from ignorance of the meaning of words, but that in others the source of the error is a mis- apprehension of things; that a person who has not the use of language at all may foiTn 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 ;t though he will not allow such eiToneous belief to be called * " From hence also this may he 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 rrean 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. t " Men are subject to err not only in affirming and denying, but also in perception, and 66 NAMES AND PROPOSITIONS. falsity, but only eiTor. And, moreover, 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 de- notes 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 man- ner by which anything works upon ovu- senses, but by most men they are called accidents^* It is strange tliat 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 hecavse of an attribute (or, as he calls it, an accident), our object is not to affimi 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 attri- bute which is possessed by the individual object designated by the words, "summit of Chimborazo," which attribute consists in the phys- ical fact of its exciting in human beings the sensation which we call a sensation of white. It will be admitted that, by asserting the propo- sition, we wish to communicate information of that physical fact, and are not thinking of the names, except as the necessary means of ma- king that communication. The meaning of the proposition, therefore, is, that the indixddual thing denoted by the subject, has the attiibutes 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 further 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 in), is, ot 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, the beings possessing the attributes con- noted by the name man; and the only thing known of them may be those atti-ibutes : 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 atti-ibutes which the predicate connotes are possessed by any given individual, or by any number of individuals previously known as John, Thomas, Richard, &c., but that those attributes are possessed by each and every individual possessing certain other attri- in silent cogitation Tacit errors, or the errors of sense and cogitation, are made by passing from one imagination to the imagination of another diflerent thing ; or by feigning that to be past, or future, which never was, nor ever shall be; as when, by seeing the im- age 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 thmgs that have sense." — Computatian or Logic, ch. v., sect. 1. * lb., ch. iii., sect. 3. IMPORT OF PROPOSITIONS. G7 butes ; that whatever has the attributes connoted by the suDJcct, has also those connoted by the predicate ; that the latter set of attxibutes constanlhj accompanij the foiiner set. Wliatever has the attributes of man has the atti-ibute of mortality ; mortality constantly accompanies the attributes of man. If it be remembered tliat every attiibute is grounded upon some fact or phenomenon, either of outwai'd sense or of inward consciousness, and that to possess an attinbute is another phrase for being the cause of, or fonnuig 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, does really assert thereby no other thing than this, that one phenomenon alway* accompanies another phenomenon ; inso- much 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 o^vn. 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 connota- tion of the word mortal goes no further than to the occurrence of the phe- nomenon 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 propo- sition, when it asserts anything more than the meaning of words, is generally, as in the cases which we have examined, either the coexist- ence 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 refeiTing to it. Take the following example : A generous person is worthy of honor. "VTho 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 fonner, are physical facts, or perceptions of the senses. Worthy of honor, admits of a similar analysis. Honor, as here used, means a state of approving and admiring emotion, followed upon occasion by corresponding out- ward acts. " Worthy of honor" connotes all this, together with our approval of the act of shoAving honor. All these are j^hcnomenaj 68 NAMES AND PROPOSITIONS. States of internal coixsciousness, accompanied or followed by physical facts. When we say, A generous person is worthy of honor, we affinn 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, honor, 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 mean- ing of the proposition, but in the meaning of the names which compose it ; in the complicated nature of the 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 asser- tion 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 Phe- nomena ; we make propositions also respecting those hidden causes of phenomena which ai"e 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 ti-ue, mutatis mutandis, of attributes ; no assertion can be made, at least with a meaning, concerning these unknown and unknowable entities, (beyond their mere existence), except in virtue of the Phenomena by which alone they manifest themselves to our faculties. When we say, Socrates was contemporary 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 earthly 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 noumcnon Socrates, was existing, and doing or experiencing those various facts, during the same time. Coexistence and sequence, therefore, may be affimied or denied not only between phenomena, but between noumena, or between a noume- non and phenomena. And there is one kind of assertion which may be made respecting noumena, independently of the phenomena which are their sensible m8.nifestation ; the assertion of their simple exist- ence. But what is a uoumenon 1 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 t\ie 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. IMPORT OF PROPOSITIONS. 69 § 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 analyze ; for which wo fundament um, distinct fi-om the objects themselves, could be assigned. In addition to prop- ositions which assert a secpience or coexistence between two phenom- ena, there arc therefore, also, propcjsitions which assert resemblance between them : as. This color is like that color ; — The heat of to-day is equal to the heat of yesterday. It is tnle that such an assertion might with some plausibility be brought within the description of an affirma- tion of sequence, by considering it as an assertion that the simulta- neous contemplation of the two colors is Jhllowcd by a specific feeling termed the feeling of resemblance. But tliere 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 analyze things into their ultimate elements. Resem- blance 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 resem- blance. 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 resembles 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 7na7i, is grounded indeed upon a resemblance among the things which are placed in the same class, but not upon a mere general resemblance : the resemblance it is grounded upon 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 1 might still assert the proposition \vith the same mean- ing 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 ; or as the expression, Jehovah is God, might be used by the firmest believer in the unity of the godhead. Propositions, therefore, in which objects are refeiTed to a class because they possess the attributes constituting the class, are so far from asserting nothing but resemblance, that they do not, prop- erly speaking, assert resemblance at all But we remarked some time ago (and tho reasons of the remark will be more fully entered into in a subsequent Book), that there is some- times a convenience in extending the bound.aries of a class so as to include things which possess in a very inferior degree, if in any, the characteristic properties of the class, — provided they resemble that class more than any other, insomuch that the general propositions 70 NAMES AND 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 recognized ; 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 concern- ino- 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 eveiy case in which we jjredicate a general name, we affirm, not absolutely that the object possesses the properties designa- ted 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 ranlcrsons ? No ; except in so far forth as they are prudent ; for prudent persons who are scoundrels can seldom on the whole be beneficial to society, nor acceptable to even finite wisdom. Is it upon prudential conduct, then, that divine approbation and benefit to mankind are invariably consequent ] Nei- ther 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 j^rudential conduct, although in so far as it is pru- dential it is beneficial to society, may yet, by reason of some other of its qualities, be productive of an injury outweighing the benefit, and of a divine 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 antec-edent upon which the other tenn of the sequence is universally consequent. But the propo- sition, " Prudence is a virtue," is an universal proposition. What is it, then, upon which the proposition aflSrms 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 coiTect fore- sight of consequences, a just estimation of their importance to the object in view, and repression of any unreflecting impulse at vai'iance 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, which are 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 asser- tion respecting an attribute may be transformed into an assertion exactly equivalent respecting the fact or phenomenon which is the grotmd of the attribute. And no case can be assigned, where that which is pre- dicated of die 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, VERBAL AND REAL PROTOSITIONS. 73" And as these five 9,re the bnly things which can be affirmed, so arc they the only things which can be denied. '.' No horses are web- footed," denies that the attributes of a horse ever coexist \vith web-feet. It is scarcely necessary to apply the same analysis to Particular affirm- ations and negations. " Some birds are web-footed," affirms that, \vith the atti-ibutes connoted by bird, the phenomenon web-fcet is sometimes coexistent : " Some birds are not web-footed," asserts that there are other instances in which this coexistence does not have place. Any farther explanation of a thing which, if the previous exposition has been assented to, is so obvious, may well be spared. CHAPTER VI. OF PROPOSITIONS BIERELY VERBAL. § 1. As a preparation for the inquiiy 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 Prop- ositions, we examined the opinion of the Conceptualists, that a propo- sition is the expression of a relation between two ideas ; and the doc- tiine of the Nominalists, that it is the expression of an agreement or disagi-eement 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. AVe then examined the different kinds of prop- ositions, and we found that, w\x\\ the exception of those which are merely verbal, they assert five different kinds of matters of fact, name- ly. Existence, Order in Place, Order in Time, Causation, and Resem- blance ; 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 as- serted 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, suscep- tible of tnith 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 sim- ple and unimportant a.s those which served as for examples when ex- amining Hobbes' theory of predication, viz., those of which the subject and predicate are proper names, and which assert only that those names K 74 NAMES AND PROPOSITIONS. 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 ; compre- hending 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 es- sence of man, becalise 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 Proposi- tion, 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 proposi- tions in which any of these were predicated of it were called Acciden- tal Propositions. A connexion may be traced between this distinction, which originated with the schoolmen, and the well knoA\-n dogmas of substanticE secundce, or general substances, and substantial forms, doc- trines which under varieties of language pervaded alike the Aristote- lian 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 ^-iews 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 ha\"ing 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 winch 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 ; it is one of the attributes connoted by the name. The essence of man, simply means the whole of the attributes VERBAL AND REAL PROPOSITIONS. 75 connoted by the word ; and any one of those attributes taken singly, is an essential property of man. The doctiines 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 tiiie views of the subject in the writings of the ancient Aristotelians than in their more modem followers. Poi-phyry, in his Lsagoge, approached so near to the true conception of essences, that only one step remained to be taken, but this stej?, 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 Poq>hyry, made a differ- ence in it ; you made it dXXolov : but by altering any property which was of its essence, you made it another thing, aXko* To a modei-n it is obvious that between the change which only makes a thing diiferent, 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 aXXolov : melt it, and it becomes aXXo, another thing, namely, water. Now it is really the same thing, i. e., the same paiticles of matter, in both cases ; and you cannot so change an\1;hing that it shall cease to be the same tiling 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 constitutes it ice, is gone; while, so 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 AristoteliaiLS 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 sub- stance, together with all the propoities that belonged to it, inhered in every indi\-idual piece of ice. As they did not consider these univei-sal substances to be attached to all general names but only to some, they thought that an object boiTowed only a part of its properties fi'om an universal substance, and that the rest belonged to it individually : the fonner they called its essence, and the latter its accidents. The scho- lastic doctrine of essences long sur%'ived the theory on which it rested, that of the existence of real entities corresponding to general terras ; and it was reserved for Locke, at the end of the seventeenth century, to convince philosoj^hers that the supposed essences of classes were merely the signification of their names; nor, among the signal services which that great man rendered to philosophy, was there one more needful or more valuable.! ♦ KaQolov /isv ovv rruaa (Jta^opri vpoiryivo/xhfT) rivl irepoiov ttoieV ulV a! fiiv kocvu^ re Kai I6iu^ (differences in the accidental properties) uM.oiov noiovGiv al 6e idiairara, (differences in the essential properties) uX?m. — Porph., Isag., cap. iii. t Few among the great names in philosophy have met with a harder measure of justice from the present generation than Locke; the unquestioned founder of the analytic philos- ophy of mind, but whose doctrines were first caricatured, then, when the reaction arrived, ca^t 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 favor of Hobbes ; a great writer, and a great thinker for his lime, but inferior to Locke not only in sober judgment but even in profundity and origi- 76 NAMES AND PROPOSITIONS. Now, as the most familiar of the general names predicable of an object usually connotes not one only, but several attributes of the object, each of which atti'ibutes 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 con- notes only one of these atti-ibutes, or some smaller number of them than all. In such cases, the universal affiiTuative proposition will be true ; since whatever possesses the whole of any set of attributes, must pos- sess 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, Eveiy man is a corporeal being. Every man is a li\'ing 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 coiTesponding 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 ex- istence 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 shoAV 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 exist- ence 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 -vrishes to be believed really to have 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 rneaning of a name, what they really flow from is tlie tacit assumption of the real existence nal 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. VERBAL AND UEAL mOPOSITIONS. 77 of the object so named. Apart from this assmnption of real existence, the class of propositions in which the predicate is of the essence of the subject (that is, in which the ])redicate connotes the whole or j)art of Avhat the subject connotes, but nothing besides), answers no purpose but that of unfolding the whole or sonae part of the meaning of the name, to those \vho did not previously know it. Accordingly, tlu; 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 pur- pose equally well. The various kinds of definition which these dis- tinctions give rise to, and the pui-poses to which they are respectively subservient, will be minutely considered in the proper place. § 3. According to the above view of essential propositions, no prop- osition 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 imphed 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 ; ^. e., of the class to which it was most familiarly referred, and to which, therefore, they conceived that it by natm-e belonged. Thus, because the proposition, Man is a rational being, was an essential proposition, they affirmed the same thing of the proposition, Julius Ctesar is a rational being. This fol- lowed veiy naturally if genera and species wei'e 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 accom- pany it ; to inhere in John Thompson, and form the common essence of Thompson and Julius CcBsar. It might then be fairly said, that ra- tionality, 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 proper- ties, 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 gi'ound, 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 aiising from a misapprehension of the essences of classes, yet even Locke, when he extirpated the parent error, could not shake liimself free from that which was its fruit. He distinguished two sorts of essences. Real and Nominal. His nominal essences were the es- sences 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 perfect 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 78 NAMES AND PROPOSITIONS. connected with the thoughts, contained in that immortal Third Book.* But, besides nominal essences, he admitted real essences, or essences of individual objects, which he supposed to be the causes of the sensi- ble properties of those objects. We know not (said he), what these are (and this acknowledgment rendered the fiction comparatively in- nocuous) ; 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 con- ditions under which one property of a thing admits of being demon- strated 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 coi-puscular stiiicture : what it is now supposed to mean in the case of any other entities, I would not take upon my- self 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 infonnation, 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 con- notes any atti-ibute not connoted by the subject. All these, if true, add to our knowledge : they convey infonnation not already involved in the names employed. Wlien I am told that all, or even that some objects, w^hich 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 propo- sitions only which are in themselves instructive, or fi-om which any instructive propositions can be infeiTed. Nothing has probably conti'ibuted more to the opinion so commonly prevalent of the futility of the school logic, than the circumstance tliat almost all the examples used in the common school books to illustrate the doctrines 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 : Ovme corpus est suhstantia, Omne animal est corpus, Omnis homo est corpus, Omnis homo est ani- mal, Omnis homo est rationally, and so forth. It is far from wonderftil * The always acute and often profound author of .4rt OntUne 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 upon 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 ex- presses the point of difterence respecting the import of Propositions, between my view and what I have called the Conceptualist view of them. \Vhere 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. VERBAL AND REAL TROPOSITIONS. 79 that the syllogistic art shovikl have been thought to be of no use in assisting coiToct reasoning, when almost tlie 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 compre- hended the meaning of the words : and stood exactly on a level, in point of evidence, with the premises fi-om which they were drawn. I have, therefore, throughout this work, studiously avoided the employ- ment 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 specula- tive ti-uth, or as memoranda for practical use. According as we con- sider 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 mor- . tality : No men are gods, means that the attributes of man are never accompanied by the attributes, or at least never by all the attributes, of a 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 oflfice which the proposition pei'foiTns. The practical use of a proposition is to apprise or remind us what we have to expect in any individual case which comes within die assertion contained in the proposition. In reference to this pui'- pose, the proposition, All men are mortal, means that the attributes of man are evidence of, are a marJc of, mortality ; an indication by which the presence of that attribute is made manifest. No men are gods, means that the atti'ibutes of man are a mark or evidence that some or all of the attributes of a god are not there ; that where the fonner are, we need not ex])ect to find the latter. These two forms of expression are at bottom equivalent ; but the one points the attention more directly to what a jjroposition 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 proposi- tions. We may expect, therefore, that the mode of exhibiting the import of a general proposition which shows it hi its application to practical use, will best express the fimction which propositions per- form in Reasoning. And accordingly, in the theory of Reasoning, the mode of vie\\dng the subject wliich considers a Proposition as asserting that one fact or phenomenon is a marh or evidence of another fact or phenomenon, will bo found almost indispensa])le. Ff)r tlie purposes of tliat Theory, the best mode of defining the import of a proposition is not the mode which shows the 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. 80 NAMES AND 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 vi^ith 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 projjositions. We have considered general names as having a mean- ing, 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, hipj30gi-iff, chimera, mennaid, 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 atti'ibutes, the things, be they more or fewer, which happen to possess those attri- butes, 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 alb 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 existing things 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 intro- duced 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 be- cause 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 gi'oup of objects should be thought of together. A naturalist, for purposes connected with his particular science, sees reason to dis- tribute 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 sig- nification, from other connotative names. The classes which they de- note are, as much as any other classes, constituted by certain common atti-ibutes ; and their names are significant of those attributes, and of nothing else. The names of Cuvier's classes and orders, Planti- grades, Digitigrades, &c., are as much the expression of attiibutes, as CLASSIFICATION A\D THE PREDICABLES. 81 if those names had. preceded, Instead of gi'owing out of, his Classifica- tion of Animals. The only peculiarity of the case is, that the conve- nfence of classification was here the primary motive for liitioducing the n'aimes ; while in other cases the name is introduced as a means of predication, and the formation ef a class denoted by it is only an indi- rect consequence. The principles which ought to regulate Classification as a logical process subservient to the investigation of truth, cannot be discussed to any pm-pose until a much later stage of oui* inquiry. But, of classifi- cation as resulting from, and im2)lied 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 oredication, mutilated and formless. § 2. This portion of the theory of general language is the subject of what is teiTned the doctrine of the Predicables ; — a set of distinctions handed down from Aristotle and his follower. Porphyry, many of which have taken a finn root in scientific, and some of them even in popular, phraseology. The Predicables are a five-fold division of Gen- eral Names, not grounded as usual upon a difference in their mean- ing, that is, in the attribute which they connote, but upon 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 {yevog). A species (eldog). A differentia (dicupopd). A proprium {I6i6v^. An accidens (avfi[3E(i7]K6g). 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 predi- cated. There are not some names which are exclusively genera, and others which are exclusively species, or differentia? : but the same name is refen-ed to one or another Predicable, according to the sub- ject of which it is predicated on the particular occasion. Animal, for instance, is a genus with respect to Man, or John ; a species with re- spect to Substance or Being. Rectangular is one of the Differentia of a geometrical square : it is merely one of the Accidentia of the table on which I am wiiting. The words, genus, species, &c., are therefore relative terms ; they ai'e names applied to certain predicates, to ex- press the relation between them and some given subject : a relation grounded, as we shall see, not upon what the predicate connotes, but upon the class which it denotes, and upon the place which, in some given classification, that class occupies relatively to tlie particular subject. § 3. Of these five names, two. Genus and Species, arc not only used by naturalists in a technical acceptation not precisely agreeing with their philosophical meaning, but have also acquired a popular accep- tation, much more general than either. In this popular sense any two classes, one of which includes the whole of the other and. more, may l)e called a Genus and a Species. Such, for instance, are Animal and Man; Man and Mathematician. 'Animal is a genus; Man and Brule L 82 NAMES AND PROPOSITIONS. are' its two. species; or we may divide it into a greater number of epecies, as man, horse, dog, &c. Biped,, ot two-footed anmuil, may also be considered a genus, of which man and bird are two species. Taste is a genus, of which sweet taste, sour taste, sak 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 jjopular "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 aggi-egate whole ; the names 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 fonn of expression ; nor is it of any import- ance 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 th6 name niortal ; 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 belongi'ng to the class. By the Ai-istotelian logicians, the terms genus and species were used in a more restricted sense. They did not iidmit 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 : hiped would not have been admitted to be a genus with reference to man, but a proprium or accidens ohly. It was requisite, according to their theory, that geiius and speciesxshould be of the essence of the subject. Animal was of the essence of man ; hiped was not. And in every classification they considered some one class as the lowest or injima 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 dis- tinction 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 charac- ter was formerly, and by many wi'iters is still, attached, — amounts to CLASSIFICATION AND TUB PREDICABLES. 83 nothing more than the JifTerence 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 schoohnen chose to call the essence of an indi- ^■idual,'wa6 simply the essence of the class to which that individual was most familiarly referred. Is there no difference, then, except this merely verbal one, between the classes which the schoolmen admitted to be genera or species, and those to which they refused the title i Is it an error to regai"d some of the differences which exist among objects as differences in kind (genere or specie), and others oidy as differences in the accidents 1 Were the schoolmen right or wrong in giving to some of tlie classes into which things may be divided, the name of kinds, and considering others as secondary divisions, grounded upon differences of a comparatively supei-ficial 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) differ- ence to found a distinction upon. Take any attribute whatever, and if some things have it, and others have not, we may ground upon the attribute a di^nsion 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 general names, positive and negative together. But if we contemplate any one of the classes so fonned, 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 nmnbered ; 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 characterize them by, except precisely what is connoted by the name : white things, for example, are not distii\guishcd by any common properties except whiteness-; or if they are, it is only by such as are in some way dependent upon, 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 obsei-vations and experi- ments, in the full confidence of discovering new properties which were by no means implied in those we previously knew. Wliile, if any one were to propose for investigation the common properties of all things which are of the same color, the same shape, or the same specific gravity, the absurdity would be palpable. We have no ground to believe that any such common propeities exist, cXcejJt such as maybe shown to be involved in the supjiosition itself, or to be derivable from 84 NAMES AND PROPOSITIONS. 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 h^ 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 them- selves, 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 conve- nience, he will be right ; pro\"ided he means no more than this — that where a certain apparent difference between things (although perhaps in itself of little moment) answers to we know not what number of other differences, pei'\'ading not only their known properties but prop- erties yet undiscovered, it is not optional but imperative to recognize 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 atten- tion 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 upon the importance or unimportance of the particular qualities in which the difference happens to consist. Now, these classes, distinguished by unknown multitudes of prop- erties, 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 to a certain property or proper- ties, and there tenninated, they considered as differences only in the accidents of things ; but where any class differed fi-om 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 ex- pression 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-dis- tinctions, I shall not only retain the di\'ision itself, but continue to express it in their language. According to that language, the proxi- mate (or lowest) Kind to which any individual is referable, 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 in- cluded in the class man, to which Sir Isaac 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 fixjra 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, CLASSIFICATION AND TUB TREDICABLES. 85 uncoTinocteJ with Christianity, are common to all Christians and pe- culiar to them ; while in regard to all Men, physiologists are perpetu- ally caiTying on such an inquiry ; nor is the answer ever likely to be completed. Man, therefore, we may be permitted to 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 Kind^, or logical species, of man. The various races and temperaments, the two sexes, and even the various ages, may be differences of kind, within our meaning of the term. I say, they may be ; I do not say, they are. For in the progress of jihysiology it may be made out, that the differences which distinguis.i different races, sexes, &c., fi'om one another, follow as consequences, under laws of nature, fi-om some one or a few primai-y differences which can be pre- cisely 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 Chris- tian, Jew, Mussulman, and Pagan, a difference which also can-ies 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 shall turn out, that the differences are not capable of being accounted for, then man and woman, Caucasian, Mongolian, and Ne- gro, &c., are really different Kinds of human beings, and entitled to be ranked as species by the logician ; though not by the naturalist. For (as already hinted) the word species is used in a very different signification in logic and in natural history. By the naturalist, organ- ized beings are never said to be of different species, if it is supposed that they could possibly have descended fi-om the same stock. That, however, is a sense aitificially given to the word, for the technical pur- poses of a particular science. To the logician, if a negro and a white man differ in the same manner (however less in degi'ee), 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 both descended fi-om Noah or not. But if their differences can all be traced to climate and habits, they are not, in the logician's view, specifically distinct. ^Vlien the injima s^pecics, or proximate Kind, to which an indi^^dual belongs, ha.s 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 refemble. Let the indi\'id- ual, for example, be Socrates, and the pi-oximate 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 prop- erties 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 fat-nosed ; that being a class which includes Socrates, without including all men. To detei-mine 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 1 If they had ; if a flat nose were a mark or index to an in- definite number of other peculiarities, not deducible fi-om the former by any ascertainable law ; then out of the class man we might cut an- other class, flat-nosed man, which, according to our definition, would 88 NAMES AND PROPOBITIONS. be a Kind. But if we coxild do this, man would not be, as it was as- sumed to be, the pi-oxiraate Kind. Therefore the properties of the proximate Kind do comj^rehend 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 re- lation of a genus, according to even the popular acceptation of the terms genus and species ; that is, it wall be a larger class, including it and more. We are now able to fix also the logical meaning of these terms. Every class which is a real Kind, that is, which is distinguished fiom all other classes by an indeterminate multitude of properties not deriv- able from another, is eitlier 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 indi- viduals 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 quadiTiped 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 b.egin with Differentia. This word is correlative with the words genus and species, and as all agree, it signifies the attribute which distinguishes a given species from every other species of the same genus. This is so far clear: but which of the distinguishing attributes does it signify 1 For we have seen that eveiT^ 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 gen- erally assigned by logicians as the Differentia; and doubtless this attribute serves the pxu-pose of distinction : but it has also been re- marked 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 differeutia ] The Aristo- telians 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 gi'ounded in the nature of the things themselves, which maybe 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 school- men 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, ?'. 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 cam^ to be looked at more closely, nobody could discover what caused the thing to have all those properties, nor even that there was CLASSIFICATION AND THE PREDICABLES. 87 anything which caused it to have them. Logicians, liowever, not hking 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 connnon to the class man, a j)oition oidy, and of course, a very small portion, are connoted by its name: these few, however, will naturally have been thus distinguished fioni the rest cither for their gi'eater obviousness, or for greater su^iposed importance. These proiieities, 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 iuvAisadual too; for it was their maxim, that the species contained the "_ whole essence" of the thing. Metaphysics, that fertile field of delu- sion 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 Acci- dens, 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, <^fiiotes 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 fi-om denoting individuals not included in the genus. And it must connote something besides, other- wise it would include the whole genus. Animal denotes all the indi- viduals denoted by man, and many more. Man, therefore, must coji- note all that animal connotes, otherwise there might be men who were 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 prop- osition 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 com- mon with animal, also connotes rationality, and at least some approxi- mation 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 Aristotehans 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. But, so far as it is possible to determine how language would be used in a case which is purely imaginary, we may say that the Houyhnhms would not be called men, and that the term man, therefore, rc(juiros other conditions besides rationality. The schoolmen, however, were satisfied with taking such a portion of the differentia as sufficed to distinguish the species from 88 NAiMES AND PROPOSITIONS. all other existing things,' although by so doing they might not exhaiist the connotation of the name. § 6. And here, to prevent the notion of differentia from being restricted within too naiTow 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 pui-pose which presides over the particular classification. For ex- ample, 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, it is desirable that his ideas should an'ange themselves. With this view he finds it ad\asable that one of his fundamental divisions should be into warm-blooded and cold-blood- ed animals ; or into animals which breathe with lungs and those which breathe with gills ; or into carnivorous, and frugivorous or graminivor- ous ; 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 Cu\'ier's fami- lies are founded. In doing this, the naturalist creates as 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 preconcerted purpose of scientific con- venience. And to the liberty of doing this there is no limit. In the examples we have given, the new 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 other- wise— 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 division upon them. If, however, practical convenience is a sufficient wai'rant for making the main demarcations in our aiTangement 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 distinc- tion between them by those of their properties which considerations of practical convenience most sti'ongly recommend. If we cut a species out of a given genus — the species man, for instance, out of the genus anim.al — 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 particidar 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 w^hich 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 CLASSIFICATION AND THE PREDICABLES, 89 marked out from that genus by an assignable differentia, the najne 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 Linna?an system it connotes the number of incisor and canine teeth, but does not connote rationality nor any ])articular form. The word man has, therefore, two diftbrent meanings ; al- though not commonly considered as ambiguous, because it happens in both cases to denote the same individual objects. But a case is con- ceivable in which the ambiguity would become evident : we have only to imagine that some new kind of animal were discovered, having Linna^us'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 Linngean 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 coiTesponding to a certain sensation ; but if we are making a classification of colors, and desire to justify, or even merely to point out, the particular place assigned to whiteness in our aiTangement, we may define it, " the color 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.* The differentia, tlierefore, of a species, may be defined to be, that part of the connotation of the specific name, whether ordintuy, or special and technical, which distinguishes the species in question fiom all other species of the genus to which on the pai'ticular occasion we are referring it. § 7. Ha\'ing 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. 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 differ- entia, 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 jiredicated of the species only accidental hi. l^oth va'e Acci- dents in the wider sense, in which the accidents of a thing are opposed to its essence ; although, in the doctrine of the Predicables, Accidena is used for one sort of accident only, Proprium being another sort. * 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 fol- lows, that although attributes may be put into classes, those classes can be admitted to be genera or species only by courtesy. M 90 NAMES AND mOPOSITIONS. Proprium, continue the sclioolmeri, is predicated accidentally, indeed, but necessarily; or, as tliey further explain it, signifies an attribute which is not indeed part of the essence, but which flows fi-om, or is a consequence of, the essen'ce, and is, therefore, inseparably attached to the species ; e. g., the various properties of a ti'iangle, which, though no part of its definition, must necessarily be possessed by whatever comes under that definition. Accidens, on the contrary, has no con- nexion 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 upon 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 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 Parallelogi'am, 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 num, since, without being connoted by the word, it follows from an atti'ibute which the word does connote, viz., from the attribute of rationality. But this is a Proprium of the second kind, which fol- lows 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 hut 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 in- volved. 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 DEFINITION. 91 Bpccies, 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 con- cise mode of expressing the same meaning is, that inseparable acci- dents are properties which are universal to the species but not neces- sary to it. Thus, blackness is an attribute of a crow, and, as far as we know, an 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, there- fore, 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 wc 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 fiom the species ; which are not only not neces- sary, but not even universal. They are such as do not belong to every individual of the species, but only to some indi^•iduals ; or if to all, not at all times. Thus, the color 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 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 Sepa- rable accidents. CHAPTER VIII. OP DEFINITION. § 1. One necessary part of the theory of Names and of Proposition^ remains to be treated of in this place ; the theory of Definitions. As being the most important of the (;lass of propositions which we have characterized as purt^ly 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 jjurpose. § 2. The simplest and most correct notion of a Definition is, a prop- osition declaratory of the meaning of a word; namely, either the meaning which it bears in common acceptation, or that Avhich 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 92 NAMES AND PEOPOSITIOXS. 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 individ- ual 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. Nei- ther 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 propo- sition in this &>xm : " Man" (or whatsoever 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 attri- butes by that thing." Or thus : JNIan is everything which possesses such and such attributes : Man is everything which possesses corpo- reity, organization, life, rationality, and a form resembling that of the descendants of Adam. 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 pe- dantic 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 aggi'egation 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 con- notative 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 simi 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 num- ber. It is, therefore, not -without reason that Condillac and other ^\Ti- ters have affirmed a definition to be an analysis. To resolve any complex whole ijitQ_the elements of which it is comp^Sfded, is the" meaning of analysis ; and this we do when we fepTacl§t>fie"word which connotes a set of attributes collectively, by two or more which connote the same attributes singly, or in smaller gl'oups. § 3. From this, however, the question naturally arises, in what man- ner are we to define a name which connotes only a single attribute 1 DEFINITION. 