UC-NRLF 
 
 B 3 T2fi D71 
 
THE THEORY OF INFERENCE 
 
by the same author. 
 
 Principles of 
 Natup-al and Supernatural Morals. 
 
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 Vol.11. "Supernatural Morals. " 12s. 
 
 Vol. I. 
 
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 giving to all students of ethics as a treatise in the best manner of one of the 
 best schools." — Manchester Guardian. 
 
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 ingenious." — Guardian. 
 
 Vol. II. 
 
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 chester Examiner. 
 
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 VOL.S. I. AND II. 
 
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 himself. Every chapter abounds with good things ; and, in particular, we 
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 chapter which sets forth 'The New Morality' and 'The New Command- 
 ment of Love.'" — James Iverach in British Weekly. 
 
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 as to the subject in its totality, Mr. Hughes must not be deprived of his 
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 which the superiority of the Christian revelation is urged, the acute treat- 
 ment of sin, and the clear style in which the argument is presented through- 
 out, are deserving of high commendation."— R. M. Wenley in Critical 
 Revieiu. 
 
THE 
 
 Theory of Inference 
 
 BY THE 
 
 REV. HENRY HUGHES, M.A. 
 
 AUTHOR OF "PRINXIPLES OF NATURAL AND SUPERNATURAL MORALS' 
 
 LONDON 
 KEGAN PAUL, TRENCH, TRUBNER, & CO. Li'' 
 
 PATERNOSTER HOUSE, CHARING CROSS ROAD 
 1894 
 

 7 (^ o ^ t. 
 
 The rights of trans latiott and of reprodtictio7i are reserved. 
 
PREFACE 
 
 This book, a wholly secular composition, was originally 
 designed to form part of a treatise on religious faith. But 
 it so grew in the course of being written, in material size 
 and intellectual weight, that at length it seemed desirable 
 to publish it as an independent volume. 
 
 Although the argument is primarily intended to serve a 
 special purpose, and the form in which it is cast has to 
 a certain extent been determined by that purpose, yet the 
 author ventures to hope that it will be found to have a 
 general and scientific value. He offers it to the thinking 
 public, not merely as a defence and explanation of the habit 
 of assenting to propositions which are not capable of being 
 demonstrated by one man to another, but as an impartial 
 investigation of the whole of that part of mental science 
 which has to do with inference. He has endeavoured to 
 set forth with all needful clearness and precision the nature 
 and the limits of induction and deduction, as well as to 
 vindicate the essential reasonableness of what he has called 
 illation. Induction and deduction, on the one hand, he has 
 sought to exhibit as the kinds of inference which are appro- 
 priate to, and only possible in, the field of natural law : 
 illation, on the other hand, he has striven to expound as the 
 
vi PREFACE 
 
 kind of inference, and the only kind, which leads to the dis- 
 covery of causes and effects in the field of history. It has 
 seemed to him that, in order to win general acceptance for 
 the theory of illation which it was his primary purpose to 
 establish, it was necessary to make it evident to his readers 
 that induction and deduction are unequal to, and are not as 
 a matter of fact employed in the performance of, the work of 
 drawing conclusions about real and concrete things. And 
 thus it has come to pass that logical inference, from its foun- 
 dations upwards, has been made the subject of careful and 
 minute investigation. 
 
 The book being such as has been described, the author 
 asks for it the attention of other readers besides those scien- 
 tifically interested in the question of religious faith. He 
 thinks that it may prove to be of use, not onl}- to the 
 theologian, but also to the general student of logic and 
 philosophy. 
 
CONTENTS 
 
 CHAPTER I. 
 CA USA TION. 
 
 PAGE 
 
 I. In order to establish satisfactorily the thesis, that men 
 
 may reasonably give unqualified assent to undemonstrable 
 
 propositions, it is necessary to investigate the general 
 
 subject of the mind's action in making inferences . . i 
 
 II. This involves at the outset inquiry into the origin of the 
 
 principles of causation and of uniformity in nature . . 4 
 
 III. We may notice four different kinds of cause, viz., efficient 
 
 cause, final cause, phenomenal cause, and formal cause . 7 
 
 IV. It is with the phenomenal cause — henceforth to be spoken 
 
 of simply as the cause — that this investigation is con- 
 cerned . . . . . . ■ ■ • .10 
 
 V. The principle of causation is in some way an object of 
 
 immediate knowledge 13 
 
 VI. The root idea of the relation of effect to cause is one, not 
 of observed succession to, but of procession from in 
 accordance with the design of nature . . . -15 
 VII. It is by means of simple observation, at a time when it 
 already entertains the conception of causation, that the 
 mind first becomes cognisant of particular causes and 
 particular effects 17 
 
 CHAPTER II. 
 UNIFORMITY IN NATURE. 
 
 I. The conception of the relation of particular effect to parti- 
 cular cause, as one of procession from in accordance 
 with the design of nature, includes the further concep- 
 tion of it as independent of time and place ... 20 
 
viii CONTENTS 
 
 PAGE 
 
 II. And this further conception leads, by means of an act of 
 deductive inference, to apprehension of the principle of 
 uniformity in nature 21 
 
 III. Mill's view of uniform causation, as a conception derived 
 
 from experience, and yet including the idea of necessity, 
 and being the basis of inference, is clearly untenable, 
 since it involves contradiction ...... 23 
 
 IV. And his view that, while a cause is invariably followed by 
 
 the same effect, an effect is not invariably preceded by 
 
 the same cause, cannot be sustained .... 36 
 
 CHAPTER III. 
 
 INFERENCE. 
 
 I. Inference is the mind's passage from the known to the 
 
 unknown in the light of principles closely bound up with 
 
 the principle of causation. Practically it consists almost 
 
 entirely in the discovery of causes and effects . . 39 
 
 II, The word 'therefore' is not always indicative of an act of 
 
 inference . . . . . . . . . -41 
 
 III. There are four kinds of inference, viz., induction, deduction, 
 
 illation, and delation. The former two are based upon 
 the principle of uniformity in nature, the latter two upon 
 the principle of continuity in nature .... 43 
 
 IV. In induction and in illation, the phenomenon having an 
 
 ancestry of causes or a posterity of effects, the mind 
 seeks for some one cause or some one effect which shall 
 be felt to really explain in some way the phenomenon 
 in question 44 
 
 CHAPTER IV. 
 
 INDUCTION. 
 
 I. Induction is the discovery, or the approximate discovery, 
 within a selected range of circumstances, of a cause or 
 an effect by means of the comparison, or contrast, or 
 comparison and contrast, of the set of circumstances 
 containing the phenomenon with other sets known also 
 to contain, or known not to contain, an instance of it . 47 
 
CONTENTS ix 
 
 PAGE 
 
 II. Examples of easy and almost unconscious induction . . 49 
 
 III. The process consists of several distinct steps ... 52 
 
 IV. Examples of conscious and deliberate induction . . 53 
 V. Recapitulation 56 
 
 CHAPTER V. 
 
 DEDUCTION. 
 
 I. Deduction is a recognition of the fact that, there is uni- 
 formity in nature. It consists in ascertaining a cause or 
 an effect by apprehending it to be precisely similar to 
 the known cause or effect of a precisely similar effect or 
 cause .......... 59 
 
 II. The meaning of universal propositions requires to be care- 
 fully examined. Upon it depends the meaning of syllo- 
 gistic argument ........ 62 
 
 III. In the syllogism there is — as Mill also holds — no inference 64 
 
 CHAPTER VI. 
 
 MILL'S ''FOUR METHODS." 
 
 I. Mill recognises only one kind of inference, which he calls 
 induction. It consists principally in the discovery of 
 causes and effects. For their correct discover}' he pre- 
 sents four only methods ....... 66 
 
 II. His first, the method of agreement, is substantially the 
 same as our method of comparison. He makes, how- 
 ever, two grand mistakes in connection with it . -69 
 
 III. His second, the method of difference, is exhibited in two 
 
 forms. In the joint method of agreement and difference 
 
 it is nearly allied to our method of contrast . . -71 
 
 IV. Exhibited alone — and including, as it then does, his third 
 
 method, that of residues — it is another thing. The 
 practical operation which it chiefly professes to represent 
 seems really to be, not a method of inference, but a 
 process of observation and reflection .... 74 
 V. His fourth method, that of concomitant variations, seems 
 
 to be merely a process of observation and reflection . 77 
 
CONTENTS 
 
 FAGB 
 
 VI. Induction by means of the four methods is based upon the 
 principle of universal causation, which is nevertheless, 
 according to Mill, itself a product of induction . . 78 
 VII. He urges, however, a distinction between rigorous induc- 
 tion, which is based upon the principle, and loose 
 generalising from experience, by which the principle is 
 inferred. But this position he quite fails to sustain . 80 
 
 CHAPTER VII. 
 
 THE GREAT FALLACY IN MILVS ''LOGIC:' 
 
 I. One special fallacy pervades Mill's Logic. It consists in 
 his complete, though not easily detected, failure to 
 justify his contention, that he is explaining to his 
 readers the one universal type of inference ... 88 
 
 II. Analysis of the subjective process of arriving at conclusions, 
 having been promised, is afterwards abandoned ; and 
 induction is treated as the having arrived at conclusions 
 that are true in fact . . . . . . . • 91 
 
 III. He gives in different places different definitions or descrip- 
 tions of induction ........ 92 
 
 IV. The alleged universal type represents not only inference 
 from a number of similars, but also inference from two 
 dissimilars ; and not only inference to a particular con- 
 clusion, but also inference to an abstract or general 
 conclusion ......... 97 
 
 V. Further, although it is professedly based upon the uni- 
 formity of the course of nature, yet it represents processes 
 of inferring that are quite independent of this principle . 100 
 
 CHAPTER VIII. 
 
 THE TWO FIELDS OF INVESTIGATION. 
 
 I. There are, having each its own distinct kinds of inference, 
 
 two distinct fields of investigation, namely, the field of 
 
 natural law, and the field of history . . . . .103 
 
 II. A relation of causation established in either field can only 
 
 be affirmed in the other under certain reservations or 
 
CONTENTS xi 
 
 PAGE 
 
 restrictions. Kno\vleclj,re difters in character according 
 
 to the field in which it is accjuired io6 
 
 III. In the field of natural law, in which induction and deduc- 
 
 tion are employed, phenomena are dealt with as abstract, 
 not in the concrete form in which they really present 
 themselves ..... ... 
 
 IV. And they are dealt with as individual, not as they really 
 
 present themselves in relation to other things . 
 
 109 
 
 CHAPTER IX. 
 
 CONTINUITY IN NATURE. 
 
 I. As the principle of uniformity in nature is the basis of infer- 
 ence in the field of natural law, so in the field of history 
 the basis of inference is the principle of continuity in 
 nature. It is, that causes continue to act, and to be 
 grouped, in substantially the same manner as the)- have 
 hitherto acted, and have been grouped . . . .117 
 II. A characteristic formula of the field of history, expressing 
 
 the premises of illative inference, is, some X is Y . . 121 
 
 CHAPTER X. 
 
 DELATION. 
 
 I. Delation is a recognition of the fact that there is continuity 
 in nature. It consists in arriving at knowledge of an 
 event by means of the consideration, that it must, in 
 respect of the time and manner of its appearance, main- 
 tain the traditions of past e.xperience . . . .124 
 II. "The observation of the ebb and flow of the tide for ages 
 together gives us a full assurance that it will happen 
 again to-morrow " . . . . . . . .127 
 
 III. "No man can make a question but that the sun will rise 
 
 to-morrow, and be seen, where it is seen at all, in the 
 figure of a circle, and not in that of a scjuare" . .127 
 
 IV. "The prince who had always lived in a warm climate 
 
 naturally concluded that there was no such thing as water 
 becoming hard " . . . . . . . -134 
 
:ii CONTENTS 
 
 V. "We conclude that it is supposable there may be frost in 
 England any given day in January next ; probable that 
 there will on some day of the month ; and that there is 
 a moral certainty, that is, ground for an expectation, 
 without any doubt of it, in some part or other of the 
 winter" 135 
 
 CHAPTER XL 
 
 ILLA TION. 
 
 1. Illation is the discovery of a cause, or an effect, by means 
 of associating with the phenomenon a number of other 
 facts, and formulating some event which explains them 
 all in congruity with past experience . . . .137 
 II. Examples of the discovery of a cause 142 
 
 III. Examples of the discovery of an effect ■. . . .146 
 
 IV. Illation considered relatively to induction .... 149 
 V. Assenting to propositions on the evidence of testimony is a 
 
 notable exemplification of illative inference . . .154 
 
 CHAPTER XII. 
 
 NEWMAN'S ''GRAMMAR OF ASSENT." 
 
 I. Newman's division of assent into notional and real corre- 
 sponds, in the main, to the distinction between assent 
 in the field of natural law and assent in the field of 
 
 history . . • '59 
 
 II. In insisting, as he does, that assent is something quite 
 different from inference, he uses the term inference, or 
 logical or formal inference, in a sense almost identical 
 with syllogistic reasoning. . . . . . .165 
 
 III. His objection, that inferred conclusions are only probable 
 
 conclusions, is based on two grounds. The first — the 
 generally undemonstrable character of syllogistic pre- 
 mises — is untenable . . . . . . . .170 
 
 IV. And the second— the uncertain applicability of general 
 
 laws — is not satisfactory. With the general position, 
 however, which he is seeking to defend, namely, that 
 
CONTENTS xiii 
 
 PAGE 
 
 abstract argument cannot lead to concrete truth, we are 
 substantially in full accord . . . . . .173 
 
 V. Real assent, or assent to propositions about concrete things, 
 he considers to arise from informa' inference, that is, 
 from the mind's instinctive dealing with a cumulation of 
 
 probabilities .182 
 
 VI. The mind thus acting he names, in so far as it judges 
 correctly, the illative sense. This restriction of the tenii 
 to correct judging is not to be commended . . .186 
 VII. A critical examination of his position, exhibiting the 
 measure of agreement or disagreement with our own, 
 demands, what on other grounds is now desirable, an 
 investigation of the subject of probability . . . 190 
 
 CHAPTER XIII. 
 
 PROBABLE CONCLUSIONS. 
 
 I. Butler quoted ,and probability defined. A probable event 
 
 is one of a number of alternatives . . . . .192 
 II. "A man's having observed the ebb and flow of the tide 
 to-day, afifords some sort of presumption that it may 
 happen again to-morrow" . . . . . .197 
 
 III. "We conclude that it is supposable there may be frost in 
 England any given day in January next ; probable, that 
 there will on some day of the month ; and that there is a 
 moral certainty, that is, ground for expectation, without 
 any doubt of it, in some part or other of the winter " . 199 
 
 I\'. "We believe that a child, if it lives twenty years, will grow 
 up to the stature and strength of man ; that food will 
 contribute to the preser\'ation of its life, and the want of 
 it for such a number of days be its certain destruction" . 201 
 
 CHAPTER XIV. 
 
 THEORY OF PROBABILITY. 
 
 I. The realised probability of a sequence between two con- 
 crete phenomena is the result of an impression existing 
 in the mind of the naturalness of this sequence . . 204 
 
siv CONTENTS 
 
 PAGE 
 
 11. Numerical values assigned to probabilities of alternative 
 events represent the strength of impressions of natural- 
 ness produced by experience. They express the degree 
 of expectation of a particular event on a given occa- 
 sion ; or they may express the degree of frequency with 
 which a particular event is expected to happen in the 
 future .......... 206 
 
 III. In the absence of experience, any one of a number of known 
 
 alternatives is contemplated as natural in the same 
 degree as any other. Hence equal probabilities are 
 derivable from ignorance as well as from experience . 209 
 
 IV. Estimates of the comparative values of probabilities are 
 
 for the most part both implicit and subjective . .211 
 
 V. In acting on probabilities there are two principles. If the 
 several alternatives are merely alternatives connected 
 with the same event or end, we choose as the basis of 
 action that which has the highest probability. If, how- 
 ever, they are means to different ends, our choice falls on 
 that which gives, through multiplying by its probability 
 the value of its end, the largest product .... 213 
 VI. The mathematical cumulation of probabilities all in favour 
 of one event gives a resultant probability higher than 
 any of those from which it is derived. The process, how- 
 ever, involves assumptions ; and the conclusion does not 
 really represent any impression of experience . . .218 
 
 CHAPTER XV. 
 
 PROBABILITY AND ILLATION. 
 
 I. Mill quite fails to make out his case, that induction leads 
 to the ascertainment of concrete facts through the instru- 
 mentality of probable evidence in the form of approxi- 
 mate generalisations . . . . . . -223 
 
 II. Mathematical cumulation of probabilities cannot, in the 
 nature of things, lead to the establishment of facts 
 indicated by masses of circumstantial evidence . . 228 
 III. Illation is free from the defects of the method of probability. 
 It provides a causal explanation, consonant with experi- 
 ence and acceptable to the mind, of a multiplicity of 
 concurrent facts . . . . . . . .2^4 
 
CONTENTS XV 
 
 CHAPTER XVI. 
 ASSENT AND BELIEF. 
 
 PAGE 
 
 I. The assent of illation ........ 239 
 
 II. The assent of illation compared with that of induction in 
 respect of their subjective, demonstrative, and objective 
 
 values 243 
 
 III. Mill's view of proof 249 
 
 IV. Belief 254 
 
THE 
 
 THEORY OF INFERENCE 
 
 CHAPTER I. 
 
 CA USA TION. 
 
 I. The reader is invited to enter upon the difficult but 
 interesting task of investigating the action of the human 
 mind in making inferences. Not merely as a useful study 
 in mental science is this large undertaking put before him ; 
 it is proposed, especially, as a means to understanding and 
 appreciating the essential reasonableness of religious faith. 
 For faith, in one of its most important aspects, is unqua- 
 lified and unconditional assent to certain undemonstrable 
 facts and doctrines. And in order to show as convincingly 
 as possible that such kind of assent is not in itself an 
 irrational procedure, it is necessary to exhibit it in relation 
 to the movements which the mind makes when it assents 
 to conclusions that satisfy the recognised formulas of logic. 
 Thus, on the one hand, will appear more plainly the nature 
 and the validity of the assent in question ; and thus, on 
 the other hand, the inadequacy of logical methods to lead 
 to and account for even that near approximation to it 
 which is accounted reasonable will become manifest. En- 
 deavour will be made in this treatise to exhibit clearly 
 these two facts : — that the mind may give to undemon- 
 
2 THE THEORY OF INFERENCE 
 
 strable propositions about concrete things a rational assent 
 which is much more than an assent to them as very highly 
 probable ; and that not even their very high probabihty can 
 be inferred by means of any formulas of the ordinary logic. 
 
 In an age when the thoughts of men are largely turned 
 to the study of laws of nature, and they have learned to 
 appreciate the importance of using with due precision the 
 methods of inference recognised in logic, it is not, per- 
 haps, surprising that they should look with suspicion upon 
 propositions which are incapable of logical demonstration. 
 Momentous doctrines are offered for their acceptance with- 
 out, as it appears to them, any such evidence as amounts 
 to proof. They feel that in physical investigation to place 
 implicit credence in propositions thus presented to them 
 would be an act of folly. How then, they ask, can these 
 alleged truths of religion be unhesitatingly accepted by 
 thinking men ? 
 
 In physical science a conclusion, in order that it may be 
 generally received as true, must be presented as having 
 been reached by a way of inference over which any other 
 man may travel, or which he may picture to himself as 
 having been travelled over by the original investigator. 
 In physical science facts and arguments are, so to speak, 
 the common property of many, if not of all : the same 
 conclusions are regarded as being drawn, or as capable of 
 being drawn, by many, if not by all, from precisely the 
 same facts by means of precisely the same modes of argu- 
 ment. Hence a fact or doctrine of religion — merely because 
 its advocate cannot, by addressing himself to the intuition 
 and the senses and the logical understanding of any inter- 
 locutor, demonstrate to him how step by step his conclu- 
 sion has been reached — is apt to be looked upon as one 
 which is at the best no more than very highly probable, 
 as one to which no soundly reasoning man could possibly 
 
CAUSATION 3 
 
 accord an unqualified and unconditional assent. A proposi- 
 tion, conviction of whose truth can be arrived at only by 
 a path more or less private and peculiar to each individual 
 inquirer, is apt to be regarded as having necessarily no 
 certain claim to the adhesion of any sound logician. And 
 a person in the present day, permeated with or assuming 
 the tone of thought appropriate to investigation in the 
 domain of physical science, may thus on grounds of reason- 
 ableness, as he would have it appear, refuse to give credence 
 to, or may begin to have misgivings about, the teachings 
 of Christianity. In proportion, therefore, as we hold that 
 assent to the truths of Christianity is a matter of immense 
 importance, we must, it would seem, hold it to be important 
 that it should plainly appear that full acceptance of them 
 is not in itself an unreasonable course of conduct. 
 
 But let it be noted, that it is not by any means in relation 
 to all matters that there is any wide-spread disposition to 
 contest the validity of inferences merely because they are 
 not made according to the rules of logic. In the ordinary 
 concerns of common life, even persons most wedded to 
 logical methods of ascertaining truth do habitually give 
 their full assent to facts and propositions which they 
 cannot prove. Of this there can, apparently, be no possible 
 doubt. Who is there, for example, who does not entertain 
 a firm conviction of the truth of some such propositions as 
 the following: — that his children love him, or that his 
 friend is worthy of being trusted, or that he himself was 
 born in a certain 3-ear at a certain place, or that a battle 
 was once fought between England and France at Waterloo, 
 or that a person named Marcus Aurelius was an emperor 
 of Rome ? And 3'et of these propositions no strict proof, 
 in a logical sense, is possible ; no proof which would not 
 involve assumptions, themselves neither matters of imme- 
 diate knowledge nor capable of being absolutely proved. 
 
4 THE THEORY OF INFERENCE 
 
 We might well argue, therefore, that, since persons en- 
 dowed with high powers of reasoning do habitually assent 
 to propositions other than those which can be strictly 
 demonstrated, there can really be no question that such 
 a procedure in relation to matters of religion is entirely 
 legitimate, and not in the least unworthy of a philosophic 
 mind. Nevertheless, this argument, though obvious and 
 apparently unanswerable, seems practicall}' insufficient to 
 overthrow men's contrary opinions. 
 
 II. Wishing, then, to obtain as clear and intimate a view 
 as may be possible of the philosophic reasonableness of 
 inferring and believing facts that lie outside the range both 
 of immediate knowledge and of logical demonstration, we 
 may proceed to examine the various movements of the mind 
 in making inferences. We may proceed to investigate the 
 laws which govern it in passing from knowledge of one or 
 more facts or truths to the consequent knowledge of some 
 other fact or truth. Our starting-point will be the mind's 
 position, so to speak, when it is ready to make its first 
 inference. We suppose it to have acquired a certain stock 
 of ideas such as are the objects of immediate knowledge, 
 ideas which come to it directl}', whether by intuition or 
 sensation. There is no occasion for us to go behind this 
 position, penetrating into the inner regions of metaphysics, 
 and opening up the whole question of the origin of ideas. 
 The subject of our inquiry is not mental science in general, 
 but only that part of mental science which has to do with 
 inference. And, provided it be understood that we are con- 
 templating the mind's position at a time when as 3^et it has 
 made no inferences, when whatever ideas it may possess 
 belong in some way or other to the region of immediate 
 knowledge, it is immaterial to us in what precise" manner 
 these ideas have been acquired. 
 
 Nor need we (except in special cases afterwards to be 
 
CAUSATION 5 
 
 mentioned) concern ourselves with the further f[uestion 
 whether certain elementar}' and axiomatic truths — such, for 
 example, as that three and four are seven, or that two 
 straight lines cannot enclose a space — are truths of immedi- 
 ate knowledge, or whether the}^ are reached by inference in 
 the obscure time of the mind's first making itself acquainted 
 with the external world. If these or any other first prin- 
 ciples of science have been reached by inference, still there 
 must have been an earlier time in the mind's history when 
 its knowledge was wholly independent of its power of 
 inferring. And from this earlier time our inquiry makes 
 its start. 
 
 We need not, as has been explained, in fixing upon a 
 starting-point for our investigation, go farther back in the 
 mind's history than to the time just preceding its beginning 
 to infer. It is, however, quite necessary that we should 
 go back thus far. Or — and this is practically the same 
 thing — we must at least conceive the mind, in whatever 
 period of its history it may be, as making inferences without 
 any dependence whatever upon ideas that have been obtained 
 by means of former inferences. We must conceive it as 
 using for its instruments or for its guides only such ideas 
 as are in one way or another the objects of immediate 
 knowledge. Unless we thus divest the mind of all ideas 
 and axioms which have themselves been gained by infer- 
 ence, and which, having been once gained, might seem to 
 be employed as useful aids to making further inferences, it 
 might be expected to be extremely difficult, if not impossible, 
 to trace the natural and original course taken by the mind 
 in passing from the apprehension of one or more facts to 
 the consequent apprehension of another. If we were to 
 contemplate the mind as entertaining, while engaged in 
 inference, one or more ideas, which, though made use of, 
 are not essential to the act, it might be expected to .be 
 
6 THE THEORY OF INFERENCE 
 
 extremely difficult, if not impossible, to expose fully to view 
 that wherein lies the essence of inferring, that which the 
 mind necessarily does on every occasion when an inference 
 is made. 
 
 If, in seeking to divest the mind, within the sphere of 
 its operations of inferring, of all previously inferred ideas, 
 we should meet with one or more ideas which we find not 
 only useful but indispensable means to an act of inference ; 
 if, notwithstanding any seeming likelihood of their having 
 been obtained by inference, we should find ourselves unable 
 to conceive of a real inference being made independently 
 of them ; how is it reasonable to regard them ? Must we 
 not conclude that any presumption in favour of their being 
 inferred ideas is misleading, and that they are in fact a 
 part of the mind's immediately acquired stock of knowledge ? 
 If they are inferred, we must put them away ; if we cannot 
 put them away, they are not inferred. 
 
 Now the principle of causation is, in relation to all 
 inferences, one such necessary idea. And the principle of 
 uniformity in nature is, in relation to one class of inferences, 
 another. Every phenomenon, we say, is the effect of some 
 cause, and the cause or condition of some effect. And 
 similar causes, we say, produce similar effects, while similar 
 effects are the products of similar causes. These proposi- 
 tions, expressing correctly (it is here maintained) the two 
 ideas, may be described as axiomatic truths. And with 
 regard to them it is necessary to our purpose — as it is not 
 in the case of most other axioms — to discuss their origin 
 as acquisitions of the human mind. The view that will be 
 taken of them is, as was suggested above, that they are 
 objects of immediate knowledge; the former, that is, being 
 an idea antecedent to all inference whatsoever, the latter to 
 all inference that depends upon it. If this view were 
 generally accepted, discussion of it would lie outside the 
 
CAUSATION 7 
 
 limits of this treatise. Well-known writers, however, on 
 philosophic subjects contend that the law of uniform causa- 
 tion — corresponding in the main to the aforesaid principles 
 — is itself an inference from uniform experience. It thus 
 becomes necessary to make a serious attempt to show that 
 the principles in question have in fact another origin. 
 
 And here it may be stated that the investigation upon 
 which we are engaged will be carried on for some time with 
 much explicit reference to J. S. Mill's views concerning 
 inference. As a foremost champion of the position, that 
 conclusions which are incapable of being established by 
 the methods of logic have no proper claim to be implicitly 
 beheved, his main contentions require and deserve to be 
 thoroughly examined. If the}^ can be shown to be erroneous, 
 the way will be very considerably cleared for the favourable 
 reception of a constructive argument in support of the 
 opposing thesis. Together, then, with direct investigation 
 of our subject — which will issue, it is hoped, in our obtain- 
 ing a satisfactory view, on the positive side, of the reason- 
 ableness of assenting to undemonstrable propositions — 
 critical attention will be devoted to those of Mill's arguments 
 which seem, in relation to our thesis, to be the most dan- 
 gerous and destructive. 
 
 III. We are called upon, then, to institute an inquiry 
 into the origin, first, of the idea of causation, and secondly, 
 of the idea of uniformit}' in nature. Further, it seems to 
 be most desirable, if indeed it is not necessary, that some 
 clear and full account should be before us of the meaning 
 of the relation between effect and cause. Accordingly we 
 ma}^ now proceed to consider with some care what is the 
 origin, and what the meaning, of the idea or principle that 
 every phenomenon is the effect of some cause and the cause 
 or condition of some effect. 
 
 To questions such as the following — why does an oak- 
 
8 THE THEORY OF INFERENCE 
 
 tree shed its fruit in autumn ? why does a pond dry up in 
 summer ? why do birds build nests in spring ? why does 
 a person take food when he is hungry ? why is it the lot 
 of man to suffer pain ? — four different kinds of answers may 
 be given, each kind containing its own conception of causa- 
 tion. The inquirer is regarding the phenomenon, of which 
 he speaks, as the effect of some cause, as standing in some 
 relation of seeming dependence to something outside itself; 
 and he is seeking to ascertain the nature of this cause, 
 and of this relation of dependence. And a person who 
 replies to him may indicate any one of four quite different 
 kinds of cause, any one of four quite different modes of 
 accounting for the phenomenon. 
 
 Three of these modes have reference to the Power that 
 manifests itself in nature. In order to preserve the secular 
 character of this treatise, it will perhaps be well to personify 
 nature, and speak of this Power simply as nature. The 
 meaning of what is said concerning cause will — relatively to 
 the main subject of our investigation — be unaffected by this 
 mode of speaking. With this preliminary observation we 
 proceed to notice the four kinds of answer that may be given. 
 
 1. A person intent upon magnifying nature as an 
 operating agent may reply to each question. Nature has 
 willed that it should be so. Phenomena being thus referred 
 to nature, as having in her will their final and sufficient 
 explanation, she is, in the technical language of philosophy, 
 their efficient cause. 
 
 2. Or a person having the operating agency of nature 
 in his mind, and being at the same time impressed with 
 the evidences of purpose and design which he sees around 
 him, may prefer to account for a phenomenon by exhibiting 
 it as a means to some given end. An oak-tree, he may 
 say, sheds its fruit, partly in order that new trees may 
 spring up, and partly in order that animals may find food; 
 
CAUSATION 9 
 
 a pond dries up, in order that thus the cartli may be 
 supplied with rain in due season ; birds build nests, in 
 order that their young may be safely hatched and reared ; 
 man is supplied with food for the satisfaction of his 
 appetite, in order that he may find enjoyment in an act 
 which is necessary to sustain his vigour; pain is inflicted 
 upon man, in order that character may be disciplined and 
 wrong-doing checked. The definite purpose which nature 
 is thus considered to have in view, in designing and order- 
 ing the phenomena of the world, is termed the final cause. 
 
 3. Again, a person having some knowledge of relations 
 of dependence seen to exist between one phenomenon and 
 another may point to some particular phenomenon, as con- 
 taining in itself an answer to the question. Thus he may 
 account for the oak-tree shedding its fruit, by saying that 
 the bond which unites the fruit to the tree is gradually 
 relaxed as the year progresses, until at length the wind 
 and rain of autumn sever it altogether ; for the drying up 
 of the pond, by saying that water evaporates under the 
 influence of the sun's heat ; for the birds building nests, 
 by saying that they are moved thereto by a force within 
 them which is spoken of as instinct ; for persons eating 
 when they are hungry, by saying that the desire to eat is a 
 motive acting on the will and inducing it to resolve upon 
 the necessary steps for giving satisfaction to the desire ; for 
 its being the lot of man to suffer pain, by saying that pain 
 is often the manifest consequence of inattention to the laws 
 of physical well-being. The phenomenon thus adduced, as 
 being in some way an explanatory phenomenon, may be 
 called the phenomenal cause. 
 
 4. Lastly, if a person should have in mind the general 
 idea of an order of nature regulating the dependence of one 
 phenomenon upon another, he ma^^, instead of pointing to 
 a phenomenon which seems to contain in itself an answer 
 
lo THE THEORY OF INFERENCE 
 
 to the question, express his conviction that an explanatory 
 phenomenon somewhere has existence. He ma}^ while per- 
 haps admitting that he cannot see behind the phenomenon 
 which is the subject of the question, assert that there is, 
 nevertheless, a phenomenon somewhere behind it to which, 
 by the design of nature, it stands in a relation of depend- 
 ence. In other words, he may reply that it is natural, or 
 in accordance with relations of dependence that exist in 
 nature, that this or that event should happen. It is natural, 
 he ma}' be supposed to say, that a tree should shed its fruit, 
 that water should dr}' up, that a bird should build a nest, 
 that a person being hungry should partake of food, that a 
 man should often be obhged to suffer pain. The design of 
 nature, thus regarded as containing somewhere in itself a 
 phenomenal explanation of an observed event — or, which 
 is nearly the same thing, the alleged naturalness of the 
 event happening when and as it does — may be designated 
 the formal cause. 
 
 IV. The general remark being made, that of the four t3'pes 
 of answer just considered, one will seem, in any particular 
 case, more pertinent than another according to the nature 
 of the subject and the mental standpoint of the two inter- 
 locutors, we proceed to notice some points in connection 
 with them. 
 
 Our investigation does not require that anything further 
 should be said concerning the efficient cause, and the final 
 cause, of any phenomenon. It may, however, be observed 
 that not nature alone, and nature's purpose, but man also, 
 and man's purpose, are capable of being thus spoken of; 
 if, that is, as believers in free-will, we credit man with being 
 endowed with some absolute power of initiating action. Thus 
 man, eating when he is hungry, may be regarded as to some 
 extent resolving to do so independently of the influence of 
 appetite upon the will. And he may be regarded as to 
 
CAUSATION II 
 
 some extent resolving to do so in order to fulfil a purpose 
 which he has made his own. 
 
 With reference to the formal cause, it must be pointed 
 out that the way in whicli the term is here employed, to 
 signify design in the mind of nature, is not quite in accord 
 with the definition of it usually given. The idea, it is said, 
 in a sculptor's mind is the formal cause of the statue he has 
 made ; the plan in an architect's mind is the formal cause 
 of the house he has erected. But in the discussion of the 
 preceding section nature is regarded as the sole artificer, 
 and the motives and actions of man — (his freedom of will 
 not being taken into account) — are reckoned among her 
 phenomena. Moreover, it is not merely nature's planning 
 an event to happen, but nature's planning it to happen in 
 consequence of some antecedent phenomenon, that is looked 
 upon as constituting its formal cause. The term is thus 
 not strictly applicable to the design of man, even in so far 
 as he is free to execute his design. For it is not within 
 his power to determine what kinds of antecedent shall be 
 the phenomenal causes of his realised idea. 
 
 The term phenomenal cause, it may next be remarked, 
 has not, perhaps, a recognised place fti mental philosophy. 
 Nevertheless, in the absence of a better, it seems convenient 
 to employ it here. It distinctly points, as it is intended 
 that it should point, to some phenomenon as the cause of 
 a given effect ; and it is sufficiently general to include all 
 possible varieties of this kind of cause. As, however, it is 
 with this cause alone that our argument is much concerned, 
 it will, in general, be unnecessary to speak of it by the full 
 name : it may, when it is quite evident that no one of the 
 three other kinds is referred to, be spoken of simply as the 
 cause, without the prefix of the distinctive adjective. 
 
 Let us now turn to the various instances of phenomenal 
 cause suggested by way of answer to the questions of the 
 
12 THE THEORY OF INFERENCE 
 
 preceding section. We seem to have (i) decay, wind, and 
 gravitation, all gradually loosening the hold of fruit upon 
 a tree; (2) heat vaporising water; (3) instinct inciting 
 birds to active effort ; (4) a desire producing through the 
 intervention of the will various movements of the human 
 body; (5) some of the forces of which vital energy is 
 composed acting, in consequence of improper treatment, 
 irregularl}^ in the physical organism, whether in excess or 
 in defect. Now a careful examination of these instances 
 seems to show that one kind of idea, whether in a positive 
 or in a negative form, is present in and gives character to 
 them all. In wind and gravitation acting on the stalk of 
 fruit, in heat acting on water, in instinct acting on the limbs 
 of birds, in will incited by desire acting on man's bodily 
 frame, in some part of vital energy operating in excess : — 
 in all these we seem to find different expressions of one and 
 the same idea ; all appear to be but different manifestations 
 of one and the same thing, namely, force acting upon matter. 
 And the decay of an acorn's stalk, and the failure of some 
 part of vital energy to act efficiently, seem to signify but the 
 absence of this one thing, the absence of that which has 
 hitherto been present, namely, force — here a quickening and 
 health-sustaining force — acting upon matter. 
 
 From these five instances, not at all selected with any 
 special view to making good this point, it would seem as if 
 an approximately true definition of a positive cause is, force 
 acting upon matter ; and of a negative cause, force ceasing 
 to act upon matter. And this twofold description, positive 
 and negative, seems to cover sufficiently well for the purpose 
 of our argument the whole body of causes. Without pro- 
 fessing to be strictly applicable to each without exception, 
 it represents correctly their general character, and gives 
 the needful definiteness to thought. 
 
 It will perhaps further tend to clearness of view, if we 
 
CAUSATION ,3 
 
 can now find for the phenomena which we call effects or 
 consequences some simple conception which shall include 
 them all. In the illustrations that have been given we have 
 the following effects: — an acorn falling from a tree, water 
 assuming the form of vapour, a bird engaged in building 
 its nest, a person taking food, another suffering pain. Can 
 these be included in some one idea ? An idea which 
 apparently includes them all, and which seems to be 
 sufficiently definite for our purpose, is that of an active 
 or passive state of being. And this conception of effect 
 will apparently cover all phenomena whatsoever, all facts 
 and events of which we become cognisant. 
 