93 for instance, "white," which connotes nothing but whiteness; "ra- tional," 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 tei'm, if any such can be found ; or in the direct way already alluded to : " White is a name connoting the attri- bute whiteness." Let us see, however, whether the analysis of the meaning of the name, that is, the breaking down of that meaning into separate parts, admits of being carried further. Without at present deciding this question as to the word white, it is obvious that in the case oi rational some further explanation may be given of its meaning than is contained in the proposition, " Rational is that which possesses the attiibute of reason ;" since the attribute reason itself admits of be- ing 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 ex- press attributes of those attributes, there is no difficulty : like other connotative names, they are defined by declaring their connotation. Thus, the word Jiiult 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 ob' tain the definition of the names which belong to them all taken together ; a definition which will correspond exactly to that of the coiTesponding 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 ab- stract one, the same enumeration will serve for the definition of both. Thus, if the definition of a Imvian being be this, " A being, corporeal, animated, rational, and shaped so and so," the definition of 7i«w?a??zVy wall 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 upon some fact or phenomenon, from which and which alone it derives its meaning. To that fact or phe- nomenon, called in a former chapter the foundation of the attribute, we must, therefore, have recourse for its definition. Now, the foun- dation of the attribute may be a phenomencoi of any degree of com- plexity, consisting of many different parts, either coexistent or in succession. To obtain a definition of the attribute, we must analyze the phenomenon into these parts. Eloquence, for example, is the name of one attribute only ; but this atti'ibute is grounded upon exter- nal effects of a complicated nature, flowing fi-om 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 defi- nition of elo^iieiice, viz., thjLJjOwer of influencing the affections of hu- man beinggljy means of speech or writing. A name, thefefbre, wli ether coiici'^Te'lof abstract, admits of defini- tion, provided we are able to analyze, that is, to distinguish into parts, the attribute or set of attributes which constitute the meaning both of the concrete name and of the coiTesponding abstract : if a set of attri- butes, by enumerating them ; if a single attribute, by dissecting the 94 NAMES AND PROPOSITIONS. fact or phenomenon ^vhether 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 there- fore unsusceptible of analysis, the names both of the object and of the atti'ibute still admit of definition ; or, rather, would do so if all our Bimple 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 them- selves. 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 whith to recall tliose former sensations, except the very word which we seek to de- fine, 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 tlie personal experience of the individual whom we address. § 4. 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 the above. The only adequate definition of a name is, as already remarked, one which declares the fiicts, 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. aJad_^cpjiyen- tion. AhytTimg, thereft)re,'Ts to them a sufiicientltelTnition of a term, which will serve as a correct index to wl>at the term (denotes ; although not embracing the whole, and sometimes, perhaps, not even any part, of what it connotes. This gives rise to two sorts of unperfect, or un- scientific definitions ; namely, Essential but incomplete Definitions, and Accidental Definitions, or Descriptions. In the fofmer, a connotative name is defined by a part only of its connotation ; in the Jatter, by something which forms no part of the connotation at all. An example of the first kind of imperfect definitions is the follow- ing : 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 suf- ficient 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 wliicliJs-^wiformableJ.o-as^^^ are as well indicated by the inadequate definition as by an adeqiiafe" one. Such definitions, however, are always liable to be overthrown by the discovery of new objects in natm'e. DEFINITION. 95 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 different iam. Pift'erentia 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 j)C)- genus et dffercnfias, rather than different'uim. 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 tlie name of the superior genus has not already implied. The asser- tion, however, that a definition must of necessity consist of a genus and difierentice, is not tenable. It was early remarked by logicians, that the sunnnuiii 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 fortli in words the constit- uent parts of the fact or phenomenon, of which the connotation of every word is ultimately composed. § 5. Although the first kind of imperfect definition (which defines a cohnotative term by a part only of what it connotes, but a part sufficient to mark out con-ectly the boundaries of its denotation), has been con- sidered 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 conno- tation— has been rejected from the rank of genuine Definition by all philosophers, and has been termed Description. This kind of imperfect definition, however, takes its, rise frortl the same cause as the other, namely, the willingness to accept as a defini- tion 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 with- out 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 attri- butes which may happen to be peculiar to it, although separately each of those attributes may be common to it with some other things. It ia only necessary that the definition (or description) thus formed, shcmld be convertible with the name which it professes to define ; that is, should 1x3 exactly co-extensive with it, being predicable of everything of ^vhich it is predicable, and of nothing of which it is not predicable : although the attributes specified may have nc^ connexion with those which men had in view Avhen they foi-pied or recognized the class, and gave it a name. The following are coiTect definitions of Man, according to this test : Man is a mammiferous animal, baring (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. 96 NAMES AND PROPOSITIONS. "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 views, 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 connota- tion, though in genqral 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 maramiferous animal having two hands," which is the scientific definition of man con- sidered 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 inci- dental to a plan of arranging animals into classes on a certain principle, that is, according to a certain set of distinctions. And since the defi- nition 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 Avhich 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 upon 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 continua,lly rnodified as' scientific knowledge iadvances, the defi- nitions in the sciences are also constantly varying. A striking mstance is afforded by the words Acid and Alkali, especially the foniier. 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 ele- ment in the connotation of the word. But carbonic acid, silica, sulphu- rous acid, have no hydrogen in their composition ; that property can- DKFIMTION. 97 not 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 fonnation of neutral bodies by combination with alkalis, together with such electro-chemi- cal peculiarities as this is supposed to imply, are now the only differ- entia; 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 word^ 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 coimected with the same power which is the cause of what our senses recognize as heat, but has not yet taught us the laws of those phenomena with sufficient accuracy to admit of our determinhig under what characteristics the whole of those phenomena shall ultimately be embodied as a class : which characteristics would of course be so many diffisrentice for the definition of the power itself AVe have advanced far enough to know- that one of thee 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 d.efinition 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, we showed in the Introductory Chapter of this work, that the definition of a science must necessarily be progi'essive 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 paiticulars 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, as we have now shown, a special or technical definition has for its object to expound the artificial classi- fication 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 defi- nition must necessarily be per genus et differentiam, and would also explain why any one differentia was deemed sufficient. But to expound, or exjiress in words, a distinction of Kind, has already been shown to be an impossibility : the very meaning of a Kind is, that tin; properties which distinguish it do not grow out of one another, and cannot therefore be set forth in words, even by implication, othei"wise than by enumerating them all : and all are not known, nor ever will be 60. It is idle, therefore, to look to this as one of the pui-poses of a definition : while, if it be only required that the definition of a Kind should indicate what Kinds hiclude it or are included by it, any defi- nitions which expound the connotation of the names will do this : for the name of each class must necessarily connote enough of its proper- ties to fix the boundaries of the class. If the definition, therefore, is N 98 NAMES AND PROPOSITIONS. a full Statement of the connotation it is all that a definition can be required to be. § 6. 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 ofjxutlu- 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 fonner 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 fol- lowers, 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 cer- tain extent in abeyance, still continuing, however, to breed confusion in logic, by its consequences indeed rather than by itself Yet the docti'ine in its own proper form now and then breaks out, and has ap- peared (among other places) where it was scarcely to be expected, in a deservedly popular work, Archbishop Whately's Logic. In a re- view of that work published by me in the Westminster Review for January 1828, and containing some opinions wliich I no longer enter- tain, I find the following observations on the question now before us ; obsex'vations with which my present views on that question are 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 dis- tinguished 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 qual- ity 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 ap- parent, 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 cen- taur 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 Vford means fori*. In the first expression, ' A centaur means an an- DEFINITION. 99 imal,' &:c., the sense would remain unchanged : in the second, ' A tri- angle means,' &c., the meaning would bo altered, since it would be obviously impossible to deduce any of the truths of geometry from a proposition expressive only of the maimer in which we intend to em- ploy 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 temi. But it is not correct to call an expression of this sort a peculiar kind of definition. Its difference fi-om the other kind consists in this, that it is not a definition, but a definition and sometliing 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 figui'e may be termed a triangle.' The former of these pro- positions is not a definition at all : the latter is a mere nominal defini- tion, or explanation of the use and application of a term. The first is susceptible of truth or falsehood, and may therefore be made the foun- dation 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 discon- formity to the ordinary usage of language." There is a i-eal 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 degi-ee of importance. It affii-ms 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 ti'uth. 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 ra- tional 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 fi-om definitions. This, so long as a definition was considered to be a proposition " unfoldino- the nature of the thing," did well enough. But Hobbes came, and re- jected utterly the notion that a definition declares the natm-e of the thing, or does anything but state the meaning of a name ; yet he con- tinued to affirm as broadly as any of his predecessors, that the dpxac, principia, or original premisses of mathematics, and even of all science, are definitions ; producing the singular paradox, that systems of scien- tific truth, nay, all truths whatever at which we airive by reasoning, are deduced fiom 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 firamed con- formably to the phenomena of nature ; that is, that they ascribe such 100 NAMES AND PROPOSITIONS, meanings to terms as shall suit objects actually existing. But this is \ only an instance of the attempt, too 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 ne- cessary, from which of the two is the inference really drawn 1 from the existence of a thing having the properties 1 or from the existence of a name meaning them 1 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 analyzed, 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 B C D." Here is an assump- tion, that a figure, such as the definition expresses, ma^/ 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 im- plied in it ; Avithout 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. — The admissibility of these assumptions may be intuitive, or may admit of proof; 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 geometi-ical truths, though every definition in Euclid, and every technical terai therein defined, were laid aside. It is, perhaps, superfluous to dwell at so much length upon what is so nearly self-evident ; but when a distinction, obvious as it may appear, has been confounded, and by men of the most powerfid intel- lect, it is better to say too much than too little for the purpose of rendering such mistakes impossible in fiiture. AVe will, therefore, detain the reader while we 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 coiTectly from true premisses, and amve at a false conclusion. We should only have to assume as a premiss the definition of a non-entity : or rather of a name which has no entity con-esponding 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 DEFINITION. 101 coiTcct. A dragon is a serpent breathing flame : the word means tliat. The, tacit assumption, indeed (if there were any such understood assertion), of the existence of an object with properties conesponding 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 : But a dragon is a sei-jjent : From which the conclusion is, Therefoie 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 con-ect, the j^rcmisses cannot be true. But the premisses, considered as parts of a definition, are true : there is no possibility of controverting them. 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 pre- sents 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 : A dragon is a word meaning a thing which breathes flame : A dragon is a word meaning a serpent : From which the conclusion is. Some word or words whieh 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. If it relate to anything else, we may know that it does not follow from the definition, but from the tacit assumption of a matter of fact. It is only necessary further to inquire, in what cases that tacit as- sumption is really made, and in what cases not. Unless we declare the contrary, we always convey the impression that we intend to make the assumption, 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 defini- tion of a circle. § 7. 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 pos- tulates, 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 realized by art. People had a difficulty, therefore, in conceiving that the most certain of all conclusions could rest upon premisses which, instead of being certainly true, are certainly not true 102 NAMES AND PROPOSITIONS. to the whole 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 occuiTed, or whom it did not satisfy, have thought it indispensable that there should be found in definitions something morn 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 fi'om 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 figurfe with its radii exactly equal. Conformably to this it is said, that the subject matter of mathemat- ics, 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 mere 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 docti'ine respecting the nature of demonstrative truth to be correct (which, in a subsequent place, I shall endeavor 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. According to what appears to me the sounder opinion, 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 quali- ties, 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 doc- trine on the subject, leaves the conclusion that pur reasonings are grounded upon the matters of fact postulated in definitions, and not upon the definitions themselves, entirely unaffected ; and accordingly I am able to appeal in confirmation of this conclusion, to the authoi-ity of Mr. Whewcll, in his recent treatise on The Philosophy of the In- ductive Sciences. On the nature of demonstrative truth, Mr. Whewell's opinions are gi-eatly at variance with mine, but on the particular point DEFINITIONS. 103 in question it gives me great pleasure to observe, that there is a com- plete agieement between us. And here, as in many other instances, I gladly acknowledge that his writings are eminently serviceable in clearing from confusion the initial stej)s in the analysis of the mental processes, even where his views respecting the ultimate analysis (a matter generally of far less importance) are such as (though with un- feigned respect) I cannot but regard as fundamentally eiToneous. § 8. Although, according to the views here presented, Definitions are properly of names only, and not of things, it does not follow that definition is an easy matter. How to define a name, may not only be an inquiry of considerable difficulty and intricacy, but may turn upon considerations going deep into the nature of the things which are denoted by the name. Such, for instance, are the incjuiries which form the subjects of the most important of Plato's Dialogues; as, *' What is ihetoric ]" the topic of the Gorgias, or " What is justice ]" that of the Republic. Such, also, is the question scornfully asked by Pilate, " AVliat is truth 1" and the fundamental question with specula- tive moralists in all ages, " What is virtue V It would be a mistake to represent these difficult and noble in- quiries as having nothing in view beyond ascertaining the conven- tional 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 deejily, into the prop- erties 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 derivatives of the concrete names which coiTespond to them. Connotative names, therefore, were, after proper names, the first which were used : and in the sim])ler 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 wkife, as applied to snow or to any other object, knew, no doubt, very well what quality he in- tended to predicate, and had a perfectly distinct conception in his mind of the attribute signified by the name. But where the resemblances and diffijrences on which our classifi- cations 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 accustom- ed 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, whei-e the things to be named are complex wholes, a philosopher is not content with noticing a gen- eral resemblance ; he examines what the resemblance consists in ; and he only gives the same name to things which resemble one another in 104 NAMES AND PROPOSITIONS. 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 discrim- inated, 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, nohle or mean of any sentiment, expressipn, or demeanor, 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 recognize, as they think, some likeness, more or less vague and loose, between them 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 gi'ows." 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 gi-eat force and clearness by Dugald Stewart, in his Philosophical Essays), a name not unfrequently passes by suc- cessive 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 ebjects, 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 pui-jioses 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 inconve- niences of a language which " is not made, but gi'ows." Like 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 1 and, in the first place, whether mankind agree sufficiently with one another as to the particvilar 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 alono is an inquiry into usage and convention ; the other two ai-e inquiries DEFINITION. 105 into matters of fact. Ami if the second question (vvhethex* the actions form a class at all), has been answered negatively, there retnains a fourth, often more arduous than all the rest, hamely, how best to form a class arliticially, which the name may denote. And here it is fitting to remark, that the study of tlie spontaneous growth of languages is of the utmost importance to the philosopher 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 many of his purposes. When compared with the classifica- tions of a philosopher, they are like the customary law of a country, which has gi'own 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 the greater part of the materials out of which the systematic body of written law may and ought to be fomied. In like manner, the established grouping of objects under a common name, though it may be founded only upon 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 sei'ies of years and ages. Even when a name, by successive extensions, has come to be applied to things among which there does not exist even a 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 even of philosophers ; of those at least who, from using a different language, or from any difference in their habitual associations, have fixed their attention in preference upon some other aspect of the things. The history of philosophy abounds in examples of such oversights, which would not have been committed if a philosopher had seen the hidden link that connected together the seemingly disparate meanings of some ambiguous word.* Whenever the inquiry into the definition of the name of any real ob- ject consists of anything else than a mere comparison of authorities, we tacitly assume that a meaning must be found for the name, com- patible 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 com- monly predicated. The inquiry, therefore, into the definition, is an inquiry into the resemblances and differences among those things : whether there be any resemblance running though them all; if not, through what portion of them such a general resemblance can be traced : * "Few people" (I have said in another place) "have reflected how great a knowledge of Things is required to enable a man to aflirin 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 ditlerent from one another. IJetween two of these ideas a sagacious and penetrating mind will discern, as it were intuitively, an unobvious link of connexion, upon which, though per- haps 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." 106 NAMES AND PROPOSITIONS. and finally, what are the common attributes, the possession of which gives to them all, or to that portion of them, the character of resem- blance which has led to their being classed together. Wlien these common attributes have been ascertained and specified, the name which belongs in common to the resembling objects, acquires a dis- tinct 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 endeavor to fix upon such atti-ibutes as, while they are common to all the things usually denoted by the name, are also of greatest impor- tance in themselves, either directly, or from the number, the conspic- uousness, or the interesting character, of the consequences to which they lead. He will select, as far as possible, such differentice as lead to the greatest number of intei-esting 2>ropria. 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 deter- mine the groups into which they naturally fall. But to mount up to the more hidden agreement upon which these obvious and superficial agreements depend, is often one of the most difficult of scientific prob- lems. 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 respect- ing 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. Aiupianivuv 6e tovtuv, Tih/ufiEv f/671, diu rivuv, Kai nore, Kat nuc yivtrai rruf troAAo- yicT/idc' varepov 6^ XeKriov nKpl utto Jtjff wf. JlpoTepov yap Tvepl (TV%?.oyiaiiWV TiEKriov, fj TTfpl uTToihiieuc, ^lu to KaOo'Aov fiuA?iOV eival rov avX'koyLaiiov. 'H fiiv yap uK6dei^i(, ort of each sort, and have ascertained the nature of the things they relate to, and the nature of what they sever- ally 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 phe- nomena 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 abstnise expression for it, which though stopping short in an earlier stage of the; analysis, is sufficiently scientific for many of the puqioses for which such a general expression is required. 108 REASONING. This expression recognizes the commonly received distinction between Subject and Attribute, and gives the follow^ing 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 inquir}', and proceed to the peculiar problem of the Science of Logic, namely, how the assertions, of which we have analyzed the import, are proved, or disproved : such of them, at least, as, not being amena- ble to direct consciousness or intuition, are appropriate subjects of proof We say of a fact or statement, that it is proved, when we be- lieve its ti-uth by reason of some other fact or statement fi-om which it is said to folloic. 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 pre- viously 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 nan'ower 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 teim 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 prop- erly 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 ■A'as contained in the first. All the cases mentioned in books of Logic, as examples of yEquipollency 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 ai'c 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 fi-om another, but to repeat a second time something which had been asserted at fii'st ; 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 some- thing already connoted by the fonner -predicate : eus, Socrates is a INFERENCE IN GENERAL. 109 man, therefore Socrates is a living creature ; where all tliat is connoted by living creature was aflirmcd of Socrates when he was asserted to be a man. If the propositions are negative, we must invcit their order, thus : Socrates is not a living creature, therefore he is not a man ; for if we deny tlie less, the greater, which includes it, is already denied by implication. These, therefore, are not really cases of infer- ence ; and yet the trivial examples by which, in manuals of Logic, the rules of the syllogism are illustrated, arc often of this ill-choscu kind ; demonstrations in form, of conclusions to which whoever understands the terms used in the statement of the data, has already, and con- sciously, assented. The most complex case of this sort of apparent inference is what is called the Conversion of Propositions ; which consists in making the predicate become a subject, and the subject become a predicate, and framing out of the same terms, thus reversed, another j^roposition, which must be true if the former is true. Thus, fi-om 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 conveitible into Some B is A. This process, which converts an universal propo- sition into a particular, is termed conversion per accidens. From the proposition. Some A is not B, \ye 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 asquipollent with it. Some A is " a thing which is not B ;" and the proposition, being now no longer a paiticular 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 infei'ence ; there is m the conclusion no new truth, nothing but what was already asserted in the premisses, and obvious to whoever apprehends them. The fact as- serted in the conclusion is either the very same fact, or part of the fact, asserted in the original proposition. This follows fi'om our previous analysis of the Import of Propositions. When we say, for example, that some la\vful sovereigns arc tyrants, what is the meaning of the assertion ? That the attributes connoted by the temi " lawful sover- eign," 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 fool, we mean that the attributes connoted by " great general," and those con- 110 REASONING. noted by "fool," never coexist in the same subject; which is also the exact meaning which we express when we say, that no fool is a great general. Wlien we say that all quadrupeds are wann-blooded, we as- sert, not only that the atti'ibutes connoted by "quadruped" and those connoted by " warm-blooded" sometimes coexist, but that the former never exist without the latter : now the proposition. Some wann- blooded creatures are quadrupeds, expresses the first half of this mean- ing, dropping the latter half; and, therefore, has been already affirmed in the antecedent proposition, All quadrupeds are wann-blooded. But that all wann-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 infened. In order to reassert, in an inverted form, the whole of what was affii-med in the proposition, All quadrupeds are warm-blooded, we must convert it by contraposition, thus. Nothing which is not wann- blooded is a quadruped. This proposition, and the one from which it is derived, are exactly equivalent, and either of them may be substitu- ted 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 gi-eater length upon the conversion and Eequipollency 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 pi'ovince of the ait 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 distinguisliing the different kinds or modes of opposition, are of use chiefly for this purpose. Such considerations as these, that conti-ary propositions may both be false, but cannot both be tnie ; 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 subal- ternate 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 versci;* 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 pai'ticulai- 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 pai'ticular 'fo iSlho-traries. «JL^ ^ ^-^ Lf -a \ contradictories, some A is not B J Some A is B 5 ^^^° contradictories. tielis ^ S -'^ilelSnot b | -spectxvely subaltemate. INFERENCE IN GENERAL. Ill 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 sei-ves to bridge over. Yet no one has ever censured writers on geometiy, for placing a list of these elementaiy genci-aliza- tions at the head of their treatises, as a first exercise to the leanier of the faculty which -will be required in him at every step, that of appre- hending a general truth. And tlie student of logic, in tiie discussion even of such truths as we have cited above, acquires habits of circum- spect intei-}5retation of words, and of exactly measuring the length and breadth of his assertions, which are among the most indispensable con- ditions of any considerable attainment in science, 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 Rea- soning or Inference properly so called, the cases in which the progress 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 ai'e cases of inference in the proper acceptation of the term, those in which we set out from known tniths, to anive at others really distinct from them. Reasoning, in the extended sense in which I use the terra, and in which it is synonymous with Inference, is popularly said to be of two kinds : reasoning from particulars to generals, and reasoning from gen- erals to particulars ; the fonner being called Induction, the latter Ratiocination or Syllogism, It will presently be shown that there is a third species of reasoning, which falls imder neither of these descrip- tions, and which,- nevertheless, is not only valid, but the foundation of both the others. It is necessary to observe, that the expressions, reasoning from par- ticulars to generals, and reasoning from generals to particulars, are recommended by brevity rather than by precision, and do not ade- quately mark, without the aid of a commentary, the distinction between Induction and Ratiocination. The meaning intended by these expres- sions is, that Induction is infemng a proposition from propositions less general than itself, and Ratiocination is infeiTing 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 fi-om 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 geuerahty wiih itself, or a less general proposition, or a proposition merely individual, the process is Ratiocination. Wlien, in short, the conclusion is more general than the largest of the prem- isses, 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 wiU, however, be advantageous, iii a science which 112 EEASONING. aims at tracing our acquired knowledge to its sources, that the inquirer should commence with the later rather than with the earlier stages of the process of constructing our knowledge ; and should trace deriva- tive ti-uths backward to the ti'uths from which they are deduced, and upon 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 ne- cessity 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 conclu- sion 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 we have specifically observed in the individual cases that we have examined ; it is a generalization grounded on those cases, and expressive of our belief, that what we there found ti'ue is true in an indefinite number of cases which we have not examined, and are never likely to examine. The nature and gi'ounds 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 obsen^ed ; future facts, for example : but which we do not hesitate to believe upon 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, me- mories causd, the leading results of that analysis, as a foundation for the remarks to be afi:erwards made upon the functions of the syllogism, and the place which it holds in philosophy. To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or propo- sition 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 pred- icate of the conclusion, and another called the middleterm, which must RATIOCINATION, OR SYLLOGISM. 113 be found in both premisses, since it is by means of it that the (tthcr two terms are to be connected together. The predicate of the conchi- sion is called the major tenn of the syllogism; the subject of the con- clusion is called tlie minor term. As theie 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 mnjt)r term is called the major premiss ; that w^hich contains the middleterm and the niinor term is called the mmor premiss of the syllogism. Syllogisms are divided by some logicians into throe Jigures, by oth- ers 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. Tlie most common case is that in which the middleterm is the subject of the major prem- iss and the predicate of the minor. This is reckoned as the first figure. When the middleterm is the predicate in both premisse.s, 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 WTiters who reckon no more than tluree figures, include this case in the first. Each figure is subdivided into modes, according to what are called the quantity and qimlitij of the propositions, that is, according as they are universal or particular, aflirmative or negative. The following are examples of all the legitimate modes, that is, all those in which the. conclusion coiTectly follows from the premisses; A is the minor term, C the major, B the middleterm. ' FiKST 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. Xo 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 NoBisC Some B is C All Bis C iSomeBisnotC No B is C All B is A All Bis A All Bis 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 not C Some A is C Some A is C Some A is not C Some A is 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 Bis A All Bis A All B is A Some Bis A therefore therefore therefore therefore therefore Some A i^C Some A i.s C Some A is C Some A is not C Some A is not C In these exemplars, or blank fonns for making syllogisms, no place is assigned to singular propositions ; not, of course, because such pro- positions 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 — 114 REASONING. 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 ipossihle 7?iode, 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 di%Tiiing 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 peculiar perspicuity, the whole of the common docti'ine of the syllogism. ' AH valid ratiocination ; all reasoning by which, from general propo- sitions previously admitted, other propositions equally or less general are infeiTed ; 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, regidar in mode and figure. • Although a syllogism framed according to any of these formulffi is a valid argument, all correct ratiocination admits of being, stated in syllo- gisms of the first figure alone. The rules for throwing an argument in any of the other figures into the first figiire, are called rules for the re- duction 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 O is B, being an uni- versal negative, admits of siniple conversion, and may be changed into No B is C, which, as we showed, is the veiy same assertion in other words — the same fact differently expressed. This ti-ansformation hav- ing been effected, the argument assumes the followdng fonn : — No B is C AH A is B therefore No A is C, which is a good syllogism in the second ode 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 dawn in the last chapter respecting universal afflnnatives, does not ad- mit of simple conversion, but may be converted ^er accidens, thus; Some EATIOCINATION, OR SYLLOGISM. 115 A is B ; wliich, though it does not express. the whole of what is assert- ed in the proposition, All B is A, expresses, as was formerly sliown, part of it, and must therefore lie true if the whole is true. We have, then, as the result of the reduction, the following syllogism in the third mode of the lirst figiu'e : — 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 rrtode 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 expnissiug them. Eveiy 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 ) • -p All A ) • T5 Some A } ''^' Some A J ^^ ^ therefore therefore All A. I is c No A is I C Some A ) ■ Some A-is not ) •Or, if more significant symtjols are preferred,—^ To prove an affii:;rnative, the argument must %dmit of being stated in this form : — y All animals are mortal ; All men ^ Some men > arc animals ; Socrates. . ) ' therefore All men ") Some men > are mortal. Socrates ) 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 negi-oes ) Some negroes > are capable of self-control ; Mr. A's negro ) therefore No negroes are i Some negroes are not > necessarily vicious. Mr. A's negro ,is not ) Although all ratiocination admits of being thrown into one or the other of these fontis, and sometimes gains considerably by the trans- formation, both in clearness and in the obviousness of its consequence ; there axe, 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 into the first. Thus, if the proposition were that pagans may be vir- 116 REASOXING. tuous, 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 \artuous, would be a more natural mode of stating the argument, and would carry conviction more instantly home, than the same ratiocination sti-ained into the first figure, thus — Aristides was virtuous, Some pagan was Aristides, therefore Some pagan was virtuous. A German philofsopher, Lambert, whose Neues Organon (published in the year 1TC4) contains among other things the most elaborate and complete exposition of the syllogistic doctrine which I have happened to meet with, has expressly examined what sorts of arguments fall most naturally and suitably into each of the four figures ; and his solu- tion is characterized by great higenuity and clearness of thought * The argument, however, is one and the same, in whichever figure it is expressed ; since, as Ave have already seen, the premisses of a syllo- gism in the second, thuxl, or fourth figm-e, and those of the syllogism in the first fip-ure to which it may be reduced, are the same premisses, in everything except language, or, at least, as much of them as con- tributes to the proof of the conclusion is the same. We are therefore at liberty, in conformity with the general opinion of logicians, to con- sider the two elementary fonns of the first figure as the universal types of all coiTect ratiocination ; the one, when the conclusion to be proved is affinnative, the other, when it is negative ; even though cer- tain aro-uments may have a tendency to clothe themselves in the forms of the second, third, and fourth figures ; which, however, cannot possi- bly happen with the only class of arguments which are of fii'st-rate scientific importance, those in which the conclusion is an universal affinnative, such conclusions being susceptible of proof in the first figui'e alone. § 2. On examining, then, these two genei-al formulae, we find that in both of them one premiss, the major, is an universal proposition ; and * His conclusions are, " The first figure is suited to the discovery or proof of the proper- ties 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 ditferent species of a genus." The reference of syllogisms m the last three figures to the dictum de omni et nulla is, in Lambert's view, strained and unnatural : to each of the three belongs, according to him, a separate axiom, coordinate 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 dictuin de reciproco for the fourth. See part i. or Dianoiologie, chap. iv. % 229 et seqq. . Were it not that the views I am about to propound on the functions and ultimate foun- dation of the syllogism render such distinctions as these of very subordinate importance, I should have availed" myself largely of this and other speculations of Lambert ; who has displayed, within the limits of the received theory of the syllogism, an ongmahty for which it was scarcely to be supposed that there could still have been room on so exhansted a subject, and whose book may be strongly recommended to those who may attempt still further to improve the excellent manuals we already possess of this elementary portion the Art of Reasoning. RATIOCINATION, OR SYLLOGISiM. 117 according as tins is affirmative or negative, the conclusion is so too. AH 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 hidehnite number of objects, distin- guished by a common characteristic, and designated, in consequence, by a common name. • Tlie other premiss is alv/ays 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 vs^hich 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 ia precisely the assertion made in the conclusion. Whether or not the foregoing is an adequate account of the coii- stituent parts of the syllogism, will be presently considered; but as far as it goes it is a true account. It has accordingly been generaUzed 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 su|)posed to be one and the same thing. The maxim is. That what- ever can be affinned (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, thovigh thei-e have not been wanting, in our o^^^r 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 upon 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 inider it, was then no identical proposition, but a statement of what was conceived as a fimdamental law of the uni- verse. The assertion that the entire nature and properties of the substantia secunda fonnod part of the properties of each of the bidividual 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 viean all men, but something inherent in men, and vastly superior to them in dignity. Now, how- ever, 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 \vq leani by being told, that whatever can bo affirmed of a class, may be affinned of every object contained in the class? The class is nothing but the objects contained in it: and the 118. REASONING. dictum de omrii merely amouiits to the identical proposition, that what- ever 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 diction 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 sionilicance to the cognate aphorism, "It is impossible for the same thino- to be and not to be ;" since this is, at the lowest, equivalent to the logical axiom that contradictory propositions cannot both be ti'ue. To o-ive 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 science, 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 pennanent 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 re- jected, 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 con- sisted entirely or partly in some kind of conjuration or juggle with those names. Wlien a philosopher adopted fully the Nominalist view of the signification of general language, retaining along with if 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 Avi'iters of deserved celebrity, that the process of ari'iving at new truths by reasoning consists in the mere substitution of one set of arbiti-ary signs for another ; a doctrine which they supposed to derive irresistible confirmation fi'om the example of algebra. If there were any process in sorcery or necromancy more preternatural than this, I should be much surprised. Tlie culminating point of this philosophy is the noted aphorism of Condillac, that a science is nothing, or scarcely anything, but une langue hien faite : in other words, that the one suflJi- cient 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 im- possible 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 tnvial knowledge with respect to RATIOCINATION, OR SYLLOGISM. 119 Things, ever was or could be originally got at by any conceivable manipulation of mere names : and that wlit^t can be learnt from names, is only what somebody who used the names, knew before ? Philoso- phical analysis confirms the indication of common sense, that the func- tion of names is but that of enabling us to remcmher and to communi- cate our tlioughts. 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 con- sidered 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 ejxercised. We think, indeed, to a con- siderable extent, by means of names, but what Ave think of, are the things called by those names ; and there cannot be a greater eiTor than to imagine that thought can be canied 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 coiTesponding to the erroneous Anew which Hobbes took of propositions. Because there are some propositions which are merely verbal, Hobbes, in order (ap- parently) that his definition might be rigorously universal, defined a proposition as if no propositions declare'd 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 some- thing belongs to a class, and if, as consistency would require us to suppose, 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 Avith itself. But Ave have seen that it is no sufficient account of the meaning of a proposhion, to say that it refers something to, or excludes something from, a class. EAory proposition Avhich conveys real infoi-mation asserts a matter of fact, dependent upon the laAvs of nature and not upon artificial classification. It asstits that a given object does or does not possess a given attribute ; or it asserts that tAvo attributes, or sets of attributes, do or do not (constantly or occasionally) coex- ist. Since such is the purport of all propositions AA'hich convey any real knowledge, and since ratiocination is a mode of acquir- ing real knowledge, any theory of ratiocination Avhich does not re- cognize this import of propositions,.cannot, we may be sure, be the true one. Applying this vieAV of propositions to the two premisses of a syllo- gism, Ave obtain the foUoAving results. The major premiss, which, as already remarked, is ahvays universal, asserts, that all things Avhich have a certain attribute (or attributes) have or have not along- Avith it, a cer- tain other attribute (or attributes). The minor premiss asserts that the thing or set of things Avhich 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, 120 REASONING. 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 un- less 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 atti-i- bute mortality. Or, if both the premisses are general propositions, as All men are m6rtal, 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 attiibutes are never found without the attribute of mortality. The conclusion is, that wherever the atti-ibutes of kingship are found, that of mortality is found also. If the major premiss were negative, as. No men are gods, it would assert, not that the attributes connoted by " Man" never exist without, but that they never exist with, those connoted by " God :" fi-om which, together with the minor premiss, it is concluded, that the same incom- patibility exists between the atti-ibutes constituting a god and those con- stituting a king. In a similar manner we might analyze any other ex- ample 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 umneaning 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 afiinnative syllo- gisms, 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 con- ventions : and one or other of them is the gi-ound of the legitimacy of every argument in which facts and not conventions are the matter treat- ed of. § 4. It only remains to translate this exposition of the syllogism from the one into the other of the two languages in which we foiTnerly remarked* that all propositions, and of course therefore all combina- tions of propositions, might be expressed. We observed that a propo- sition might be considered in two difterent 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 at- * Supra, p. 157. RATIOCINATION, OK SYLLOGISM. 121 tribute lias a certain other attribute. Under the other aspect, it is to be regarded not as a part of our knowledge, but as an aid tor our prac- tical 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 mcUfk 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 Ims the mark A, therefore The given object has the attribute B. RefeiTed to this type, the ai'guments 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 mortahty. 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 attributes of a god. 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 attributes signified by the word god : (or, are evidence of the absence of those attributes). 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 safely 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 ascertain- ment of a truth by ratiocination. 128 REASONING. CHAPTER III. OF THE FUNCTIONS, AND LOGICAL VALUE, OF THE SYLLOGISM. § 1. We hav« shown what is the real nature of the truths \%'itli which the Syllogism is conversant, in contradistinction to the rriore- supei-ficial 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 progi-ess 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 an- swering 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 kno^vn, 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 I 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 acknowl- edgment so explicitly made, has not prevented one set of writers from continuing to represent the syllogism as the coiTect 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 gi'ound 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 func- tions 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. Wlien 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 were previously certain of the FUNCTIONS AND VALUE OF THE SYLLOGISM. 123 mortality of every individual man : tliat if it be still doubtful whether Socrates, or any other indi-v-idunl you choose to name, be morta:l 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 caso comprised with it, is dispelled by evidence aliunde.; and then what remains for the syllogism to prove ] that, in short, no reasoning fi-om 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 foreknown. This doctrine is 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 argu- ment itself, but because the contrary opinion seemed to rest upon 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 boiid fide a new truth 1 Is it not matter of daily exjjerience that truths previously undreamt of, facts which have not been, and cannot be, directly observed, are amved 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 yet dead. If we were asked how, this being the case, we know the duke to be mortal, we should probably ajiswer. Because all men are so. Here, therefore, we ari'ive at the knowledge of a truth not (as yet) susceptible of obsei-vation, 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 have cleared up the difficulty which arises fi-om the inconsistency between that assertion and the principle, that if there be anything in the conclusion which was not already as- serted in the premisses, the argument is ricious. For it is impossible to attach any serious scientific value to such a mere salvo, as the dis- tinction drawn between being involved by impUcation in the premisses, and being directly asserted in them. When Archbishop Whately, for example, says,* that the object of reasoning is "merely to expand and unfold the assertions wrapt up, as it were, and impHed in those with which we set out, and to bring a person to perceive and acknowledge the full force of tliat which he lias admitted," he docs not, I think, meet the real difficulty requiring to be explained, namely, how it hap- pens that a science, like geometry, can be all " wTSpt 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, whert they charge it with being of no use except to those who seek to press * Logic, p. 216. 124 REASONING. the consequences of an admission into which a man has been entrapped without having considered and understood its full force. When yoti 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 kuow you were asserting it ; but, if so, the difficulty re- vives in this shape — Ought you not to have known ] Were you war- ranted in asserting the general proposition without having satisfied yourself of the truth of eveiything which it fairly includes 1 And if not, what then is the syllogistic art but a contiivance for catching you in a trap, and holding you fast in it 1 § 3. From this difficulty there appears to be but one issue. The proposition, that the Duke of Wellington is mortal, is e\idently an in- ference ; it is got at as a conclusion fi'om something else ; but do we, in reality, conclude it from the proposition, All men are mortal ? I an- swer, no. The eiTor committed is, I conceive, that of overlooking the distinc- tion between the two parts of the process of philosophizing, the infer- ring part, and the registering part ; and ascribing to the latter the functions of the former. The mistake is that of refen'ing a man to his own notes for the origin of his knowledge. If a man is asked a ques- tion, and is at the moment unable to answer it, he may refi-esh his memory by turning to a memorandum which he cames about A\dth 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 A\Titten, 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 ] No super- natiu'al aid being supposed, the answer must be, by observation. Now, all which man can obsei-A'e are individual cases. From these all gen- eral truths must be drawn, and into these they may be again resolved : for a general truth is but an aggregate of particular truths ; a compre- hensive 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 mem- ory a number of pai'ticular 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 fi-om 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 obser- vations and inferences, and instructions for making innumerable infer- ences in unforeseen cases, are compressed into one short sentence. ^V^aen, therefore, we conclude from the death of John and Thomas, and every other person we ever heard of in whose case the experi- ment had been fairly tried, that the Duke of WeUington is mortal like FUNCTIONS AND VALUE OF THE SYLLOGISM. 125 the rest -y. wo 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 ittfercncc resides. The inference is finished when we have asserted that all men are mortal. What remains to be performed afterwards is merely deciphering our own notes. Archbishop Whately has contended that syllogizing, or reasoning from generals to particulars, is not, agreeably to the vulgar idea, a pe- culiar 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 tbe deference due to so high an authority, I cannot helji thinking that the vulgar notion is, in this case, the more con-ect. If, from our experi- ence of John, Thomas, &c., who once were li\'ing, 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 fi-om 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 intei-polating 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 gi'eater than it is ; and since that evidence is either sufficient in itself, or, if in- sufficient for 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 can- not 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, affi)rding a commanding view of the suiTounding country ; but for the inere 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 intelli- gence 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 bums. He knows from memory that he has been burnt, and on this evidence believes, when he sOes 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 infemng a particular from particulars. In the same way, also, brutes reason. There is little or no ground for attributing to any of the lower animals the use of conventional signs, without which general propositions are impossible. But those anima;ls 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 bui'nt 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 126 REASONING. books or tradition, We'much oftener conclude from particulars to par- ticulars directly, than tJirough 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 obsei-vations 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 men in general, or men of some paiticular character, are accustomed to feel and act ; but much oftener from having known the feelings and conduct of the same man in some previous instance, or from considering how we should feel or act oui'selves. It is not only the village matron who, when called to a consultation upon the case of a neighbor's child, pronoun- ces on the evil and its I'emedy 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 impres- sions 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. Tliis 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 coiTesponding general prop- ositions. An old waiTior, on a rapid glance at the .outlines of the ground, is able at once to give the necessary orders for a skillful ar- rangement of his troops ; though if he has received little theoretical instruction, and has seldom been called upon to answer toother people for his conduct, he may never have had in his mind a single general theorem i-especting the relation between ground and array. But his experience of encampments, under circumstances more or less similar, has left a numbesr 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 man- ner most suited to his purpose, under the operation of all tlie 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 cer- tainly never framed into any verbal theorems or rules. It is the same in all extraordinary manual dexterity. Not long ago a Scotch manufac- turer procured from England, at a high rate of wages, a working dyer, famous for producing very fine colors, 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 talcing them up in handflils, while the common method was to weigh them. The manufacturer sought to make him turn liis FUNCTIONS AND VALUE OF THE SYLLOGISM. 127 handling system into an equivalent weighing system, that the general principle of his peculiar mode of proceeding might be ascertained. This, liowever, the man found himself quite unable to do, and therefore could impart his skill to nobody. He had, from the individual cases of his o^vn experience, established a connexion in his mind between fine effects of color, and tactual perceptions in handling his dyeing materi- als ; and from these perceptions he could, in any particular cases, infer the means to be employed, and the effects which would be produced, but could not put others in possession of the gi'onnds on which he pro- ceeded, from having never generalized them in his own. mind, or ex- pressed them in language. Almost every one knows Lord Mansfield's advice to a man of prac- tical 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 ad\-ice 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 wi-ong. 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 fi-om 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 de- rived by legitimate induction from tliat experience, would have been greatly preferable as a judge, to one, howpver sagacious, who could not be trusted with the explanation and justification of his own judg- ments. The cases of able men performing wonderful things they know not how, are examples of the less civilized and most spontaneous form of the operations of superior minds. It is a defect in them, and often a somxe of eiTors, not to have generalized as they went on ; but gen- eralization is a help, the most impoitant indeed of all helps, yet not an essential. Even philosophers, 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 upon the axioms, it is by no means necessary to our seeing the conclusiveness of the proof, that the axioms should be expressly adverted to. Wlien 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 imderstood, would assent to the inference, without having ever heard of the general truth that " things which are equal to the same thing ai-e 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 stopped short at a much more limited application of it. He saw that the general propo- sitions on which a reasoning is said to depend, may, in certain cases, be altogedier omitted, without impaii'ing its probative force. But he imagined this to bo a peculiarity belonging to axioms ; and argued from it, that axioms are not the foundations or first principles of geometry, 128 REASONING. from which all the othei* truths of the science are synthetically deduced (as the laws of motion and of the composition of forces in mechanics, the equal mobility of fluids in hydrostatics, the laws of refle.ction and refraction in optics, are the first princijiles of those sciences) ; but are merely necessary assumptions, self-evident indeed, and the denial of which would annihilate all demonstration, but firom which, as premisses, nothing can be demonstrated. In the present, as in many other in- stances, 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 ti'ue 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 defi- nition, 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 ai"e 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 diagi'am. What assumption, in fact, do we set out fi'om, to demonsti'ate by a diagi'am 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 you should grant the assumption in the case of the par- ticular circle supposed. From this, which is not a general but a sin- gular proposition, combined with other propositions of a similar kind, some of which when generalized are called definitions, and others axiqms, 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 con- ditions, 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. ]3ut this only means, that if we can prove an individual conclusion by assuming an individual fact, then in Avhatever case we are waiTanted 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, FUNCTIONS AND VALUE OF THE SYLLOGISM. 129 which we lay down at the beginning of our reasonings, are merely abi-idged statements in a kind of short hand, of the particular facts, which, as occasion aiises, we either think we may proceed upon 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 state- ment 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 upon it, but yet if we deny it the demonstration fails. The proof does not rest upon the general assumption, but upon 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 theo- rem, there can be no gi'ound 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 fonn, and these will be explained presently, so far as explanation is requisite. But, that an unpractised learner, even in making use of , one theorem to demon- strate another, reasons rather from particular to particular tlian from the general proposition, is manifest from the difiiculty he finds in ap- plying a theorem to a case in which the configuration of the diagram is exti'emely unlike that of the diagi'am 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 conclu- sions seem to be established: All inference is from particulars to par- ticulars : General propositions are mei-ely 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 in- ference drawn according to the formula : the real logical antecedent, or premisses, being the particular facts firom which the general propo- sition was collected by induction.. Those facts, and the individual in- stances 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 pui-poses, a conclusion from the forgotten facts. For this it is essential that we should read the rccoi-d correctly : and the rules of the syllogism are a set of precautions to insure our doing so. This \dew of the functions of the syllogism is confinned by the con- sideration of precisely those cases which might be expected to be least favorable to it, namely, those in which ratiocination is independent of any previous induction. We have already obsei-\'ed that the syllogism, in the ordinary course of our reasoning, is only the latter half of the process of ti-avelling fi'om premisses to a conclusion. There are, how- evex", some peculiai' cases in which it is the whole process. Particu- 130 REASONING. lars alone are capable of being subjected to observation ; and all knowl- edge which is derived from observation, begins, therefore, of necessity, in particiilai-s ; but our knowledge may, in cases of a certain descrip- tion, be conceived as coming to us from other sources than observa- tion. It may pi'esent itself as coming from revelation ; and the knowl- edore, thus supernaturally communicated, may be conceived to com- ' prise not only particular facts "but general propositions, such as; occur so abundantly in the A\Titings of Solomon and in the apostolic epistles. 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 supe- rior, that we, or any number of other persons, shall conform our con- duct to certain general instriictions. 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 de- scription therein contained of the conduct which it is the Avill of the legislator that his subjects should observe, is general. The proposi- tion asserts, not that all men ore anything, but that all men sJiall do something. These two cases, of a truth revealed in general terms, and a command intimated in the like manner, might be exchanged for the more extensive cases, of any general statement received upon testimony, and any general practical precept. But the more limited illustrations suit us better, being drawn from subjects where long and complicated trains of ratiocination have actually been grounded upon premisses which came to mankind from the first in a general form, the subjects of Scriptural Theology and of positive Law. In both these cases the generalities are given to us, and the pattic- ulars 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. It is a search for ti-uth, no doubt, but through the medium of an inquiry into the meaning- of a fonn of words. 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 presetit case among others, or not. This is a question, as the Gennans express it, of hermeneutics ; it relates to the meaning of a certain fonn of discourse. The operation is not a process of inference, but a pro- cess 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 intei-preting the signs in which the one has intimated hife assertion and the other his command. In like man- ner, when the premisses are derived from observation, the function of Reasoning is to ascertain w'hat we (or our predecessors) formerly thought might be infen-ed from the observed facts, and to do this by intei-preting 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 infeiTed 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 tcnn man, aie FUNCTIONS AND VALUE O^ THE SYLLOGISM. 131 a mark of mortality. But wlicn we conclude tliat the Duke of Wel- lington is mortal, we Jo 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 pixiposition,) concerning the inferences which that former experience would waiTant. 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 defendei's of the syllogistic doctrine, respecting the limits to which its functions are confined. They all 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 gi'ound which a syllogism aftbrds 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 beheving the facts which we leani from reasoning, in contradistinction to observation. The true reason why we believe that the Duke of Wellington ^\'ill die, is that his fathers, and our fathers, and all other persons wlio were contemporary 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, not- withstanding, live for ever. But there would be a contradiction if we first, on the gi'ound 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 Avhich may be justly drawn in future 'cases, and the inferences we actually draw in those cases when they arise. With this vaew we interpret our own formula, precisely as a judge intei-prets a law: in order that we may avoid drawing any inferences not confoi'mable to our former intention, as a judge avoids giving any decision' not con- formable 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 coiTect analysis of that process of reasoning or inference ; which is, on the contrary, (when not a mere inference fi-ora testimony,) an inference from partic- ulars to particulars; authoi-ized by a previous inference from particu- lars 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 132 REASONING. Whately himself, against the doctrine that the syllogistic art is useless for tiie purposes of reasoning. The reasoning lies in the act of gen- eralization, not in intei-preting the record of that act ; but the syllogistic form is an indispensable collateral security for the con-ectness 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 obser- vation 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 indefi- nite multitude of facts : the expei'ience which justifies a single predic- tion 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 gen- eral 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 genei'ality, is felt as of ,gi-eater 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 coiu'se of individ- ual 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 pecu- liar interest ; there is very little to prevent us from giving way to negligence, or to any bias which may affect our wishes or our imagina- tion, and, under that influience, accepting insufficient evidence as suffi- cient. But if, instead of concluding sfcfaight 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 inferable 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 Avill comprise within it some fact or facts the reverse of which we already know to be true ; and we shall thus discover the eiTor in our generalization, by what the schoolmen termed a reductio ad impossihile. Thus if, during the reign of Marcus Aurelius, a subject of the Roman empire, under the bias naturally given to the imagination and expec- tations 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. FUNCTIONS AND VALUE OF TlIK SYLLOGISM. 133 But if lie reflected that this conclusion could not be justifi;il>lc unless from the same evidence he was also warranted in concluding some gen- eral 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 whetlier any controvei'ted 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 ad- vantageous, to divert our argument into the circuitous channel of an induction from those known cases to a general proposition, and a subse- quent application of the general proposition to the unknown case. This second part of the operation, which, as before observed, is essen- tially a process of intei-pretation, 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 our 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 obser- vations, 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' ai'e 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 coiTectly, 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 reason- ings may always be represented, and which is admirably calcu- lated, 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 eiTor, we may, and do, reason at once from the known particular cases to unknown ones. These are the uses of the 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 ; inten'ogation of experience may suffice, and the result may be regis- tered in the form of a general proposition, which is committed to 134 KEASONING. memory or to writing, and fi'om wliicli afterwards we have only to syl- loo-ize. The particulars of om- experiments may then be dismissed from the memory, in which it woulcl 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 obser- vations were forgotten, or as their record became too bulky for refer- ence, is retained in a commodious and immediately available shape by means of general language. A.fainst this advantage is to be set the countei-vailing inconvenience, that inferences originally made on insufficient evidence, become conse- crated, and, as it were, hardened into general maxims ; and the mind cleaves to them from habit, after it has outgi'own 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 trifling 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. AVe can reason without them ; in simple and obvious cases we habitually do so ; minds of great sagacity can do it in cases not simple aiid obvious, provided their exj^erience supplies them with instances essentially similar to every combination of circumstances likely to arise. But other men, or the same men when without the same preeminent 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 of us would get hiuch beyond those simple infer- ences 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 fbniiulce ; and the rules of the syllogism are a system of securities for the con-ectness of the application. § 6. To complete the series of considerations connected with the pnilosophical 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 inteiTuediate 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 pait. FUNCTIONS AND VALUE OF THE SYLLOGISM. 135 It is perhaps worth while to notice here a speculation of one of the philosophers to whom mental science is must indebted, hut 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 "pctltio 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 imnrense advantage, in point of secmity for coiTectness, which is gained by interposing this step between the real evidence and the conclusion ; but he thought it incumbent upon him to strike out the major altogether from the reason- ing 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 suppress- ing, as an unnecessary step in the argument, the appeal to foniier experience. The absurdity of this was disguised from him by the opinion he adopted, that reasoning is merely analyzing 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 recog- nizing the notion of mortality, as al^-eady 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 fi-om 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 mor- tality 1 Dr. Brown could not help seeing this difficulty, and in order to avoid it, was led, contrary to his intention, to reestablish, under another name, that step in the argument which corresponds to the major, by affinning the necessity oi 'previously perceiving the relation between the idea of man and the idea of mortal. If the reasbner 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 upon a supposition of which we have recognized the radical incoiTectness, namely, that the meaning of a proposition relates to the ideas of the things spoken of, and not to the things themselves ; and conceding for a moment, the existence of abstract ideas, I must yet observe, that the 136 REASONING. idea of man, as an universal idea, the common property of all rational crealures, 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 conseqvxence of experi- ence after having satisfied himself that all men possess that attribute : so that wiiatever the idea contains, in any person's mind, beyond what is included iu the conventional signification of the Avord, 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 obsei'vations, 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 exjjression in different words of the observed fact that they have died. This is the major premiss, divested of the petitio princ'qni, 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 fol- lowing : " 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 attribvites connoted by the word man. And fi-om 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 indixddual or individuals resemble the former in certain other attri- butes ; therefore they resemble them also in the given attribute. This type of ratiocination does not claim, like the syllogism, to be conclu- sive 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 expres- sion, that is, from a comparison of the language ; but when the two propositions assert facts which are bonajide different, whether the one fact proves the other or not can never appear from the language, but must depend upon 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 recognize as tests of the coirect 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 TRAINS OF BEASONING. 137 who resemble the observetl iiulividiuvls in the same attributes in which lie resembles them ; that is (to express t,he thing concisely), of all men. It" thert^tbre, the argument be conclusive in the case of Socrates, we are at liberty, once for all, to treat the possession of tlie attributes of man as a mark, or satisfactory evidence, of the attribute of mortality. This we do by laying down tlie 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 di\-ision of the jentire logical operation into two steps ; first, that of ascertaining what attributes are marks of mortality ; and, secondly, A\'hether any given individuals possess those marks. And it will, gener- ally be ad\-isable, in our speculations on the reasoning process, to consider this double operation as in fact taking place, and all rfeason- ing as carried on in the form into which it must necessarily be thrown to enable us to apply to it any test of its coiTect 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, confonoiably 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 intei-}5reting the general pro- position, 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 Deduc- tion ; because, although the process needs not necessarily be earned 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. CHAPTER IV. OF TRAINS OF REASONING, AND DEDUCTIVE SCIENCES. § 1. In our analysis of the syllogism it appeared that the minor prem- iss 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 we exclusively employed in the pi'eceding chapter; if the Te-~ semblance, 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 upon observed cases, to other cases in which we not only cannot directly observe what is to be proved, but cannot di- rectly observe even the mark which is to prove it. S 13S REASONING. § 2. Suppose tlie syllogism to be, All cows ruminate, tlie animal wliicli 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 iiujuiry, is the major; and provided the induc- tion of which that premiss is the expression was correctly performed, the conclusion resj^ectiiig 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 pre- cipitate with nitrate of silver, is arsenic ; the substance before me con- forms 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 ta- ken 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 con- tained in the majors of the two syllogisms. First, we, or others before us, have examined various objects which yielded under the given cir- cumstances the given precipitate, and found that they possessed the properties connoted by the word arsenic ; they were metallic, volatile, their vapor had a smell of garlic, and so forth. Next, we, or others be- fore us, have examined various specimens which possessed this metallic and volatile character, whose vapor had this smell, &c., and have inva- riably found that they were poisonous. The first observation we judge that we may extend to all substances whatever which yield the precipi- tate : the second, to all metallic and volatile substances resembling those we examined ; and consequently, not to those only which ai'e seen to be such, but to those Avhich 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 par- ticulars,; 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 some- what more complicated : — No government, which earnestly seeks the good of its subjects, is liable to revolution ; the Prussian government earnestly seeks the good of its subjects, therefore it is not in danger of revolution. The. major premiss in this argument we shall suppose not to be derived from considerations a priori,, hut to be a generaliza- tion from history, which, whether correct or erroneous, must have TRAINS OF REASONING. 139 been founded upon observation of governments concerning wlioso desii'o of the good of their subjects there was no doubt. It has been found, or thought to be found, that these were not liable to revolution, and it has been deemed that those instances wari'anted 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 Pinissian government thus resemble them 1 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 sen- timents and desires of the persons who conduct the government of that country. To prove the minor, therefore, we require an argument in this form : Every government which acts in a certain manner, de- sires the good of its subjects ; the Prussian government acts in that particular manner, therefore it desires the good of its subjects. But is it true that the Prussian government acts in the manner supposed? This minor also may require proof; still another induction, as thus :■ — . What is asserted by many disinterested witnesses, must be believed to be true ; that the Prussian government acts in this manner, is as- serted by many disinterested witnesses, therefore it must be believed to be true. The argument hence consists of three steps. Having the evidence of our senses that the case of the Prussian government re- sembles a number of fonner cases, in the circumstance of having something asserted respecting it by many disinterested witnesses, we infer, first, that as in those former instances, so in this instance the asser- tion is true. Secondly, what was asserted of the Prussian government being that it acts in a particular manner, and other governments or persons having been observed to act in the same manner,. the Prussian, government is brought into kno^vn resemblance with those other gov- ernments or persons ; and since they were known to desire the good of the people, we thereupon, by a second induction, infer that the Prussian government desires the good of the people. This brings that government into known resemblance -with, the other governments which were observed to escape revolution, and thence, by a third induction, we predict that the Prussian government will in like manner escape. And thus we are enabled to reason from the well-intentioned govern- ments which we historically know as having escaped revolution, to other governments which, when we made the induction, we may have known nothing about : yet if the induction was good, and therefore applicable to all governments of which we know the intentions but do not know the fortunes, it must be no less applicable to those whos6 intentions we do not know, but can only infer, provided this inference also rests upon a good induction. We ai-e still reasoning from particu- lars to particulars, but we now reason to the new instance from three distinct sets of fonner instances : to one only of those sets of instances do we directly perceive the new one to be similar ; but from that sim- ilarity we inductively infer that it has the attribute by which it is as- similated to the next set, and brought within the corresponding induc- tion ; when 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 ccmclusion. § 3. Notwithstanding the superior complication of these examples, compared with those by which in the preceding chapter we illustrated 140 REASONING. the general theory of reasoning, every doctrine which we then laid down holds equally true in these more intricate cases. ' The succes- sive general propositions are not steps in the reasoning, are not inter- mediate 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 jjropositions ; they are mere formula? for infemng particulars from particulars. The principle of general reasoning is (as before explained), that if from observation of certain kno^^^l particulars, what was seen to be true of them can be infeiTod to be time of any others, it may be in^ fened 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 dra^vTi coiTectly, and may avoid drawing it when it cannot, we determine once for all what are the distinguishing marks by which such cases may be recognized. 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 fi-om particu- lars 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 drawai. 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 knowTi, the induction would have been deemed to extend. These marks we either recognize at once, or by the aid of other marks, which by another previous induction we col- lected to be marks of f/icm. Even these marks of marks may only be recognized 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 gi-ounded on particulars its simifarity to which is only ascer- tained in this indirect manner. Thus, in the argument concerning the Prussian government, the ulthnate inductive inference was, that it was not liable to revolution : this inference was drawn according to a formula in which desire of the public good was set down as a mark of not being liable to revolution ; 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 many disinter- ested witnesses : this mark, the Prussian government was recognized by the senses as possessing. Hence that government fell within the last induction, and by it was brought within all the others. The per- ceived 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, k a mark of b, i of c, c of d, therefore a a mark of d. They consist (to TRAINS OF REASONING. 141 caiTy on tlve same metaplior) of several chains united at the extremity, as thus : a a mark of d, h of e, c o^f, d ef of n; therefure ahc a mark of«. Suppose, for example, the following combination of circum- stances: 1st, rays of light impinging on a reflecting surface; 2(1, that sijrface parabolic ; 3d, 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 circum- stances is singly a mark of somQthing 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 para- bolic form of the surface is a mark that, fi'om any point of it, a line drawn to the focus and a line parallel to the axis will make equal an- gles with the surface. And finally, the parallelism of the rays to the axis is a mark that theu- 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 reflection must coincide with the other of the two equal angles, that fonned by a line drawn to t!ie focus ; and this again, by the fundamental axiom concerning sti'aight 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 ai'e abundant, as in all propositions where the hypothesis includes numerous conditions : " If a circle be taken, and //"within that circle a point be taken, not the centre, and //"straight lings 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 othervidse have seemed not easily reconcilable with the fact that there are De- ductive or Ratiocinative Sciences. It might seem to follow, if all rea- soning 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 difficvilties in science. The existence, for example, of an extensive Science of Mathematics, requiring the highest scientific ge- nius 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 partic- .ular case which is the subject of inquiry comes within them ; and am-, pie room for scientific ingenuity in so combining various inductions, as, by means of one within which the case e^^dently 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, detennining 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 ap- plied to the new case, and the business is ended. But new cases ai'e continually arising, which do not obviously come within any 142 REASONING. formula whereby the questions 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 endeavor 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 induc- tions we have, from which we can infer equality or inequalit}'. For iufen-ing equality we have the following fonnulae : — 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 dif- ferences of equal things are equals. There are no other fonnulse 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 ob\-iously come within any of these. The formulas specify certain marks of equality and of in- equality, 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 recognizing these angles as the differences of equal things'? Be- cause each of them is the difference not of one pair only, but of in- numerable 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 formulcB. By an exercise of ingenuity, which, on the part of the first inventoi, deserves to be regarded as considerable, two pairs of angles were hit upon, which united these requisites. First, it could be per- ceived 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, how- ever, was not peiceived intuitively, but infeired, in conformity to another formula. To make all clear, we subjoin an analysis of the demonstration. Euclid, it ^^■^.\l be remembered, demon- strates his fifth proposition by means of the fourth. This it is not allov.'able for us to do, because we are undertaking to ti-ace 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 con- clusion, and prove the fifth directly from first principles. To do so requires six for- mulas. (We must begin, as in Euclid, by prolonging the equal sides A B, AC, to equal distances, and join- ing the extremities B E, D C.) TRAINS OF REASONING. 