 We may consider, then, cause to be force acting (or 
 ceasing to act) on matter, and producing (or ceasing to 
 produce) an active or passive state of being. 
 
 V. We now come to the crucial questions of a theor}^ of 
 causation. What is the origin of this idea or principle of 
 causation in the human mind ? And what is the true 
 character of the relation of dependence between effect and 
 cause ? 
 
 As regards the origin of the idea of causation, or the path 
 by which there first enters into the mind a conviction that 
 any phenomenon taken note of is dependent upon some 
 other, and has some other dependent on it, all that we are 
 here concerned to know is, that the mind becomes possessed 
 of the idea before it has in any way exercised its power of 
 making inferences. The idea of causation, it is here main- 
 tained, is an essential means to the making any real infer- 
 ence whatsoever; and therefore it must be insisted on, as 
 a fact of human nature, that it is in some way an object 
 of immediate knowledge. Further than this it is not neces- 
 sary that we should inquire. 
 
 Mill, however, holds that the conception arises from 
 observation of a number of similar pairs of consecutive 
 
14 THE THEORY OF INFERENCE 
 
 phenomena; a being seen time after time to be followed by 
 by until at length b is looked upon as standing to a in the 
 relation of effect to cause. The difficulties which beset 
 this theory we shall have to notice presently. At present it 
 is sufficient to remark that it derives the conception of cause 
 and effect in general from the mind's acquaintance with the 
 repetition of particular sequences. But the view which it is 
 necessary to the success of our argument that we should 
 be able to take is, that the conception is essentially indepen- 
 dent of such knowledge. It is contended that if the mind 
 had no experience of the repetition of phenomena ; if each 
 phenomenon as it occurred was invariably something new ; 
 yet it would be in some measure aware, at a very early 
 period indeed of its development, that there is somewhere 
 among things and movements external to itself a precedent 
 explanation of any particular thing or movement which it 
 sees. And also it would be aware, though perhaps at a 
 less early period, that some change of circumstances arises 
 as the consequence of any particular exercise of force which 
 it observes. The human mind, it is maintained, begins at 
 a very early period of its existence — before it can have 
 learned by any experience to associate phenomena in pairs — 
 to seek for the fellow, so to speak, of any one by which it is 
 impressed. It is somehow conscious, apart from any teach- 
 ing of experience, that any given phenomenon has its ex- 
 planation in some other upon which it is dependent, or in 
 some other which is dependent on it. It anticipates a re- 
 lation of dependence between the thing it sees and some 
 other portion of the world around it. 
 
 This view seems to account satisfactorily for the constant 
 questionings and the practical curiosity of childhood ; it 
 seems, as perhaps will become apparent, to be a basis on 
 which a consistent theory of inference can be erected ; 
 and it seems to be free from logical difficulties such as 
 
CAUSATION 15 
 
 those with which, as we shall see, Mill's exposition is en- 
 cumbered. 
 
 VI. Passing to the second of the two questions, we at 
 once see that the relation of effect to cause is, in part, one 
 of succession in time. Effect is certainly conceived of as 
 coming- after cause in point of time, though the interval 
 between them may be in some cases inappreciably small. 
 Thus far we are in accord with Mill, who describes cause 
 as the unconditional invariable antecedent. He, however, 
 maintains that conception of this relation is derived solely 
 from experience of similar pairs of consecutive phenomena, 
 and is thus a conception of succession only. A more correct 
 view seems to be that, as the existence of cause and the 
 existence of effect, so the relation of effect to cause is a matter 
 which would be equally apprehended by the mind if all 
 phenomena were but of single occurrence. The true re- 
 lation appears to be one of absolute dependence ; one of 
 procession from, not of mere succession to. A cause is 
 not merely that which is, according to experience, the un- 
 conditional invariable antecedent ; but it is that without 
 which the consequent could not possibly exist. It appears 
 to be the case that there is a certain true sense in which 
 the effect or consequent is an actual portion of the cause. 
 The phenomenon, consisting of force acting upon matter, 
 which constitutes the cause, seems to expend and part with 
 a portion of its own energy in producing the state of being 
 which constitutes the effect. 
 
 The relation of effect to cause must indeed, if the con- 
 ception of it is derived otherwise than from experience of 
 repeated sequences, be something more than one of mere 
 succession. For a single instance of a phenomenon would 
 stand in this same relation of mere succession to every 
 other phenomenon that has gone before. To that imme- 
 diately preceding it, it has a relation of succession which 
 
i6 THE THEORY OF INFERENCE 
 
 is certainly unique ; but immediate succession is clearly no 
 necessary part of the conception of the relation of effect to 
 cause. No doubt every phenomenon is immediately pre- 
 ceded by a cause ; but it is by no means always to this 
 immediate cause that the mind looks, or is able to look, as 
 containing the explanation of it. If, for example, we affirm 
 that eating unripe fruit creates gastric disturbance, or that 
 a good education makes a man a useful citizen, we by no 
 means intend to imply that the cause is immediately followed 
 by its effect : there intervene other causes set in motion by 
 the first. An explanatory cause may be separated by some 
 interval of time and by a chain of intervening causes from 
 the phenomenon which it explains. Every effect has, indeed, 
 an ancestry of causes, and every cause a posterity of 
 effects ; and the mind fixes its attention upon one cause or 
 one effect, rather than another, as the cause or the effect, 
 according to the circumstances of any given case. 
 
 The view thus taken — that the relation of effect to cause 
 is one of procession, and not of succession only — seems to 
 be essential to a sound theory of inference ; while that 
 which it opposes appears to be incapable of being sustained. 
 It is not, be it understood, by any means asserted that, 
 when we think of cause and effect, the idea of procession 
 is invariably present in the consciousness. For some pur- 
 poses, perhaps, we do not seek to penetrate beneath the 
 superficial notion of succession. But it is contended that 
 for the establishment of an exhaustive and consistent theory 
 of inference there is need to penetrate ; and that, when we 
 do penetrate, we find that the root idea, from which that of 
 succession springs, is the idea of effect proceeding forth 
 from cause. 
 
 Further, this procession seems to be apprehended as 
 taking place in accordance with the design of nature. That 
 which the mature mind distinctly recognises as the formal 
 
CAUSATION 17 
 
 cause of every phenomenon — viz., the plan or the orderly 
 design of nature, in accordance with which the phenomenon 
 follows upon some chosen antecedent — appears to be no 
 less an essential part of a full conception of causation than 
 is the procession of effect from cause. A given effect is 
 apprehended as proceeding from its own cause, and a given 
 cause as producing its own effect, not by any haphazard, 
 but because it belongs to the settled order of the world that 
 things should make their appearance as they do. Concep- 
 tion of a relation between effect and cause, other than one 
 of immediate succession or of observed invariable succession, 
 would, indeed, seem to be impossible except on the hypo- 
 thesis — however feebly it may be grasped — of a designing 
 mind manifesting itself in all phenomena of nature. If we 
 reject these notions of succession as explaining the relation, 
 the idea of purpose and design in nature seems, together 
 with that of procession, to be forced upon us. Together 
 with apprehension that an observed event has proceeded 
 from some cause, or will be productive of some consequence, 
 there seems necessarily to be an apprehension also, in how- 
 ever inchoate a form, that it is according to the settled order 
 and the design of nature, according to the constitution of 
 things as in themselves they are, that it has proceeded from 
 that which has produced it, or will produce that which will 
 be its consequence. 
 
 VII. Entertaining the conception of causation, as a re- 
 lation of procession of effect from cause, the mind seems 
 prepared to receive very readily the further notion of a 
 particular event having its origin in some particular assign- 
 able cause, and of a particular manifestation of energy pro- 
 ducing some particular assignable effect. Some conspicuous 
 antecedent in close proximity to a phenomenon it easily 
 welcomes as the explanatory cause; some notable conse- 
 quent occurring shortly after it, it easily regards as the 
 
i8 THE THEORY OF INFERENCE 
 
 anticipated effect. Let us suppose, for example, a person 
 to take notice of the fact that a peal of thunder has been 
 immediately preceded by a flash of lightning, or that a 
 sensation of bodily pain has been immediately preceded 
 by the reception of a blow. Then his mind, trying in the 
 exercise of its natural activity to account to itself for the 
 occurrence of the thunder or of the feeling of pain, is likely 
 enough to see in the lightning the source of the one, or 
 in the blow the origin of the other. Observation is likely 
 enough to mark the antecedent named as the explanatory 
 cause, to which the existence of the effect is due. Or again, 
 let us suppose a person to have bitten an apple and experi- 
 enced immediately afterwards a sensation of sweetness, or 
 to have listened in the night to the roaring of the wind and 
 discovered in the morning that a tree has been uprooted. 
 Having a conception of causation, he is likely enough to 
 see in the sensation of sweetness something created by 
 the biting of the apple, and to recognise in the uprooting of 
 the tree the work accomplished by the storm of wind. 
 
 What has been said must not be taken to imply, that 
 the mind consciously entertains the idea of causation for 
 any length of time before it has cognisance of particular 
 causes and particular effects. It may even be that it first 
 awakens to the idea in consequence of observing together 
 the two phenomena to which it first assigns the relation 
 of effect and cause. But it is contended that there is some 
 interval of time, however inappreciably small, between recog- 
 nition of the fact that the one phenomenon has a cause, or 
 has an effect, and recognition of the fact, or supposed fact, 
 that the other is the cause, or is the effect ; the two acts 
 of recognition occurring in the order given. The course 
 of reasoning certainly appears to be, B has a cause and A is 
 its cause, or A has an effect and B is its effect ; not, A and 
 B are related, and the relation is one of cause and effect. 
 
CAUSATION 19 
 
 The latter argument, though no doubt a reasonable one, 
 would seem to belong to a much later period of the mind's 
 development, impl^nng, as it does, acquaintance with, and 
 comparison between, various possible relations among phe- 
 nomena. 
 
 It may be worth while to remark, in conclusion, that it 
 appears to be more congenial to the human mind to start 
 from an effect and travel backwards to its cause, than it is 
 to start from a cause and travel forwards to its effect. As 
 in the case of persons, so in the case of phenomena in 
 general, it is their ancestry, rather than their posterity, in 
 which the inquiring mind is chiefly interested. Phenomena 
 which attract attention to themselves in their aspect of effects 
 seem to be commonly selected by the mind for investigation, 
 in preference to those which present themselves as causes. 
 
CHAPTER II. 
 
 UNIFORMITY IN NATURE. 
 
 I. We have supposed the mind to have reached the stage 
 of ascertaining by observation — whether faultily or cor- 
 rectly, whether tentatively or certainly, we need not consider 
 — that some particular manifestation of force is the cause of 
 some particular state of being, or that some particular state 
 of being is the effect of some particular manifestation of 
 force. And we have supposed it to be conscious that the 
 effect has its origin in the cause, or that the cause gives 
 birth to the effect, in accordance with the settled order and 
 constitution of the world. 
 
 The conception of particular cause and particular effect 
 being thus linked together in the design of nature, the concep- 
 tion of them as partaking of a common orderly existence, as 
 constituting together (we might almost say) a natural organic 
 whole, seems to include yet another conception of the re- 
 lation between them, besides that, already noticed, of the 
 one being followed by the other in point of time. It seems 
 to include the conception of the relation being, relatively to 
 all outside them, independent of time and place. Whenever 
 and wherever, during the reign and in the realm of nature, 
 the particular effect might have been found, its cause must 
 have been the same ; and whenever and wherever the par- 
 ticular cause might have been observed in action, it must 
 have produced the same effect. Into the mind's conception 
 
UNIFORMITY IN NATURE 21 
 
 of the one being naturally and necessarily followed by the 
 other, time and place do not appear to enter. The two 
 phenomena are inseparable : the existence of either, as a 
 part of nature, at any time and at any place necessarily 
 involves the existence of the other. That the mind which 
 has marked the cause of some effect, or the effect of some 
 cause, should conceive that it has marked it because the 
 time is ' now ' and the place ' here,' would seem to be 
 impossible. 
 
 II. In what has just been said there seems to be virtually 
 contained the principle of uniformity in nature. Apparently, 
 the mind has but to recognise a second effect precisely similar 
 to the first, in order to know that it must have been produced 
 by a second cause precisely similar to the first ; or to 
 recognise a second cause precisely similar to the first, in 
 order to know that it must give rise to a second effect 
 precisely similar to the first. For the mental picture of a 
 second effect or cause precisely similar to the first would 
 seem to be undistinguishable from the mental picture of the 
 first divested of conditions of time and place. And the 
 mental picture of the corresponding cause or effect, neces- 
 sarily rising in association with the picture of the first effect 
 or cause, would indicate also a cause of the second effect, 
 or an effect of the second cause, precisely similar to the first. 
 The mind, having once associated together a particular cause 
 and particular effect, has virtually associated all effects 
 precisely similar to the effect with causes precisely similar to 
 the cause, and all causes precisely similar to the cause with 
 effects precisely similar to the effect. It knows of each 
 particular cause and of each particular effect, as it comes to 
 be acquainted with them and contemplates the existence 
 of others like them, that there is in their case uniformity in 
 nature. 
 
 When particular similar causes or similar effects are 
 
22 THE THEORY OF INFERENCE 
 
 under contemplation, so immediate and inevitable does the 
 conclusion — that similar efifects will follow, or that similar 
 causes have gone before — appear to be, that it may almost 
 be accounted a necessary part of the conception of the 
 similarity of the causes or of the efifects. At all events, it 
 seems to afiford a sufificient test of similarity. And the 
 general or universal statement, that all similar causes or 
 effects produce or are produced by similar effects or causes, 
 seems to be, in respect of the ground we have for making 
 it, a statement of much the same character as, that all rivers 
 are composed of flowing water, and that all branches are 
 offshoots from the trunks of trees. As water that does not 
 flow is not what we mean by a river, and wood taken from 
 the trunk itself is not what we call a branch, so a pair of 
 causes giving rise to dissimilar effects, or a pair of effects 
 proceeding from dissimilar causes, is not what we under- 
 stand by a pair of similar causes, or a pair of similar effects. 
 But, though the idea of similarity of effects practically 
 becomes a part of the conception of similar causes, and vice 
 versa, it cannot, apparently, be said to be contained in the 
 first conception of them. There seems to be a distinct 
 onward movement of the mind from the apprehension of 
 the fact that a particular wind, for example, has blown down 
 a particular tree to apprehension of the fact, that the next 
 wind observed to be blowing under similar conditions will 
 uproot any tree that happens to be similarly situated, or 
 that the next tree found to be similarly uprooted has been 
 blown down by a similar wind. The movement is indeed 
 a necessary movement, so soon as the notion of the second 
 wind as a similar cause, or of the uprooting of the second 
 tree as a similar effect, enters the mind ; but nevertheless 
 it is a movement. It is a movement from the known to the 
 hitherto unknown ; a movement by which the mind, availing 
 itself of the fact that throughout nature there are repetitions 
 
UNIFORMITY IN NTWE^JRE --^ 23 
 
 of causes and of effects, passes from the knowledge of a 
 causal relation between two consecutive phenomena, and 
 the knowledge of a third phenomenon similar to one of 
 them, to knowledge of a fourth similar to the other. Such 
 a movement, concerning which more will have to be said in 
 following chapters, we may speak of as an act of deductive 
 inference. 
 
 The reader may here be referred to Charles Lamb's well- 
 known essay on Roast Pig for a very graphic illustration 
 of early marking, by means of observation, the cause of 
 an effect, and inferring that a repetition of the cause will 
 be associated with a repetition of the effect. It would serve 
 to enliven this discussion to quote the story in full in these 
 pages, but unfortunately it is much too long. The sub- 
 stance of it is as follows. A swineherd's hut, containing 
 a litter of new-farrowed pigs, having been accidentally set 
 on fire by his son, the luxury of roast pig was thereby for 
 the first time discovered. It being concluded by the swine- 
 herd and his son that the cause of this most agreeable 
 phenomenon was the burning of a hut containing a litter 
 of pigs, it is perceived by them — whether reasoning from 
 similar cause to similar effect, or from similar effect to 
 similar cause — that, if any other hut with a litter of pigs 
 in it were set on fire, a similar result will be produced. 
 Accordingly, " as often as the sow farrowed, so sure was 
 the house of Ho-ti to be in a blaze." The neighbours learn 
 the secret, and follow the example of Ho-ti and his son, and 
 " this custom of firing houses continued, till in process of 
 time a sage arose who made a discovery that the flesh of 
 swine, or indeed of any other animal, might be cooked 
 without the necessity of consuming a whole house to 
 dress it." 
 
 III. If the exposition which has been given of the two 
 principles of causation and uniformity in nature commends 
 
24 THE THEORY OF INFERENCE 
 
 itself as reasonable, Mill's views, being in opposition to it, 
 must be dissented from. But not on this account only is 
 it suggested that they are unsound. A more convincing 
 reason for holding them to be erroneous is, that they con- 
 tain internal inconsistencies, from which he vainly seeks to 
 show that they are free. If this position can be made good, 
 if independently of the argument of these chapters it can be 
 shown that a certain opposite theory cannot be successfully 
 maintained, we shall have indirect evidence in favour of 
 the theory expounded here, additional to whatever direct 
 evidence the exposition itself may seem to contain. And 
 since a true theory of causation and uniformity may be said 
 to be an essential part of a true theory of inference, it is 
 important for the establishment of the main thesis of this 
 book that this indirect evidence should not be neglected. 
 
 Now Mill's contention is, that the idea of causation is 
 derived from experience of the uniform course of nature. 
 Instead of causation being, as has been here represented, 
 the designed procession of one phenomenon from another 
 — a conception leading on to the conception of a uniformity 
 in nature which is a uniformity of procession — instead of 
 this, uniformity in nature is, with Mill, an observed fact, 
 and is no more than a uniformity of succession. And the 
 principle of causation is only a particular expression or 
 enunciation of this fact of uniformity of succession. Causa- 
 tion is but the invariable relation of sequence seen, or 
 inferred, to exist between any two phenomena. One 
 phenomenon is perceived to be invariably followed by 
 another ; and, this being so, the antecedent is termed the 
 cause, and the consequent the effect. "The o»ly«|p'iO|ijien 
 of a cause which the theory of induction requir|p AhA^ch 
 a notion as can be gained by experience. The Law of 
 Causation, the recognition of which is the main pillar of 
 inductive science, is but the familiar truth that invariability 
 
UNIFORMITY IN NATURE 25 
 
 of succession is found by observation to obtain between 
 every fact in nature and some other fact which has pre- 
 ceded it, independently of all considerations respecting the 
 ultimate mode of production of phenomena, and of every 
 other question regarding the nature of 'Things in them- 
 selves.'" ^ 
 
 We have now to note with the greatest care the meaning 
 which is to be attached to the words observation and ex- 
 perience. In a strict and proper sense, they have reference 
 onl}^ to things that have already presented themselves as 
 apparent to the intelligence. Experience is of things that 
 have been actually experienced, and observation is of things 
 that have been actuallv observed. There is, however, a 
 looser way of employing these terms, in which they are 
 made to cover a wider range. Thus we may say. Experi- 
 ence teaches me that if I eat this kind of food it will make 
 me ill, or, Observation shows that no self-seeking man can 
 at all times be relied on. Here it will be seen that the 
 terms in question are used to cover facts other than those 
 which the}' strictly refer to. There is, together with a 
 statement of certain known facts, an inference from them 
 to other contemplated facts. In strict language, experience 
 only teaches a person that a certain kind of food has made 
 him or others ill in time past ; and he infers that it will, if 
 now partaken of, also make him ill in the future. Observa- 
 tion onl}' teaches a person that among the self-seeking men 
 he is acquainte^Ufcth, there is not one who is alwa3's to be 
 relied on ; and lMd|ifers that any other self-seeker, whoever 
 ^ he may be, is similarly unreliable. There is in either case 
 I a' passage' of the mind from the known to the unknown. 
 
 In which, then, of the two senses are we to understand 
 the terms in the above passage ? Mill, as we shall see, 
 would decline to acknowledge that common-place predictions 
 
 ^ .4 System of Logic, Ijy John Stuart Mill, Bk. III. ch. v. § 2. 
 
26 THE THEORY OF INFERENCE 
 
 or generalisations of the kind just noticed are valid inductive 
 inferences, resting, as such, on a recognition of causation. 
 But let it be observed, that this is a crucial question of a 
 theory of inference, and that the correctness of his view can 
 by no means be admitted. It will here be maintained, that 
 any real inference whatsoever, not merely is not valid, but is 
 not even possible, apart from a conception of causation. To 
 understand, therefore, Mill as using, in a first description of 
 causation as the basis of true inference, certain terms in a 
 loose sense implying that inferences of some kind form a 
 part of the conception of causation, would be to see in his 
 argument an altogether inadmissible pctitio principii. And 
 let it be further noted that he appears in general to be 
 anxious to insist on the sufficiency of sense experiences, 
 to the exclusion of innate ideas, to account for men's con- 
 ceptions of nature's order. Under these circumstances we 
 are surely entitled — nay, we may indeed regard ourselves 
 as bound — even if we are not altogether intended, to con- 
 sider that he is here declaring actual experience to be the 
 basis of the conception of causation, and that he is not 
 introducing into the conception any kind of innate or of 
 inferred idea. Upon the two grounds indicated we may 
 reasonably interpret the terms experience and observation, 
 in the passage before us, in their literal and simple sense, 
 and we may reasonably refuse to interpret them in any 
 other. 
 
 Nevertheless, Mill endeavours to show that the true 
 principle of causation, while it is derived from experience 
 and observation, and while it is the necessary basis of in- 
 ductive inference, contains more than the direct results 
 of experience and observation. Having, in effect, asserted 
 that the true conception is one of experienced and observed 
 succession, not of imagined procession, he claims for this 
 conception that it none the less includes the ideas of neces- 
 
UNIFORMITY IN NATURE 27 
 
 sity and universality, ideas upon which inductive inferences 
 are founded. A cause, he holds, is an antecedent which, 
 not only has been, but must always be, followed by a certain 
 consequent. Not only among observed phenomena, he holds, 
 but among all phenomena whatsoever, there is a certain 
 necessary sequence. " To certain facts, certain facts always 
 do, and, as we believe, will continue to, succeed. The 
 invariable antecedent is termed the cause ; the invariable 
 consequent the effect. And the universality of the law of 
 causation consists in this, that every consequent is con- 
 nected in this manner with some particular antecedent or 
 set of antecedents. Let the fact be what it may, if it has 
 begun to exist, it was preceded by some fact or facts with 
 which it is invariably connected. For every event there 
 exists some combination of objects or events, some given con- 
 currence of circumstances, positive and negative, the occur- 
 rence of which is always followed by that phenomenon." ^ 
 
 Parentheticall}^, another objection to Mill's theory of causa- 
 tion may here be pointed out. He is careful, it will be 
 noticed, to speak of the necessar}^ and universal relation of 
 causation as if it were only half of what in truth it seems to 
 be. He holds that a cause is invariably followed by its own 
 particular effect, but he does not hold that an effect is in- 
 variably preceded by its own particular cause. " To certain 
 facts," he says, " certain facts always do, and, as we believe, 
 will continue to, succeed ; " but he avoids sa3ang, " By certain 
 facts certain facts always are, and, as we believ^e, will con- 
 tinue to be, preceded." Discussion of this point will be 
 better reserved for another section. 
 
 Let us now return to the consideration of his strange 
 position, that a cause, on becoming known to the mind solel}' 
 b}^ experience and observation as an invariable antecedent, 
 at the same time becomes known to it as the antecedent of 
 
 1 Bk. III. ch. V. g 2. 
 
28 THE THEORY OF INFERENCE 
 
 a necessary consequent. We are not yet prepared to take 
 in hand the further question of universahty — the question, 
 that is, how, in his view, experience and observation teach 
 that to every phenomenon whatsoever throughout nature 
 there is a cause, an antecedent which is invariably followed 
 by a similar effect. 
 
 The proposition, A always has been followed by a, in- 
 cludes the proposition, A always will be followed by a. 
 "To certain facts, certain facts always do, and, as we be- 
 lieve, will continue to, succeed." This idea, not only of an 
 observed, but of a necessary relation between cause and 
 effect, is without doubt a part of men's actual conception of 
 causation, and it is a part which is essential to it as the 
 basis of a certain class of acts of inference. But, unless the 
 conception of causation is derived otherwise than from ex- 
 perience, it seems impossible to account for this idea of 
 necessity which enters into it. Let us, however, see how 
 far Mill succeeds in what appears to be the hopeless 
 endeavour to show that the idea is in fact a product of 
 experience. He writes as follows : — 
 
 '' When we define the cause of anything (in the only sense 
 in which the present inquiry has any concern with causes) 
 to be ' the antecedent which it invariably follows,' we do 
 not use this phrase as exactly synonymous with ' the ante- 
 cedent which it invariably has followed in our past ex- 
 perience.' Such a mode of conceiving causation would be 
 liable to the objection ver}^ plausibly urged by Dr. Reid, 
 namel}'', that according to this doctrine night must be the 
 cause of day, and day the cause of night ; since these 
 phenomena have invariably succeeded one another from 
 the beginning of the world. But it is necessary to our 
 using the word cause that we should believe not only that 
 the antecedent always has been followed by the consequent, 
 but that as long as the present constitution of things 
 
UNIFORMITY IN NATURE 29 
 
 endures it always zi^'ill be so. And this would not be true 
 of day and night. We do not believe that night will be 
 followed by day under all imaginable circumstances, but 
 only that it will be so provided the sun rises above the 
 horizon. If the sun ceased to rise, which, for aught we 
 know, may be perfectly compatible with the general laws of 
 matter, night would be, or might be, eternal. On the other 
 hand, if the sun is above the horizon, his light not extinct, 
 and no opaque bod}^ 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. . . . Invariable sequence, therefore, is not 
 1 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 conjunc- 
 tions in some sort accidental. Such, to an accurate thinker, 
 is that of day and night. The one might have existed for 
 any length of time, and the other not have followed the 
 sooner for its existence; it follows only if certain other 
 antecedents exist ; and where those antecedents existed, it 
 would follow in any case. No one, probabl}^, ever called 
 night the cause of day ; mankind must so soon have arrived 
 at the very obvious generalisation, that the state of general 
 illumination which w^e call day would follow from the pre- 
 sence of a sufficientl}' luminous bod}^ whether darkness had 
 preceded or not. We may define, therefore, the cause of a 
 phenomenon to be the antecedent, or the concurrence of 
 antecedents, on which it is invariably and Jinconditionally 
 consequent."^ 
 
 With reference to this we have to make the following 
 inquiries. First, what possible warrant have we for intro- 
 ducing the idea of unconditionaJity or necessity into the 
 1 Bk. III. ch. V. §6. 
 
30 THE THEORY OF INFERENCE 
 
 definition of cause, when it has already been stated that the 
 idea of causation is based only on experience of succession ? 
 Secondly, if this idea is legitimately introduced, as a pro- 
 duct of experience, how are we to account for its absence 
 from our conception of the relation between night and day ? 
 Or thirdly, if in fact it is not absent from this conception, 
 why do we still not call night the cause of day ? 
 
 I. We find what is practically Mill's answer to the first 
 question in a foot-note appended to a subsequent chapter. 
 " Dr. Ward's last, and, as he says, strongest argument, is 
 the familiar one of Reid, Stewart, and their followers — that 
 whatever knowledge experience gives us of the past and 
 present, it gives us none of the future. I confess that I see 
 no force whatever in this argument. Wherein does a future 
 fact differ from a present or a past fact, except in their 
 merely momentary relation to the human beings at present 
 in existence ? The answer made by Priestley, in his exami- 
 nation of Reid, seems to me sufficient, viz., that though we 
 have had no experience of what is future, we have had 
 abundant experience of what ivas future. The ' leap in the 
 dark ' (as Professor Bain calls it) from the past to the 
 future is exactly as much in the dark, and no more, as the 
 leap from a past which we have personally observed to a 
 past which we have not. I agree with Mr. Bain in the 
 opinion that the resemblance of what we have not experi- 
 enced to what we have, is, by a law of our nature, presumed 
 through the mere energy of the idea, before experience has 
 proved it."-'- Let us examine the value of this reply. 
 
 He seems to contend, that experience of the past both 
 warrants and contains assurance that what has invariably 
 been will still continue to be. In the first place, he seems 
 to say, experience warrants the assurance, because we find, 
 on looking back to many a past date, that what had 
 1 Bk. III. ch. xxi., foot-note. 
 
UNIFORMITY IN NATURE 31 
 
 invariably been before that date did, in fact, continue to be 
 after it, though at the time we had no certain knowledge 
 that it would do so. Hence we may legitimately conclude, 
 that what has invariably been up to the present time will 
 continue to be in the future, though otherwise we have no 
 certain knowledge of this. And in the second place, he 
 seems to sa^', existing experience itself contains this assur- 
 ance, though subsequent experience is needed to really 
 prove the fact. His first contention appears to be, that a 
 given relation between two phenomena may be confidently 
 looked for in the future, because the continuity of this 
 relation is seen to have remained unbroken in the past. 
 His second appears to be, that a given relation may be 
 looked for, because the relation itself is seen to have in- 
 variably existed in the past. In the first he seems to regard 
 the mind as following, in some degree, the manifestations of 
 an antecedent throughout their course, and discovering no 
 instance of its being succeeded by another consequent. In 
 the second he seems to regard it as simply knowing of no 
 consequent but one. The too contentions agree in the point 
 that the mind has legitimate ground for looking in future for 
 the consequent to which it has become accustomed. But 
 otherwise they appear to be inconsistent with each other; 
 and we had better treat them as if they were presented as 
 alternatives. 
 
 With regard to the first, it is no doubt true that there are 
 cases in which the uninterrupted occurrence of any given 
 phenomenon or combination of phenomena gives rise to a 
 conviction that the occurrence will continue in the future. 
 Such cases we shall have to notice in a later chapter of this 
 treatise. It may here be said of them that the principle 
 which they exemplify is something quite different from the 
 uniform relation between cause and effect. To expect A, or 
 B, or A and B, to go on happening from time to time in the 
 
32 THE THEORY OF INFERENCE 
 
 manner that they do, because they have never yet been 
 known to happen otherwise or to cease to happen, is a very 
 different thing from expecting that, whenever A happens, B 
 will happen in succession to it. That an idea of certainty 
 or necessity should be born of experience of the continuous 
 manifestations of phenomena is no ground whatever for 
 introducing the same idea into experience of the happening 
 of one phenomenon being uniformly followed by the happen- 
 ing of another. It must altogether be denied that it is 
 admissible to transfer the idea of certainty or necessity from 
 the absolute continuity of a phenomenon, or of a collection or 
 succession of phenomena, to the contingent continuity of a 
 relation of succession between one phenomenon and another. 
 Further, even if we could transfer it, its existence would 
 first need to be accounted for. 
 
 And with regard to the second contention, it is no doubt 
 true that there are cases in which experience of an in- 
 variable relation of succession between one phenomenon and 
 another leads to expectation that the relation will continue. 
 But then, it is here maintained, this is because, together 
 with experience, there is present in the mind another con- 
 ception which makes it possible for experience to be utilised. 
 The question, be it observed, is just that which has recently 
 been spoken of as a crucial question of a theory of inference. 
 It is contended, that thus to found expectation of the future 
 upon experience of the past is a mode of generalising, a 
 genuine act of inference, which is only possible because 
 the mind is in possession of a conception of causation un- 
 derived from uniform experience. It cannot for a moment be 
 allowed, that there is in experience itself any kind or degree 
 of knowledge concerning anything except that which is 
 already past. 
 
 2. But supposing Mill to have silenced our questionings 
 as to the unconditionality or necessity of one phenomenon. 
 
UNIFORMITY IN NATURE 33 
 
 whenever it may happen, being succeeded by another ; so 
 that we cease to dispute the possibility of the idea being 
 contained in or evolved from the simple experience of the 
 past ; supposing this, we have still to confront him with the 
 following dilemma. Since day has invariably succeeded 
 night, and yet we do not call night the cause of day, either 
 invariableness of succession does not, as a matter of fact, 
 give rise to the idea of unconditionality, or unconditional 
 invariableness of succession does not constitute what we 
 understand by causation. For one reason or the other (if 
 not, as we must maintain, for both) invariableness of suc- 
 cession does not, in this particular case, give rise to the 
 notion of causation. If the former alternative be chosen, 
 then his view of causation is such as to be useless for the 
 purposes of a theory of inference ; if the latter, then his view 
 needs to be entirely reconsidered. 
 
 Mill does not shrink from encountering this objection. 
 He holds that in the special case of the succession of night 
 and day invariableness does not give rise to the idea of 
 unconditionality, but that this peculiarity may be accounted 
 for consistently with the maintenance of his theory of 
 causation. In addition to his remarks upon the subject in 
 the passage already quoted, he writes as follows: — "To 
 some it may appear, that the sequence between night and 
 day being invariable in our experience, we have as much 
 ground in this case as experience can give in any case for 
 recognising the two phenomena as cause and effect ; and to 
 say that more is necessar}' — to require a belief that the 
 succession is unconditional, or, in other words, that it would 
 be invariable under all changes of circumstances — is to 
 acknowledge in causation an element of belief not derived 
 from experience. The answer to this is, that it is experi- 
 ence itself which teaches us that one unifomiity of sequence 
 is conditional and another unconditional. When we judge 
 
34 THE THEORY OF INFERENCE 
 
 that the succession of night and day is a derivative sequence, 
 depending on something else, we proceed on grounds of 
 experience. It is the evidence of experience which con- 
 vinces us that day could equally exist without being followed 
 by night, and that night could equally exist without being 
 followed by day. To say that these beliefs are "not gene- 
 rated b}^ our mere observation of sequence," is to forget that 
 twice in every twenty-four hours, when the sky is clear, 
 we have an experiinoitiLUi cnicis that the cause of day is the 
 sun. We have an experimental knowledge of the sun which 
 justifies us on experimental grounds in concluding, that if 
 the sun were always above the horizon there would be day, 
 though there had been no night, and that if the sun were 
 always below the horizon there would be night, though there 
 had been no day. We thus know from experience that the 
 succession of night and day is not unconditional. Let me 
 add, that the antecedent, which is onl}' conditionally invari- 
 able, is not the invariable antecedent. Though a fact may, 
 in experience, have always been followed by another fact, 
 yet if the remainder of our experience teaches us that it 
 might not alwa^-s be so followed, or if the experience itself 
 is such as leaves room for a possibility that the known 
 cases may not correctly represent all possible cases, the 
 hitherto invariable antecedent is not accounted the cause ; 
 but why ? Because we are not sure that it is the invari- 
 able antecedent." ^ 
 
 Now what does this argument amount to ? Experience, 
 it says, teachies us that the sun, rather than night, is the 
 unconditional invariable antecedent, or cause, of da3^ But 
 how can this circumstance, obviously inconsistent with the 
 position that presumption or expectation is born of invariable 
 experience, possibly explain the failure of expectation to be 
 in this case born ? How can an exception to the law of 
 1 Bk. III. ch. V. § 6. 
 
UNIFORMITY IN NATURE 35 
 
 nature, that experience of a uniform past involves assurance 
 of a uniform future, explain itself, leaving the law substan- 
 tially intact ? It must be pointed out, that the experience 
 which discriminates between the sun and night, as the cause 
 of day, can, apparently, be no other than the experience of 
 a mind already possessed of an idea of causation as some- 
 thing more than a relation of succession. But if we waive 
 this difficulty — a difficulty perhaps sufficient in itself to 
 upset Mill's theory — and assume that a mind, knowing only 
 of a relation of succession, can distinguish between an in- 
 variable succession that is conditional, and an invariable 
 succession that is unconditional, how does its refusing to 
 see in the sequence of night and day the quality of uncondi- 
 tionality release this pair of phenomena from the operation 
 of the other mental process which pronounces that the quality 
 must be present ? It appears to be simply a case of contra- 
 diction, a case of one kind of experience refuting the alleged 
 teaching of another kind. To say that expectation of the 
 future is naturally engendered by uniform experience of the 
 past, and then to excuse a manifest exception to this alleged 
 fundamental principle by the plea, that it is by a discrimi- 
 nating experience that the exception is demanded, appears 
 to be no sound defence whatever of the principle in question. 
 The principle, having an exception, must be abandoned as a 
 principle. 
 
 We may now, perhaps, look upon Mill's doctrine of causa- 
 tion — that it is a conception which, being the basis of infer- 
 ence, is one of observed and yet unconditional succession — as 
 sufficiently refuted. The three terms — basis of inference, 
 product of experience, unconditionality of sequence — cannot 
 possibly be harmonised into one conception. A conception 
 of causation derived from experience, and existing prior to 
 all inference, cannot possibly comprise any reference to the 
 future : a conception of unconditional sequence, forming the 
 
36 THE THEORY OF INFERENCE 
 
 basis of inference, cannot possibly be derived only from 
 experience : a conception of the future, inferred from the 
 experience of the past, cannot possibly be the basis of all 
 inference. 
 
 Let us, then, consider it sufficiently established, that a 
 cause is an antecedent phenomenon from which the effect is 
 considered to proceed, and that this procession, being con- 
 ceived of as in accordance with the orderly design of nature, 
 presents itself to the mind as necessary or unconditional. 
 Investigation of Mill's argument on the question of univer- 
 sality as appertaining to causation must be postponed until we 
 have discussed the processes of induction and deduction. 
 