143 First Formula. The sums of equals arc equal. A D and A E arc sums of equals by the supposition. Having that niai-k of equahty, they are concluded by this formula to be equal. Second Formula. Equal straight Inics being aj)j)licd to one another coincide. AC, AB, are within this formula by supposition; AD, AE, have been brought within it by the preceding step. Both these pairs of sti'aight lines have the property of e(}uality ; which, according to the second formula, is a mark that, if applied to each otlier, they will coin- cide. Coinciding altogether means coinciding in every part, and of coui'se at their extremities, DE and BC. Third Formula. Straight lines, having their extremities coincident, coincide. BE and DC have been brought within this formula by the preceding induction ; they will therefore coincide. Fourth Formula. Angles, having their sides coincident, coincide. The two previous inductions having shown that BE and DC coin- cide, and'that AD, AE, coincide, the angles ABE and ACD are thereby brought within the fourth formula, and accordingly coincide. Fifth Formula. Things which coincide are equal. The angles ABE and ACD are brought within this formula by the induction immediately preceding. This train of reasoning being also applicable, mutatis mutandis, to the angles E BC, D CB, these also are brought within the fifth formula. And, finally. Sixth Formula. The differences of equals are equal. The angle ABC being the difference of ABE, C BE, and the angle ACB being the difference of ACD, DCB; which have been proved to be equals ; ABC and ACB 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 ABC, as remainders made by cutting one pair of angles out of another, while each pair shall be con-esponding angles of ti'iangles which have two sides and the inter- vening angle equal. It is by this happy contrivance that so many dif- ferent 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 arc not obyiou,sly included in it ; and how long, and numerous, and complicated, may be the processes, necessary for bringing the inductions together, even wheu each induction may itself be very easy and simple. All the inductions involved in all geometry are comprised in those simj^le ones, the for- mula 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 144 REASONING. language) for proving the minors necessary to complete the syllogisms; the majors being the definitions and axioms. In ^hose definitions and axioms are laid down the whole of .the marks, by an artful combina- •tion of which men have been able 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 diflftculty 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 De- ductive Science as. possible ; for endeavoring to construct the science from the fewest and the simplest possible inductions, and to njake these, by any combinations however complicated, suffice for pro^dng even such truths, relating to complex cases, as could be proved, if we chose, by inductions from specific experience. Every branch of nat- ural philosophy was originally experimental ; each generalization, rested upon 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 consist of no more than one step, and are ex- pressed 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 knowta 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 cir- cuitous mode of proceeding, for a process apparently much easier and more natural, is held, and justly, to be the greatest triumph of the in- vestigation of nature, we are not, in this stage of our inquiry, .prej)ared to examine. But it is necessary to' remark, that although, by this progi-essive 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 Experi- mental. . 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 ascer- taining 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 be- tween sciences which can be made Deductive, and those which must as yet remain Experimental. The difference consists iji 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 h marks of one another, c a mark of d, or c and d marks of one another, vnthout any- TRAINS OF REASONING. 115 thing to connect a or b with c or d: we have a science of detached and mutally independent generalizations, such as these, that acids redden vegetable blues, and that alkalis color 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 knowl- edge, has not yet thrown oft" this character. There are other sciences, however, of which the propositions are of this kind : a a mark of Z», i 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 tlie objects concerning which we are inquiring ; bat 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 transforms 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 6, c a mark of ut we srip- pose that they do so, for the sake of tracing the consequences which follow fiom the supposition. The opinion of Dugald Stewart respect- ing the foundations of geometry, is, I conceive, substantially correct ; that it is built upon 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 con- clusions as certain as those of geometiy, that is, as strictly in accord- ance with the hypotheses, and as in'esistibly compelling assent 07i 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 ques- tioned. In this relation, of course, the derivative truths of every de- ductive 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 svipposed certain for the purposes of the particular science. And therefore the conclusions of all deduc- tive sciences were said by the ancients to be necessary propositions. We have obsei-^'ed already that to be predicated necessarily was char- acteristic of the predicable Propiium, 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 en- . deavored to enforce, has been contested by a living philosopher, Mr. Whewell, both in the dissertation appended to his excellent Mechani- cal Enclid, 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 gi'eat scientific emi- nence), in which Stewart'^ opinion was defended against his foirner strictures. Mr. Whewell's mode of refuting Stewart is to prove against him (as has also been done in this work), that the premisses of geom- etry are not definitions, but assumptions of the real existence of things corresponding to those definitions. This, however, is doing little for Mr. Whewell's purpose, for it is these very assixmptions which we say are 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 trian- gles are bounded, those of which jiarallelism may be predicated, and the like."* And this is true; but this has never been contradicted. * Whewell's Mechanical Euclid, p. 149, et segq. DEMONSTKATION, AND NECESSARY TRUTHS. 151 Those who say that the premisses of geometry are hypotheses, arc not bound to maintain them to be hypotlieses which have no r^jlation what- ever to fact. Since an hypothesis framed for the purpose of scientific inquiry must relate to something whicli has real existence (for there can be no science respecting non-entities), it folliows that any hypothe- sis we make respecting an object, to faciUtatc onr study of it, must, not involve anything which is distinctly false, and repugnant to its real nature : we must not ascrilx) 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 diilerence in the truth of our conclusions. Of this nature, accordingly, are the fir^it 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 inas- much 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 illusti'ate 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 commonwenlth, and from the elements composing it, might argue what would be its fate. And the conclu- sions 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 : while on the contrary, if the hypothesis merely divests a real object of some portion of its properties, \Vithout clothing it in false ones, the conclu- sions will always express, under known liability to correction, actual truth. § 3. But although Mr. Wliewell has not shaken Stewart's doctrine as to the hypothetical chai'acter of that portion of the first principles of geometry which are involved in the so-called definitions, he has, I con- ceive, gi'esLtly the advantage of Stewart on another important point in the theory of geometrical reasoning; the necessity of admitting, among those first jn-inciples, axioms as well as definitions. Some of the axioms of Euclid might, no doubt, be exhibited in the form of defi- nitions, or might be deduced, by reasoning, fi-om propositions similar to ivhat 9,re so called. Thus, if instead of the axiom. Magnitudes which can be made to coincide are equal, we introduce a definition, " Equal magnitudes arc 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 imaginai'y superposition, resembling that by which the fourth proposition of the first book of Euclid is de- monstrated. But although these and several others may be struck out of the list of first princi])les, because, though not requiring demon- stration, they are susceptible of it ; there will be found in the list of axioms two or three fundamental trutJis, not capable of being demon- strated : among which I agree with Mr. WTiewell in placing the prop- 152 REASONING. osition 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."* The axioms, as well those which are indemonstrable as those which admit of being demonstrated, differ from that other class of funda- mental 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 is 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 move- ment once impressed, until stopped or slackened by some resisting force,) is true without a particle of qualification or error ; it is not affected by the frictions, rigidities, and miscellaneous disturbing causes, which qualify, for example, the theories of the lever and of the pulley. 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 accu- rately true : but along with them there are others, as for instance the propositions respecting the figure of the earth, which are but approxi- mations to the truth ; and in order to use them for the further advance- ment of our knowledge, we must feign that ihey are exactly true, although 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 1 I answer, they are ex- perimental truths ; generalizations from observation. The proposition, Two straight lines cannot inclose a space — or in other words. Two sti'aight 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 philosophic prejudice of long stand- ing and great strength, and there is probably no one proposition enun- ciated in this work for which a more unfavorable reception is to be ex- pected. 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 Mr. Whewcll, has recently found occasion for a most elaborate treatment of the whole theory of axioms, in attempting to construct the philosophy of the * We might, it is true, insert this property into the definition of parallel lines, framing- the definition so as to require, bo/h 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. P'or if it were possible that they should not, that is, if any straight lines other than those which are parallel according fo the defini- tion, had the property of never meeting although indefinitely produced, the demonstrationa of the subsequent portions of the theory of parallels could not be nijdntained. DEMONSTRATION, AND NECESSARY TRUTHS. 153 mathematical ami physical sciences on the basis of the doctrine against which I now coiUcnil. Wlioever is anxious that a discussion should go to the bottom ot'the subject, must rejoice to see the opposite side of the question worthily represented. If what is said by such a man as Mr. Whewell, in support of an opinion which he has made the founda- tion 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 Mr. Whewell, and by all, in recent times, who have adopted 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 miaid itself, from the first moment when the meaning of the proposition is appre- hended ; and without any necessity for verifying it by repeated trials, as is requisite in the case of ti-uths really ascertained by observa- tion. 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. Wliether 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 inter- sect one another, without seeing that fi-om 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 con- fessedly learn from the evidence of our senses. Independently of a priori evidence, we should certainly believe it with an intensity of con- viction 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 al- most any part of our acquired knowledge, and much too early to admit of our retaining any recollection of the history of our intellectual ope- rations 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 be- lief itself is superior 1 The burden of proof lies upon 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 have 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 wnthin the reach of memory, and too obscure for external observation. The advocates of the a priori theory are obliged to have recourse to other 154 REASONING. arguments. These are reducible to two, which I shali endeavor to state as clearly and a^ forcibly, as possible. § 5. In the first place it is said, that if ovir 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 liijes ; whereas in fact it is seen to be ti-ue by. merely thinking of them. That a stone thrown into water goes to the bottom,'may be perceived by our senses, but mere think- ing of a stone thrown into the water will never lead us to that conclu- sion : not so, however, with the axioms relating to sti'aight lines : if I could be made to conceive what a straight line is, without having seen one, I should at once recognize that two such lines cannot inclose a space. Intuition is "imaginary looking;"* 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 can- not 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 evi- dence of it from actual ocular inspection, is not only unnecessary, but unattainable. What says the axiom 1 That two straight lines cannot inclose a space ; that after having once intersected, if they are pro- longed to infinity they do not meet, but continue to diverge fi-om one another. How can this, in any single case, be proved by actual observation 1 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 furthest 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 under- stating, 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 wordsi, 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 upon 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 accu- rate, 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 talvO some objects to serve, as representatives of aU whjich resemble them ; and in * Whewell's Philosophy of the Inductive Sciences, i., 130. DEMONSTKATIOV, AXD NECCSSAUY TRUTHS. 155 the present case the conditions which qualify a real, object to be the representative of its clas*, arc completely fulfilled by an object existing only in our fancy. "Without denying, therefore, the possibility ot satisfying ourselves that two sti-aight lines cantiot inclose a s])ace, by merely thinking of straight lines without actually looking at them ; I contend, tluit we do not beUeve this truth on the ground of the imagi- nary 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 obsei-Vation. And we should not be authorized to substitute obsenation of the image in our mind, for obsei-vation of the reality, if we had not learnt by long continued experience that all the properties of the reality are faithfully represented in the image ; just as we should be scientifically warranted, in describing the sliape and color of an animal Nvhich we had never seen, fi-om a plaotogenic picture made of it with a daguerreotype ;• but not until we had leanit by ample exj>erience, that observation of such a picture is precisely equivalent to observation of the original. These considerations also remove the objection aiising from the impossibity 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 A\'ithout doing so we may know that if they ever do meet, or indeed if, after diverging fi-om 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 upon as being precisely similar to the reality. Now, -^vhether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we have had occasion to make fi'om fonner ocular obser\-atic»n, we shall either way be equally satisfied, that a line which, after diverging fi-om 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." § 6. The first of the two great arguments in support of the theory that axioms are a priori truths, having, I tliink, been sufficiently an- swered ; I proceed..to the second, on which most stress is usually laid, and which is chiefly insisted upon by Mr. ^Vliewell. Axioms (it is asserted) are conceived by iis not only as tnie, but as universally and necessarily true. Now, experience cannot possibly give to any propo- sition this character. I may have seen snow a hundred times, and may have seen that it was white, but this cannot give me entire assur- ance 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 156 REASOXING. may be, they can show nothing with regard to the infinite number of cases in which the experiment has not been made." Moreover, axioms are not only universal, they are also necessary. Now " experience cannot offer the smallest ground for the necessity of a proposition. She can obseiTO 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 rea- son 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 ex- perience, and to see it to be necessarily true, are two altogether different processes of thought."* And Mr. 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."t In order to leani what the distinction is, the non-recognition of which incurs this denunciation, let us refer again to Mr. Whewell. " Neces- sary truths are those in which we not only learn that the proposition is true, but see that it 7nust 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."* Although Mr. W^hewell 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 necessaiy 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 INIr. ^Vhewell's 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 woi-ds, which we can- not figure to ourselves as being false, must rest upon evidence of a higher and more cogent description than any which expeiience 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 upon 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 upon the past history and habits of our own minds. There is no more generally acknowledtred fact in human nature, than the extreme difficulty at first felt in con- ceiving anything as possible, which is in contradiction to long estab- * Whewell's Philosophy of the Inductive Sciences, i., 5&— 61. t njid-, 57. t Ibid., i., 54, 55. DEMONSTRATION, AND NECESSARY TRUTHS. 157 lisbed and familiar experience ; or even to old and 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 laws of asso- ciation an increasing difficulty, which in the end becomes 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 man of the most practised intellect is not exempt from the universal laws of our concep- tive faculty. If daily habit presents to him for a long period two facts in combination, and if he is not led during that period either by accident or intention to think of them apart, he will in time become incapable of doing so even by the strongest effiart ; 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. There are remarkable instances of this in the history of science : instances, in which the wisest men rejected as impossible, because inconceivable, things which their posterity, by earlier practice and longer perseve- rance in the attempt, found it quite easy to conceive, and which every- body 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 can- not 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.* 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 * It would be difficult to name a man more remarkable at once for the greatness and the universality of his intellectual powers, than Leibnitz. Yet this great man gave as a reaspn for rejecting Newton's scheme of the solar system, that God could not make a body revolve rouiid 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 crea- tures, est miraculeux. II no suffit pas de dire: Dieu a fait une telle loi de nature : done la chose est naturelle. II faut que la loi soit executable par les natures des creatures. Si Dieu donnait cette loi, par exemple, a un corps libre, de toumer a I'entour d'un certain centre, il faudrait ou qu'il y joignil d'aulres corps q-ui par Icur impulsion Vobligeasscnt de rcster toujours dans son orbite circidaire, ou qu'il nut un ange a ses trousses, ou enfm il faudrait qu'il y concourut extraordinairement ; car naturellement il s'ecartera par la tangente." — Worlui iff Leibnitz, ed. Dutens, iii., 4-lC. 158 REASONING. ether; the occult cause of gravitation ; and his writings prove, that although he deemed the particular nature of the inteiTnediate agency a matter of conjecture, the necessity of some such agency appeared to him indubitable. It would seem that even now the majority of scien- tific men have not completely got over this very difficulty ; for though they have at last learnt to conceive the sun attracting the eaith with- out 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 its highest 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 confiraied, and more familiar, and in which nothing ever occurs to shake our conviction, or even suggest to us any concep- tion at variance with the association, the acquired incapacity should continue, and be mistaken for a natural incapacity 1 It is true our ex- perience 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 imahe inconceivableness of the tliiuff, under such circumstances, proves anything against the ex- perimental origin of the conviction I Is it not clear that in whichever mode our beUef in the pi'oposition may have originated, the impossi- bility of our conceiving the negative of it must, under either hypothesis, be tJic same ? As, tlien, Mr. Whewell oxliorts those who have any difficulty in recognizing the distinction held by him between necessary and contingent ti'uths, 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 Mr. Whewell, 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 inductioHS fi'om experience, and measures the possibility of things in themselvea, by the human capacity of conceiving them. I hope to be pardoned for adding, that Mr. "Wliewell himself has both confirmed by his testimony the effect of habitual association in giving to an experimental truth the appearance 6f a necessary' one, and attbrded a striking instance of that remarkable law in his own person. In h\s Philosajjhy of the Inductive Sciences he continually asserts, 'that propositions which not only are not self-evident, but whicli we know to have been discovered gradually, and by gieat efforts of genius and pa- tience, have, when Once established, appeared so self-evident that, but for historical evidence, it would have been impossible to conceive that they had not been recognized from the first by all pereons in a sound state of tlieir faculties. " We now despise those who, in the Coperni- can controversy, could not conceive the appai'ent motion of the sun on the heliocenti'ic hypothesis; or those who, in opposition to Galileo, thought that a uniform force might be tliat which generated a velocity proportional to the space ; or those who held there was something ab- surd in N'ewtoii's doctrine of the different refrangibility of differently colored 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 fii|d a difficulty in admitting what is to us so plain and simple. We have a latent perstiasion that we in their place should have been Aviser and moro clear-sighted ; that we should have taken the right side,. and given our assent at once to the truth. Yet in reality such a persuasipn 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 beiYig persons more prejudiced, or ,stupid, or naiTow-minded, than the greater part of rpankind 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 ima- gine die struggle to have been necessary. The very essence of these tri- umphs is, that they lead us to regard tltc views we reject as not only false, hut inconceivahle.^'* This last proposition is precisely what I contend for ; and I ask no * Philosophy of the Indwtive Sckivce^, vol. ij., p. 174. 160 REASONING. more, m order to overthrow the whole theory of Mr. Whewell 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 Mr. Whewell himself says, that we are continually led by the natural progress of thought, to regard as incon- ceivable what our forefathers not only conceived but believed, nay, even (he might have added) were unable to conceive the contrarv of. Mr. Whewell 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 e\"ident at all. After so complete an admission that inconceivablenesa is an accidental thing, not inherent in the phenomenon itself, but de- pendent 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 gi'ound than its inconceivableness ? Yet he not only does so, but has unintentionally afforded some of the most remarkable exam- ples which can be cited of the very illusion which he has himself so clearly pointed out. W^e select as specimens, his remarks on the evi- dence of the three laws of motion, and of the atomic theory. With respect to the laws of motion, Mr. Whewell says : " No one can doubt that, in historical fact, these laws were collected from expe- rience. 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."* After such a testimony, to adduce evidence of the fact would be supei-fluous. 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 con- tinue for ever to move in the same direction with undiminished velo- city unless acted upon by some new force, was a proposition which mankind found for a long time the gi'eatest 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 Mr. Whewell observes, speedily began to believe that laws, thus conti-adictory 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 demonsti'able necessity, compelling them to be such as they are and no other ;" and ]Mr. Wliewell, though he has " not ventured absolutely to pronounce" that all these laws " can be rigorously traced to an ab- solute necessity in the nature of things, "t 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 kno\\Ti to be true, independ- ently of experience."! Can there be a more striking exemplification than is here afforded, of the effect of association which we have de- scribed \ Philosophers, for generations, have the most exta-aordinary 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 * Philosophy of the Liduxtiue Sciaices, i., 238. t Ibid., 237. t Ibid, 213. DEMONSTRATION, AND NECESSARY TRUTHS. 161 which at last, by the coutlnuation of tlie same progress, becomes an im- possibility, of severing them from one another. If such be the pro- gress 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 femiliar from the first dawn of intelligence, and of the coijclusiveness of which, from the earliest records of human thought, no skeptic has suggested even a mo- mentary doubt 1 The other instance which we shall quote is a truly astonishing one. and may be called the reductio ad ahsurdum of the theory of inconceiv- ableness. Speaking of the laws of chemical composition, Mr. Wlie- well says :* " That they could never have been clearly understood, and therefore never firmly established, without laborious and exact exper- iments, is certain ; but yet we may venture to say, that being once kno\\'n, they possess an evidence beyond that of mere experiment. For Jtoic, in fact, can tve conceive combinations, othenvise than as defi- nite in kind and qicantity 1 If we were to suppose each element ready to combine with any other indifferently, and indifferently in any quan- tity, we should have a world in which all would be confusion and in- definiteness. 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, capa- ble of being classified and named, and of having general propositions asserted concerning them. And as xoe cannot conceive a world in which this should not he 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." That a philosopher of Mr. Whewell's eminence should gravely as- sert that we cannnot conceive a world in which the simple elements would combine in other than definite proportions ; that by dint of med- itating on a scientific truth, the original discoverer of which is 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 in- timate as to be unable to conceive the one fact without the other ; is so signal an instance of the law of human nature for which I am contend- ing, that one word more in illustration must be quite superfluous. I shall, only, therefore, express my satisfaction that so long as the pro- gi'ess of scientific instmction has not rendered this association as indis- soluble in the minds of most people as Mr. Whewell finds it, the majority of mankind will be fairly able to judge, from this example, of the value of the evidence which he deems sufficient to prove that a scientific proposition might be known to be true independently of experience.! * Philosophy of the Indtictive Sciences, i., 384, 385. + The Quarterly Review for June, 1841, contains an article, of great ability, on Mr. 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 oripinahty which may or may not belong to any portion of my own speculations, but to obtain for an opinion which is opiiosed to reigning doctrines, the recommendation derived from a striking concurrence of sentiment between two inquirers entirely independent of one another. 1 have much pleasure in citing from a writer of the extensive acquirements in physical and metaphysical knowledge and the ca- 162 REASONING. CHAPTER VL 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 pacity 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 straight- ness is uniformity of direction, for space in its ultimate analysis is nothing but an assem- blage of distances and directions. And (not to dwell on the notion of continued contem- plation, 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 propo- sition 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, ivithout vi- olating 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 homo- geneity 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, i/i virtue of the extreme simplicity of these primary relations, being called up by the imagination with as 7nuch 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 acon- trary 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 be- ing 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 con- clude, 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 ^ priori reasoning can possibly assure us that they do act under precisely similar cir- cumstances? 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 por- tion 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 DEMONSTRATIOV, AND NECESSARY TRUTHS. 163 character of necessity in any sense beyond this, as implying an evidence independent of and snporior to observation and experience, must depend upon the previous estabHshment of such a claim in favor of the defini- tions and axioms themselves. With regard to axioms, we found that, considered as experimental truths, they I'est upon superabundant and obvious evidence. We inquired, whether, since this is the case, it be necessaiy to suppose any other evidence of those truths than experi- mental evidence, any other origin for our belief of them than an experi- mental 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 war- ranted in concluding that axioms are but a class, the highest class, of by the counterpressure 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 fun- damental 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 tire 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 sus- tains 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 de- cide 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 ex- perience and all our knowledge, surely these are the truths which, if experience suggests 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 plan- etary 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 re- cognition of such truths, as general propositions, coextensive at least with all human expe- rience. That they pervade all the objects of experience, must ensure their continual sug- gestion by experience ; that they are true, must ensure that consistency of suggestion, that iteration of uncontradicted assertion, which commands implicit assent, and removes all oc- casion 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 setitiment 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 menial picture or idea of that object which we may on any occasion stimmon before our imagination. . . . All propositions, therefore, become not only untrue but inconceivable, if . . . axioms be violated in therr enunciation." Another high authority (if indeed it be another authority) may be cited in favor of the doctrine that axioms rest upon the evidence of induction. " The axioms of geometry them- selves 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 tune, and body, and again, in linear, and su- perficial, and solid space. Again, when we say, the equals of equals are equal, we men- tally 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 ex- perience, they would not present themselves to the mind. The only diilerence between these and axioms obtained from extensive induction is this, that, in raising the axioms of geometry, the instances oifer themselves spontaneously, and without the trouble of search, and are few and simple ; in raismg those of nature, they are infinitely numerous, compli- cated, 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 Htudy of Natural Philosophy, pp. 95, 96. 164 BEASONIVG. inductions from experience : the simplest and easiest cases of generali- zation 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, qf 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 j^roperty or prop- erties 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 most or even in 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 circum- stances, when their influence is of too trifling amount to be worth con- sidering, or adjourning it, when important, to a more convenient moment. From these considerations it would appear that Deductive or De- monstrative 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 formulae according to which their inductions are made. Hypothetical Sciences. Their conclusions are only true upon 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 demon- stration. What we have now asserted, however, cannot be received as univer- sally true of Deductive or Demonstrative Sciences vmtil verified by being applied to the most remarkable of all those sciences, that of Num- bers ; 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 d priori, but experimental truths, or that their pe- cuHm- certainty is o\\nng to their being not absolute but only conditional truths. This, therefore, is a case which mei'its examination apart; and the more so, because on this subject we have a double set of doctrines to contend with; that of Mr. Whewell and the d priori philosophers on one side ; and on the other, a philosophical theory the most opposite to theirs, which was at one time very generally received, and is still far fi-om 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 lan- guage, substitutions of one expression for another. The proposition, Two and one are equal to three, according to these philosophers, 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 agi-eed 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 substi- tuted one for another ; a series of translations of the same fact, fi-om DEMONSTRATION, AND NECESSARY TRUTHS. 1G5 one into another language : though how, after such a series of transla- tions, 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 arc peculiarities in the processes of arithmetic and algebra which render tho abine theory very plausi- ble, 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 reconcilable 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 upon paper; AB, AC, are present to our imagination as lines, inter- secting other lines, forming an angle with one another, and the like ; but not so a and h. These may represent lines or any other mao-ni- tudes, but those magnitudes are never thought of; nothing is realized in our imagination but a and h. 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 pretend that the reasoning process has to do with anything more ] We seem to have come to one of Bacon's Pre- rogative Instances ; an experimcntuvi 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 infer- ence 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 some- thing : 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 tPROPERLY SO CALLED. § 1. Induction, then, is that operation of the mind, by which v^e in- fer that what we know to be true in a particular case or cases, ^\all be ?,rue in all cases which resemble the former in certain assignable respects. In other words. Induction is the process by which we con- dude that what is tiiie of certain individuals of a class is tnie of the INDUCTIONS IMPROPEULY SO CALLED. 175 whole class, or that what is true at certain times will be true under 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 px'oceeds from the known to the unknown ; and any operation involving no in- ference, 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 ad- mits 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, un- less 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 ti'ue of Peter, Paul, John, and eveiy other apostle — these, and such as these, would, in the phrase- ology in question, be called pez-fect, 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, wlilch we have quoted, are not generalizations ; the propositions pur- porting to be conclusions from them, are not really general proposi- tions. 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 prop- erties connoted by the subject of tlie proposition. "AH men are mor- tal" does not mean all now living, but all men past, present, and to come. ^Vhen the signification of the term is limited so as to render it a name not for any and every individual falling under a certain gen- eral description, but only for each of a number of individuals desig- nated 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 pait of the investigation of ti-uth, 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 matliematicians 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 caimot meet it in more than two points, and when the same tiling has been successively proved of the ellipse, the parabola, and the hyj>cr- 176 INDUCTION. bola, 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, thouo-h 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 we formerly observed*) does not prove directly the general theorem ; it proves only that the con- clusion, which the theorem asserts generally, is true of the particular ti-iangle 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 jjrojDosition. 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 A B C, but for the same reason which proved it to be true of A B C. If this were to be called Induction, an appro- priate 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 gi'ound 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 upon 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 ascer- tained what is called the Icnv 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 fi-om 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 fonnation 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 upon record in which it has led to false results. It is said that Newton discovered the binomial theorem by induc- tion ; 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 foi-mula 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 mind like Newton's, which seemed to aiTive per saltuvi at principles and conclusions that ordinary mathe- maticians 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 suf- ficiently the nature of multiplication to venture upon multiplying several lines of figures or symbols at one operation, cannot but perceive * Supra, p. 127, 128. INDUCTIONS IMl'KOrERLY SO CALLED. 177 that in ra,isina- a binomial to a jiower, the co^fficieiits must dcpciul upon the laws of permutation and lombination : and as soon as this is recognized, the theorem is demonstrated. Indeed, wheii once it was seen that the law j)revailed in a few of the low^ powers, its identity with the law of permutation would at once suggest the considerations which prove it to olrtain universally. Even, therefore, such cases as these, are but examples of what I have called induc-tion by parity of reasoning, that is, not really induction, because iu)t involving any infer- ence 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, to no ordinai-y 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 obser\"«d separately, aiul as it were piece- meal. Wlien the observations have been inade, there is a convenience . (amounting for many purposes to a necessity) in obtaining a represen- tation 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 per- ceive that this land was entirely suiTounded 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 I Certainly not. That the land in question is an island, is not an inference fi-om 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 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 (jf our supposed navigator. The object of Kepler was to determine the real path described by each of the planets, or let us say the planet Mars (for it was of that body that he first established two of the three gi-eat astronomical truths which bear his name). To do this there was no other mode than that of direct obsei-v'atron : 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 success- ively all these positions, or at all events, positions which produced the * I am happy to be able to refer, in confirmation of this view of what is called induction in mathematics, to the highest English authority on the philosophy of algebra, Mr. Pea- cock. See pp. 107-8 of liis profound Treatise on Algebra. z 278 INDUCTION. same impressions on riie 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 ioined together. He expressed the whole series of the observed places of Mars by what Mr. Whewell calls the general conception of an ellipse. This operation was far fi-om being as easy as that of the navio-ator 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 re- volve in that same ellipse ; and even in concluding that the position of the planet during the time which intervened between two observa- tions, must have coincided with the intermediate points of the curve. But this really inductive operation requires to be carefully distin- guished from the mere act of bringing the facts actually observed under a o-eneral description. So distinct are these two operations, that the one might have been performed without the other. Men mio-ht and did make correct indvictions concerning the heavenly mo- tions, 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. Men early remarked that the same set of apparent positions returned pe- riodically. 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 ti'Uth) add anything to the power of predic- tion which they already § 4. The descriptive operation which enables a number of details to be summed up in a single proposition, Mr. "Whewell, by an aptly- chosen expression, has termed the Colligation of Facts.* 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; a,nd laying down, throughout his work, as principles of induction, the principles of mere colligation. Mr. Whewell maintains that the general proposition which binds to"-ether 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,t " are not merely brought to"-ether, but there is a new element added to the combination by the ve!ry act of thought by which they are combined. . . .When the Greelvs, after long observing the motions of the planets, saw that these motions might be rightly considered as produced by the motion of one wheel • Philosophy of the Inductive Sciences, ii., 213, 214. t Ibid. IXDUCTIONS IMPROrERLY SO CALLED. 179 revolving in tlio inside of anollier wheel, these wheels were creations of their minds, added to the facts which tliey 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 most certain, and Mr. Whewell has rightly stated elsewhere, 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 coiTesponds to, something conceived ; and although 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 oar 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 j 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 undefvalued as Mr. Whe- well supposes it has. 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 litnitcd 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 Mr. Whewell's language, it is afterwards called in to coimect. This, Mr. Whewell himself admits, when he observes, (which he does on several occasions,) how great a service would be ren- dered to the science of physiology by the philosopher " who should establish a 2:)recise, tenable, and consistent conception of life."* 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 ctjnception from the very phenomena which we are attempting to colligate, we selec't it from among those which have been, jireviously collected by abstraction fiom other facts. In the instance of Kepler's laws, the latter was the case. * Philosophi/ of the Inductive Sciences, vol ii., p. 173. 