 IV. We may now take up the question of the discrepancy 
 between Mill's view and ours as to what the uniformity of 
 causation properly consists in. A cause, he says, is invariably 
 followed by the same effect, but an effect is not invariably 
 preceded by the same 'cause. " It is not true, then, that one 
 effect must be connected with only one cause, or assemblage 
 of conditions ; that each phenomenon can be produced only 
 in one way. There are often several independent modes in 
 which the same phenomenon could have originated. One fact 
 may be the consequent in several invariable sequences ; it may 
 follovf, with equal uniformity, any one of several antecedents, 
 or collections of antecedents. Many causes may produce 
 mechanical motion : many causes may produce some kinds 
 of sensation : many causes may produce death. A given 
 effect may really be produced by a certain cause, and yet be 
 perfectly capable of being produced without it."^ 
 
 In writing thus he certainly appears to be in error. There 
 seems to be no sound reason for assigning less uniformity to 
 the cause which produces a given effect, than to the effect 
 which proceeds from a given cause. Doubtless it is a fact 
 that mere experience fails to show that similar effects are in 
 1 Bk. III. ch. X. § I. 
 
UNIFORMITY IN NATURE 37 
 
 all cases the results of similar causes. But no less is it a fact 
 that mere experience fails to show that similar causes in all 
 cases give rise to similar effects. If in truth our apprehen- 
 sion of uniformity, even in relation to things that happen 
 before our eyes, were derived only from experience, it would 
 surely be, as regards the effects of causes no less than 
 the causes of effects, an apprehension consistent with the 
 recognition of manifold exceptions. Mill himself writes thus : 
 " All laws of causation are liable to be in this manner counter- 
 acted, and seemingly frustrated, b}^ coming into conflict with 
 other laws, the separate result of which is opposite to theirs, 
 or more or less inconsistent with it. And hence, with almost 
 every law, many instances in which it really is entirely ful- 
 filled do not, at first sight, appear to be cases of its operation 
 at all." ^ He proceeds to explain that the cause must be held 
 to be acting normally, even though the effect is not visible to 
 the senses : it is followed by a tendency to something, even 
 though the tendency is prevented from being realised. "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." ^ 
 
 If it is a reasonable explanation of the failure of a cause 
 to produce always the same apparent effect, to say that the 
 tendency to this effect has been neutralised or concealed 
 by the action of some other cause, why may not the circum- 
 stance of an effect not proceeding always from the same 
 apparent cause be somewhat similarly accounted for ? Why 
 may it not be said that the true and only cause of a 
 particular single effect exists in combination with other 
 causes among which it is concealed ? Death, for example, 
 is produced, so far as simple experience teaches, by various 
 causes ; but at the same time the death which proceeds 
 from one kind of cause is not in all respects precisely the 
 1 Bk. III. ch. X. §5. 
 
38 THE THEORY OF INFERENCE 
 
 same phenomenon as the death which proceeds from another 
 kind. Death is, in each instance of it, a compound effect. 
 And why may we not hold that the element, which the 
 various manifestations of death have in common, has its 
 own particular corresponding element in each of the various 
 kinds of compound cause ? 
 
 Of course, to take this view and under all circumstances 
 to maintain it, is to pass beyond the limits of mere experience 
 and observation. But so also must we sometimes pass 
 beyond these limits, in order to maintain the view that, 
 even in relation to matters which come under our notice, 
 similar causes are invariably followed by similar effects. 
 And consequently, Mill's theory of causation — in insisting 
 that experience is the basis of the conception, in going 
 outside experience to justify the assertion that a cause is 
 invariably followed by its own consequent, and in refusing 
 to recognise, on the ground of its not being consonant with 
 experience, the correlative truth that an effect is invariably 
 preceded by its own antecedent — appears to involve, here 
 as elsewhere, inconsistency or contradiction. 
 
CHAPTER III. 
 
 INFERENCE. 
 
 I. It appears to be a main part of the proper business 
 of the mind to make itself acquainted with the world in 
 which it has existence. Facts and occurrences outside 
 itself, and the relations in which phenomena stand to one 
 another are, in its regard, natural and proper objects of 
 attention and inquiry. 
 
 Besides the knowledge which it attains by means of 
 observation, and of subsequent reflection on the things 
 observed, there is a knowledge of which it becomes pos- 
 sessed b}^ means of a special kind of movement. This 
 movement has its starting-point only in things observed ; 
 its goal lies in some new object found to satisfy certain 
 conditions of relation between itself and the things already 
 in a manner known. And this movement is what we call 
 an act of inference. It is a passage from the known to 
 the unknown, made in the light of certain conditions that 
 have to be fulfilled. It is the discovery of some new object, 
 knowledge of which is felt to be needed to amplify and 
 complete our knowledge of objects already partially revealed. 
 It is the fastening upon some new object, with which the 
 old ones are perceived to be indissolubly connected. It is 
 an activity to which the mind is urged by its own inherent 
 curiosity, as well as by consideration of the practical benefits 
 of extending knowledge beyond the limits of experience and 
 immediate obsei'vation. 
 
40 THE THEORY OF INFERENCE 
 
 The principle of causation has been represented in the 
 preceding chapters as the essential basis of an act of infer- 
 ence. And it is for the following reason that it is thus 
 spoken of Principles closely bound up with the principle 
 of causation are essential means to the mind's making the 
 passage from the known to the unknown. They are the 
 conditions of relation between the new and the old, which 
 the mind recognises as having to be fulfilled. And further, 
 an act of inference is for the most part connected in a more 
 direct manner with the principle of causation. For it is, 
 in the vast majority of cases, the making discovery of the 
 cause of a given effect or of the effect of a given cause. 
 
 By way of illustrating to ourselves the position that infer- 
 ence is the discovery of causes and effects, we may take 
 a few simple statements of inferred fact, and see how 
 they really express a relation of causation between two 
 phenomena. 
 
 (i.) Let the statement be — I travelled with a person 
 yesterday, whom I knew, from his emaciated appearance, 
 to be very ill. Here the inference conveyed is, that the 
 emaciated appearance of a certain person was an effect which 
 had grave illness as its cause. (2.) The inference — You 
 must be hungry, as you have had nothing to eat for some 
 hours — might be expressed thus : In any person — and the 
 expression ' any person ' includes you — want of food such 
 as you have now experienced is a natural cause of a feeling 
 of hunger. (3.) The following sentence — I have just learned 
 from the newspaper, that there was an eclipse of the sun 
 yesterday visible in America — is an instance of inference 
 from testimony. Its meaning is, I see in the actual fact of 
 an eclipse having taken place an essential part of the cause 
 of its being reported in the newspaper that it did take 
 place. (4.) The inference — It is evident from his successful 
 campaigns, that Napoleon was an extremely able general — 
 
INFERENCE 41 
 
 is equivalent to the statement, Great strategic ability in Napo- 
 leon is an explanatory cause of the success which attended 
 his campaigns. (5.) The inference expressed in the words 
 — If it is fine to-morrow evening, there will be light enough 
 for walking home, as the moon will have risen and will be 
 full — is an inference that light is a natural effect of any in- 
 stance of a shining full moon. 
 
 The example last given leads to notice of the comparatively 
 limited class of inferences which do not express a relation 
 between cause and effect. If the sentence ran thus — When 
 we walk home to-morrow evening, the moon will have risen 
 and will be full — there would be an implied inference which 
 is not, or at all events need not be, an inference from cause 
 to effect or from effect to cause. The rising and the fulness 
 of the moon are the facts inferred. And the inference is not, 
 at all events in the case of uneducated people, that these 
 will be the certain effects of causes known to be in operation. 
 It is, that these phenomena will certainly take place to-morrow 
 evening, since the time of their regular recurrence will have 
 arrived. It is unnecessary at present to say more in this 
 connection. 
 
 II. All inferred statements are capable of being concisely 
 expressed in the form, A is a fact, therefore B is a fact. And 
 this may be regarded as their typical form of expression. 
 If the inference is from effect to cause, the word ' therefore ' 
 introduces the conclusion, as that which the mind has now 
 discovered. If the inference is from cause to effect, it 
 serves to introduce the effect itself, as well as the mind's 
 discovery of the effect. In the former case we have a 
 sentence like the following : His appearance was emaciated, 
 therefore he was verj'- ill. By which conclusion is meant. 
 Therefore I knew him to be very ill. In the latter case we 
 have a sentence such as this : You have been long without 
 food, therefore you are hungry. Which conclusion covers 
 
42 THE THEORY OF INFERENCE 
 
 the two meanings, Therefore I know that 3^ou are hungr}^ 
 and, You are hungry in consequence of your long fast. 
 
 But we must be on our guard against mistaking every 
 operation of the mind, the conclusion of which may be 
 introduced by the word ' therefore,' for an act of inference. 
 There are many instances in which there is no semblance 
 of a movement from the known to the unknown. If we say, 
 for example, Four is the double of two, therefore two is the 
 half of four ; or, A window is a pane of glass framed in a 
 wall, therefore this pane of glass framed in a wall is a 
 window; or, Two straight lines cannot enclose a space, 
 therefore AB and AC cannot enclose a space ; we seem, 
 in these cases, to have no more than a dealing by the mind 
 with knowledge of which it is already in possession. 
 
 There are, however, other instances, in which the mind 
 may appear at first sight to move onwards from the known 
 to the unknown, and yet not in dependence upon the prin- 
 ciple of causation. This appearance is misleading. If the 
 supposed movement is not in fact made in dependence upon 
 this principle, it is not made at all. The following is, perhaps, 
 a case in point. A person says, we may suppose. This fruit 
 is a ripe orange, therefore it has juice inside. And it may 
 seem that in saying this he is making a genuine act of in- 
 ference without any regard to causes and effects. But it 
 must be objected that, either there is here no movement 
 from the known to the unknown, or there is a movement 
 dependent upon the principle of causation. Is a ripe orange 
 a fruit which presents externally certain marks by which 
 it is known ? or is internal juiciness a material part of the 
 conception ? If the former is the case, it must be maintained 
 that if the mind passes on to the knowledge of the new fact, 
 that there is juice inside, it can only be in dependence upon 
 the principle of causation. But if the latter, then there is 
 no proper movement of the mind from the known to the 
 
INFERENCE 43 
 
 unknown ; for, until the juice is discovered, it does not 
 really know that the fruit is a ripe orange. The argument 
 expresses no more than a tentative movement, resulting in 
 the probable conclusion that the fruit, being in appearance 
 what it is, is a ripe orange, and, as such, has juice inside. 
 
 III. Of inference there appear to be four different kinds. 
 That is to say, there are four different ways by which the 
 mind, starting from the known, may reach, in dependence 
 upon the principle of causation, the hitherto unknown. The 
 four kinds or ways may be named induction, deduction, 
 illation, and delation. The last term, it must be explained, 
 is not known as a word expressing inference. It is intro- 
 duced here on account of its form, which seems to mark it 
 as a word that may be fitly used, in the absence of a better, 
 to signify a kind of inference which is connected with illation 
 in much the same way as deduction with induction, and 
 differs from deduction in much the same wa}^ as illation from 
 induction. The first three kinds of inference consist in the 
 discovery of the causes of effects and effects of causes. 
 
 Induction and deduction — as the terms are here employed 
 — are in strict dependence upon that principle, closely bound 
 up with the principle of causation, which we have already 
 discussed as the principal of uniformity in nature. Illation 
 and delation are in strict dependence upon another principle, 
 also closely bound up with that of causation, hereafter to be 
 discussed as the principle of continuity in nature. 
 
 For the present we may dismiss from further considera- 
 tion the two last-mentioned kinds of inference, and concen- 
 trate our attention upon induction and deduction. It may 
 sometimes be convenient to think and speak of these two 
 under one common name ; and ' logical inference ' seems a 
 fairty suitable name by which to call them. In one respect 
 the term seems satisfactory, since it is likely to suggest to 
 the general reader inference of a formal and demonstrable 
 
44 THE THEORY OF INFERENCE 
 
 character. In one respect it seems unsatisfactory, since 
 writers on logic are not agreed as to what constitutes the 
 real province of logical science. If we elect to include in 
 logic, besides deduction, induction understood to be based 
 upon the principle of uniformity in nature, we shall be in 
 substantial accord with Mill; seriously differing from him, 
 however, in holding that there are two valid kinds of 
 inference lying outside the domain of logic. 
 
 It may lastly be remarked that, philosophically, the order 
 in which the two kinds of logical inference have been 
 mentioned should be reversed ; since, as we shall see, an 
 act of deduction appears to be precedent to the completion 
 of every induction. But, inasmuch as most deductive infer- 
 ences are subsequent to those of induction, it seems on 
 the whole convenient to treat of induction before deduc- 
 tion ; and the order of naming them has been determined 
 accordingly. 
 
 IV. Before proceeding to consider the process of discover- 
 ing causes and effects by the method of induction, let us 
 take the preliminary step of realising clearly what it is that 
 the mind, when at any time it begins to infer, is seeking to 
 discover. What is about to be said, though said with special 
 reference to induction, is mostly applicable to illation also. 
 
 It has already been pointed out that every phenomenon, 
 regarded as an effect, has, not one cause, but an ancestry 
 of causes ; and that every phenomenon, regarded as a cause, 
 has, not one effect, but a posterity of effects. Even if every 
 effect that we notice was a single effect, produced by only 
 one immediate cause, this cause being in turn the effect of 
 a cause behind it, we should still have a chain of causes, or 
 line of ancestry, reaching from the effect to the primeval 
 cause ; any cause whatever in this chain being in a true 
 sense a cause of the effect in question. Any cause in the 
 chain is a cause from which the effect ultimately proceeds. 
 
INFERENCE 45 
 
 and without which it could not possibly have existence. 
 And similarly, if every cause that we notice was a single 
 cause, producing immediately only one effect, this effect 
 being in turn the cause of another succeeding to it, we 
 should still have a number of effects, each of which is in 
 a true sense an effect of the cause in question. 
 
 But the truth, that for every effect there is a multiplicity 
 of causes and for every cause a multiplicity of effects, 
 becomes much more conspicuously evident when we con- 
 sider how, in fact, causes join with other causes to produce 
 effects, and several distinct effects are at once the products 
 of the same causes. For example, manual labour and 
 showers of rain join with other causes to produce good 
 crops ; while both manual labour and showers of rain have 
 in their turn proceeded each from some combination of 
 causes. So again, manual labour and showers of rain, 
 besides contributing together to the growth of crops, have 
 their quite separate influence upon the life of the agricul- 
 turist, being thus in various ways factors in the production 
 of a number of subsequent effects not otherwise connected 
 with each other. Thus every ordinary effect, being a com- 
 pound effect, has — exactl}^ in the same wa}', it would seem, 
 as living creatures have — a spreading ancestry behind it, 
 every individual member of which has been essential to its 
 production. And similarly every ordinary cause, being a 
 compound cause, has a widening posterity succeeding to it, 
 every individual member of which owes its existence in 
 some measure to this cause. 
 
 This being so, when the mind inquires the cause of a 
 given effect or the effect of a given cause, what it is seeking 
 to discover is really no more than a ver}' small part of the 
 history of the phenomenon under consideration. Some one 
 link in a chain of causes joining the phenomenon in some 
 direction to the distant past, or in a chain of effects leading 
 
46 THE THEORY OF INFERENCE 
 
 in some direction to the distant future, is for the most part 
 all that it aims at ascertaining at any given time. 
 
 And yet the mind, in endeavouring to unite the pheno- 
 menon which excites its curiosity to some one other as its 
 cause, or to some one other as its effect, must not be re- 
 garded as indifferent as to where, or of what sort, the cause 
 or the effect shall be. It is searching for information which 
 it can understand, for information which can be felt by it 
 really to advance its acquaintance with the world around it. 
 It looks for a cause which shall answer more or less plainly 
 to its notion of a cause as giving birth to the effect, or for 
 an effect which it can in some measure realise as proceeding 
 from the cause. It asks for a cause so nearly related to the 
 effect, or for an effect so nearly related to the cause, in re- 
 spect of apparent kinship or of proximity of time or place, 
 that some approach to a vivid apprehension of the relation 
 of causation between them may be possible. Of no other 
 does it, in ordinary circumstances, much care to know. 
 
CHAPTER IV. 
 
 INDUCTION. 
 
 I. Understanding that the mind commonly looks for 
 one cause or one effect at a time, and that the cause or 
 effect looked for is one which, by reason of some kind of 
 nearness to the effect or cause, shall seem to be intelligible, 
 we proceed to consider the process of inferring causes and 
 effects by the method of induction. The essence of the 
 method may be said to consist in a work of comparison and 
 contrast. The phenomenon whose cause or whose effect 
 we are seeking to discover is regarded as being, in every 
 instance of it, contained in or surrounded by a set of 
 circumstances among which the cause or the effect must 
 lie. Taking then some instance of the phenomenon, and 
 neglecting all those of its surrounding circumstances among 
 which we have no interest in finding a cause or an effect, 
 we have remaining a certain limited range of circumstances 
 within which our investigation is to be carried on. The 
 circumstances, other than the phenomenon itself, within this 
 range are such as have preceded it, if we are looking for 
 a cause, and such as have succeeded it, if we are looking 
 for an effect. We next bring under observation other sets 
 of circumstances preceding or succeeding instances of the 
 phenomenon, and we ascertain which of the circumstances 
 are common to all the sets, including the first. Or we 
 bring under observation other sets of circumstances bearins: 
 
48 THE THEORY OF INFERENCE 
 
 a general resemblance to the set before us, but known not 
 to have after them or to have had before them an instance 
 of the phenomenon, and we ascertain which of the circum- 
 stances in the given set are present in any one of these 
 sets. In the one case, we compare our first set with others, 
 in order to ascertain what it has in common with them all, 
 and what it has that is not common to them all. In the 
 other case, we contrast it with others, in order to ascertain 
 what it has in common with any one, and what is therefore 
 left to it that is absent from them all. In the one case, we 
 judge that the cause or the effect is contained somewhere 
 among the common circumstances, the remainder being with 
 certainty disregarded. In the other case, we judge that it 
 is contained somewhere among the circumstances which are 
 found in the first set only, those which are common to it 
 and any other set being certainly such as may be set aside. 
 The one form of the method may be spoken of as the 
 method of comparison, the other as the method of contrast. 
 The two may often be employed in connection with the 
 same inquiry. 
 
 To illustrate roughly what has just been said, let us 
 suppose it to be required to find the cause of good health. 
 We might take some person in good health, and turn our 
 attention to such of his personal habits as seemed at all 
 likely to have a bearing upon health. We might then take 
 a number of other persons whose health is good, and 
 ascertain, by striking out from the list of habits we have 
 drawn up every one which any individual among these 
 persons is found not to practise, which of the habits of the 
 first person are common to them all. These we should 
 judge to contain collectively the required cause. Or we 
 might contrast the habits of the first person with those 
 of a number of persons not in the enjoyment of sound 
 health, and ascertain, by striking out every habit which 
 
INDUCTION 49 
 
 any one of them has in common witli liimsclf, by wliicli 
 of his habits it is that he is distinguished from all of them. 
 Among these we should judge the required cause to lie. 
 Both forms of the method would be made use of, if we 
 were first to find habits common to the observed healthy 
 persons, and then eliminate some of these as being shared 
 also by persons not in good health. 
 
 It must here be explained, that in the examples of induc- 
 tion given in this chapter no attempt is made to trace 
 particular causes and particular effects with scientific ac- 
 curacy. To make such an attempt would be to enhance 
 largely and unnecessarily the difficulty of the discussion 
 both for author and for reader. It would enhance it largely, 
 because the complexity of causes and effects as they appear 
 in nature is so great — cause combining with cause and 
 effect with eftect — that in almost every phenomenon there is 
 an assemblage of causes producing an assemblage of effects, 
 or an assemblage of effects proceeding from an assem- 
 blage of causes. And to single out a quite definite effect 
 or cause, and follow it correctly to some definite factor of 
 a compound cause or effect, is mostly a special work re- 
 quiring careful and patient labour. The attempt to do 
 this, moreover, is here quite unnecessary, since the sub- 
 ject of our investigation is the science of inference only, not 
 any of the other sciences in which inference is employed. 
 How the mind deals, not with certain particular facts, but 
 with any facts, is what we are here concerned to know. 
 All, then, that is aimed at is to state accurately the method of 
 the mind's procedure, and to adduce such rough and popular 
 illustrations as may suffice to make the statement clear. 
 
 II. Among the earliest and simplest conclusions, in arriv- 
 ing at which induction is employed, are general conclusions 
 such as, Any nest is built by a bird, Any bird builds a nest. 
 These conclusions may be incorrect relatively to the whole 
 
50 THE THEORY OF INFERENCE 
 
 of the facts of nature, and yet may be perfectly sound as 
 the tentative and immature conclusions of a person under 
 whose notice only a limited number of facts has come. 
 They have the same interest for the purposes of this dis- 
 cussion as conclusions of the most unimpeachable correct- 
 ness. For our main business is to see what is the natural 
 action of the mind in making inferences. Flow far its 
 operations can be relied upon as leading to objective truth 
 will to some extent appear as we proceed. 
 
 If the mind, having observed several instances of a nest, 
 proceeds to investigate — it may be almost unconsciously — 
 the cause, it apparently reasons substantially as follows: — (i.) 
 Each nest being built by a bird, there must be in or connected 
 with the bird the cause of its being built. (2.) The effects 
 being similar, the causes must be similar. (3.) The common 
 cause is to be found in those antecedent circumstances 
 which are common to all the birds whose nests have been 
 observed. (4.) The common circumstances appear to be 
 comprised in the bird-nature which is common to them all. 
 (5.) Since each of the observed nests has its cause in the 
 nature of a bird, any other nest, being an effect similar to 
 it, likewise has its cause in the nature of a bird. 
 
 Or if a number of birds — whose bird-nature constitutes 
 a set of causes common to them all — are watched, and the 
 mind seeks to discover something which as birds they do, 
 the reasoning is, apparently, of a very similar character, 
 (i.) The nature of each bird is a cause leading to its doing 
 something. (2.) There being a cause common to them all, 
 there must be a corresponding effect common to them all. 
 (3.) The common effect is to be found in something which 
 all are observed to do. (4.) Such a common effect is the build- 
 ing of a nest. (5.) Nest-building, being an attribute of each 
 bird brought under observation, is an attribute of any crea- 
 ture of like nature, that is, of any bird. 
 
INDUCTION 51 
 
 Let us now, before discussing this analysis, pass on to 
 consider a very simple case of inferring by induction a more 
 particular cause of a given effect, or a more particular effect 
 of a given cause. Let us take the case of a boy learning 
 by experience to associate together industry and a master's 
 favour and regard. Expressions of his master's good-will, 
 he comes to know, have their cause in his industry ; or he 
 gradually perceives that his industry produces as its effect 
 these expressions. 
 
 The course of reasoning may be as follows : — (i.) Expres- 
 sions of good-will, noticed from time to time, have their 
 causes. (2.) So far as they are in character the same, their 
 causes must be the same. (3.) A similar or common cause 
 must be found in the sets of circumstances which precede 
 and are in some connection with them. (4.) Such a cause 
 is my industr3\ Or the argument may run thus: — (l.) My 
 industry produces some effect. (2.) So far as it is day by 
 day the same, the effect must naturally be the same. (3.) 
 The uniform effect lies in circumstances connected with the 
 master's examination of the work done. (4.) Such an effect 
 are his expressions of approval. 
 
 The method of contrast, it may be pointed out, may also 
 be supposed to be employed in such a case as this; and 
 we may alter the above chains of reasoning accordingly. In 
 finding the cause we shall now have this argument: — (i.) 
 Expressions of good-will have a cause. (2.) This cause 
 cannot be present when the expressions are absent. (3.) 
 The cause must be found among circumstances of my con- 
 duct which are present when the expressions are present, 
 and absent in their absence. (4.) Such a cause is my 
 industry. And in finding the effect the mind will argue 
 thus: — (i.) My industry produces some effect. (2.) The 
 effect, whatever it is, must be absent whenever the cause 
 is absent. (3.) It must be found among some circumstances 
 
52 THE THEORY OF INFERENCE 
 
 of my school life which follow industry, but do not follow 
 idleness. (4.) Such an effect are my master's expressions 
 of approval. 
 
 The employment of the method of contrast belongs, 
 perhaps, to a later period of the mind's development than 
 the employment of the method of comparison. And it 
 would seem to depend a great deal upon the circumstances 
 of any given case whether, and how far, the mind makes 
 use of it in addition to, or instead of, the earlier method. 
 
 III. The above analysis of the process of discovering 
 by induction causes and effects indicates several distinct 
 steps. First, if this may be called a step, the mind takes 
 up the conception of causation and prepares to look for a 
 cause or for an effect. Secondly, it brings together a number 
 of sets of circumstances each containing an instance of the 
 effect or cause, or a number of sets not containing an 
 instance, but otherwise bearing some resemblance to sets 
 containing it. Thirdly, it makes a deductive inference, say- 
 ing that the looked-for cause or effect must be present in 
 every one of the first named sets, or that it must be absent 
 from every one of the last named sets. Fourthly, it searches 
 among the sets for an antecedent or a consequent, in some 
 sort of proximity to the effect or cause, fulfilling the condition. 
 Fifthly, having found one, it pronounces — more or less con- 
 fidently and more or less correctly — that it is the required 
 cause or effect. 
 
 In the case of an act of generalisation there is yet a sixth 
 step. There is a second act of deductive inference, in which 
 the mind pronounces that the cause of the observed effect, 
 or the effect of the observed cause, is a type-cause of all 
 similar effects, or a type-effect of all similar causes. 
 
 The first deductive inference — which is always made — 
 and the second — which is made whenever the mind passes 
 from the facts before it to others like them — are, be it 
 
INDUCTION 53 
 
 observed, made in dependence upon or in accordance with 
 the principle of uniformity in nature. So soon as the mind 
 has before it similar effects or similar causes, it knows from 
 memory, or at the moment realises, that the}^ proceed from 
 some similar or common cause, or give rise to some similar 
 or common effect. It likewise knows, it may be added, by 
 means of an act of reflection, that the cause or the effect 
 cannot be present in a set of circumstances from which the 
 effect or the cause is absent. 
 
 Mill, it may now be remarked, regards the whole move- 
 ment of the mind, in its passage from particular facts to a 
 general proposition grounded on these facts, as consisting 
 of but one operation ; and this he speaks of as induction. 
 His view will presently be commented on. What is here 
 meant by induction is only that part of the mind's move- 
 ment which it makes when, carrying with it the conception 
 of causation, it searches for and lights upon, within a certain 
 limited range, some particular circumstance or group of 
 circumstances antecedent to an effect or subsequent to a 
 cause ; the circumstance or group of circumstances being 
 common to all sets containing a similar effect or cause, or 
 absent from all sets not containing an instance of it. It is 
 the simple work of comparison or contrast engaged in, and 
 consummated, for the purpose of tracing, in the light of the 
 principle of uniformity in nature, a cause or an effect. 
 
 IV. The method, which has been represented as followed 
 by an immature mind more or less unconsciousl}', is sub- 
 stantialh' that which a trained intelligence consciously and 
 deliberately adopts. A trained intelligence adopts it, not 
 merely for the sake of acquiring additional knowledge of the 
 ways of nature, but also for the sake of turning acquired 
 knowledge to practical account. It seeks to ascertain the 
 cause of an effect or the effect of a cause, not merely that it 
 mav the better understand the world in which it lives, but 
 
54 THE THEORY OF INFERENCE 
 
 also that it may learn how causes can be directed and con- 
 trolled, to the furtherance of effects that are beneficial and 
 the hindrance of such as are injurious. Let us now take 
 a case of deliberate search for the cause of an effect. 
 
 Let it be required to find the cause of a certain person 
 exhibiting symptoms of being poisoned. If it should be 
 found that other persons are suffering with like symptoms, 
 we may make use, or begin by making use, of the method 
 of comparison. If there is no other, the method of contrast 
 must be employed. We are looking, be it remembered, not 
 for the recondite immediate cause, the discovery of which 
 is a matter for physiological science; nor for any very dis- 
 tant cause, such as the original production of the poison ; 
 nor for any merely modifying or contributory cause, such 
 as the constitution of the patient, by which the effect of 
 the poison is in some degree determined. But we wish 
 to find a cause which shall not be so remote from familiar 
 occurrences of daily life, or so apparently unconnected with 
 the effect, as to fail to be explanatory. We wish to find 
 the cause among circumstances which we have opportunity 
 of bringing satisfactorily under observation, and which 
 stand in some kind of recognised proximity to the effect. 
 The eating of some special article of food, for example, 
 would be a cause of the kind required. 
 
 Taking the case in which there are a number of persons 
 suffering together, we bring under observation the several 
 sets of circumstances which constitute the lives, antecedent 
 to the event, of the several patients; dismissing as irrele- 
 vant all circumstances that are inaccessible to the unscientific 
 observer, and all that appear to be remote from the effect, 
 and being especially careful to keep in view all that are 
 connected with the patients' dietary. Among the reduced 
 sets before us, and especially among those parts of them 
 which have to do with diet, we make search for circum- 
 
INDUCTION 55 
 
 stances common to the lives of all ; and among these 
 common circumstances, when they are found, we judge 
 the common cause to lie. If the cases which come under 
 observation are fairly numerous, and their circumstances 
 various, the common circumstances will be few ; so that 
 the cause may be looked upon as almost found. Otherwise 
 their number may be lessened by now introducing the 
 method of contrast. All the common circumstances, which 
 are found in the case of any person who is not a sufferer, 
 may be eliminated. 
 
 All has now been done towards the discovery of the 
 cause that induction can do. Unless there is but one ante- 
 cedent left, or unless we can learn by experiment, or by 
 the evidence of other facts, that it is in this one, and not 
 in that, of the group of residual antecedents that the cause 
 lies, we must be satisfied with having nearly, but not quite, 
 discovered its location. 
 
 But it must now be pointed out that — apart from experi- 
 ment or other evidence — the certainty of a cause being 
 contained in the small set of residual antecedents depends 
 upon two things. It depends not only upon the accuracy 
 of our work of comparison and contrast, but also upon our 
 not having unduly restricted the range of investigation. We 
 propose to ourselves to find in some article of food the 
 cause of symptoms of being poisoned. But it may very 
 well be that the explanatory cause really lies elsewhere, 
 and possibly among circumstances which we have over- 
 looked. It is conceivable that we might in some particular 
 case, unless we were extremely careful, dismiss at the 
 outset every one of the causes among the circumstances 
 deemed irrelevant. Only, perhaps, if it were possible for 
 all or nearly all the antecedents, which for the attainment 
 of any practical result it is necessary to get rid of, to 
 be eliminated by systematic and accurate comparison and 
 
56 THE THEORY OF INFERENCE 
 
 contrast, could it be properly affirmed that the residuum 
 infallibly contains a cause. 
 
 The method of ascertaining the effects of causes is similar 
 to that whereby the causes of effects are made known. 
 Let the subject of inquiry be, for example, the special 
 effect of militar}^ training upon young men. We should 
 proceed, by means of a comparison of all soldiers who 
 come under our observation, to take note of certain salient 
 points of character and conduct that appear to be common 
 to them all. We should then, by contrasting them with 
 persons who have not received a military training, discover 
 that, while some of the common points are to be met with 
 elsewhere, yet there are one or more among them which 
 seem to be peculiar to the military calling. Thus we may 
 suppose that all soldiers are found, by the method of 
 comparison, to be loyal and patriotic, to have a keen sense 
 of comradeship, to be indifferent to danger, to be prompt 
 in obeying orders, to have an erect carriage and precise 
 deportment. And we may suppose it to be found, by the 
 method of contrast, that of these characteristics only one, 
 namely, the last, is peculiar to the soldier; since there are 
 evidently large numbers of persons possessing one or more 
 of the others, while sailors ma}' be held to possess them 
 all. We should then conclude that an erect carriage and 
 precise deportment is the one noticeable result of military- 
 discipline as distinguished from all other kinds of training. 
 
 V. The results of this discussion ma}" now be recapitu- 
 lated before we pass on to the subject of deduction. 
 
 The method of induction is the mind's method of approach- 
 ing the discovery of causes and effects, by gradually con- 
 tracting within very close limits the area or range of 
 circumstances in which it has purposed to seek for a cause 
 or an effect. And induction, or inductive inference, is the 
 mind's discovery, with the aid of deduction, that a cause 
 
INDUCTION 57 
 
 or an effect lies, so to speak, somewhere within a certain 
 very narrow space. The contraction is accomplished by 
 excluding or eliminating from the selected body of cir- 
 cumstances, antecedent to the effect or subsequent to the 
 cause, all those which are not found in every other instance 
 in which the effect, or the cause, is observed to be present, 
 and likewise all which are found in any one instance in 
 which the effect, or the cause, is observed to be absent. 
 This exclusion or elimination is justified by the principle of 
 uniformity in nature. Upon the number and variety of 
 the sets of circumstances with which the first set is compared 
 and contrasted will, in general, depend the completeness 
 of this process of eliminating the circumstances in which 
 a cause, or an effect, cannot possibly reside. 
 
 When the process of elimination has been carried 
 correctly as far as we can carry it, we have before us 
 one of three cases. Either (i) no circumstance remains, 
 in which case it follows that the presumption of a cause 
 or an effect being contained in the selected body was a 
 mistaken presumption ; and we must begin our search 
 anew among some other body. Or (2) one circumstance 
 remains, in which case, in so far as cause or effect is pre- 
 sumably contained somewhere in the selected body, this 
 presumably is a cause or an effect. Or (3) several circum- 
 stances remain, in which case, unless some independent 
 evidence can be adduced, connecting one of them rather 
 than another with the phenomenon whose cause or effect 
 we are seeking to discover, we must stop short of full 
 discovery. We must be content to know that, in so far as 
 cause or effect is presumably contained somewhere in the 
 selected body, there is presumably in the small residue 
 before us a cause or an effect. 
 
 Induction can, in general, do no more than show us a 
 small number of circumstances among which presumably 
 
58 THE THEORY OF INFERENCE 
 
 the cause or the eftect must he. Evidence of a different 
 kind from that afforded by other instances of the presence, 
 or instances of the absence, of a given phenomenon is 
 commonly required in order, not only that we may lay our 
 hands with certainty upon a cause or an effect, but also that 
 we may learn with certainty within what narrow space it 
 lies concealed. Induction cannot, in general, give complete 
 assurance, even that the locality of the cause or effect has 
 been discovered. Only in the cases, if any such there can 
 be, in which it might be possible to say with certainty, not 
 only that all the real causes or effects had not been rejected 
 as circumstances irrelevant to the inquiry — so that the 
 residue would contain at least one — but also that all the 
 really irrelevant circumstances had been rejected or elimi- 
 nated — so that the residue would contain none that are 
 irrelevant — would it be possible to say with certainty that 
 the cause or effect had been discovered by the process of 
 induction only. In such cases every one of the residual 
 circumstances would be a cause, or an effect. 
 
CHAPTER V. 
 
 DEDUCTION. 
 
 I. In dealing with induction we have had occasion to 
 notice two acts of deductive inference; the one being an 
 essential aid to the process of induction, the other transform- 
 ing the conclusion into a law of nature. The one declares 
 that if X represents the unknown cause or effect of the 
 observed phenomenon, X likewise represents the cause or the 
 effect of every other instance of the phenomenon : it declares 
 also, if need be, that in the absence of an instance, X must 
 be absent also. This is a recognition of the uniformity that 
 exists in nature. The other deduction is supposed in the 
 illustration given to pronounce as follows. From the induc- 
 tion, that all observed nest-building is done by birds, it 
 draws the conclusion, that any nest is built by a bird. And 
 from the induction, that all observed birds build nests, it 
 draws the conclusion, that any bird builds a nest. 
 
 These acts of deductive generalisation, to us obviously 
 erroneous, are natural to a person of limited experience. 
 It is concluded in the one case, that the faculty of nest- 
 building exists only, and in the other case, that it exists 
 always, in the nature of a bird. If we take A to represent 
 this faculty, B the remainder of the nature of a bird, and 
 P a nest, we have, as the results of our inductions, (i) P in 
 each observed case has its cause in AB, (2) AB in each 
 observed case produces P. From (i) we may make the 
 
6o THE THEORY OF INFERENCE 
 
 deductive inference, Any P has its cause in either A or 
 B ; but obviously not — as in the example given — Any P has 
 its cause in AB. For if A is the actual cause, P might be 
 produced by AC or AD; it being possible, as we now 
 know or consider, for A to enter into other combinations 
 besides AB. From (2) we may infer, Any AB produces 
 P ; but obviously not — as in effect the example does — 
 Any B produces P. For A may be the actual cause, and 
 need not, as we now know or consider, be an invariable 
 accompaniment of B. 
 
 And universally, if in ascertaining a cause we find that, 
 in a particular case, AB contains the cause of P, we may 
 go on to say. Any AB produces P, Any P has its cause 
 either in A or in B. Similarly, if in ascertaining an effect 
 we find that, in a particular case, A has as its specific effect 
 either P or Q, we may go on to say. Any A produces either 
 P or Q, Any PQ has A as one of its causes. 
 
 In the case of our having knowledge, howsoever obtained, 
 that two single phenomena, this A and this P, are cause 
 and effect, then we may infer. Any P has its cause in A, and, 
 Any A produces P. We may likewise make the inferences. 
 That other P has its cause in A, That other A produces P. 
 
 Deduction, whether from a pair of particulars to another 
 pair of particulars, or from a pair of particulars to a pair of 
 abstract phenomena, appears to be neither moi"e nor less 
 than a necessary movement of the mind by which it reaches 
 (/again and again, in relation to particular instances that come 
 ^before it, the truth that uniformity exists in nature. If the 
 mind has before it a particular A as the known cause of 
 a particular P, and sees, or conceives the idea of, another 
 phenomenon precisely similar to P, proceeding from some 
 cause, then it cannot but picture to itself, as this cause, 
 particular or abstract as the case may be, a phenomenon 
 precisely similar to A. Or if it has before it P as the known 
 
DEDUCTION 6r 
 
 effect of A, and contemplates another instance of A acting 
 as a cause, it cannot but picture to itself as the effect, 
 particular or abstract as the case may be, a phenomenon 
 precisely similar to P. According!}^ as the newl}^ contem- 
 plated effect or cause is particular or abstract, so the newly 
 ascertained relation of causation will take a particular or 
 an abstract form. From the proposition, My father was 
 mortal because he was a man, the mind can pass, either 
 to the particular truth, I am mortal because I am a man, 
 or to the abstract truth, Any man is mortal because he 
 is a man. 
 