180 INDUCTION. The facts being out of the reach of being observed, in any such man- ner 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 phe- nomenon, 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 descrip- tion of the phenomenon : if not, it was necessarily abandoned, and another tried. It is such a case as this which gives color to the doc- trine 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 concejjtion of an ellipse, or (to express the meaning in less technical language) knowing what an ellipse was, Kepler tried whether the ob- served 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 ob- served ; it was the sum of the different observations. It superadded nothing to the particular facts which it served to bind together: ex- cept, indeed, the knowledge that a resemblance existed between the planetary oi'bit and other ellipses ; an accession the nature and amount of which will be fully considered hereafter.* Having stated this fundamental difference between my views and those of Mr. 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 " concep- tion" of an ellipse, he tried nineteen other imaginaiy paths, which, finding them inconsistent with the observations, he was obliged to re- ject. But as Mr. Whewell truly says, the successflil hypothesis, although a guess, ought not to be called a lucky, but a skillful guess. The guesses which serve to give mental unity and wholeness to a chaos of scattered particulars, are accidents which occur to no minds but those abounding in knowledge and disciplined in scientific combi- nations. How far this tentative method, so indipensable as a means to the col- ligation of facts for pui^j^oses 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 tc distinguish * Vide infra, book iv., ch. I. INDUCTIONS IMPROPERLY SO CALLED. 181 this process of colligation from Iridvulion properly so called : and that the distinction may be made clearer, it is well to advert to a curions and interesting remark of Mr. Whewcll, which is as strikingly true of the former operation, as it is vineqviivocally false of the latter. In different stages of the progress of knowledge, philosophers have employed, for the colligation of the same order of facts, difterent con- ceptions. The early and rude observations of the heavenly bodies, in which minitte precision was neither attained nor sought, presented no- thing 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 reconcilable with this simple supposition, fw the colligation of those additional facts, the supposition was varied ; and vaiied again and again as facts became more numerous and precise. The earth was removed fi-om the centi'e to some other point within the circle ; the planet was sup- posed to revolve in a smaller circle called an epicycle, round an im- aginary point which revolved in a circle round the earth : in proportion as observation elicited fresh facts contradictory to these representations, other epicycles and other eccentrics 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 coiTectness the accurate observations of the present day, which disclose many slight deviations from an orbit exactly elliptical. Now Mr. Whewell has remarked that tliese suc- cessive 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 tuni served as a correct des.criptioYi 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 fi-aming 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 coiTectness of the former expression, considered as a general state- ment 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 gen- eralizations, even the rudest and most imperfect of them, that of uni- fonn movement in a circle, ai'e so far from being entirely false, that they are even now habitually employed by astronomers when oYily a rough approximation to correctness is required. " L'astronomie mo- derne, en detruisant sans retour Ics hypotheses primitives, envisagees comme lois reelles du monde, a soigneusement maintenu leur valeuiv positive et permanentc, la ]n-opriete de representer commodement les phenome'.nes quand il s'agit d'une premiere ebauche. Nos ressources a cet egard sent meme bien plus etendues, precisement a caiise quie nous ne nous faisons ancune illusion sur la realite des hypotheses ; ce qui nous permet d'employer sans scrupule, en chaque cas, celle que nous jugeons la plus avantageuso."* Mr. Wliewell's remark, therefore, is as just as it is interesting. Suc- *■ CoMTE, Cours de Philosophie Positive, vol, ii., p. 202, 182 INDUCTION. cessive expressions for the colligation of observed facts, or, in other words, successive descriptions of a phenomenon as a v^^hole, w^hich 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 con- flicting inductions. The jihilosojjhic study of facts may be undertaken for three dif- ferent purposes : the simple description of the facts ; their explana- tion ; 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, Mr. Whewell's observation is true of the first alone. Considered as a mere description, the circular theory of the heavenly motions repre- sents perfectly well their general features ; and by adding epicycles without limit, those inotions, even as now known to us, might be expressed with any degree of accuracy that might be required. The only real advantage of the elliptical theory, as a mere description, would be its simplicity, and the consequent facility of conceiving it and reasoning about it : for 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 explana- tions, 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 we said of the different descriptions, that they are all true as far as they gol Is it not clear that one only can be true in any degree, and the other two must be altogether false 1 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 ex- pressing real facts with unequal degrees of accuracy] Assuredly the one is true, and the other absolutely false. In every way, therefore, it is evident that when Mr. Whewell explains induction as the colligation of facts by means of appro- priate conceptions, that is, conceptions which will really express them, he confounds mere description of the observed facts with in- ference from those facts, and ascribes to the latter what is a char- acteristic property of the former. There is, however, between Colligation and Induction, a real correlation, which it is important to conceive coixectly. Colligation is not always induction; but induction is always colligation. The assertion that the planets move in ellipses, was but a mode of rep- resenting 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 saui© GROUND OF INDUCTION. 183 facts, whicb Kepler had connected by his conception of an elhpse, 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. Moreover, 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, excejit in the case of phenomena of very limited compass. "VVe should not be able to affirm any predicates at all, of a subject in- capable 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 necessaiy accuracy, but also that the results of these obsen'ations 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 rep- resented. To suppose, however, that nothing more is required from the concep- tion than that it shall sei-\e to connect the obsei-vations, would be to substitute hypothesis for theory and imagination for proof The connecting link must be some character which really exists in the facts themselves, and which would manifest itself therein if the conditions could be realized which our organs of sense require. What more may be usefully said on the subject of Colligation, or of the correlative expression invented by Mr. Wliewell, 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 fi-om Experience. It consists in inferring from some individual instances in which a phe- nomenon is obsei-ved 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 fi-om 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 state- ment of what Induction is ; an assumption with regard to the course 184 INDUCTION. of nature and the order of the universe : namely, that there are such things in natui'e as parallel cases ; that what happens once, \n\l, under a sufficient degree of similaTity of circumstances^ happen again, and not only again, but always. 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 waiTanted ; the fact is so. The universe, we find, is so. constituted, that whatever is tine in any one case, is true in all cases of a certain description ; the only difficulty is, to find u'//at description. This universal fact, which is our waiTant for all inference from expe- rience, has been described by diflerent 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 philo- sophers as an instinct of om- nature — they usually describe under the name of " our intuitive conviction that the future ^^:ill resemble the past." Now it has been well pointed out by Mr. Bailey,* that (whether the tendency be qr 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 bunied to-day and yesterday; but we believe, on precisely tlie same gi-ounds, that it burned before we were born, and that it burns this very day in Cochin-China. It is not fi-om the past to the future, as past and fiiture, that we infer, but from the known to the unkno-wn ; from facts observed to facts unob- served ; 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 fliture ; 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 proce&s. 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 opportu- nities of remarking, have its extent and limits been always very justly conceived. Yet this principle, though so far from being our. earliest induction, must be considered as our wan'ant for all the ojhers, in this sense, that unless it were true, all other inductions would be fallacious. And this, as we have ah'eady seen, is the sole mode in which the gene- ral propositions which we place at the head of our reasonings when we throw them into syllogisms, ever really contribute to their validity. Archbishop Wliately has well remarked, that every induction is a syUogism with the major premiss suppressed ; or (as I prefer express- * Essays on the Pursttit of TnitL GROUND OF INDUCTION. 185 ing it), that every imluctioii may be thrown into the form of a syllo- gism, by supplying a major premiiss. If this be actually clone, the principle which Ave are now considering, that of the uniformity of the cour^^e of nature, will appear as the ultimate major premiss of all in- ductions ; ami will, therefore, stand to all inductions in the rplation 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 it» being proved ; since no conclusion is. proved for which there cannot be found a true major j^remiss.* It was not to be expected that in the case of this axiom, any more than of other axioms, there should be unanimity among philosophers with respect to the gi'ounds upon 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 * From the fact, that every induction maybe expressed in the form of a syllogism. Archbishop Whately concludes that Induction itself is but a peculiar case of ratiocination, and that the universal type of all Inference, or Reasoning, is the Syllogism. Our own inquiries have led us to a directly opposite result. Instead of resolving Induction into Ratiocination, it has appeared to us that Ratiocination is itself resolvable into Induction. The Archbishop's theory may, I think, be shown to be fallacious by following out his ovvn train of thought. The induction, " Johi>« Peter, Thomas, &c., are mortal, therefore all mankind are mortal," may, as he justly says, be thrown into a syllogism by preti.xing as a major premiss (what is at any rate a necessary condition of the validity of the argument) namely, that whatever is true of John, Peter, Thomas, &c,, is true of all mankind. So far the case is made out ; and Archbishop Whately (who, endowed with a penetrating and active rather than a patient and persevering intellect, seldom fails to cast his sounding line to a greater depth than his predecessors, and when he has done this, scarcely seem? to care whether he reaches the bottoui or not) omitted to ask himself the further question, How we come by the 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, then, on the Archbishop's princi[)le&, it is by ratiocina- tion still, that is, by a previous syllogism. This previous syllogism it is, therefore, necessary to construct. There is, in the long run, only one possible construction : the real proof that whatever is true of John, Peter, &c., is true of all mankind, can onf>' be, that a different supposition would be inconsistent with the uniformity which we' kndvv to exist in, the course of nature." Whether there would be this iuconsistcncy or nqt, 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. Having reached this point, wc have the whole field of induction laid out in syllogisms, and every instance of inference from experience exhibited as the conclusion of ratiocination, except one ; but that one, unhappily, includes all the rest. Whence came the universal major? What proves to' us that nature is governed by general laws ? Where are the premisses of the syllogism of which that is the conclusion? Here, at least, is a case of induction which cannot be resolved into syllogism. And undoubtedly it would be the ideal perfection of Inductive Philosophy if all other general truths could be exhibited as conclusions tjeduced from that widest generalization of all. But such a mode of presenting them, however useful in giving coherence and systematic unity to our thoughts, would be an inversion of the real order of proof. This great generalization must itself have been founded on prior generahzations : 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 dared to affirm 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. .\rciii>ishop Whately's theory, therefore, implying, as it does, the consequence that we never could have had a single well-grounded induction unless we had already reached that highest generalization, must, I conceive, be regarded as untenable. Aa 186 INDUCTION. controverted point in regard to the fundamental axiom of induction, until a more advanced period of our inquiry* 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, pos- sesses rather the brevity sviitable to popular, than the precision requi- site in philosophical, language : its terms require to be explained, and a stricter tlian 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 al- ways expect uniforaiity in the course of events; he does riot always believe that the unknown will be similar to the known, that the fu- ture 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 extraor- dinary, if the course of nature is constant, and resembles itself, in these particulars. To look for constancy where constancy is not to be ex- pected, as, for instance, that a day which has once brought good for- tune'will always be a fortunate day, is justly accounted superstition. The course of nature, in truth, is' not only uniform, it is also infi- nitely 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 upon 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 ad- mitted 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 induc- tion, if it deserves the name, which is natural to the mind when unac- customed to ■ scientific methods. The tendency, which some call an instinct, and which others account for by association, to infer the fu- ture from the past, the known from the unknown, is simply a habit of expecting that what has been found true once or several times, * Infra, chap, xxi. GROUND OF INDUCTION. 187 and never yet found false, will be found true again. Wlietlicr the instances are few or many, conclusive or inconclusive, does not much affect the matter : these are considerations which occur only on re- flection : the unprompted tendency of the mind is to generalize its ex- perience, 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 take the facts which present themselves, without taking the trouble of searching for more : it is a superior mind only which asks itself what facts ai-e needed to enable it to come to a sure conclusion, and then looks out for these. But although we have always a propensity to generalize from un- varying experience, we are not always warranted in doing so. Be- fore we can be at liberty to conclude that something is universally true because we have never known an instance to the contrary, it must be proved to us that if there were in nature any instances to the contrary, we should have known of tliem. 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 remark- able cases amount to full proof.* No such assurance, however, can be had, on any of the ordinary subjects of scientific inquiry. Popular notions are usually founded upon induction by simple enumeration ; in science it carries us but a little way. We are forced to begin with it ; we must often rely upon 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 funda- mental errors) his wi'itings 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 reason- ing 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 indicctio per emuncrationcm simplicem which he condemns ; and the experience, which we hear so confidently appeidcd to by all sects, parties, and in- terests, 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 Induc- tion, 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 * Infra, chap, xxi, xxii. 188 INDUCTION. the conclusion has turned out erroneous. The experience, however, on which the conclusion rested was genuine. From the earhest records, the testimony of all the inhabitants of the known world was unanimous on the point. The uniform experience, therefore, of the in- habitants of the known world, agreeing in a common result, without one known instance of deviation from that result, is not alwaysr suffi- cient 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 vve conclude that all men's heads grow above their shoulders, and never below, in spite of the conflicting testimony of the naturalist Pliny 1 As there were black swans, although civilized men had existed for three thousand years on the earth without meeting with them, may there not also be " men whose heads do gi'ow beneath their shoulders," notwithstanding a father less perfect unanimity of negative testimony from all observers ? Most persons would answer No ; it was more credible that a bird should vary in its color, than that man should vary in the relative posi- tion of his principal organs. And there is no doubt that in so saying they would be right : but to say why they are right, would be impos- sible, 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 fi-om the in- stances which we have 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 chem- ist announces the existence and properties of a newly-discovered sub- stance, if we confide in his accuracy, we feel assured that the conclusions he has amved 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 fi"om 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, in- feired without hesitation fi-om a single instance ; an universal pi'opo- sition 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 suffiijient presumjjtion of the truth of the proposition, to outweigh the testimony of one unexcep- tionable 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 gray. Why is a single instance, in some cases, sufficient for a complete in- duction, 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 1 Whoever can 'answer this ques- tion knows more of the philosophy of logic than the wisest of the an- cients, and has solved the great problem of induction. LAWS OF NATURK. 189 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 exjierience, one of the iirst observations that present themselves is, that the uniformity in question is not properly uniformity, but uniformities. The general regularity results from the coexistence of partial regularities. The course of na- ture 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 gilways accompanied by D, B by E, and C by F, it follows that AB is accom- panied by D E, A C by i) 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 regai'ded 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 em- ployed, there were seven uniformities ; all of which, if considered suf- ficiently certain, would, in the more lax application of the term, be called laws of nature. But of the seven, three alone are properly dis- tinct and independent ; these being presupposed, the others follow of course : the three first, therefore, accoi'ding 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, there- fore, to result from them : whoever affirras those three has abeady affiimed 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 an equal pressure in a contrary direction, produces motion, which does not cease imtil equilibi'ium 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 phra-se', 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 occur- rence by which they could all be fulfilled. If the mercury were not sustained in the barometer, and sustained at such a height that the col- umn of mercury were equal in weight to a column of the atmosphere, of the same diameter j here would be a case, either of the air not 190 INDUCTION. 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 simjile 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 sec- ond, and the second within the third, in the manner which we so fully illustrated 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 : al- though, for reasons which will appear hereafter, verification by specific experience would still be desirable, and might possibly be indis- pensable. \ Complex uniformities which, like this, are mere cases of simpler ones, and have, therefore, been virtually inferred in affimiing 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 of philosophers, wherever they can trace regularity of any kind, 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, is generally employed by scientific men with a sort of tacit reference to the original sense of the word latv, namely, the expression of the will of a superior ; the superior, in this instance, being the Ruler of the universe. When, therefore, it appeared that any o^ the uni- formities which were observed in nature, would result spontaneously from cei'tain other uniformities, without any separate act of creative will, the former have not usually been spoken of as laws of nature. According to another mode of expression, the question. What are the laws of nature 1 may be stated thus : — What are the fewest and sim- plest assumptions, which being granted, the whole existing order of nature would result 1 Another mode of stating it would be thus : What are the fewest general propositions from which all the uniformi- ties which exist in the universe might be deductively inferred ? As has already been hinted (and will be more fully discussed here- after) every gi'eat 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 akeady made, with- out any fresh extension of, the inductive inference, is already an ad- vance 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 volitions, by which, instead of a much greater number, it appeared that the whole scheme of the heavenly motions, so far as yet observed, might be conceived to have been produced. 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 LAW3 OF NATURE. 191 a ceitain instantaneous impulse originally impressed upon tliem. After this great discovery, Kepler's three propositions, though still called laws, would hai'dly, by any person accustomed to use language with precision, be temied laws ot' nature : that phrase would be reserved for the simpler laws into which Newton, as the expression is, resolved them. According to this language, every well grounded inductive generali- zation is either a law of nature, or a result of laws of nature, capable, if those laws are knowai, of being predicted from them. And the prob- lem 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 1 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 expi'ession, 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 sepa- rate 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 pur- pose it is often necessary to unravel some portion of the web, and ex- hibit the fibres apart. The rules of experimental inquiry are the con- trivances for um-aveling the web. § 2. In thus attempting to ascertain the general order of nature by ascertaining the particular order of the occuiTence 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 imderstanding, as yet undirected by science. When men first formed the idea of studying phenomena according to a stricter and surer method than that which they had in the first instance spontane- ously adopted, they did not, conformably to the well meant but imprac- ticable 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 ta observation, as to force themselves upon men's involuntary recognition. Some facts are so perpetually and familiarly accompanied by certain others, that manr kind learnt, as children now 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 be- tween those phenomena. No science was needed to teach men that food nourishes, that water drowns, or quenches thirst, that the sun gives light and heat, that bodies fall to the ground. The first scien- tific 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 192 INDUCTION. their truth to be conthigent upon some other circumstance not origi- nally 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 impractica- ble : since it is impossible to frame any scientific method of induction, or test of the correctness of inductions, vmless ujjon the hypothesis that some inductions of unquestionable certainty have been already made. Let us revert, for instance, to one of our foraier illustrations, and consider why it is that, with exactly the same amount of evidence, both negative and positive, we did not reject tlie as.sertion that there are black swans, while we should refuse credence to any testimony which assexted that there were men weai'ing their heads underneath their shoulders. The first assertion was more ci'edible 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 1 Apparently, because there is less con- stancy in the colors of animals, than in the general structure of their internal anatomy. But how do we know this ] Doubtless, fi-om experience. It appears, then, that we need experience to inform us, in what cases, or in what sorts of cases, experience is to be relied upon. 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 expei'ience in general ; but we make experience its own test. Experience testifies, that among the uni- formities which it exhibits or seems to exhibit, some are more to be relied upon than others ; and uniformity, therefore, may be presumed, from any given number of instances, with a gi'eater degree of assurance, in proportion as the case belongs to a class in which the nniformities have hitherto been found more uniform. •This mode of coixectihg one generalization by means of another, a narrower generalization by a wider, which common sense suggests and adopts in practice, is the i-eal 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 ai:)plying such a test as that above described, unless we already possess a general knowledge of tlie prevalent character of the uniformities existing throughout natiu'e. 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, pei-vading all nature, and what ai'e 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 considera- tion, that the stronger inductions are the touchstone to which we always endeavor 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 LAWS OF NATURE. 193 evidence of the truth of the better established law in which it is now found to be included. We may have infeiTed, from historical evidence, that the uncontrolled government of a monarchy, of au aristocracy, or of the majority, will commonly be a tyranny : but we are entitled to rely upon this generalization with much gi-eater assurance when it is shown to be a corollary from still better established truths ; the infirmity of human nature, and the impossibility of maintaining the predominance of reason and conscience over the selfish propensities by any means except such as the supposition of absolute power neces- sarily excludes. It is at the same time obvious that even these great facts in human nature 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 sti-onger inductions, or with conclusions capable of being correctly deduced from them, then, unless upon reconsideration it should appear that some of the stronger inductions have been sti'etched too far, the weaker one must give way. The opinion so long prevalent that a comet, or any other unusual ap- peaiance in the heavenly regions, was the precursor of calamities to mankind, or to those at least who witnessed it ; the belief in the vera- city of the oracles of Delphi or Dodona ; the reliance on astrology, or on the weather-prophecies in almanacs ; were doubtless inductions sup- posed to be grounded on exj)erience : and faith in such delusions seems quite capable of holding out against a gi-eat multitude of failures, pro- vided 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 Avith the stronger in- ductions subsequently obtained by scientific inquiry, respecting the causes upon which terrestrial events really depend ; and where those scientific truths have not yet peneti-ated, 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 together by a ratiocination, are confirmatory of one another : while any which lead deductively to con- sequences that are incompatible, become mutually each other's test, showing that one or other must be given up, or, at least, more guard- edly 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 fi-om which it is deduced; while in general all are more or less increased in certainty. Thus the Torricellian experiment, though a mere ease of three more general laws, not only strengthened gi'eatly the evidence on which those laws rested, but converted one of them (the weight of the atmosphere) fi-om a doubtful generalization into one of the best-established doctrines in the range of physical science. If, then, a sui-vey of the uniformities which have been ascertained to exist in nature, should point out some which, as far as any human pur- pose requires ceitainty, may be considered as absolutely certain and absolutely universal ; then by means of these uniformities, we may be able to raise raultitudas 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 Bb 194 INDUCTION. admit of an exception : the former generalization will attain the same absolute 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 phenom- enon 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 phenome- na. 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 branch- es,) 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 com- prehension 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 imchangeably 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 the other a cylin- der, 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 rela- tively to each other, of whatever nature the bodies be, may be uner- ringly 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 recognize, 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 LAW OF CAUSATION. 195 exception to them; and philosophers have been led, although (as I have endeavored to show) erroneously, to consider their evidence as lying not in experience, but in the original constitution of the human intellect. If, therefore, from the laws of space and number, we were able to deduce unifermitics of any other description, this would be conclusive evidence tu us that those other unifonnities possessed the same degi-ee 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 j)henomena, 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. Moreover, motions, forces, or other influences, and times, arc numerable quantities ; and the properties of number are applicable to them as to all other things. But although 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 proposi- tions : that bodies acted upon by an instantaneous force move with uniform velocity in straight lines ; tliat bodies acted upon by a con- tinuous 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 parallelo- grams, (as that a tnangle 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 propor- tional 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 of what cannot be explained. 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 that rigorous certainty and universality of which we are in search. "We must endeavor 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 uniformi- ties of succession. This fundamental law must resemble the truths of geometry in their most remarkable peculiarity, that of never being, in 196 INDUCTION. any instance whatever, defeated or suspended by any change of cir- cumstances. 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 inde- feasibility : and of those few, one only has been found capable of com- pletely sustaining it. In that one, however, we recognize 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. It is an universal truth that every fact which has a beginning has a cause. 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 upon some law." We must not, however, conclude that the generality of the principle is merely verbal : it will be found upon inspection to be no vague or unmeaning assertion, but a most import- ant and really fundamental truth. § 2. The notion of Cause being the root of the whole theory of Induc- tion, 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 purposes of induc- tive 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 con- sidered desperate, for a long time to come. But in this as in most other respects, the science of the Investigation of Truth by means of Evidence, has no need to bon-ow any premisses from the science of the ultimate constitution of the human mind, except such as have at last, though often after long controversy, been incoi-porated into all the existing systems of mental philosophy, or all but such as may be re- garded as essentially effete. 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 ontolo- gical cause of anything. To adopt a distinction familiar in the wri- tings 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 may be 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 myste- rious and most powerful tie, such as cannot, or at least does not, exist between any physical fact and that other physical fact upon 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 tiue 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 \\\\\ there be found anything incompatible with it. We are in no way LAW OF CAUSATION. 197 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 wliicli is the main pillar of inductive philosophy, is but the familiar truth, that inva- riability of succession is found by observation to obtain between every fact in nature and some other fact which has preceded it ; independ- ently 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 wo said in speaking of the general uni- formity of the course of nature, this web is composed of separate fibres ; this collective order is made up of particular sequences, obtaining inva- riably among the separate parts. To certain facts, certain facts always do, and, as we believe, always will, succeed. The invariable antece- dent is termed the cause ; the invariable consequent, the effect. And the universality of the law of causation consists in this, that every con- sequent 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 invaria- bly connected. For every event, there exists some combination of objects or events, some given concurrence of circumstances, positive and negative, the occurrence of which will always be 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. Upon the universality of this truth de- pends 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 one single an- tecedent, that this invariable sequence subsists. It is usually between a consequent and the sum of several antecedents ; the concurrence of them all being requisite to produce, that is, to be certain of being fol- lowed by, the consequent. In such cases it is very common to single out one only of the antecedents under the denomination of Cause, call- ing the others merely Conditions. Thus if a man eats of a particular dish, and dies in consequence, that is, would not have died if be 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 inva- riable connexion between eating of the dish and death ; but thex'e certainly is, among the circumstances which took place, some combi- nation or other upon which death is invariably consecjuent : as, for instance, the act of eating of the dish, comliined 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 phenom- enon, 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 vyhole of these antecedents ; and we have, philosophically speak- 198 INDUCTION. ino-, 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 incor- rectness of the expression, is this : that the various conditions, except the single one of eating the food, were not events (that is, instantaneous chano-es, 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 closer connexion between the effect and that one antecedent, than between the effect and the remaining conditions. But although 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 begi7i 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 ex- posure 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 caiise of his attack was ex- posure 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 condi- tions, it is only because some of them will in most cases be imder- stood 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, although no one now regards it as the principal one. When the deci- sion of a legislative assembly has been detennined by the casting vote of the chaimian, we often 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 that of fixing him with the responsibility, the share which any other person took 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 show the absence of any scientific ground for the distinction between the cause of a phe- nomenon 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 LAW OF CAUSATION. 199 any of them which may not, according to the purpose of our immediate discourse, obtain that nominal preeminence. This will be seen by analyzing 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 suppo- sitions 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 ma- terial 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 say- ing that it is caused by the earth ; or, lastly, the earth's atti-action; 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 fi'om 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 woi'ds 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 upon at the moment. So great is the force of this last consideration, that it often induces us to give the name of cause even to one of the negative conditions. We say, for example, The cause of the army's being surprised was the sentinel's being oft' his post. But since the sentinel's absence was not what created the enemy, or made the soldiers to be 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 (^ 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 oi 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 cer- tain other positive facts do not exist. Since, then, mankind are accustomed, with acknowledged propriety 200 INDUCTION. SO far as the ordinances of language are concerned, to give the name of cause to almost any one of the conditions of a phenomenon, or any portion of the whole number, arbitrarily selected, without excepting even those conditions which are purely negative, and in themselves incapable of causing anything ; it will probably be admitted without longer discussion, that no one of the conditions has more claim to that title than another, and that the real cause of the phenomenon is the as- semblage of all its conditions. There is, no doubt, a tendency (which our first example, that of death from taking a particular food, suffi- ciently 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 phe- nomenon ; 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 philosophers, 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 ^ force exerted by the earth, or an attraction by the earth, abstractions which they can represent to themselves as exhausted by each eftbrt, and therefore constituting at each successive instant a fresh act, simultaneous with, or only immediately preceding, the effect. Inasmuch as the coming of the circumstance which com- pletes 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 contiary, any one of the conditions, either positive or negative, is found, upon occasion, completely to accord. The cause, then, philosophically speaking, is the sum total of the con- ditions, positive and negative, taken together ; the whole of the contin- gencies of every description, which being realized, the consequent invariably follows. The negative conditions, however, of any phenom- enon, a special enumeration of which would generally be very prolix, may be all summed up under one head, namely, the absence of pre- venting or counteracting causes. The convenience of this mode of expression is grounded mainly upon 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 eftect, 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 LAW OF CAUSATION. 201 preventing the effects of other causes by virtue (for the most part) of the same laws, according to which they produce their own,* 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 con- sideration 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 upon 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 dra\vn between somethhig 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 in- cident 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 ia the phrase by which the effect is spoken of, so that if it were also reckoned as part of the cause, the seeming incon- gruity would arise of its being supposed to cause itself. In the in- stance which we have already had, of falling bodies, the question was thus put : — What is the cause which makes a stone fall 1 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, accord- ing 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 if we do but alter the mere wording of the question, and express it thus, What is the cause which produces vertical motion towards the earth ? we might now, without any incongruity, speak of the stone or other heavy body as the agent, which, by virtue of its own laws or properties, commences moving towards the earth ; 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 caase is not the stone itself, but the weight or gravitation of the stone. * 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, so 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 efl'ects, but of an agency vvhicfi manifests itself in no other way than in defeating the effects of another agency. If we knew upon wnat other relations to light, or upon what peculiarities of structure opacity depends, we might find that this is only an apparent, not a real, excep- tion 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; although, if all counteracting agencies were of this description, there would be no pur- pose 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 con- tained in the positive laws of the various other agencies in nature. Cc 202 INDUCTION. 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 license 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 philosophical truth. Even those of the attributes of an object which might seem with greatest propriety to be called states of the object itself, its sensible qualities, its color, 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 the states of objects, are always sequences into which those 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 last example, that of a sensation produced in our organs, are not the laws of our organization, and even those of our minds, as directly operative in determining the effect produced, as the laws of the outward object] Though we call prussic acid the agent of a man's death, are not the whole of the vital and organic properties of the patient as actively instrumental as the poison, in the chain of effects which so rapidly terminates his sentient existence 1 In the process of education, we may call the teacher the agent, and the scholar only the matei'ial acted upon ; yet in truth all the facts which preexisted in the scholar's mind exert either cooperating 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 degi'ee as to react most 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 con- ditions 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 incon- sistency. § 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 thi;: phrase as exactly LAW OF CAUSATION. 203 synonymous with " tlie antecedent which it invariably has followed in our past experience." Such a mode of viewing 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 ante- cedent always has been followed by the consequent, but that, as long as the present constitution of things endurcss, 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 any imaginable circumstances, but only that it will be ?>o,prov.idcd 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 com- bination 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* 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 super- fluous 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 neces- sity, it is unconditionalmss. 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 upon the occurrence of other antecedents. That which wDl be followed by a given consequent when, and only when, some third circumstance also exists, is not the cause, oven although no case should have ever occuiTed 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 a philosopher, 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 fi)llows 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 * I use the words " straight line" for brevity and simplicity. In reality the line in ques- tion is not exactly straight, for, from the effects of refraction, we actually see the snn for a short interval during which the opaque mass of the earth is interposed in a direct line be- tween the sun and our eyes ; thus realizing, though but to a limited extent, the coveted desideratum of seeing round a corner. 204 INDUCTION. would follow tlie presence of a sufficiently luminous body, whether darkness had preceded or not. We may define, therefore, the cause of a phenomenon to be the an- iecedent, or the concurrence of antecedents, upon which it is invariatly and uncondUionally consequent. Or if we adopt the convenient modi- fication of the meaning of the word cause, which confines it to the as- semblage 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 uncondition- ally 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 ^vill exist together ; and if many causes coexist, these causes (by what we shall term here- after, 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 con- sequents, 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, there- fore, though a case of sequence invariable within the limits of human experience, is not a case of causation. It is not unconditional. To distinguish these conditionally uniform sequences from those which are uniform unconditionally ; to ascertain whether an apparently invariable antecedent of some consequent is really one of its conditions, or whether, in the absence of that antecedent, the effect would equally have followed from some other portion of the circumstances which are present whenever it occurs ; is a principal part of the great problem of Induction ; and is one of those questions, the principles of the solu- tion of which will, it is to be hoped, result from the inquiry we have undertaken. § 6. Does a cause always stand \%ath its effect in the relation of an- tecedent 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 1 It is certain that a cause does not necessarily perish because its effect has been produced ; the two, therefore, do very generally coexist ; and there are some appearances, and some common expres- sions, seeming to imply not only that causes may, but that they must, be contemporaneous with their effects. Cessante causd, cessat ct effec- tus, 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 general doctrine among philosophers. Mr. Whe- well observes that Kepler's numerous attempts to account for the motion of the heavenly bodies on mechanical principles, were rendered abortive by his always supposing that the force which set those bodiea LAW OF CAUSATION. 205 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 in open contradiction to this supposed axiom. A coup de soleil gives a man 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 contin- uance 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 counter- poised 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. The solution of these difficulties will be found in a very simple dis- tinction. 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 neg- ative 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 are enabled to avoid 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 continu- ance 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 we have quoted,*) we think the inquiry an unimportant one. There certainly are cases in which the effect follows without any interval perceptible to 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 af- fected. Whether the cause and its effect be necessarily successive or not, causation is still the law of the succession of phenomena. Every- thing 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 * The reviewer of Mr. Whewcll in the Quarterly Review. 206 INDUCTION. origin of phenomena, and all the successions of phenomena must be resolvable into causation. These are the axioms of our doctrine. If these be gi-anted, we can afford, though I see no necessity for doing so, to drop the words antecedent and consequent as applied to catrse and effect. I have no objection to define a cause, the assemblage of phenomena, which occuning, some otlier phenomenon invariably com- mences, 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 degi-ee dependent or conditional upon one another, are found all to depend, as the phrase is, upon 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 w^hich 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 gray color, and many others between w^hich we can trace no interdependence. The pui-pose to which the phraseol- ogy 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 differ- ent 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 dis- tinguish the attractive, or gravitative, property of the earth, and its magnetic property ; the gravitative, luminiferous, and calorific proper- ties of the sun ; the color, shape, weight, and hardness of the crys- tal. These are mere phrases, wdiich explain nothing, and add nothing to our knowdedge of the subject; but considered as absti'act 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 us to a conception which we shall find of great importance in the interpretation of nature ; that of a Per- manent Cause, or original natural agent. There exist in nature a num- ber of permanent causes, which have subsisted ever since the human race has been in existence, and for an indefinite and probably enonnous length of time previous. The sun, the earth and jilanets, with their various constituents, air, water, and the other distinguishable substances, whether simple or compound, of which nature is made up, are such Peraianent Causes. These have existed, and the effects or consequen- ces 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, scientifically speaking, no account of the origin of the Permanent Causes themselves. Wliy these particular nat- LAW OF CAUSATION. 207 ural agents existed originally and no others, or why they are commin- gled 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 spaco, we could conjecture whether a similar distribution prevails in another. The coexistence, therefore, of Primeval Causes, tanks, 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 upon 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 re- quisite 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 conjectm-ally) for the rotation itself, it is entitled to be ranked as a pi'imeval cause. It is, however, only the origin of the ro- tation which is mysterious to us : once begun, its continuance is account- ed for by the first law of motion (that of the permanence of rectilineal motion once impressed) combined with the gi-avitation 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 universe, which is not con- nected 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 an- tecedent phenomena, again, were connected in a similar manner with some that preceded them; and so on, until we reach, as the ultimate step, either the properties of some one primeval cause, or the conjunc- tion of several. The whole of the phenomena of nature were therefore the necessary, or in other words, the unconditional, consequences of the original 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 if we knew all the agents which exist at the present moment, their colloca- tion in space, and their properties, in other words the laws of their agency, we could predict the whole subsequent history of the universe, at least unless some new volition of a power capable of controlHng the universe should supei-vene.* And if any particular state of the entire * 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 detennina- tions of which a large class of metaphysicians are not willing to regard as following the 208 INDUCTION. universe should ever recur a second time, (which, however, all experi- ence combines to assure us will never happen,) all subsequent states would retui-n too, and history would, Uke a circulating decimal of many- figures, periodically repeat itself: — Jam redit et \irgo, redeunt Saturnia regna Alter eiit turn Tiphvs, et altera quae vehat Argo Delectos heroas ; eruntqooque 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 infinitely 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 in the universe is determined by laws of causation and collocations of the original causes, it follows that the coexistences which are obsei-vable among effects cannot be them- selves the subject of any similar set of laws, distinct from laws of causa- tion. Uniformities there are, as well of coexistence as of succession, among the 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 pi-imeval 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 coex- isted. The only independent and unconditional coexistences which are sufficiently invai'iable to have any claim to the character of laws, are between diff'erent 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 ti-eatedof in the latter part 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. 3). In the mean time I may remark that these metaphysicians, who, it must be observed, ground the main part of their objection upon 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-e.xam- ination, 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 thinking highly objec- tionable. But if they would consider that by saying that a man'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, ahd 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. LAW OF CAUSATION. 209 of the pi-esent Book, under the name of the Specific Properties of Kinds. § 9. Before concluding this chapter, it seems desirable to take notice of an apparent, but not a real opposition between the doctrines which I have laid down respecting causation, and those maintained in a work which I hold to be far the greatest yet produced on the Phi- losophy of the Sciences, ]M. Comte's Cours dc Phdosophie Positive. M. Comte asserts as his first principle, that the causes of phenomena are beyond the reach of the human faculties, and that all which is ac- cessible to us is their laws, or, as he explains the term, their constant relations of succession or of similarity. Accordingly M. Comte sedu- lously abstains, in the subsequent part of his work, from the use of the word Cause : an example which I have not followed, for reasons which I will proceed to state. I most fully agree with M. Comte that ulti- niatc, or, in the phraseology of metaphysicians, efficient causes, which ai'e conceived as liot being jjhenoraena, nor perceptible by the senses at all, are radically inaccessible to the human faculties : and that the " constant relations of succession or of similarity" which exist among phenomena themselves, (not forgetting, so far as any constancy can be traced, their relations of coexistence,) are the only subjects of rational investigation. When I speak of causation, I have nothing in view, other than those constant relations : but I think the terms causation, and cause and effect, important to be preserved, for the purpose of distinctively designating one class of those relations, namely, the rela- tions of succession which so far as we know are unconditional ; as contrasted with those which, like the succession of day and night, de- pend upon the existence or upon the coexistence of other antecedent facts. This distinction corresponds to the great division which Mr. 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, altogether vicious, inasmuch as the ascertainment of causes, sucli causes as the human faculties can ascertain, namely, causes which are themselves phenomena, is, therefore, merely the asceitaiimicnt of other and more universal Laws of Phenomena. And I cannot but look upon the revival, on English soil, of the doctrine (not only refuted by the school of Locke and Hume, but given up by their great rivals Reid and Stewart) tliat efficient causes are within the reach of human knowl- edge, as a remarkable instance of what hag been aptly called " the peculiar zest which the spirit of reaction against modern tendencies gives to ancient absurdities." Yet the distinction between those constant relations of succession or coexistence which Mr. Whewell tenns Laws of Phenomena, and those which he tenns, as I do. Laws of Causation, is grounded (how- ever incorrectly expressed) upon a real difference. It is no doubt with great injustice that Mr. Wliewell (who has evidently given only a most partial and cursory inspection to M. Comte's work,) assumes that M. Comte has overlocdced this fundamental distinction, and that by excluding the investigation of causes, he excludes that of all the most general truths. No one really acfjuainted with M. Comte's admirable speculations could have so completely misapj)rehended their whole spirit and purpoit. But it does appear to me tlaat his disinclina- Dd 210 INDUCTION. tion to employ the word Cause has occasionally led him to attach less importance than it deserves to this great distinction, upon which alone, I am convinced, the possibility rests of framing a rigorous Canon of Induction. Nor do I see what is gained by avoiding this particular ■word, when M. Comte is forced, like other people, to speak continually of the properties of things, of agents and their action, oi forces, and the like ; terms equally liable to perversion, and which are partial and inadequate expressions for what no word that we possess, except Cause, expresses in its frill generality. I believe, too, that when the ideas which a word is commonly used to convey are overclouded with mysticism, the obscurity is not likely to be so effect,ually dispelled by abstaining from its employment, as by bringing out into full clearness the poition of real meaning which exists in the various cases where the terin is most familiarly employed, and therelay giving a legitimate satisfaction to that demand of the intellect which has caused the term to remain in use. 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 frinda- mental, 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 pro- duction 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 kijow 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 fi'om 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 coiTectly express the part due to that cause, of the effect which follows from the two together. This condition is realized in the extensive and impoitant class of phenomena commonly called mechanical, namely, the phenomena of the communi- cation of motion (or of pressure, which is tendency to motion) fr'om one body to another. In this important class of cases of causation, one cause never, properly speaking, defeats or frusti-ates 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 du'ections as COMPOSITION OF CAUSES. 211 the two forces would separately have camcJ 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 mechanical philosophy, 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 jio means prevails in all departments of the field of natui'e. 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 of both of them taken together. Not a trace of the properties of hydro- gen 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 color of green viti-iol a mixture of the colors of sulphuric acid and copper. This explains why mechanics is a deductive or demonstrative science, and chemisti-y not. In the one, we can compute the effects of all combina- tions of causes, Avhether real or hypothetical, from the laws which we know to govern those causes when apting sej?arately ; because they continue to obsei've the same laws when in combination, which they observed when separate ; whatever would have happened in conse- quence of each cause taken by itself, happens when they are together, and we have only to cast up the results. Not &o 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 it by specific experiment. If this be true of chemical combinations, it is still more time of those far more complex combinations of elements which constitute organized bodies ; and in which those extraordinary new uniformities arise, which are called the laws of life. All organized 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 iife, 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 ingi-edients 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 wc ever predict that it could taste, unless gel- atine 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 212 INDUCTION. 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 gunpow- der 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 exJn-emity 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,* and the stream had flowed in for as long after- wards. Each agent produced the same amount of -effect as if it had acted separately, though the contrary effect which was taking plafce during the same time obliterated it as fast as it was produced. Here, then, we have two causes, producing by their joint operation an effect which at first seems quite dissimilar to those which they produce sep- arately, 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 dif- ference, but which is in reality the result of the addition of opposites ; a conception to which, as is well known, mankind are indebted for that admirable extension of the algebraical calculus, which has so vastly in- creased its powerxS 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 na- ture in which, even when the eoncuiTent 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 two agen- cies 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, in- stead 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 ease 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 prin- ciple of the Composition of Causes ; none that have not some laws which are rigidly fulfilled in eveiy 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 * I omit, for simplicity, to take into account the effect, in this latter case, of the diminu- tion of pressure, in diminishing the flow of the water through the drain ; which evidently iu no way allects the truth or applicability of the principle. COMPOSITION OF CAUSES. 213 the weights of the elements which compose it. The weight either of the elements or. of" the compound will vary, if they be carried fur- ther from their centre of attraction, or brought nearer to it ; but what- ever affects the one affects the other. They always remain precisely equal. So again, the component parts of a vegetable or animal sub- stance do not lose their mechanical and chemical properties as sepa- rate agents, when, by a peculiar mode of juxtaposition, 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 jiew laws which govern them as organized beings. When, in short, a concurrence of causes takes place whicli calls into action new laws, bearing no analogy to any that we can trace in the separate operation of the causes, the new laws may supersede one portion of the previous laws but coexist with ancither portion, and may even com})ound the effect of thosfe previous laws with their own. Again, laws which were themselves generated in the second mode, may generate others in the fir^t. 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, het.eropathic laws, are not capa- ble of composition with one another. The causes which by one com- bination 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 de- duce all chemical and physiological truths from the laws or properties of simple substances or elementary agents, they may probably be de- ducible from laws whicli 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 ingi-edients, but the prodigiously complex Facts of Life may all be deducible from comparatively simple laws of life ; which laws (depending indeed upon combinations, but upon compara- tively simple combinations, of antecedents), may in more complex circumstances be strictly comjiounded wjth 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 pi'oportion as these phenomena are more ac(;urately studied, there aj)pears more and more reason to believe tliat the same laws which operate in the simpler combinations of circumstances do, in fact, continue to be obsei-ved in the more com- plex. * This will be found c(jually 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 * For abundant illustrations of this remark, I may refer to the writings of Dr. W. B. Carppnter, of Bristol, and ospecially his treatise on General Physiology, in which the high- est generalizations which the science of life has yet reached, and the best modern concep- tion of that science as a whole, are exhibited in a manner equally perspicuous and philo- sophical. On the details of such a treatise the present writer would be an incompetent wit- ness : these however have been sufficiently vouched for by some of the highest living authorities ; while of the genuinely scientific spirit which pervades it, those ipay be per- mitted to express an opinion, who v/ould not be entitled to ofler to a work on such a sub- ject, any other praise. 214 INDUCTION. 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 sum 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 com- bination before we have actually tried it, and.to jiulge of what sort of elements some new substance is- compounded before we have analyzed it : a problem, • the solution of which has been propounded by M. Comte as the ideal aim and purpose of chemical speculation. The gi-eat law of definite proportions, first discovered in its full generality by Dalton, is a complete solution of this problem in one single aspect (of secondary importance it is ti-ue), that of quantity : and in respect to quality, we have already some partial generalizations sufficient to indicate "the possibility of ultimately proceeding further. We can predicate many 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 very curious law, discovered by Berthollet, that two soluble salts mutually decompose one another whenever the new combinations w^hich result produce an insoluble compound : or one less soluble than the two former. Another imifonnity has been obsei-v^ed, com- monly 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 o-eneration of laws from others dissimilar to them; and in chem- istry, 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 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 actino- singly : but that this rule, though genei'al, is not universal ; that in some instances, at some particular points in the transition fi'om sep- arate 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 fi'om the separate agency of the same causes ; the Ia\vs 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, although it is encumbered 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 brue, enters as a COMPOSITION OF CAUSES. 215 particular case into tlic gcjioral principle of the Composition of Causes : tlie causes compounded being, in this instance, liompgeneous ; in which case, if in any, their joint elfect might be expected to" be identical with the sum of their separate eflects. 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, we know, raise two bodies exactly similar, and thus the effect is proportienal 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 apait, would sepa- rately raise the two bodies in (juestion i The fact, therefore, that wlien 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 eflects to their causes cannot of course be applicable to cases in which the augmentation of the cause alters the ki?id of effect; that is, in which the su7-j)lus quantity superadded to the cause does not become compounded with it, but the two together generate an alto- gether' new phenomenon. Su^jpose 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 eflects being heterogeneous, no ratio, whether corresponding or not to that of the quantities of heat applied, can be established between them. Thus we see that the supposed axiom of the proportionality of effects to their causes fails at the precise point whei?e the principle of the Composition of Causes also fails ; viz., where the concuiTence 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 of existence. 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 seqmed necessary as an introduction to the theory of the inductive process, may here termi- nate. That process is essentially an inquiry into cases of causation. All the uniformities which exist in the succession of plienomena, and most of those which prevail 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 recjuisite 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 eveiy 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. 216 INDUCTION. CHAPTER VII. OF OBSERVATION AND EXPERIMENT, § 1. It results from the preceding exposition, that the process of ascertaining what consequents^ in natui-e, 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 pi'ocess of analysis. Tha.t every fact which begins to exist has a cause, and that this cause must be found somewhere among the facts which immediately pre- ceded its occuiTence, may be taken for certain. The whole of the present facts are the infallible result of all past facts, and more inmie- diately 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 whole 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 that portion of the consequent which is attendant upon 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 men- tal partition is an indispensable first step. The order of nature, as per- ceived at a first glance, presents at every instant a chaos followed by another chaos. We must decompose each chaos into single facts,' We must leai-n to see in the chaotic antecedent a multitude of dis- ' tinct 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 endeavor to effect a sej)aration of the facts from one another, not in our minds only, but in nature. The mental analysis, however, must take ]ilace first. And every one knows that in the mode of performing it, one intellect diflers im- mensely fi-om another. It is the essence of the act of obsei-\'ing ; 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 hind of all the circum- stances, 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 obsei-ver ; that, however, is a question not of Logic, but of the. theory OBSERVATION AND EXPEUIMRNT. 217 of Education, in the most enlarged sense of the term. There is not properly an Art of Observing. There may be rules for observing. J)ut these, like rules for inventing, are projjorly instructions for the preparation of one's own mind ; for putting it into the state in which it will be mnst 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 limlTS, 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 njental analysis, depend upon the particular purpose in view. To ascertain the state of the whole universe at any particular m-oment is impossible, but would also be useless. In making chemical experi- ments, we should not think it necessary to note the position of the planets; because experience has shown, as a very superficial experi- ence is sufficient to show, that in such cases that circumstance is not material to the j-esult : and, accordingly, in the age when men believed in the occult influences of the heavenly bodies, it might have been un- philosophical to omit ascertaining the precise condition of those bodies . at the momeirt of the experiment. As to the degree of minuteness of the mental subdivision ; if we were obliged to break down what we obsen^e 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 can-ied the subdivision as far as the point at which we are able to see what observations or ex})eri- ments 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 cany it further as occasion requires, and should not allow the freedom of our discriminating faculty to be im})risoned 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" pos- sibility of decomposing the facts of the universe into any elements but those which ordinaiy language already recognized. § 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 fi'om one another except in thought, or if those consecjuents 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 eil'ect, 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 consctpients, and^ observe by what they are preceded. We must, in short, follow the Baconian rule of varying E E 218 INDUCTION. the circumstances. This is, indeed, only the Jirst rule of physical inqui- ry, and not, as some have thought, the sole rule ; but it is the founda- tion of all the rest. Foi- 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 upon what it is in itself, not upon the mode in which it is obtained : its employment for the puqioses of induction depends upon 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, moreover, 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 ser- vice which nature, being constrvicted 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 atmos- phere enables it to sustain life, the variation we require is that a living animal should be immersed in each component element of the atmos- phere 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 even for our knowledge of the very existence of the two ingredients. Thus far the advantage of experimentation over simple obsez'vation is universally recognized : 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 experi- ments 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 any means at our disposal, we can generally determine at our own discretion, so far as js 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 every- thing else which is within the reach of A's influence, we have only to observe what alteration is made in that state by the prissence of A. For example, by the electrical machine we can produce in the midst OBSERVATION AND EXPERIMENT. 219 of known circumstances, the plienomena which nature exhibits on a grander scale uncUn- the form of lii^hrniniT and thunder. Now let any one consider wirat amount of kiu)wled'u;e ot'riie etfects and laws of elec- tric agency mankind could ever 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 produc- tion to enable it to be studied ; while the fact is so much tlie contrary, that without the electric machine, the voltaic l?attery, and the Leyden jar, we should never have suspected tile 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 super- natural, 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-dis- covered substance in a pure state, (that is, having made sure that there is nothing present whicn 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 phe- nomenon, and we have to seek for instances in which nature produces it, the task before us is one of quite another kind. Instead of being able to choose what thq concomitant circumstances shall be, we now have to discover what they are ; which, when we go beyond the sim- plest and most accessible cases, it is next to impossible to do, with any precision and completeness. Let us take, as an exemplification of a phe- nomenon 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 suppo.se the subject of investigation to be a human society or State all the same difficulties recur in a greatly augmented degree. 220 INDUCTION. We have thus ah-eady 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 astron- omy), or in which they have a very limited range (as in physiology,' m^'ental philosophy, and the social science), indviction from dhect 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 tlie first of the sciences we have men- tioned, astronomy ; that it is not generally recognized as true of the others, is probably one of the reasons why they are still in their infancy. But any further notice of this topic would at present be premature. § 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 caiises of a given effect. The fact that light blackens chloride of silver might have been discovered, either by experiments upon 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 dieorotical discussion, that artificial experimentation is applicable only to the former of these modes of investigEttion. We can take a cause, and try what it will produce : but we cannot take an effect, and try what it will be pro- duced by. We can only watch till we see it ]iroduced, or are enabled to produce it by accident. This would be of little importance, if it always depended upon our choice from which of the two ends of the sequence we would under- take 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 contiive, instances of th,e 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 resoui'ce but to comjiare 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 the light. If we knew nothing of the Indian arrows but their fatal OBSERVATION AND EXPERIMENT 221 effect, accident alone could turn our attention to experiments on the urali : in the regular course ofinvestisration, 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 o])liged to set out from the eftect, and to apply the rule of varying the circum- stances 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 there- fore 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 although this is certainly the most favorable case for sciences of pure observation, as contrasted with those in which artificial experi- ments are possible, there is in reality no case which more strikingly illustrates the inherent imperfection of direct induction when not founded upon 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 pro- duce the antecedent artificially, and if, when we do so, the effect fol- lows, the induction is complete; that antecedent is the cause of that consequent.* But we then have added the evidence of experiment to that of simple observation. Until we had done so, we had only proved invariaole antecedence, but not unconditional antecedence, or causa- tion. Until it had been shown by the actual production of the antece- dent under kno\Mi 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 con- sequent might be successive stages of the effect of an ulterior cause. Observation, in short, without experiment (and without any aid from deduction) can ascertain uniformities, 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, thei'e is an immense number of uniformities ascertained, some of coexistence, othei-s of succession, to many of which, notwithstanding considerable variations of the attendant circum- stances, we know not any exception : but the antecedents, for the most part, are such as we cannot artificially produce ; or, if we can, it * 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. 222 INDUCTION. is only by setting in motion tlie exact process by which nature pro- duces 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 1 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 uliiformity. We know not, in the case of almost any of the phenom- ena 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 all of them" 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 aiTangement, premature in this place, it seemed that a few general remarks upon the difierence between Sciences of mere Observation and Sciences of Experimentation, and the extreme disad- vantage 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 INaUIRY. § 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 eftects or properties of a given c^use. 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 con-esponding 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 must, it would seem, be the effect of A. Suppose, for example, that A is tried along with B and C, and that the effect is abc; and suppose that A is next THE FOUR EXPERIMENTAL METHODS. 223 tried with T) and E, but without B and C, and that the effect is ade. Then wo may rouson thus : b and c are not effects of A, for they were not produced hy it in the second experiment; nor are .cZ 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 K, 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 coiu'duded 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, ;vve 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 suqli a random trial it could only be by accident. But if we can observe a in two different combinations, aic and ade; and if we know, or can discover, that the antecedent circumstances in these cases respectively were ABC and ADE; we may conclude by a reasoning similar to that in the pre- ceding example, that A is the antecedent connected with the consequent (i by a law of causation. B and G, 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 crystalizatioUi. We compare in- stances in which bodies are known to assume crystaHne structure, but which have no other point of agreement; and we find thdm 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 crystalization. In this example we may go further, and say, it is not only the invariable antecedent but the cause. For in tliis 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. never more strikingly- manifested than when, by keeping a phial of water charged with siliceous particles undisturbed for years, a chemist (1 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 inten-ogation of her. But if we cannot artificially produce the phenomenon A, the con- 224 INDUCTION. elusion that it is the cause of a remains subject to very considerable doubt. Though an invai-iable, it may not be the unconditional ante- cedent of a, but may precede it as day precedes night or night day. This uncertainty arises from the imjjossibility 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 antece- dents, we might be sure that the unconditional invariable antecedent, or cause, mustbe found somewhere among them. Unfortunately it is hardly ever possible to ascertain all the antecedents, unless the phe- nomenon 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 analyze 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 when she produ- ces any 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 upon the following axiom : Whatever circumstance can be excluded, without prejudice to tl>e phenomenon, or can be absent notwithstanding it presence, is not connected with it in the way of causation. The casual circumstances being thus elimi- nated, if only one remains, that one is the catise 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 jxhenomenon. '• 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 endeavored to obtain in- stances which agreed in the given circumstance but differed in every other : in the present method we require, on the contrary, two in- stances 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 ABC, and having noted the effects produced, compare them with the efiect of the rernaining circumstances B C, when A is absent. If the effect of A B C is ahc, and the effect of BC, he, it is evident that the effect of A is a. So THE FOUR EXPKRI.MENTAL METHODS. 225 again, if we begiji at the otUcr end, and desire, to investigate the gause of an .ctfect a, wo must select an instance, as abc, in which the effect occurs, .and iiL which the antecedents were ABC, and we must look out for another inatance in which the remaining circumstances, he, occur without a. If the antecedents, in that instance, are BC, we know that the cause of a must be A : either A alone, or A in conjunc- tion with some of the other circumstances present. It is scarcely necessary to give examples of a logical process to Avhich 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 fullness of life immediately before, all' circumstances being the same, except the wound. The axjoras which ai^e taken for gi-anted in this method are evidently the following : Whatever antecedent camiot be excluded without pre- venting the phenomenon, is the cause, or a condition, of that phenom- enon ; Whatever consequent can be excluded, with no other differ- ence in the antecedents than the absence of a particular one, is the effect of that one. Instead of comparing diffei"ent instances of a jahe- nomenon, to discover in what they agree, this method compares an instance of its occurrence with an instance of its non-occuri'ence, to discover in what they difler. The canon which is the regulating prin- ciple 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 save ane i?i common, that one occurring only in the former ; the circumstance in which alone the two instances differ, is the effect, or cause, or a neces- sary part oftflie caiise, 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 tcim (which is enrploycd 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 upon the relation between the remaining elements only,) is well suited to express the operation, analagous 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 wliich 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 Diffc;renco is more particularly a method of artificial experiment ; while that of Agreement is more especially the resource we employ 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, Fp 226 INDUCTION. that the nature of the combinations which it requires ns much more strictly defined than in the Method of Agi-eement, The two instances which are to be compared with one another must be exactly similar, in all circumstances except the one which we are attemj)ting to inves- tigate : they must be in the relation of ABC and BC, or of a Z»c and be. 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 leani at once, from the most ordinary experience, that most of the coexistent phenomena of the universe may be either present or absent without affecting the given phenome- non ; 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, ABC and BC, to snch circumstanceis 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 spon- taneous 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. AVlaen, 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, j^rovided the process does not last a long time. A certain state of sun-ounding circumstances existed before we commenced the experiment : this is BC. We then hitroduce A ; say, for instance, by merely bringing an object from another part of Hie room, before there has been time for any change in the other ele- ments. It is, in short (as M. Comte obsei-\-es), the very nature of an experiment, to introduce into the preexisting 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 we in general are entitled to feel complete assurance, that the pre- existing state, and the state which we have prodviced, differ in nothing except in 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 ail events after one or two repetitions) that no circumstance capable of causing suffocation had supei-vened 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 we 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 vohmtary 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 FOUR EXPERIMENTAL METHODS. 227 The reverse of this is the case with the Method of Agreement. We do uot here require instances of so special and dcterininale a kind. Any instances whatever, in which nature presents us with a phenom- enon, may be examined for tlic purposes of this method ; and if all such instances agree ia anything, a conchision of considerable value is already jittained. We can sekhmi, indeed, be sure that this one point of agreement is the only one ; but our ignorance does not, as irt 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 ABC, ADE, AFG, are all eqilally followed by a, then a is an invariable f(':ascqaGntof A. If «ir, a.'tc, ({f^, all nunibcr A iimong their ante- cedents, then A is connected as an antecedent, by some invariable law, with a. But to detei-mine 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 any- thing, namely, an instance in which the effect, a, has come into exist- ence, with no other change in the preexisting 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 Agi-eement. 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 Agi-eement leads only to laws of phenomena, as Mr. Whewell calls thenx, but which (since laws of causation are also laws of phenomena) I prefer to designate as uniformities in which the ques- tion 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 com- parison of ABC, ADE, AFQ, suggested that A was the antecedent on which to try the experiment ^vhethe^ 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 Agi-eement, although applicable in principle to either case, is more emphatically the method of investigation on those subjects where arti- ficial expei-imentation is impossible ; because on those it is, generally, our only resource of a directly inductive nature ; while, in the phenome- na which we can produce at pleasure, the Method of Difference gene- rally affords a more efficacious process, which will ascertain causes as well as mere laws. § 4. Our next remark shall be, that there are many cases in which, although 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 Agi-eement. This occurs when the agency by which we can produce the phenomenon is not that of one single antecedent, but 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 pheijomenoai,,?it^ pleasure, by employing any one of the many substances which ire' 228 INDUCTION. known to refract light in tliat peculiar manner. But if, taking one of those substances, as Iceland spar for example, we wish to detcmiine on which of the properties of Iceland spar this remarkable phenomena depends, we can make no use, for that purpose; of the Method of Dif- ference ; 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 Agree- ment ; by which, in fact, through a comparison of all the known sub- stances Avhich had the property of doubly refracting light, it was ascer- tained that they agreed in the single circumstance of being crystaline substances ; and althoiigh the converse does not hold, although all crys- taline 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 crystaline 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 Agi'eement arises a pecu- liar modification of that method,.- which is sometimes of great avail in the investigation of jiature. 