 It is not, however, by any means contended that on every 
 occasion, w^hen the mind becomes conscious of a fact of so 
 common a nature as the liability to death of this or that 
 individual, it goes through a fresh process of deductive 
 inference. Having been once led to apprehend distinctly 
 and firmly the general or abstract truth. Any man is mortal 
 because he is a man, it w^ould seem to hold it in readiness 
 for application to subsequent particular cases that come 
 before it. Or rather, perhaps — and this is much the same 
 thing — it may be said to carry about with it the idea of 
 mortality as part of an enlarged conception of the attributes 
 of manhood. The mind having once grasped, by means of 
 deduction, a general or abstract truth, seems freed from the 
 necessity of making subsequent particular deductions. It 
 remembers or it knows, when it looks upon phenomenon 
 P or A, that there is another phenomenon A or P existing 
 in causal connection with it. 
 
 Nor, again, is it necessary to suppose that the mind 
 makes a deductive inference whenever, from apprehension 
 of the fact, This A is a cause of P, it becomes conscious of 
 the fact. Any A is a cause of P. It may be that it carries 
 about with it, so to speak, as part of an enlarged conception 
 of causation, originally obtained by deduction, the idea that 
 
62 THE THEORY OF INFERENCE 
 
 a causal relation found to exist in any one pair of particular 
 phenomena exists also in any pair whatsoever of similar 
 phenomena. Having once grasped, by means of deduction, 
 the idea of uniformity in nature, it seems freed from the 
 necessity of using deduction in every fresh case in order 
 to arrive at an abstract or general conclusion. It may 
 remember, when it becomes aware of a causal relation 
 between a particular A and P, that the same connection 
 exists between any A and P, or between A and any P. 
 
 II. The subject of logical inference, to the end of which 
 we have now come, can scarcely be dismissed without 
 some notice of syllogistic argument. 
 
 In treatises on logic the major premise of a syllogism is 
 given in the form of a universal proposition, of which All 
 A is P may be taken as the type. Now it is important that 
 we should clearly understand what these universals are 
 intended to express. What warrant have we for laying 
 down such propositions as. All men are mortal, All magnets 
 attract iron ? And what are the consequences that follow 
 from them ? What is the nature and the value of the 
 argument. All men are mortal, John is a man, Therefore 
 he is mortal ? or of the argument. All magnets attract iron, 
 This is a magnet, Therefore it will attract iron ? 
 
 I. If the universals are simply loose ways of expressing 
 the inferred conclusions, Any man is mortal because he is 
 a man. Any magnet attracts iron because it is a magnet, they 
 may be interpreted in two slightly different ways. They 
 may be understood to record facts in connection with men 
 and magnets, a knowledge of which the mind has by induc- 
 tion and deduction become possessed of; or they may be 
 understood to announce new and enlarged conceptions of 
 men and magnets, which the mind henceforward entertains. 
 
 In the former case the assertion is made that, wherever 
 a man exists, that man is mortal; or, wherever a magnet 
 
DEDUCTION 63 
 
 exists, that magnet attracts iron. This is the major premise 
 of a syllogism. The minor premise, John is a man. This is 
 a magnet, points out a particular man, or a particular mag- 
 net. And the conclusion, John is mortal, This magnet will 
 attract iron, announces that the mind sees the man, or sees 
 the magnet, and repeats, with reference to him, or with 
 reference to it, the assertion which it made in the major 
 premise. The word ' therefore,' which introduces the con- 
 clusion, does not imply any inference, any passage of the 
 mind from old to new truth. It does not imply an inference 
 any more than it would imply it, if the argument were 
 worded thus : John is mortal, therefore he is mortal, or, 
 This magnet will attract iron, therefore it will attract iron. 
 The assertion of the conclusion follows from the assertion 
 of the major premise, only because it is seen to be contained 
 in it. 
 
 If we understand the universals in the latter of the two 
 senses, then the assertion is made, that the mind hence- 
 forward refuses to acknowledge as a man any creature who 
 is not mortal, or as a magnet any piece of iron or steel that 
 does not attract metal. A man is a creature who has, among 
 his attributes, that of mortality ; a magnet is a piece of iron 
 or steel which has, among its properties, that of attracting 
 iron. The major premise is in this case nothing but a 
 definition. And it is the minor premise, John is a man, 
 This is a magnet, which makes an assertion, in which the 
 assertion of the conclusion is manifestly contained. 
 
 In whichever way we interpret the general or abstract 
 proposition which constitutes the major premise of the syl- 
 logism, there is in the syllogism itself no inference. The 
 conclusion is contained in, and extracted from, either the 
 major premise made applicable by the minor to a particular 
 case, or else the minor premise read in the light afforded 
 by the major. 
 
64 THE THEORY OF INFERENCE 
 
 2. If the universals are to be taken literally as collective 
 statements, they may again be interpreted in two different 
 ways. They may be understood to announce the results 
 of observation, or they may be conceived to announce the 
 results of a thoroughly exhaustive application of an act of 
 inference. 
 
 In the former case it is declared, that all men who have 
 sufficiently come under obsei*vation have failed to live be- 
 yond a certain number of years, or that all pieces of iron or 
 steel that have been brought into a given kind of contact 
 with loadstone have, when tested, exhibited the property 
 of attracting iron. The propositions are simple statements 
 of observed fact. They are not conclusions from inference, 
 nor does the conception of causation enter into thern. If 
 they are made major premises of syllogisms, the conclusions 
 of these syllogisms can only repeat a part of what they 
 assert. The syllogisms will run thus : All observed men 
 are mortal, John is one of the observed men. Therefore he 
 is mortal ; All observed magnets have the property of attract- 
 ing iron, This is one of the observed magnets, Therefore it 
 has the property of attracting iron. 
 
 But we may suppose the inferences to have been made, 
 Any man is mortal. Any magnet attracts iron. If then the 
 mind should picture to itself man after man, or magnet after 
 magnet, it would know of each, that he is mortal, or that 
 it attracts iron. And if we imagine this process carried 
 on exhaustively, so as to include all men whatsoever, or 
 all magnets whatsoever, the mind would be entitled to pro- 
 nounce literally and absolutely, as a part of its own know- 
 ledge. All men are mortal. All magnets attract iron. These 
 true universals, if employed as major premises of syllogisms, 
 would, as in the preceding case, contain the particular con- 
 clusions that follow from them. 
 
 III. The view of the meaning of syllogistic argument con- 
 
DEDUCTION 65 
 
 taincd in tlic foregoing remarks is very mucli in accord with 
 that of Mill. That is to say, he hkewisc holds that in the 
 syllogism there is no fresh inference. He writes as follows : 
 "When, therefore, we conclude from the death of John and 
 Thomas, and every other person we ever heard of in whose 
 case the experiment had been fairly tried, that the Duke of 
 Wellington is mortal like the rest, we may, indeed, pass 
 through the generalisation, All men are mortal, as an inter- 
 mediate stage; but it is not in the latter half of the process, 
 the descent from all men to the Duke of Wellington, that the 
 inference resides. The inference is finished when we have 
 asserted that all men are mortal. What remains to be per- 
 formed afterwards is merely deciphering our own notes." ^ 
 
 The following remarks on the practical value of the syllo- 
 gism may be quoted with some approval. " The value, 
 therefore, of the syllogistic form, and of the rules for using 
 it correctly, does not consist in their being the form and the 
 rules according to which our reasonings are necessarily, or 
 even usually made ; but in their furnishing us with a mode 
 in which those reasonings may always be represented, and 
 which is admirably calculated, if they are inconclusive, to 
 bring their inconclusiveness to light. An induction from 
 particulars to generals, followed by a syllogistic process 
 from those generals to other particulars, is a form in which 
 we may always state our reasonings if we please. It is not 
 a form in which we must reason, but it is a form in which we 
 may reason, and into which it is indispensable to throw our 
 reasoning when there is any doubt of its validity : though 
 when the case is familiar and little complicated, and there is 
 no suspicion of error, we may, and do, reason at once from 
 the known particular cases to unknown ones."^ 
 
 1 Bk. II. ch. iii. § 3. - Id., § 5. 
 
CHAPTER VI. 
 MILL'S ''FOUR METHODS." 
 
 I. We must now make some examination of Mill's general 
 theory of inference. 
 
 Instead of four kinds of inference, differing essentially 
 from one another, he recognises only one, which he terms 
 induction. "We have thus obtained," he writes, "what we 
 were seeking, an universal type of the reasoning process. 
 We find it resolvable in all cases into the following elements : 
 Certain individuals have a given attribute; an individual or 
 individuals resemble the former in certain other attributes ; 
 therefore they resemble them also in the given attribute. 
 . . . Whether from the attributes in which Socrates resembles 
 those men who have heretofore died, it is allowable to infer 
 that he resembles them also in being mortal, is a question of 
 Induction ; and is to be decided by the principles or canons 
 which we shall hereafter recognise as tests of the correct 
 performance of that great mental operation. 
 
 " Meanwhile, however, it is certain, as before remarked, 
 that if this inference can be drawn as to Socrates, it can be 
 drawn as to all others who resemble the observed individuals 
 in the same attributes in which he resembles them ; that is 
 (to express the thing concisely), to all mankind. If, therefore, 
 the argument be admissible in the case of Socrates, we are at 
 liberty, once for all, to treat the possession of the attributes 
 of man as a mark, or satisfactory evidence, of the attribute 
 
 66 
 
MILL'S "FOUR METHODS" 67 
 
 of mortality. This we do by laying down the universal pro- 
 position, All men are mortal, and interpreting this, as occa- 
 sion arises, in its application to Socrates and others. By 
 this means we establish a very convenient division of the 
 entire logical operation into two steps : first, that of ascertain- 
 ing what attributes are marks of mortality ; and, secondly, 
 whether any given individuals possess those marks. And 
 it will generally be advisable, in our speculations on the 
 reasoning process, to consider this double operation as in 
 fact taking place, and all reasoning as carried on in the form 
 into which it must necessarily be thrown to enable us to 
 apply to it any test of its correct performance. 
 
 " Although, therefore, all processes of thought in which 
 the ultimate premises are particulars, whether we conclude 
 from particulars to a general formula, or from particulars 
 to other particulars according to that formula, are equally 
 Induction; we shall yet, conformably to usage, consider the 
 name Induction as more peculiarly belonging to the process of 
 establishing the general proposition, and the remaining opera- 
 tion, which is substantially that of interpreting the general 
 proposition, we shall call by its usual name, Deduction. And 
 we shall consider every process by which anything is inferred 
 respecting an unobserved case as consisting of an Induc- 
 tion followed by a Deduction ; because, although the process 
 needs not necessaril}' be carried on in this form, it is always 
 susceptible of the form, and must be thrown into it when 
 assurance of scientific accuracy is needed and desired."^ 
 
 Induction, then, or inference, is the passage of the mind 
 from certain obsen'ed facts to a new particular fact, or to a 
 general conclusion. Deduction is not a mode of inference, 
 but is only the interpretative or explanatory process pre- 
 sented in the syllogism, when the mind passes to a new 
 particular fact by this circuitous route. What we have 
 1 Bk. II. ch. iii. § 7. 
 
68 THE THEORY OF INFERENCE 
 
 regarded as deductive inference exists, if it exists at all, only 
 as a part of a comprehensive process of induction. Induc- 
 tion, in Mill's view, accomplishes the work which has been 
 assigned in this book to induction and deduction together. 
 
 Now, entirely waiving for the present the question whether 
 there are not still other kinds of inference, waiving also for 
 the present the question whether he makes out his case, that 
 all inductive inferences may be referred to one universal 
 type, let us consider carefully his exhibition of the different 
 forms which the process of induction takes. These forms 
 are methods of ascertaining causes and effects. " The 
 general remarks on causation," he writes, "which seemed 
 necessary as an introduction to the theory of the inductive 
 process, may here terminate. That process is essentially an 
 inquiry into cases of causation. ... To ascertain, therefore, 
 what are the laws of causation which exist in nature ; to 
 determine the effect of every cause, and the causes of all 
 effects, is the main business of Induction ; and to point out 
 how this is done is the chief object of Inductive Logic." ^ 
 And the principles or canons alluded to in the passage 
 previously quoted are rules for the correct discovery of the 
 causes of effects and effects of causes. 
 
 The canons or rules laid down by Mill are five in number, 
 having relation to four methods of discovery. On the 
 subject of these methods he writes as follows : — " The 
 business of Inductive Logic is to provide rules and models 
 (such as the Syllogism and its rules are for ratiocination), 
 to which, if inductive arguments conform, those arguments 
 are conclusive, and not otherwise. This is what the Four 
 Methods profess to be, and what I believe they are univer- 
 sally considered to be by experimental philosophers, who 
 had practised all of them long before any one sought to 
 reduce the practice to theory." ^ 
 
 1 Bk. III. ch. vi. § 3. " Bk. III. ch. ix. § 6. 
 
MILL'S "FOUR METHODS" 69 
 
 IL His first method is called by Mill the method of 
 agreement. It is substantially the same as our method of 
 comparison. He gives its canon thus : — " If two or more 
 instances of the phenomenon under investigation have only 
 one circumstance in common, the circumstance in which 
 alone all the instances agree is the cause (or effect) of the 
 given phenomenon." ^ And he introduces the canon with 
 the following remarks : — " The mode of discovering and 
 proving laws of nature, which we have now examined, 
 proceeds on the following axiom. Whatever circumstances 
 can be excluded, without prejudice to the phenomenon, or 
 can be absent notwithstanding its presence, is not connected 
 with it in the way of causation. The casual circumstance 
 being thus eliminated, if only one remains, that one is the 
 cause which we are in search of: if more than one, they 
 either are, or contain among them, the cause ; and so, 
 mutatis inuta?idzs, 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." 
 
 Concerning this method, only two remarks need to be 
 made, but they are both remarks of some importance. 
 
 The first is, that Mill states the principle on which the 
 method is founded — obviously the principle of uniformity 
 in nature — as an axiom. This in his case must be held to 
 be entirely inadmissible. It must be contended that, his 
 views of causation and uniformity in nature being what they 
 are, he is not in the least entitled to assume, that to any 
 phenomenon whatever that comes before him there is either 
 an invariable antecedent or an invariable consequent, present 
 in every instance of its presence. In what he offers as a 
 fundamental axiom of scientific induction he assumes the 
 universality of uniform causation, notwithstanding that this 
 is, according to him, only a truth inferred by some kind of 
 1 Bk. III. ch. viii. § I. 
 
 /S 
 
70 THE THEORY OF INFERENCE 
 
 informal induction, a kind of induction the supposed process 
 of which he scarcely does more than hint at. We shall see 
 later on in this chapter the measure of his success in indi- 
 cating a possible way by which it might come to be inferred. 
 
 The second remark is as follows. Mill speaks of a 
 characteristic imperfection of the method of agreement, which 
 does not seem to be, in fact, attendant on it. We have 
 already seen, in Chapter II., how he takes the view that, 
 although a cause is invariably followed by the same effect, 
 yet an effect is not invariably preceded by the same cause. 
 And this supposed circumstance he looks upon as to some 
 extent vitiating the method of agreement. " One of the 
 principal consequences of this fact of Plurality of Causes is, 
 to render the first of the inductive methods, that of Agree- 
 ment, uncertain. To illustrate that method we supposed two 
 instances, ABC followed by abc, and ADE followed by ade. 
 From these instances it might apparently be concluded that 
 A is an invariable antecedent of a, and even that it is the 
 unconditional invariable antecedent or cause, if we could be 
 sure that there is no other antecedent common to the two 
 cases. That this difficulty ma}^ not stand in the way, let 
 us suppose the two cases positively ascertained to have no 
 antecedent in common except A. The moment, however, 
 that we let in the possibility of a plurality of causes, the 
 conclusion fails. For it involves a tacit supposition that a 
 must have been produced in both instances by the same 
 cause. If there can possibly have been two causes, those 
 two may, for example, be C and E : the one may have been 
 the cause of a in the former of the instances, the other in 
 the latter, A having no influence in either case." ^ 
 
 Now this alleged uncertainty does not seem to have any 
 real existence, since plurality of causes, in the sense of 
 different causes leading to effects precisely similar, does not 
 1 Bk. III. ch. X. § 2. 
 
MILL'S "FOUR METHODS' 71 
 
 appear to be a fact of nature. It must be held to be the 
 case that, though we may be able to trace certain similar 
 effects up to causes that are apparently different, yet these 
 apparently' different causes certainly contain some common 
 element, from which proceeds that which is common to the 
 similar effects. So far as the concrete effects, apparent to 
 the view, really proceed from diverse causes, so far they are 
 themselves, not similar, but diverse. 
 
 "Suppose," Mill goes on to say, "that two great artists or 
 great philosophers, that two extremely selfish or extremely 
 generous characters, were compared together as to the 
 circumstances of their education and history, and the two 
 cases were found to agree only in one circumstance : would 
 it follow that this one circumstance was the cause of the 
 quality which characterised both those individuals ? Not at 
 all ; for the causes which may produce any type of character 
 are very numerous ; and the two persons might equally have 
 agreed in their character, though there had been no manner 
 of resemblance in their previous history. This, therefore, is 
 a characteristic imperfection of the Method of Agreement." 
 
 To this the following answer may obviously be made. 
 First, the greatness of one artist or philosopher, the extreme 
 selfishness or generosity of one character, is very far from 
 being, as an observed effect, precisely similar to that of 
 another. Secondly', so far as the compared phenomena are 
 different, so far they are the product of different causes. 
 But thirdly, so far as they have elements in common, so 
 far there must have been among their antecedents circum- 
 stances precisely similar, from which, as causes, these com- 
 mon elements have certainly proceeded. 
 
 III. The second method, that of difference, is presented — 
 not ostensibly, but really — in two quite different forms. In the 
 form about which least is said it is associated with the method 
 of agreement in what Mill terms the joint method of agreement 
 
x}" 
 
 72 THE THEORY OF INFERENCE 
 
 and difference. In this form, which it will be convenient to 
 consider first, it is nearly allied to our method of contrast. 
 