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 employ- ment 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 beais testimony to a connexion between A and a. In order to convert this proof 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 ABC, to leave out A, and observe whether by doing so, « is prevented. Now supposing (what is often the case) that. we are not able to try this decis\\'e experiment; yet, provided we can by any means discover what would be its result if we could try it, the advan- tage will be the same. Suppose, then, that as we previously examined a variety of instances in which a occuired, 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 innoi containing A; which establishes, by the Method of Agi-eeraent, the same connexion between the absence of A and the absence qf'aj 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 re- moved along with it, we bave by the one proposition ABC, abc, by .the other BC, ic, the positive and negative instances which the Method of Difference requires. Thus, if it be true that all animals which have a well-developed respiratory system, and therefore aerate the blood perfectly, agree in being warm-blooded, while those whose respiratory system is imperfect do not maintain a temperature much exceeding that of the surrounding medium, we may argue fi'om this two-fold expe- rience, that the change which takes place in the blood by respiration is the cause of animal heat. 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 indepen- THE POUR EXrERIMENTAL METHODS. 229 tleiit of the otlier, and corroborating it. But it is not ecjuivalcnt to a proof" by the direct JNIethod of Difleroncc. For the requisitions of the Method of Diffcreace are not satisfied, unless we can be quite sure either that the instances affirmative of a agree in no antecedent what- ever but A, or that the instances negative of « agi'ce in nothing but tlie 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 tke two sets of instances sepaiately would then be sufficient to prove causation. This indirect method, therefore, can only be viewed as a great exten- sion and improvement of the Method of Agreement, but not as partici- pating in the moi'e cogent nature of the Method of Diflerence. The tbllovving luay 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 sels of instances differ, is the effect, or cause, or a necessary ^tart of the cause, of the jihenomenon. We shall presently show that the Joint Method of Agreement and Difference constitutes, in another respect not yet adverted to, an im- provement upon the common Method of Agreement, namely, in being unatfected by a characteristic imperfection of that method, tlie 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 postJ)one it to the next 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 pi'inciple 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 elfeot of the antecedents which liad been overlooked, or of which the effect was as yet an unknown quantity. Suppose, as before, that we have the antecedents ABC, followed by the consequents a h c, and that by previous inductions, (founded, we will suppose, upon the ^Method of Dirterence,) 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 efiect of A is a, and that the effect of B is b. Subti-acting the sum of these effects from the total phenomenon, there remains c, which now, without any fresh experi- ment, we may know to be the effect of C. This Method of llesiddes is in ti-uth a peculiar modification of the Method of Difference. If the instance ABC, ahc, coidd have been compared with a single instance AB, ab, we should have proved C to be the cause of c, by the com- mon process of the Method of Diffei'ence. In the present case, how- ever, instead of a single instance A B, we have had to study sejjarately the causes A and B, and to infer from the effects which ihey produce 230 INDUCTION. separately, what effect they must 'produce in the case ABC where they act together. Of the two instances, therefore, which the Method of Difference requires — the one positive, the other negative — the nega- tive one, or that in which the given phenomenon is absent, is jiot 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 ob- tained by the same infallible method, and provided we are certain that C is the only antecedent to which the residual phenom.enon c-can be refeiTed ; 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 e\Hdence derived from the Method of Resiciues is not complete, unless we can obtain C ai-tificially and try it separately, or unless its agency, when once suggested, can be accounted for, and proved de- ductively, fi'om kno^vn 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 infonning us of sequences in which neither the cause nor the effect were su^ciently 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 Canox. Subduct from any phenomenon such part as is hnoicn by previous inductions to be the effect of certain antecedents^ aoid 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 inde- structible natural agents, which it is impossible either to exclude or to isolate : which we can neither hinder from being present, nor contrive that they should be present alone. It would appear at first sight that we could by no Tneans sepai-ate the effects of these agents fi-om 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 really due to the mountain; and beyond a certain THE FOUR EXrEKIMENTAL METHODS. 231 distance everything goes on precisely as it would do if the mountain exercised no influence whatever, which^ accordingly, we, with sullicient reason, conclude to be the tiict. ' The difliculty, therefore, in applying the methods already treated of to determine the eflects 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 fi-om the influence of the eart^h : •we cannot take away the earth from the ^)endulum, 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 evidfeuce, then, do we ascribe its vibrations to the earth's influence 1 Not on any sanctioned by the Method of Difference ; for t)ne of the tAVo instances, the negative instance, is wanting. Nor by the Method of Agreement ; for although all j)endulums 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 co- existent fact in all the experiments 1 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. Independ- ently 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 eflfect such a variation of circumstances as the foregoing three methods require; we cannot ascertain, by those methods, what por- tions of the phenomena exhibited by any body are due to the heat con- tained in it. If we could observe a bordy 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 Agi-eement ; or, if we pleased, 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 woidd be idle, for instance, to attempt to ascertain the effect of heat by subtracting from the phenomena exhibited by a body, afl 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 may fonn a part of the very results, which we affect to subtract in order that the effect of heat may be sliowii by the residue. If. therefore, there were no other methods of experimental investi- gation than these three, we should be for ever 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 232 INDUCTION. by a change in the consequent a, the other consequents h and c re- maining the same ; or, vice versCl, if every change in a is found to have been preceded by some modification in A, none being obsersable 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 quan- tity, we can increase or diminish it ; and doing so, we find by the va- rious methods of experimentation or observation already treated of, that such increase or diminution of heat is followed by expansion or conti-action of the body. In this manner we aiTive at the conclusion, otherwise unattainable by us, that one of the effectsof heat is to enlarge the diiTiensions 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 w'as, 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 teiTestrial phenomena her annihilation would put an end to ; but when we find that all the variations in the j)Ositio7i of the moon are followed by coiTesponding variations in the time and place of high water, the jilace being always either on the side of the earth which is nearest to, or on that which is most remote fi'om, 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 ah effect are coiTespondent, or anal- ogous, 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 indis- pensable 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 pei-pendic- ular 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 charactei-ized, that all terrestrial bodies tend to the earth, and not to some unkno^vn fixed point lying in the same direction. In every twenty-four hours, by the earth's rotation, the line dra\vn fi'om 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 tAvo hundred millions ofm.iles; yet in all these changes of the earth's posi- tion, the line in which bodies tend to fall continues to be directed to- wards it : which proves that teiTestrial gravity is directed to the earth, and not, as was once fancied by some, to a fixed point of space. run FOUR EXPERIMENTAL METHODS, 233 The metliotl by whicl'i tliese rosults were oLtaijied^ may he tevmcd the Method of Concomitant Variations : it is regulated by the I'ollow- " ing canon : — Fifth Canon. JV/iatcver inlienoinenon varies in any manner wJienever another phenotncnoji varies in some particu/ar manner, is cither a cause or an effect of that plienomcnon, or is connected with it tJirous^h 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, atid indeed must ha^^pen, supposing them to be two diHerent efi'ects of a common cause : and by this method alone it would never be possible to ascer- tain which of the two suppositions is the true one. The only way to solve the doubt would be that which we have so often adverted to, viz., -by endeavoring to ascertain whether we can produce the or;e 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 ; ou 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, \ye must endeavor, though it is an attempt which is seldom successful, to find them produced by nature in some case in which the preexisting 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 Avith variations in the caiuse, the same precautions must be used as in any other case of the determina- tion of an invariable sequence. We must endeavor to retain all the other antecedents unclianged, 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 generp^l, namely, that every modification of the cause is followed by a change in the effect. And it docs usually happen that when a phenomenon A causes a phe- nomenon a, any variation in the quantity or in the various relations of A, is unifoi-mly followed by a variation in the quantity or relations of a. To take a familiar instance, that of gi-avitation. 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 fi'om 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 gi'avitation, but that two of the relations of the sun, its position with re,-4pect 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 egp-th's gravita- G G 234 INDUCTION. ting at all, is simply tlie sun; but the cause of lier 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 modi- fied cause, which is in truth a different cause, should produce a differ- ent effect. But as the cause is only different in its quantity, or in some of its relations, it usually haippens that the effect also is only changed in its quantity or its relations. 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 upon whose modifica- tions, modifications of an effect are invariably consequent, must be the cause {or connected with the cause) of that effect; a proposition, the truth of vvhich 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 men, 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 Concomi- tant Variations take place in the cases in which the Method of Differ- ence, strictly so called, is impossible, its use is not confined to those cases ; it may often usefully follow after the Method of Diff'erenee, to give additional precision to a solution which that has found. When by the Method of Difference it has first been ascertained that a cer^ tain object produces a certain effect, the Method of Concomitant Va- riations 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 afiinn 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 coi-ollary from the principle of the Composition of Causes, which, as we have seen, is the general rule of causation; cases of the opposite descrijjtion, 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 j^roportional to the square of A. If, on the other hand, a is not wholly the effect o^" A, ■ but yet varies when A varies, it is probably (to use a mathematical THE FOUR EXrEHI.^IENTAL METHODS. iioO phrase) a function not of A alone but of A and something else : its changes will be such as woukl occur if part of it remained constant, or varied on some o.ber principle, and the remainder varied in some numerical relation t,> the variations of A. In that case, when A dimin- ishes, a will seem to approach not towards zero, but towards vsomc other limit : and when the series of variations is siicli as to indicate what that limit is, if constant, or the law of its vai'iation 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 drav/ing 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, detei'mine 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 that 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 can never be more than a gu6Ss, and of the most hazardous sort, not a legitimate induction; for since wc 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 u-s 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 object^;, when in motion, gradually abate their velocity and at last stop ; which accordingly the ancieiits, with their inductio per enumerationcm sim- pliccm, imagined to be the law. Every moving body, however, encounters various obstacles, as fi-iction, the resistance of the atmos- phere, &c., which we know by daily experience to be causes capable of destroying motion. It w^as suggested tlitit the whole of the retard- ation might be owing to these causes. How was this inquii*ed into ? If the obstacle^ could have been entirely retuoved, 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 accord- ingly being employed, it was found that every diminution of the obstacles diminished the retardation of the motion : and ina.s'much as in this case (unlike the case of heat) the total quantitie's 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 retard"- ation 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 fi-om a fixed point, and moved a little out of the 238 INDUCTIOiV. perpendicular, wliicli 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 susjjension, and by making the body oscillate in a Space exhausted as nearly as possible of its air. There could therefore be no hesitation in assign- ing the whole of the retardation of motion to tbe influence of the obstacles ; and since, after subducting this retardation from the total phenomenon, th© 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 infer- ence 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 uncer- tainty which enters largely into all our predictions of effects'; but it is Jiot peculiarly applicable to the Method of Concomitc^nt Variations. The uncertainty, however, of which I am about to speak, is character- istic 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 ^^■ho 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, be- comes appreciable. When, therefore, such variations in the quantity of the antecedents as we have the means of observing, are but small in comparison with the total qua:ntities, there is much danger lest we should mistake the numerical law, and be led quite 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, whidi could be founded upon those variations. Exam- ples are not wanting of such mistakes. "The formulae," says Sir John Herschel,* " 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 obsei-- vations from which they were deduced, " have almost invariably failed to support the theoretical structures which have been erected on them." Under this uncertainty j the conclusion we may draw froin the con- comitant 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 gi-eater or smaller than those whiqh we have had the means of observing, cannot be considered to rest upon 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 * Discourse on the Sludy of Natural Philosophy, p. 179, EXAMPLES OF THE TOUR METHODS. 237 the relation wlilcli wo liavo obsoivotl to exist betweeit the variations of A and a, will hold true in uU cases which fall between the same extreme; limits ; that is, wherever the ntnu)st increase or diminution in which the result has been found' by observation to coincide with thq law, is not exceeded. The four methods which it has now. been attempted to describe, arc tlie only possible modes of experimental inquiry, of direct induction d posteriori, as distinguished from deduction : at least I know not, nor am able to conceive, any others. And even of these, the Method of Residues, as\ve have seen, is not independent of deduction; though, as it retpures specific experience in addition, it may, without impropriety, be included among methods of direct observation and experiment. These, then, with such assistance as can be obtained from Deduction, co;mpose 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, accord- ingly, will form the subject of the succeeding chapter. CHAPTER IX. MISCELLANEOUS EXAMPLES OF THE FOUR METHODS. • ■ § 1. I SHALL select, as my first example, an interesting, speculation of one of the most eminent theoretical chemists of the present or any age, Dr. 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, point- ing out what property, common to all these deleterious &ubstances,. ia 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 sub- stance ; 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 quan- tity to destroy life, eschars are produced, tfiat is, certain superficial portions of the tissues are destroyed, which are afterwards thrown off by the reparative process taking jjlace in the healthy parts. 238 INDUCTION. These three sets of instances admit of being treated according to the Method of Agreement. lu all of them the metallic compounds are broii"-ht into contact with the substances which compose the human or animal body ; and the instances do not seem to agree in any other cir- cumstance. The remaining antecedents are as different, and even opposite, as they could possibly be made ; for in some the animal sub- stances 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 togetlier by so powerful a force as to resist the subse- quent action of the- ordinary causes of decomposition. Now organic lif(3 (the necessary condition of sensitive life) consisting in a- contlhiial state of decomposition and recomposition of the different organs and tissues ; whatever incapacitates them for this decomposition desti-oys life. And thus the proximate cause of the death produced by this, description of poisons, is ascertained, as far as the Method of Agree- ment can ascertain it. Let us now bring our conclusion to the test of the Method of Differ- ence. Setting out from the cases already mentioned, in which the antece- dent is, the presence of substances forming with the tissues a compound incapable of putrefaction (and u 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 of all, " many insolnble basic salts of arsenious acid are known not to be poisonous. The substance called alkargen, discovered by Bunsen, which contains a veiy 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 aixest their progi'ess to decomposition. As far, therefore, as these instances go, it appears that ^^-hen the effect is absent, it is by reason of the absence of that antecedent which we had already good gi'ound 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 vei-y same sub- stances, under cu'cumstances 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 foi-m a compound, which, being in- soluble, 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 sub- oxide, neither of which enters into combination with animal matter. EXAMPLES OF TUE FOUR METHODS. 239 The disease called painter's cqUc/ so common in manufactories of white lead, is unknown whpre the workmen are accu&tomed to take, as a preservative, sulphuric-acid-lemonade (a solution Of sugar ren- dered acid by sulphuric acid). Now diluted sulphuric acid has the property of decomposing all compounds of lead with organic matter, and (of course) of preventing them from being formed. There is another -class of instances, of the nature required by the Method of Pifference, which seem at first sight to conflict with the theory. Soluble salts of silver, such for instance as the nitrate, have the same stiftcning antiseptic effect on decomposing anifnal substances as corrosive sublimate and the most deadly metallic poisons ; and when applied to the external parts^of the body, tlie nitrate is a powerM criustic, depriv.inc" tho^o ports of rdl ertivo vitnlity/nnd musing thorn to be tlu'own otf by the neighboring 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 b^ ad- ' ministered "internally with perfect imj)unity. From this apparent exception arises the strongest confirmation which this theory of Liebig 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 org-anic actions. § 2. 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 neg- ative one which the rigor of that method requires, ought to differ only in the presence or absence of one single circumstance. Now, in the preceding argument, tliey differ in the presence or absence not of a sin- gle circumstance, but of a single substance : and as every substance has innumerable properties,, there is no knowing what number of real dif- ferences 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 proper- ties 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 in- stance. This source of uncertainty, which is a serious hindrance to all extensive generalizations in chemistry, is however reduced in tho 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 favor of the theory, all the evidence which can be ob- tained by what we termed the Indirect Method of Difference, or the Joint Method of Agreement and Difference ; the evidence of which, 240 IXDUCTION. though it. never can amount to that of the Method of Diffevence prop- erly so called, may approach indefifiitely near to it. No similar defect of completeness in proof will be found i'n the following Original investigation, for which I am indebted to ISIr. Alex- ander "Bain, at present Lecturer on Moral Philosophy in Marischal CoUeo^e, Aberdeen ; one of the men from whom science and philoso- phy have most to hope, and Avho has permitted me to lay his extensive knowledgeof every department of physical inquiry freely under con- tribution, for the purpose of exemplifying and illustrating the doctrines ofthis work..^ §■ 3. Let the object be to ascertain the law of what is termed hiduccd 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 familial- exemplification oPthe phenomenon to be investi- gated, is the following. Around the prime conductors of an electrical machine, the atmosphere to some distance, or any conducting surface suspended in. that atmosj)here, is ibund to be in an electric condition opposite to that of the prime conductoi- itself Near and around the positive prime conductor there is a 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 electiified with the opposite electricity to it ; either receiving a share from the alrfeady 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 opposi- tion; or, if withdrawn in their electrified state, they will be attracted by any other oppositely dafarged body. In like Inanner the hand, if brought near enough to the coiiductor, 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 elec- trified. In the case, therefore, of the electrical' machine, it apj^ears that the accumulation of electricity in an insulated conductor is always accompanied by the- excitement of , the contrary electricity in the sur- rounding atmosphere, and in exery 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 neighborhood of an electi'ified body. As one remai'kable 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 chai"*e 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 thoasand pieces, each piece will have its two oppositely electrified poles complete within itself In the voltaic circuit, again, we cannot have one cunent with- out its opposite. In the ordinary electric anachine, the glass cylinder or plate, aild the rubber, acquire opposite electricities. EXAMPLES OF THE FOUR METHODS. " 241 From all these instancesj treated by the Method of Agreement, a - general law appears to result. The instances -embrace all tlie known modes in whicli a body can become charged with electricity ; and in all of" thi'm tlicre is tbund, as a concx)mitant or consequent, the excite- ment ot* 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 neighboring body. As the two contrary electricities can only be produced together, so they can only cease together. Tliis may be sho\vn by an application of the Method of Difference to the example of the Leyden jar. It needs scai'cely be here remarked that in the Leyden jar, electricity can be accumulated and n^taincd in considerable quantity, by the con- trivance 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 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 elec- tricity, as the opposite surface of receiving and retaining the other : but in the machine, the neighboring 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 elcctrifiiMl, to the conductor itself, their lim- ited power imposes a corresponding limit to the capacity of the con- ductor for being charged. As the capacity of the neighboring body for supporting the opposition increases, a higher charge becomes pos- sible : and to this appears to be owing the great superiority of the Leyden jar. A further aiul most decisive confirmation by the Method of Differ- ence, is to be found in out; of Faraday's experiments in the course of his researches on the subject f)f induced electricity. Since common or machine electricity, and voltaic electricity, may be considered for the present pui-pose to be identical, Faraday wished to know whether, as the prime conductor develops opposite electri- city upon a conductor in its \icinity, so a voltaic cuiTent miming 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 cii'cumstance except the one to which Hh 242 INDUCTION. 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 neighboring body ; and the interpretation of this, in the language of cause and effect, is, that all causes which can excite the one kind of electricity, have the property of simultaneously exciting an equal amount of the other. 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 accommo- dated in one wire ; and there is no need of another wire placed be- side 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 neighboring body. Now the result of Faraday's 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 ap- peared when the two wires were moved to and from one another ; but these are phenomena of a different class. There was no in- duced electi-icity 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 cuiTent ran down the neighboring 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 Agree- ment, 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 maimer both characteristic and easily in- , telligible. § 4. Our third example shall be extracted from Sir John Herschel's Discourse on the Study of Natural Phil osopJiy, ViVfork Te^lete v/'ith. admirably selected exemplifications of inductive processes fi'om almost every department of physical science, and in which alone, of all books which I have met with, the four methods of induction are recognized, although not characterized and defined nor their correlation shown, so distinctly as has appeared to me desirable. The present example is justly 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 promul- gated by the late Dr. Wells, and now universally adopted by scien- tific men. The passages in inverted commas are extracted verbatim fi-om Sir John Herschel, * but to those who possess his work I would strongly recommend to read the entire passage in the original, and fully pos- sess themselves of the purport of the speculation as a whole, before applying themselves, with me, to the logical analysis of the different steps of the argument. * Discourse, pp. ISO — 162. EXAJIPLES OF TUK FOUR AIimiODS. 243 ■ " Suppose dew were tlie phenomenon proposed, w-liosc cause we woulJ know. In the first phice" we must determine precisely what we nicun 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 risible wet is falling." This answers to a preliminary operation which will be characterized in the ensuing book, treating of operations subsidiary to induction.* The state of the question being iixed, we come to the solution. " Now, here we have analogous phenomena in the moisture which bedews a cold metal or stone when wO breathe upon it ; that which appears on a glass of water fresh from the well in hot waather ; that which appears oil tlie inside of windows when sudden rain or hail chills the ext-ernal 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 1 " Is it a fact that the object dewed is colder than the air 1 Certainly not, one would at first be inclined to say; for what is to make it so 1 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 inva- riably 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 die 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 Agree- ment can afford us no light: we must call in a moi'e potent method. " That dews are accompanied with a chill is a common remark; but vulgar prejudice would make the cold the effect rather than the cause. We must therefore collect more facts, or which come& to the same thing, vary tlie circumstances ; since every instance in which the circum- stances differ is a fresh fact; and especially, we must note the contrary or negative cases, i. e., where no dew is produced :" for vyO are aware that 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."t Here is an instance in which the effect is pro- * Vide infra, book iv., chap. ii. On Abstraction, + This last circumstance (adds Sir John Herschel) " cxchides the fall of moisture from the sivy in an invisible form, which would naturally suggest itself as a cause." I have omitted this passage in the text, as not pertinent to the pilrpose in hand, the argument which it contains being deductive and h priori. The fall of moisture is rejected as a cause, because from its laws previously known, we inXer that it could not have produced the par- ticular phenomenon last mentioned 244 INDUCTION. duced, 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 circumstancea 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 recognize, 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 phenome- non; 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 obNaous. Those polished substances are found to be most strongly dewed which conduct heat worst ; while those which conduct well, resist dew most effectually." The compli- cation increases ; here is the Method of Concomitant Variations called to our assistance ; and no other metliod was practicable upon 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 cceteris jjaribus 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 ef the causes which assist in producing the deposition of dew upon the surface. " But if we expose rough surfaces instead of polished, we some- times find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner tlian varaished 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 stirfaccs which jiart 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 ca.teris 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 upon 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 finn textui-e, such as stones, metals, &c., as unfavorable, but those of a loose one, as cloth, wool, velvet, eider- EXAMPLES OF THE FOUR METHODS. 245 down, cotton, &(•., as eminently favorable 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 Hrm or absolutely loose. Looseness of texture, therefore, or something which is tho 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, there- fore, an induction (from fresh instances) simply curruhorative 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 rajjidly 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 fi-om the surface more rapidly than it can be restored from within. The instances, on the contrai-y, 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 sole difl'erence 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 aflibrded of this indirect method, and of the manner in which the data are prepared for it by the INIetliods of Agreement and of Concomitant Variations, is the most important of all the illustrations of induction afforded by this most interesting speculation. We might now consider the question, upon what the deposition of dew depends, to be completely solved, if we could be (juite sure that the substances on which dew is produced differ from those on which it i? not, in nothing but in the property of losing heat fi-om the surface faster than the loss can be repaired from within. And, although we never can have that complete certainty, this is not of so much import- ance as might at first be supposed ; for we have, at all events, ascer- tained that even if there be any other quality hitherto unobserved which is present in all tlie substances which contract dew, and absent in those which do not, this other pr(»perty must be one which, in all that great number of substances, is present or absent exactly where the property of being a better radiat(;r than conductor is present or absent ; an extent of coincidence which af!brds the strongest 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 accom- panies the cause, and for purposes of prediction, no ciTor will bje committed by treating it as if it were really such. Reverting now to an earlier stage of the inquiry, let us remember that wo had ascertained that, in every instance where dew is formed, there is actual coldness of the surface below the temperature of the fiurrounding air; but we vieve not sure whether this coldness was the 246 INDUCTION. 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 siairounding air. But if the dew were the cause of the coldness, that effect would be produced in other substances, and not solely in those whose own laws suffice to produce it whether there were dew or no. That supposition, therefore, is repelled. But there were only three suppositions possible ; the dew is the cause of the coldness ; both are caused by some third circumstance ; or the coldness is the cause of the dew\ The first is refuted. The second is inapplicable : the cause of the coldness is a known cause ; a radiation from the surface greater than can be supplied by conduction : now this, by its known laws, can produce no direct effect except coldness. There remains only the third supposition, that the coldness is the cause of the dew : which, therefore, may be considered as completely made out. This law of causation, already so amply established, admits, how- ever, of most efficient additional corroboration in no less than three vvays. First, by deduction from the known laws of aqueous vapor when diffused through air or any other gas ; and although we have not yet come to the Deductive Method, we will not omit what is neces- sary to render this speculation complete. It is known by direct exper- iment that only a limited quantity of water can remain suspended in the state of vapor at each degi-ee of temperature, and that this maxi- mum grows less and less as the temperature diminishes. From this it follows, deductively, that if there is already as much vapor suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapor to be condensed and become water. But, again, we know deductively, from the laws of beat, 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 gravita- tion or cohesion, attach itself to the surface of the body, thereby con- stituting 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 cxcejytions 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 imdersupplied with aqueous vapor, comparatively to its temperature, that even when some- what cooled by the contact of the colder body, it can still continue to hold in suspension all the vapor 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 produc- tion of dew, which the methods we previously made use of failed to detect, and which might have remained still undetec*ted, 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, accoi-ding to the canon of the Method of Difference. We can, by cooling the surface of anybody, 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. EXAMPLES OF THE FOUR METHODS. 247 Here, too, therefore, the causation is directly proved. We can, it is true, accomplish this only on a small scale ; hut we have ample I'eason to conclude that the same operation, if conducted iu JSTature's great laboratory, would equally produce the elVect. 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 ji^to the. previous state of things a single and pcrfec;tly definite new circumstance, and manifest- ing the ett'ect so rapidly that there is not time for any other material change in the preexisthig circumstances. Let us quote again Sir John Horschel : — " 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 \f the clouds ivithdraiv even for afow viiinitea, and have a clear opening, a deposition of dew presently begins, and goes on increas- ing 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 communi- cation 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 iluid, tliat 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 con- sequent follows accordingly : a natural experiment which satisfies the. requisitions of the Method of Difference.* The accumulated proof of which the Theory of Dew has been found susceptible, is a striking example of the fullness 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. It is unnecessary to subjoin Sir John Herschel's summary of the result, as it does not contain all the ])roofs which I have given, and our more detailed analysis of each step of the process renders such a recapitula- tion unnecessary. § 5. This admirable 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 * I must, however, remark, that this example, which seems to militate against the asser- tion we made of the comparative inapplicabihty of the Method of Difference to cases of pure observation, is really one of those exceptions which, according to a proverbial expres- sion, prove the general rule. For, be it observed, in 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 jihenomcnon, lie does so by employing com- plex means, which he is unable (lerfectly to analyze, and can form, therefore, no sutlicient judgment what portion of the ctlects 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 experi- ment 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 upon what it depends, to be certain a priori that it might not operate upon the deposition of dew inde- pendently of any thermometric effect at the earth's surface. Fhen, therefore, in a case so fkvorable as this to Nature's experimental talents, her experiment is of little value except ia corroboration of a conclusion already attained through other means. 248 INDUCTION. inquiry, as to supersede the necessity of any further exemphfication 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 eflects 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 agree- ment of its calculated with its obsei-ved 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 suflficient cause of all the phenom- ena of its orbitual motion : but when the effect of this cause is strictly calculated and subducted from the obsei'ved 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 actiially 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 Terce causm''^ (antecedents known to exist) " why it sJiould 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 fiilk thread. But the effect of these causes being exactly known by the observation made in the absence of the copper, and behig 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, how- ever, 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 coj^per. To have made it exemplify the Method of Res- idues, the effect of the resistance of the air and that of the rigidii^, of the silk should have been calculated d jjriori, fi-om the laws obtained by separate and fcu'egone experiments. " Unexpected and peculiarly striking confirmations of inductive laws frequently occm- 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 KXAMTLES OF THE FOUR METHODS. 249 of souiul. Tlu' iiKjuirv into tlio cause of soiiiul had led to coiielusioiis respecting its mode of propagation, from which its vehxity in the aix* couhl he precisely calculatecl. The c^dculations were performed; but, when compared with fact, though the agreement was quite suffi- cient to show the general cttrrectuess of the cause and mode of propa- gation assigned, yet the loholc velocity could not be shown to arise from this theory. There was still a residuid 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 condensa- tion which necessarily takes place at every vibration by which sound is conveyed. The matter was subjected to e.xact calculation, and the result was at once the complete explanation of the residual phe- nomenon, and a striking confirmation of the general law of the devel- opment 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 j)roduced from a small portion of what he considered as magnesia present in a mineral he had analyzed. It is on this principle, too, that the small concen- trated residues of great operations in the arts are almost sure to be the lurking places of now chemical ingredients : witness iodine, brome, selenium, and the new metals accompanying platina in the expeiu- ments of Wollaston and Tennant. It was a happy thought of Glauber to examine what everybody else threw away."* The disturbing effects mutually produced by the earth and planets upon each other's motions were first brought to light as residual phe- nomena, by the ditference 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 deter- mined philosophers to consider the law of gravitation as obtaining be- tween 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 Vvhose system it belonged. Again, the catastrophists, in geology, be their opinion light or wrong, support it upon 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 : if it be possible to establish, what is generally rather as- sumed than proved, that there is in one human individual, one sex, or one race of mankind over another, an inherent and inexplicable supe- riority in mental faculties, this must bo proved by subtractingfrom the differences of intellect which we in fact see, all that can be traced by known laws either to the ascertained differences of physical organiza- tion, or to the differences whi<;h have existed in the outward circum- stances in which the subjects of the comparison have hitherto been placed. Wliat these causes might fail to account for, would constitute a residual phenomenon, which and which alone would be evidence of * HERsCHEr., ul supra, pp. 78-9, and 86. I I 250 INDUCTION. an ulterior original distinction, and the measure of its amount. But the strongest assertors of- such supposed differences have hitherto been very negligent of providing 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. CHAPTER X. OF PLURALITV 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 neces- sary 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 our- selves, therefore, every effect, on the one hand as connected exclu- sively with a single cause, and On the other hand as incapable of being mixed and confounded with any other coexistent effect. We have re- garded ahcdc, the aggregate of the phenomena existing at any mo- ment, as consisting of tlissimilar 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 fi-om the multitude of antecedent circum- stances, A,B, C, D, and E. If such were the fact, it would be comparatively an easy task to in- vestigate 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 phe- nomenon 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 hornogeneous, and marked out by no assignable boundaries fi-om one another : A and B may produce not a and h, 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 cir- cumstances ; 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 ti'ue, then, that one effect must be connected with only one cause, or assemblage of conditions ; that each phenomenon can be pro- duced 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 ante- cedents. Many causes may produce motion ; many causes may pro- PLURALITY OF CAUSES, 251 duce some kinds of sensation : many causos 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 tirst of our inductive riiethods, that of Agree- ment, uncertain. To illustrate that method, we supposed two instances. A B C followoil by a h r, and A J) 1^] followed by (? d c. From these in- stances it miirht be concluded that A is an invariable antecedent of o; 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 staml 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 tin* possibility of a plu- rality of causes, the conclusion fails. For it involves a tacit suppo- sition 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 ha\'ing no influence in either case. Suppose, for example, that two great artists, or great philosophers, that two extremely selfish, or extremely generous charactei-s, were compared together as to the circumstances of ;their education and his- tory, and the two cases were found to agree only in one circumstance": would it follow that this one circuriistance was the cause of the quality which characterized both those individuals ? Not at all ; for the causes at work to produce any given type of character are innumer- able ; and the two persons might equally have agreed in their char- acter, although there had been no manner of reserabhmce in their previous history. This, therefore, is a characteristic imperfection of the INIethod of Agreement ; from which imperfeciion the Method of Difference is fre^. For if we have two instances, ABC and BC, of which BC gives be, and A being added converts it into a he, it is certain that in this instance at least A was either the cause of a, or an indispensable portion of its cause, even thoui^h the cause which produces it in other instances may be altogether different. Plurality of Causes, therefore, not only does nf»t diminish the reliance due to the Method of Difference, but does not even render a greater number of obstjrvations or experiments necessary : two instances, the one positive and the other negative, are still suffi- cient 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 suggestione, 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 accpiires any high degree of independent value. If there are but two instances, ABC and ADE, although the-se 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 proba- bility in favor of A ,• there may be causation, but it is almost equally 252 INDUCTION. probable that there was only, as the expression is, 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 AFG, AHK, &c., all entirely 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 in- stances. With each addition, therefore, to the number of instances, the presumption is strengthened in favor oi A. The inquirer, of course, will not neglect, if an opportunity present itself, to exclude A from some one of these combinations, from AHK for instance, and by trying H K separately, appeal to the Method of Difference in aid of the Method of Agreement. By the former method 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 gi-eat a multiplication, then, of varied instances, all agree- ing in no other antecedent ex<;ept 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 here- after. 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 imperfec- tion. 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 resthig contented with the results obtained by it, without attempting to confirm tliem either by the Method of Difference, or by coimecting them deductively with some law or laws already ascertained by that superior method. And, in the second place, we leaj-n from this, the true theory of the value of mere number of instances in inductive inquiry. The tendency of unscientific inquiries is to rely too much upon number, without analyzing the instances ; without looking closely enough into their nature, to ascertain what circumstar^ces 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 expe- rience on which they appear to rest : not considering that by the addi- tion of instances to instances, all of the same kind, that is, differing from, one another only in points already recognized 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 cir- PLURALITY OF CAUSES. 253 cumstanccs 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 AE^recmcnt which, as partaking in some degree of the na- ture of the Method of Diff'ercnce, 1 have called the Joint Method of Agi'eement and Dift'ei-ence, is not afi'ected by the characteristic imper- fection 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 instaTices in which a is not, agi-ee oidy in not contain- ing 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 advan- tage 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 fi-ee 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 witli it. But although this is true in principle, it is gen- erally altogether impossible to work the Method of Agreement by negative instances without positive ones : it is so much more diffi- cult 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 1 But we might hope much sooner to seize some point of resemblance among the comparatively few and definite species of objects which arc transparent ; and this being attained, we should quite naturally be put upon examining whetlKU- the ab- sence 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 Diffijrence, therefore, or, as I have otherwise called it, the Indirect Method of Difference (be- cause, like the Method of Difference properly so called, it proceeds by a.scertaining how and in what the cases where the phenomenon is present, difter from those in which it is absent) is, after the direct Method of Difference, the most powerful of the remaining instru- ments of inductive investigation • and in the sciences which depend on pure obscr\-ation, with little or no aid from experiment, this method, so well exemplified in the beautiful speculation on tin; cause of dew, is the primary resource, so far as direct appeals to experi- ence are concerned. § 3. We have thus far treated Plurality of Causes only as a possible supposition, which, until nnnoved, renders our inductiolis 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 con- sider it as a case actually occurring in nature, and which, as often as 254 INDUCTION. it does occur, our methods of induction ought to be capable of ascer- taining 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 ob- Bervationfj or experiments shows that the sun is a cause of heat, another that friction is a source of it, another tliat percussion, another that elec- tricity, 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 cu-cumstance in which they all agi'ee, and fail in doing so. We find it impossible to trace, in all the cases in which the effect is met with, any common circiuustance. 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 anal- ysis, 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 cir- cumstance in them all. Thus it might, andperhaps 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 hap- pens) we cannot take this ulterior step, the different antecedents must be set down as distinct causes, each sufficient of itself to produce the effect. We may here close our remarks on the Plurality of Causes, and pro- ceed to the still more peculiar and more complex case of the Intermix- ture 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 tJre most pait, as will appear presently, quite unequal to cope. The instrument of Deduction alone is adequate to unravel the com- plexities proceeding from this source ; and the foiu' methods have httle more in their power than t© supply premisses for our deductions. § 4. A concuiTence of two or more causes, not separately producing each its own effect, but intei^fering with or modifying the effects of one another, takes place, as has already been explained, in two different ways. In the one case, which is exemplified by the joint operation of different forces in mechanics, the separate effects of all the causes con- tinue to be produced, but are compounded with one another, and dis- apfjear in one total, ' In the other case, illustrated by the case of chem- ical 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 sub- stances, hydrogen and oxygen, on being brought together, throw off their peculiar properties, and produjce the substance called water ; in such cases the new fact may be subjected to experimental inquiry, like INTERMIXTURE OF EFFECTS. 255 any other phenomenon ; and the elements which arc said to compose it may be considered as the mere agents of its production ; the condi- tions on which it depends, tlie facts which make up its cause. Tlie ejects of th(> new phenomenon, the j^rojfertics of water, for in- stance, are as ^easily found by experiment as the effects of any other cause. But to discover the cause of it, tliat is, the particular conjunc- tion of agents from which it resuUs, is often difficult enough. In the first place, the origin, and actual production of the phenomenon, is most freqdently inaccessible to our ol)servation. 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 experi- mentation on oxygen ^nd hydrogen separately, no knowledge of their laws, could have enabled us deductively to infer that they would pro- duce 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 incjuiry directed specifically towards that end, but either to accident, or to tho gi'adual progress of experimentation on the different combinations ot which the producing agents are susceptible ; if it were not for a pecu- liarity belonging to effects of this description, tliat they often^, under some particular combination of circumstances, reproduce their causes. If water results from the juxtaposition of hydrogen and oxygen when- ever this can be made sufficiently close and intimate, so, on the other hand, if water itself be placed in certain situations, hydrogen and oxy- gen are repi'oduced from it : an abrupt termhiation is put to the n6w laws, and the agents reappear separately with their own properties as at first. AVliat is called chemital 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 Ted precipitate, while the au:, on being examined after the experiment, proved to haye 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 theit 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 irou 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: tho iron we ourselves supplied, but the oxygen must have been produced from the water. The result there- fore is that the 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 superinduption of the new-laws called the properties of water, have again started iijto existence, and the causes of water are found among its effects. 256 INDUCTION. Where tvvo plienomena, between the laws or properties of which considered in themselves no connexion can be traced, are thus recipro- cally 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 fi-ora oxygen and hydrogen, and oxygen and hydrogen are reproduced from water); this causation of the two pbenonlena by one another, each of them being generated by the .other's destruction, is properly ti-ansfonnation. The idea of chemical composition is an idea of transfomiation, but of a transfonnation which is incomplete ; since we consider the oxygen and hydrogen to be present in the water as oxygen and hydrogen, and- capable of, being discx)vered in it if our senses were sufficiently keen : a supposition (for it is no more) grounded solely upon 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 fi-om 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) 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 ajiplicable. 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 gi'ow 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 ^eiierated, 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 com- binations 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 confonns in its separate state, would have presented fewer difficulties to the inductive inquirer than that of which we have just INTERMIXTURE OF EFFECTS. 257 fiiiislieJ the consideration. It presents, however, so far as direct in- duction apart from deduction is concerned, iniinitoly grtiater diillc id- ties. Wlien a concurrence of causes f^ives rise to a new effect bearing no relatioa to the separate effects of tliosc causes, the resulting phe- nomenon at least stands forth undisguised, inviting attention to its peculia^'ity, and presenting no obstacle to (»ur recognizing its pi'esence or absence among any number of surrounding phenomena. It admits therefore of being easily brought under the canons of induction, pro- \ided 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 homoge- neous 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 dis- cernible; they are -\- a, — a, ^ b, — b, 2 b, Sec, 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 lixeil 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 appa- rently frustrate or modify one another's operation, yet in reality all are fulfilled, the collective effect being the exact sum total of the effects of the causes taken separately. A familiar instance is that of a body kept in equilibrium by two equal and contrary foixes. One of the forces if acting alone would carry it so far to the west, the other if acting alone would carry it exactly as far towards the cast : 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 caiTy 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 cjpposite to theirs, or more or less incon- sistent with it. And hence, with almost every law, many instances in which it really is entirely fulfilled, do not, at first siglit, 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 ofthe effects of two causes of motion may be rest. Again, a bcjdy 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 flhe sum of two motions in two other lines. Motion, however, is but changes of place, and at every instant the body is in the exact place it would have been in if the forces liad 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 eaeh uistant, Kk 258' INDUCTION. 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 compoimd their effects may be treated as if they produced simultane- ously 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 pi'oportioned to the force directly, and to its o^vn 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, fi-om the very first, retarded by the action of gravity and other resisting forces, and at last stopped altogether ; it is clear that the general propo- sition, although it would be true imder a certain hypothesis, would not express the facts as they actually occur. To accommodate the expres- sion 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 equiva- lent 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, the 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 fbund 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 coiTectly indicated by the expression tentlcncy. 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 w'or'ds which signify a tendency to the , particular effect with which the science is 'conversant ; thus j)resst/rc, in mechanics, is synonymous with tendency to motion, and forces are not reasoned upon as causing actual motion, but as exerting pressure. A similar improvement in terminology would be very salutary in many other branches of science. Tlie habit of neglecting this necessary element in the precise ex- pression of the laws of nature, has given birth to the popular prejudice INTERMIXTURE OF EFFECTS. 259 that all general truths have exceptions ; and much unmerited distrust has thence accrued to the conclusions of philosophy, when they have been submitted to. the judgment of persons who wei-.e not philosophers. The rough generalizations suggested by common observation usually have exceptions ; but the principles of science, or in other words, the laws of causation, have not. " What is thought to be a,n exception to a princi})le," (tii quote words used on a difterent occasion,) " is always some other and distuict principle cutting into the former ; some other force which impinges against the first force, and deflects it from its direction. Therd are not a law and an exception to that l,aw, the Itivv acting in ninety-nine cases and the exception in one.. There are two laws, each possibly acting in the whole hundi'cd cases, ai\d bringing about a common effect by their conjunct oj)ei'ation. If tl>c foixc which, being the less conspicuous of the two, is called the dhturhing 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 prqbably acts as a modifying cause in many other cases which no one will call exceptions. . " Thus if it wei'e stated to be a law of nature that all heavy bodies , fall to the ground, it wx)uld 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 excep- tion, 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 gravita,tion is", be said to prevail over the law ; but its disturbing effect is quite as real in evej-y other case, since, though it does not prevent, it retards th6 fall of all bodies whatever. The rule, and the so-called exception, do not divide the cases between them ; each of thern is a comprehensive rule extending to all cases. To call one of these c(»ncurrent principles an exception to the other, is super- ficial, 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 docs not exist another cause preponderating over it." § G. 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 eflect to the concurrence of causes in which it originated, and ascertain the conditions of its recurrence, the circumstances in which it may be expected again to occur. The conditions of a phenomenon \vhich arises from a com- position of causes, may be investigated '. either deductively or experi- mentally. 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 vosteriori method, professes to proceed according to the canons of •260 INDUCTION. experimental inquiry. Considering the whole assemblage of con- cun-ent causes which produced the phenomenon, as one single cause, it attempts to ascertain that cause in the ordinary manner, by a com- parison 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 noiethod 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 favorite maxim of Lord Chan- cellor 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 a,s 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 condi- tions of health and disease in the human body ; or (for greater simpli- city), the conditions of recovery fi-om a given disease ; and in order to nan-ow the question still more, let it be limited, in the first instance, to this one inquiry: Is, or is not some particular medicament (mer- cury, 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, tempera- ment, and other peculiarities of bodily constitution, the particular form or variety of the disease, the particular stage of its progi'css, &c., re- marking 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 h^d hot. § 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 real 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 possi- ble 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 gene- ralization can we, in a case of this desci'iption, hope to obtain. The reason is that which we have so often spoken of as constituting the INTERMIXTURE OF EFFECTS. 261 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 teqd to cure it, that there are sure to be abundant instances of recovery in which mercury lias 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 iuilure. When an effect results from the union of many causes, the Bhare 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 very exactly any onp. of the causes. Recovery from a disease is an event to which, in every case, many inffu- ences must concur. Mercury may be one such influence ; but, from the Very fact t^iat there are many other such, it will- necessarily happen that although mercury is administered, the patient, for want of other concurring influences, will oft(>n not recover, and that he often will recover when it is not administcu'ed, the other favorable influences being sufficiently powerful v/ithout it. Neither, therefore, will the instances of recovery agree in the adtainistration of mercury, nor will the instances of failure agree in the non-administration of it. It is much if, by multijilied 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 tlueory of the subject. § 8. The inapplicability of the m.ethod of simple observation to ascertain the conditions of effects dependent on many concurring causes, being thus recognized ; we .shall next hiquire whether any greater benefit can bo 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 qffect : 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 fi-om 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 may be successful although the former must necessarily fail. 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 (sverything 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 as(jcrtain the general laws of its- action upon the human body, anore easy physical sciences. Such rensoners ignore the fact of Plurality of Causes in the very case which aff'ords the most signal eiiample of it. So little could be con- cluded, 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 induc- tive 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 definite circumstance. The nearest approach to an experiment, in the philo- soj)hical sense, which takes place in politics, is the introduction of a new operative element into national affairs by some special and assign- able measure of government, such as the enactment or repeal of a particular law. But, where there are S(j m^ny influences at wol-k, 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 Ix^fore the cjffect of a new cause becomes conspicuous enough to bo a subject of induction, so many of the other influencing circumstance^ will have changed as to vitiate the experiment. Two, therefore, of the three possible methods for the study of phe- 264 INDUCTION. notnena resulting from the composition of many causes, being from the very nature of the case, inefficient and ilkisory ; there remains only the third — that which considers the causes separately, atid 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 it8el£ CHAPTER XI. OF THE DEDUCTIVE METHOD. § 1. The mode of investigation which, from the proved inapplicability of direct methods of observation ahd experiment, remains to us as the mahi source of the knowledge we possess, or can acquire, respecting the conditions, and laws of recuiTence, of the more complex phenom- ena, 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 deduc- tion 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 upon 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 phenom- ena ; and those causes are human actions, together with the general outward circumstances under the dominion of which mankind are placed, and which constitute man's position in this, world. The -De- ductive 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 a,lways, and necessarily have been ob- tained 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 te this process of study, may or may not be difficult. In the case last mentioned, this first condition is of easy fulfilment. That social ph&. nomena depended upon the acts and mental impressions of humaij THE DEDUCTIVE METHOD, 2G5 beings, never could have been a matter of any doubt, however imper- fe<'tly it may have been known either by what laWs those impressions and actions are governed, or to what social consi;quences their laws naturally lead. Neither, again, after physical science had attained a certain development, coidd there be any real doubt where to look for the laws on which the phenomena of life dejiend, since they must be the mechanical and chemical laws of the solid and fluid sul>stances composing the orgaiiized body and the medium in which it subsists, together with the peculiar vital laws of the diflcrent tissues constituting the organic structure. In other cases, really ftir more simple than these, it was much less. obvious in what quarter the causes were to be lookfd for : as in the great case of the celestial phenomena. Until, by comi)ining the laws of certain causes, it ^vtl3 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 7ccrc 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 tjic conditions of the effect. The mode of ascertaining these laws neither is, nor can be, any other than the fourfold method of experimental inquiry, already dis- cussed. 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 fotces. Even where the tendency is not, in the ordinary sense of the word, counteracted, but only modified, by having its effects comjiounded with the effects arising from some other tendency or tendencies, we are still in an imfavorable position for tracing by means of such cases, the law -of the tendency itself It would have been difficult to dis- cover 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 aftbrded 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 fbr. AccordinglyT^n the cases, unhappily very numerous and important, in which the caiises do not suffin- 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 conspicuous in the case of physiological phenomena ; it being impossible to separate the different agencies which collectively compose an organized body, without destroying the very phenomena which it is our object to investigate : following life, in creatures we dissect, We lose it, in the nioment we detect. 266 INDUCTION. And for this reason I am not quite prepared to agree with M.Cornte, in deeming the scienpe of society and government intrinsically a more difficult study than the science of organic and animal life. I cannot but incline to the opinion, that physiology is embarrassed by gi-eater natural difficulties, and is probably susceptible of a less degree of ultimate perfectipn, than the social science; 'inasmuch as it is possible to study the laws of one man's mind and actions apart from otlier men, much less imperfectly than we can study the laws of one organ or tissue df the human body apart from the other organs or tissues. It is profoundly remarked by M. Comte, that pathological facts, or, to speak in common language, diseases in their different forms and degrees, afford in the case, of physiological investigation the nearest equivalent to experimentatipn 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 the parts of the organic economy, there can be no prolonged disturbance in any one fimction without ultimately involving many of the others ; and when once it has done' so, the experirnent for the most part loses its scientific value. All ■depends upon observing the early stages of the derangement; which, unfortunately, are of necessity the least marked, Ifj 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 tvas 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 wliich 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 Qause. 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 exjjeriments are best tried, not in a state iSf disease, which is essentially a changeable state, but in the condition of. health, coxa- paratively a fixed state. In the one, unusual agencies are at work, the results of which we have no means of predicting ; in the otlier, the course of the accustomed physiological phenomena would, it may generally be presumed, remain undisturbed, were it not for the dis- turbing cause vvhich we introduce. Such, with the occasional aid of the method of Concomitant Varia- tions (the latter not less encumbered than the more elementary methods, by the peculiar difficulties of the subject), are our indue- THE DEDUCTIVE METHOD. 207 live, resources for ascertaiuing the laws of the causes considered sepa- rately, 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 ex])lain, nor could, without specilic experience, have predicted many of the facts which are certified to us by the most ordinary observation. Fortunately, wc are much better informed as to the empirical laws of the phenomena, that is, the unifonnities respecting which we cannot yet decide whether they are ■^cases of causation or mere results of it. Not oidy has the order iij ■which the facts of organization and life successively manifest them- selves, from the first genu of existence to death, been found to be uni- foiTn, and veiy accurately ascertainable ; but, moreover, by a great application of the Method of Concomitant Variations to the entire facts of comparative anatomy and physiology, the conditions of or- ganic structure corresponding to each class of functions have been determined with considerable precisiori.* Whether these organic conditions are the whole of the conditions, and whether they be con- ditions at all, or mere collateral effects of some common cause, we are quite ignorant : nor are we ever likely to know, unless we could con- struct an organized body, and Irj whether it would live. Under §uch disadvantages do we, in cases of this description, at- tempt 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 calise was not intermixed or interfered with, or not to any gieat extent, by other causes whose laws wcie unknown. And only when the induction which furnished the prem- isses to the Deductive Method rested upon 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. ^Vhen the lavvs of the causes have been -ascertained, and the first stage of the gi-eat logical operation now under discussion satis- factorily accompKshcd, the second parj, follows; that of determining, from the laws of the causes, what eflect any given combination of those causes will prod'uce. 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 celebrated problem of throe bodies gravitating towards one ♦ This great philosophical operation' has been admirably characterized in the third vol- ume of M. Comte's truly encyclopedical work. 268 tNDUCTION. another, witli 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 anything more than an approximate general solution. In a case a little more complex, but still one of the simplest w^hich arise in practice, thajt of the motion of a projectile, the causes which affect tlie velocity and range (for example) of a cannon-ball may be all known and estimated ; the force of the gunpowder, the angle of eleva- tion, the density of ..the air, the strength and direction of the sound; but it is one of the most difficult of all mathematical problems to combine all these, so as to determine the effect resulting from their collective action. i Besides the theorems of nvimber, 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 influ- ence of so many and such shifting causes as to give no room either for fijXed 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 the ratiocination from a general law to a particular case, that is, the determination, by means of the particular circum- stances of that case, what result is required in that instance to fulfill the law. Thus, in the Torricellian experiment, if the fact that air had weight had been previously kno^yn, it would have been easy, without any numerical data, to deduce from the general law of equilibrium, that the .mercury W^ould 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, eqiiilibrium 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 ques- tions: Given a certain combination of causes, what effect will follow] and, What combinatioTn of causes, if it existed, would produce a given effect ] Tti the one case, we determine the effect to be exj>ected in any complex circumstances of which the different elements are known : in the other case we learn, according to what law — -under what ante- cedent conditions — a given complex effect will recur. § 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 1 When in every single instance a multitude, often an unknown multitude, of ag'encies, are clashing and combining, what security have we that in our computation a priori we 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 THE DEDUCTIVE METHOD. 269 of each, — a condition in most cases not to be fulfilled ; and even when fulfilled, to niaki; the calculation transcends, in any but very simple cases, the utmost power of mathematical science with its most modem improvements. lliese objections truly have much weight, and would be altogether unansweiable, if there were no test by which, when we employ the Deductive Metlunl, we might judge whether an error of any of the abt)ve di'scriptious had been committed or no. 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 upon the general conclusions arrived at by' deduction, these conclusions must be found, on a careful com- parison, 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 ti-ust 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 combi- nation 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 la^vs : 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 hut c^\6t 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 pf the causes of the celestial motions, that it should lead by deduction to Kepler's laws: which, accordingly, the Newtcniian theory did. In order, therefore, to facilitate the verification of theories obtained by deduction, it is important that as many as possible of th^ empirical laws of the phenomena should be ascertained, by a comparison of in- stances, conformably to the Method of Agreement : as well as (it must be added) that the phenomima themselves should be. described, in the most comprehensive as well as accurate manner possible ; by collect- ing from the observation of parts, the simplest possible correct expres- sion for the corresponding wholes: as when the series of the observed places of a planet was first expressed 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 analyze 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 I3.W from com- 270 INDUCTION. plex 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 us to discover. It is a new trial of the principle in a different set of circumstances ; and occasionally serves to eliminate some cir- cumstance not previously excluded, and to effect the exclusion of which, might require an experiment impossible to be executed. This was strikingly conspicuous in the example formei'ly quoted, in which the difference between the observed and the calculated velocity of sound was ascertained to result from the heat extricated by the con- densation 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 certainly added materially to the proof of the uni- versality 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 men to attach rather too much value than too little. To the Dedvictive Method, thus characterized in its three constituent parts. Induction, Ratiocination, and Verification, the human mind is indebted for its most glorious triumphs in the investigation of nature.. To it we owe all the theories by which vast and complicated phenomena are embraced under a iew simple laws, which, considered as the laws, of those gz-eat 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 (ex- cept 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, only four different agents on the concurrence of which the motion's of that body depend ; a much smaller number, no doubt, than that by which any other of the gi'eat phenom- ena of nature are determined or modified. Yet how could we ever ha,ve ascertained the combination of forces upon 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 con- currence of causes ; although the periodical recurrence of exactly the same effect, affords positive proof that all the combinations of causes which occin- at all, recur periodically ; we -should never 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 analyze, 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. EXPLANATION OP LAWS. 271 CHAPTER XII. OF THE EXPLANATION OF LAWS OF NATUR6. § 1. The Jetluctive 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 he undertaken either for the purpose of discovering the law, or of explaining a law already discovered. The word es-planat'ion occurs so continually, and holds so important a place in philosophy, that a little time spent in fixing the meaning of it will he profitably em- ployed. 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 aheap of combus- tibles. And in a similar manner, a law or uniforrnity 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 acusation may be explained from, or, as it also is often ex- pressed, 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 effect 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 miiform motion in the tangent, and the law of the centripetal force, which tends to pro- duce 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 ele- ments. It is resolved into the laws of the separate causes, together with the fact of itheir coexistence. The one is as essential an ingredi- ent as the other ; whether the object be to discover the law of the effect, or only to explain it. To deduce tKe laws of the heavenly motions, we require not only to know the law of a rectilineal and that of a grav- itative force, but the existence of both these forces in the celestial regions, and even their relative ajnoimt. The complex laws of causa- tion 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 upon it at such alenj^th as dispense^ with the necessity of further insisting iipon it here. The first mode, then, of the explanation of Laws of Causation, is when the law of an effect is resolved into the va- rious tendencies of which it is the result, and into the laws of those tendencies. 272 INDUCTION. § 3. A second case is when, between what seemed the cause and what was supposied to be its effect, further observation detects an in- termediate hnk ; a fact caused by the antecedent, and in its turn caus- ing 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: man- kind 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 9. 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, prop- erly speaking, but the cause of the cause : the real cause of the sensa- tion 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. Hitherto, however, no such inter- mediate agency 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 upon contact with an object, is ascertained not to be an ultimate law ; is resolved, as the phrase is, into two other laws — the law, that contact with an object produces an affection of the neiTe ; and the law, that an affection of the nerve produces sensation. To take another example : the more powerful acids corrode or black- , en organic compounds. This is a case of causation, but of remote causa- tion ; and is said to be explained when it is shown that there is an inter- mediate 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 coloring mat- ters (whence its efficacy in bleaching), and purifies the air from infec- tion, .This law is resolved into the two following laws. Chlorine haa a powerful affinity for bases of all kinds, particularly metallic bases and hydrogen. Such bases are essential elements of coloring matters and contagious compounds ; whicli substances-, therefore, are decom- posed and destroyed by chlorine. § 4. It is of importance to remark, that when a sequence of phe- nomena 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 Sian either of the laws which connect B with C and A with B. This vdll appear from very simple considerations. All laws of causation ai-e 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 Avhen B is really followed by C, and is therefore less general than the law that EXPLANATION OF LAWS. ^73 A produces B. It is- also less general than the law that B produces . C. For B may h^vc other causes besides A ; and as A produces C only by means of B, while B produces C whether it has itself been prpduced by A or by anything else, tlie second law embraces a greater number of -instances, covers as.it were a greater space of ground, than the first Thus,- in our former cxami^lc, the ]aw 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, siuce, for aught we know^the change in- the nerve may equally take place when, from a counteracting cause, as for instance strong jneutal excitement, the sensation docs not follow ; as in a battle, where woun,ds are often re- ceived without any ctmsciousness of receiving them. And again, the law tliat change in the state of a nein-e 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 nxjt produced by contact with an object, but by some othet cause; as in the well kno>vTi case, when a person who has lost a limb feels the vevj sensation which he lias 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 se(]uencc is resolved, laws of greater generality than that law is, but (as a' consequence of, or rather a^ implied hi, .thei:t: greater generality,) they are more to bq relied ob ; tliere are fewer chances of their being ultimately found not to be universally true. From the moment when the sequence of A and C is i^hown not to be. immediate, but to depend upon an intervening phenomenon, then, how- ever 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 BC. The tendency of A to produce C may be defeated by Avhatevcr is capable of defeat- iT\g either the teVidency 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 rnore elementary tendencies ; and the generalizatioji that A j& 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 pfB, the^mmediate, antocedent of C- in the- sequencc/ , ...."■ The resolutipn 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. Assoon 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 and 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 retpiire limitation from subsequent experience, than the law which they serve U) explain. They are more nearly unconditional ; tlu^y are defeated by fewer con- tingencies ; they are a nearer approach to the universal truth of nature. The same obsen-ations are still more evidently true with regard to the M M 274 INDUCTION. first of the three modes of resolution. When the law ropagating power of chemical action is likely to exert itself ill the most markexl manner. Aecoi'dingly, first, it explains the remark- able 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 actioniipon " the wliole hnnp." 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. SQgar is a substance which, from the complexity of its composition, ha^ 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 proxim- ity of a substance of which the elements are separating from each other, and combining with the elements of water, causes sugar, to un- dergo the same change, giving out carbonic acid gas, arid becoming alcohol. It is not the elements contained-in the yeast which do this. " An acpieous 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 resi- due of the yeast, after being treated with water, possess the power of exciting fermentation. It is not the yeast itself, therefore ;■ it is the yeast in a state of decomposition. The sugar, which would noC decompose and oxidize by the mere presence of Oxygen and waterj is induced to do so when another oxidation is at work in the midst of it. ' J3y the same principle Liebig is enabled to explain rrialaria; the pernicious influence of putrid substances ; a variety of poisons; conta- gious diseases ; and other phenomena. Of all substances, those com- -posing the animal body are the most complex in their Composition, and in the least stable condition of union. The blood, in particular, is the most unstable compound known. What, therefore, can be less. sur- prising than 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 respiraticjn 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 of Liebig exemplifies the second. The laws explained are such as this, that yeast puts sugar into a state of fennentation. 280 INDUCTION. 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 ozie more comprehen- sive expression which includes them all. For the curious fact of the contagious nature of chemical action was only raised into a law of all chemical action by these very investigations ; just as the Newtohian attraction was only recognized as a law of all matter when it was found to explain the phenomena of teiTestrial 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 had 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 were brought together into one law of chemical action in general : the peculiarities of the various substances being, in fact, . elimina,ted, just as the New- tonian deduction eliminated from the instances of terrestrial gravity the circumstance of proximity to the earth. § 2. Another of Liebig's speculations, which, if it should ultimately be found to agi'ee with all the facts of the extremely complicated phenomenon to which it relates, will constitute one of the finest, examples of the Deductive Method upon record, is his theory of respi- ration. The facts of respiration, or in other words the special laws which Liebig has 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 thei'eby its color from a blackish purple to a brilliant red. The absorption and exhalation are evidently chemical phenomena ; and the carbon of the ca,rbonic acid must have been derived fi-om the body, that is, must have been ab- sorbed 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 carbonie 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 tliis vexata qucestio in a class of chemical actions in which scarcely any less acute and accurate 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 EXAMPLES OF THE EXPLANATION OF LAWS. 281 globules, then>f)re, arc concluded to bo tlio portion of the blood wliich is operative in respiration. These globules contain a certain quantity of iron, which (rom chemical tests is inferred to be in the state of oxide. Dr. Liebig recognized, in tlic known chemical properties of the oxides of iix)n, laws which, if followed out deductively, wtoiild lead to the prediction of the precise series of phencmena 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 vtmous blood we have no direct evidence which of riie oxides is ]>resent, but the considerations to be presently stated will prove that it is the prottjxide. As arterial and venous blood are in a perpetual state of alternate con- version into one another, the question arises, under what circumstances the protoxide of iron is capable of being converted into the i)croxide, and vice versd. Now the protoxide readily combines with (jxygen iii the presence of water, forming the hydrated peroxide : these condi- tions 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 phenojnena of respiration. But the arterial blood, in (juitting the luntrs, 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 (whei"e no sulphur is present) gives forth oxygen and wsiter, which oxyggn, attracting the carbon from the organic substance, becomes carbonic acid ; while the peroxide, being reduced to the state of prot- oxide, 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 add being given off, and the protoxide, by the absorption of oxygen and water, becoming again the h^-drated 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-azotized but highly carbonized animal products, in particular the bile. In these it finds the precis^ conditions required for decomposing the peroxide into oxyge\i and the protoxide. The oxygen combines with the carbon of the decaying tissues, and forms carbonic acid, which, although insufficient in amount to neutralize the whole of the protoxide, combines with a pcntion (