 " Suppose," says Mill, " that as we previously examined 
 a variety of instances in which a occurred, and found them 
 to agree in containing A, so we now observe a variety of 
 instances in which a does not occur, and find them agree 
 in not containing A ; which establishes, by the Method of 
 Agreement, the same connection between the absence of A 
 and the absence of a, which was before established be- 
 tween their presence. As, then, it had been shown that 
 whenever A is present a is present, so it being now shown 
 that when A is taken away a is removed along with it, we 
 have by the one proposition ABC, adc, by the other BC, dc, 
 the positive and negative instances which the Method of 
 Difference requires. This method may be called the In- 
 direct Method of Difference, or the Joint Method of Agree- 
 ment and Difference, and consists in a double employment 
 of the Method of Agreement, each proof being independent 
 of the other, and corroborating it."i 
 
 And of this joint method he states the following as the 
 
 /canon : — " If two or more instances in which the phenomenon 
 
 occurs have only one circumstance in common, while two 
 
 O I or more instances in which it does not occur have nothing 
 
 -JO:^ in common save the absence of that circumstance, the 
 
 .•^ ^"^ circumstance in which alone the two sets of instances differ 
 
 is the effect, or the cause, or an indispensable part of the 
 
 cause, of the phenomenon." ^ 
 
 Our method of contrast, it will be remembered, consists 
 in eliminating from the antecedents of a, or consequents of 
 A, any one which is found to be present in other sets of 
 circumstances from which a, or A, is absent. The method 
 was presented as an aid to, or a substitute for, the method of 
 comparison in the work of eliminating impossible causes or 
 1 Bk. III. ch. viii. § 4. 
 
MILL'S "FOUR METHODS" 73 
 
 effects. Mill appears to look upon his kindred method as a 
 test of the correctness of the conclusion established by the 
 method of agreement. He supposes, or seems to suppose 
 that, A having been found by the method of agreement, 
 search is made among diverse sets of circumstances not 
 containing a to see if A is in truth absent from them all. 
 .The method of contrast sa3^s that, if ADE is followed by 
 rtS, DF by /, and EG by vi, where / and in do not contain 
 a, then neither D nor E can be a cause of a. The joint 
 method of agreement and difference says, or seems to say, 
 that if (i) ADE is followed by ^S, ADF by al, AEG by 
 am, and if (2) HK is followed by /, KL by q, LM by r, 
 where/, q, r do not contain «, then (i) points to A as a 
 cause since it is always present when a is present, and (2) 
 corroborates this view by showing that A is invariably absent 
 when a is absent. The method of contrast casts out D and 
 E from ADE, instead of this being done by the method of 
 comparison ; the joint method supposes these two to be cast 
 out by the method of agreement, and then consents to let 
 A stand. In either case the principle is employed, that a 
 cause cannot be present in the absence of the effect. 
 
 But what possible ground has Mill for the statement, 
 that the two general truths — the invariable presence of A 
 when a is present, and its invariable absence when a is 
 absent — may be expressed, relatively to each other, by the 
 pair of symbols, ABC followed by abc, and BC followed 
 by bcl If A be here taken to represent all instances of 
 the antecedent, or an average instance of it, or any instance 
 of it whatsoever, how can it possibly be said, either (i) 
 that the sum, BC in ABC, of all antecedents that combine 
 with A is precisely similar to the sum, BC standing alone, 
 of all that do not combine with it ; or (2) that the average 
 of the one set of antecedents is precisely similar to the 
 average of the other; or (3) that those combining with any 
 
74 THE THEORY OF INFERENCE 
 
 given instance of A are precisely similar to those not com- 
 bining with it ? 
 
 Further, if it is conceivable that ABC and BC are legi- 
 timately employed, where is the ground for introducing here 
 the exact consequents, abc and be, of the given antecedents ? 
 
 IV. This ABC followed by abc and BC by be, leading to the 
 conclusion that A and a are cause and effect, is the other form 
 of the method of difference spoken of above. On the efficacy 
 of this method Mill lays considerable stress. The following 
 \- is its canon: — " If an instance in which the phenomenon under 
 investigation occurs, and an instance in which it does not 
 occur, have every circumstance in common save one, that 
 one occurring only in the former; the circumstance in which 
 alone the two instances differ is the effect, or the cause, or 
 an indispensable part of the cause, of the phenomenon." ^ 
 
 Concerning the method he says : " In the Method of Agree- 
 ment, we endeavoured to obtain instances which agreed in 
 the given circumstance but differed in every other : in the 
 present method we require, on the contrary, two instances 
 resembling one another in every other respect, but differing 
 in the presence or absence of the phenomenon we wish to 
 study. If our object be to discover the effects of an agent 
 A, we must procure A in some set of ascertained circum- 
 stances, as ABC, and having noted the effects produced, 
 compare them with the effect of the remaining circumstances 
 BC, when A is absent. If the effect of ABC is abe, and the 
 effect of BC, be, it is evident that the effect of A is a. So 
 again, if we begin at the other end, and desire to investigate 
 the cause of an effect a, we must select an instance, as abc, 
 in which the effect occurs, and in which the antecedents were 
 ABC, and we must look out for another instance in which 
 the remaining circumstances, be, occur without a. If the 
 antecedents, in that instance, are BC, we know that the 
 1 Bk. III. ch. viii. § 2. 
 
f 
 
 MILL'S "FOUR MErHODS^;^^>v^^^ 75 
 
 cause of a must be A : either A alone, or A in conjunction 
 with some of the other circumstances present." ^ 
 
 The method, it will be observed, consists, not in eliminating 
 one by one, from a set of antecedents ABC or of consequents 
 abc, all impossible causes or effects, but in subtracting from 
 a set of antecedents and a set of corresponding consequents 
 all those which are already known to be causally related. 
 The antecedents and consequents that remain, or the ante- 
 cedent and consequent should there be but one, will stand 
 to each other in the relation of cause and effect. 
 
 What has just been said is, perhaps, the most obvious 
 way of interpreting the remarks that have been quoted. 
 This interpretation, however. Mill appears to regard as 
 descriptive only of a secondary application of the method 
 of difference, an application which constitutes his third 
 method, namely, that of residues. Of this method the 
 canon is as follows : — " Subduct from any phenomenon such 
 part as is known by previous inductions to be the effect of 
 certain antecedents, and the residue of the phenomenon is 
 the effect of the remaining antecedents." - 
 
 What Mill looks upon as the primary interpretation of 
 the method of difference we may perhaps gather from the 
 axioms upon which he considers it to be based. He says : 
 "The axioms implied in this method are evidently the fol- 
 lowing. Whatever antecedent cannot be excluded with- 
 out preventing the phenomenon, is the cause, or a condition 
 of that phenomenon : Whatever consequent can be excluded, 
 with no other difference in the antecedents than the absence 
 of a particular one, is the effect of that one."^ 
 
 These two axioms seem to say no more than this : If a 
 detached cause obviously has no effect but the phenomenon, 
 or a detached effect obviously has no cause but the pheno- 
 menon, it is the cause, or the effect, of the phenomenon. Or, 
 ' Bk. III. ch. viii. §2. - Id., § 5. 3 Id., § 2. 
 
76 THE THEORY OF INFERENCE 
 
 in other words, If a single antecedent and a single consequent 
 can be detached from a mass of antecedents and consequents 
 without affecting the remainder of the mass, they are cer- 
 tainly related as cause and effect. The method based on these 
 axioms, or this axiom, seems to differ from that of residues 
 only in taking away, from ABC and abc, A and a instead of 
 BC and be. In the one case subtraction may be supposed 
 to be made, in order to prove the truth of a conjecture ; in 
 the other, for the purpose of ascertaining what will be left. 
 
 With regard to this method of difference, there is no 
 doubt that, if instances can be found of ABC followed by 
 abc and BC by be, we may assure ourselves at once that A 
 and a are cause and effect. But it cannot for a moment be 
 allowed that finding such instances is commonly practicable. 
 It must be contended, that in all the cases of ordinary life 
 to which this method may seem to be theoretically applicable 
 we already know, on other grounds, that A and a are 
 causally related. We do not conclude that A and a are 
 cause and effect, because we have ABC followed by abc and 
 BC by be ; but, knowing that BC is followed by be and A 
 by a, w^e may, if we will, put them together and say — if 
 we think we are justified in saying it — that we have ABC 
 and abe. Mill, however, greatly exalts the potency of this 
 method of difference as an instrument for the discovery of 
 causes and effects. " It thus appears," he writes, " to be 
 by the Method of Difference alone that we can ever, in the 
 way of direct experience, arrive with certainty at causes." ^ 
 And by way of giving a simple illustration of the employ- 
 ment of the method he says, "As a truth made known by 
 the Method of Difference, ' Fire burns ' might have sufficed. 
 Before I touch the fire I am not burnt; this is BC; I touch 
 it, and am burnt; this is ABC, rtBC."- But it cannot be 
 at all admitted that knowledge of the fact, that fire is the 
 1 Bk. III. ch. viii. § 3. - Bk. III. ch. ix. § 6. 
 
MILL'S "FOUR METHODS" 77 
 
 cause of burning, is actually arrived at in the manner indi- 
 cated. It may be safely asserted, that we have no more 
 valid reason for concluding that all the accompanying ante- 
 cedents and consequents, here represented together by BC, 
 remain after the burning exactly as they were before the 
 burning, than we have for concluding directly by means of 
 observation and reflection, without any reference whatever 
 to these accompanying circumstances, that the burning, 
 whose cause is sought, was the effect of fire. We know, 
 in fact — if, that is, we do know — that they remain the same, 
 only because we are aware that the new cause, fire, pro- 
 duces burning, and burning only, as its own proper effect. 
 
 V. Of the fourth method, called the method of concomi- 
 tant variations, something may now be said. It consists 
 in discovering, or partly discovering, a causal connection 
 between two phenomena by observing that variations in the 
 one are accompanied by variations in the other. The canon 
 is this: "Whatever phenomenon varies in any manner ^- il V^ 
 whenever another phenomenon varies in some particular 
 manner, is either a cause or an effect of that phenomenon, 
 or is connected with it through some fact of causation." It 
 is stated to be based on this axiom or proposition : " Any- 
 thing on whose modifications, modifications of an effect are 
 invariably consequent, must be the cause (or connected with 
 the cause) of that effect." And as a sufficient reason for 
 accepting this as true, it is remarked that, "if the thing 
 itself had no influence on the effect, neither could the 
 modifications of the thing have any influence."^ 
 
 A cause, then, is something, not only which precedes, 
 but which manifestly influences the effect. Modifications 
 of an effect are, not only consequent upon, but produced 
 by, modifications of the cause. The occurrence of corre- 
 sponding changes in two phenomena is sufficient to show 
 1 Bk. III. ch. viii. § 6. 
 
78 THE THEORY OF INFERENCE 
 
 that some relation of causation, direct or indirect, exists 
 between them. But surely this is a different view of causa- 
 tion from that which Mill has maintained to be the true one, 
 namely, that the relation between a cause and its effect is 
 merely one of succession. Surely, too, this fourth method 
 is no more than equivalent to this — that, if from the gradual 
 evidence of our senses we are aware that one phenomenon 
 causes another, or with another proceeds from a common 
 cause, then we know that there exists between them some 
 relation of causation. 
 
 VI. The mind, having discovered by means of the rules 
 given, from the few instances before it, that two phenomena 
 are cause and effect, is, in Mill's view, at once in possession 
 of a law of nature. Every phenomenon has a cause, and 
 an effect, with which it is connected by a law of nature ; 
 and cause and effect are to be determined, if they can be 
 determined at all, only by means of the four methods. 
 
 Of the idea of necessity, which is supposed to be in- 
 herent in the idea of observed invariableness in the past — 
 necessity, which establishes the observed invariable suc- 
 cession of phenomena as a law of nature — enough has been 
 already said in our second chapter. We have now to turn 
 our attention to the idea of universality, which we were not 
 then in a position to discuss. We have to inquire on what 
 ground it is that every effect, observed and unobserved, may 
 be held to have a cause of which it is the invariable conse- 
 quent, and every cause an effect by which it is invariably 
 followed. We have to examine into the tenability of Mill's 
 view of the origin of the idea of universal causation. He 
 admits that in induction the principle is assumed, and yet 
 he contends that it is itself an inferred truth. " 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 
 
MILL'S "FOUR METHODS" 79 
 
 a great error to offer this large generalisation as any expla- 
 nation of the inductive process. On the contrary, I hold it to 
 be itself an instance of induction, and induction by no means 
 of the most obvious kind. Far from being the first induction 
 we make, it is one of the last, or at all events one of those 
 which are latest in attaining strict philosophical accuracy." •'■ 
 In what way he considers induction to be dependent on 
 the principle of universal causation, he indicates in the 
 following passage: — "The validity of all the Inductive 
 Methods depends on the assumption that every event, or 
 the beginning of every phenomenon, must have some cause, 
 some antecedent, on the existence of which it is invariably 
 and unconditionally consequent. In the Method of Agree- 
 ment this is obvious ; that method avowedly proceeding on 
 the supposition that we have found the true cause as soon 
 as we have negatived every other. The assertion is equally 
 true of the Method of Difference. That method authorises 
 us to infer a general law from two instances ; one, in which 
 A exists together with a multitude of other circumstances, 
 and B follows ; another, in which A being removed, and 
 all other circumstances remaining the same, B is prevented. 
 What, however, does this prove ? It proves that B, in the 
 particular instance, cannot have had any other cause than 
 A ; but to conclude from this that A was the cause, or that 
 A will on other occasions be followed by B, is only allowable 
 on the assumption that B must have some cause; that 
 among its antecedents in any single instance in which it 
 occurs, there must be one which has the capacity of pro- 
 ducing it at other times. This being admitted, it is seen 
 that in the case in question that antecedent can be no other 
 than A ; but, that if it be no otlier than A it must be A, 
 is not proved, by these instances at least, but taken for 
 granted. There is no need to spend time in proving that 
 1 Bk. III. ch. iii. § I. 
 
8o THE THEORY OF INFERENCE 
 
 the same thing is true of the other Inductive Methods. The 
 universaHty of the law of causation is assumed in them all." ^ 
 
 This statement of his position in assuming the principle 
 appears to have reference only to the use made of it in 
 passing at once from the discovery, that A and a are cause 
 and effect in a particular case, to apprehension of the 
 universal law, that any A is a cause of a. He does not 
 seem, either here or elsewhere, to direct attention to his 
 assumption of it in setting forth the methods of discovery. 
 It is assumed, as we have already noticed, in the axiom 
 upon which he bases the method of agreement : it is also 
 assumed in tlie axioms of the method of difference, if the 
 BC standing by itself is not identical with that in ABC. 
 
 It is, perhaps, worth while to point out, that the intro- 
 duction of axioms as a ground of induction is itself — apart 
 from their content — an instance of basing induction upon a 
 product of induction; if, that is, we may accept his view of 
 axioms. For he writes, " We have thought ourselves war- 
 ranted in concluding that axioms are but a class, the most 
 universal class, of inductions from experience ; the simplest 
 and easiest cases of generalisation from the facts furnished to 
 us by our senses or by our internal consciousness."^ 
 
 VII. Now Mill attempts to reconcile the apparent con- 
 tradiction of basing induction upon a product of induction 
 by means of an explanation which must be accounted quite 
 impossible. He contends that there is a loose and unscien- 
 tific process of generalising, which is essentially different 
 from that of scientific induction. While the latter rests 
 upon the principle of universal and uniform causation, the 
 former is quite independent of it. And it is by means of 
 unscientific, not of scientific, generalising or induction that 
 the mind becomes possessed of the idea of universal causa- 
 tion. Being put in possession of the principle by unscientific 
 1 Bk. III. ch. xxi. § I. "- Bk. II. ch. vi. § i. 
 
MILL'S "FOUR METHODS" 8i 
 
 generalising, it employs it as the basis of induction con- 
 ducted after scientific methods. 
 
 This is what Mill says on the subject : — "As was observed 
 in a former place, the belief we entertain in the universality, 
 throughout nature, of the law of cause and effect, is itself 
 an instance of induction, and by no means one of the 
 earliest which any of us, or which mankind in general, can 
 have made. We arrive at this universal law by generali- 
 sation from many laws of inferior generality. We should 
 never have had the notion of causation (in the philosophi- 
 cal meaning of the term) as a condition of all phenomena, 
 unless many cases of causation, or, in other words, many 
 partial uniformities of sequence, had previously become 
 familiar. The more obvious of the particular uniformities 
 suggest, and give evidence of, the general uniformity, and the 
 general uniformity, once established, enables us to prove the 
 remainder of the particular uniformities of which it is made up. 
 As, however, all rigorous processes of induction presuppose 
 the general uniformity, our knowledge of the particular uni- 
 formities from which it was first inferred was not, of course, 
 derived from rigorous induction, but from the loose and un- 
 certain mode of induction per enumerationem siinplicevi ; and 
 the law of universal causation, being collected from results 
 so obtained, cannot itself rest on any better foundation." ^ 
 
 There is no occasion for us to follow the argument by 
 which he seeks to show that the law of universal causation, 
 though obtained by a method that is loose, is, in consequence 
 of the vast mass of experience with which it is in accord, 
 worthy of complete confidence, and fit to be the basis of 
 scientific operations. Its trustworthiness, as derived from 
 unscientific generalising, is not a point with which we are at 
 all concerned : what we have to be convinced of is the pos- 
 sibility of so deriving it. 
 
 1 Bk. III. ch. xxi. § 2. 
 
82 THE THEORY OF INFERENCE 
 
 It will be observed that in the passage just quoted Mill 
 speaks of the particular uniformities, from which the law is 
 inferred, as being themselves instances of loose and unscien- 
 tific generalising, or induction per sivipliccin oiumerationem. 
 By these uniformities we must apparently understand sup- 
 posed laws of nature, such as, Any A is the cause of a, Any 
 B is the cause of b. And, apparently, Mill's contention is. 
 that from the premises. Any A is the cause of a, Any B is the 
 cause of b, and a number of others of the same kind — all 
 obtained by loose generalising — the mind in some way passes 
 to the conclusion. Any phenomenon whatsoever has a cause. 
 
 Perhaps, before proceeding with the question of the exist- 
 ence of any mode of generalising other than induction proper, 
 we had better notice what Mill tells us of the employment 
 of the supposed method. He writes thus concerning it : — 
 " To an inhabitant of Central Africa fifty years ago, no fact 
 probably appeared to rest on more uniform experience than 
 this, that all human beings are black. To Europeans not 
 many years ago, the proposition, All swans are white, appeared 
 an equally unequivocal instance of uniformity in the course 
 of nature. Further experience has proved to both that they 
 were mistaken ; but they had to wait fifty centuries for this 
 experience. During that long time, mankind believed in an 
 uniformity of the course of nature where no such uniformity 
 really existed. 
 
 "According to the notion which the ancients entertained 
 of induction, the foregoing were cases of as legitimate infer- 
 ence as any inductions whatever. In these two instances, 
 in which, the conclusion being false, the ground of inference 
 must have been insufficient, there was, nevertheless, as much 
 ground for it as this conception of induction admitted of. 
 The induction of the ancients has been well described by 
 Bacon, under the name of ' Inductio per enumerationem 
 simplicem, ubi non reperitur instantia contradictoria.' It 
 
MILL'S "FOUR METHODS" 83 
 
 consists in ascribing the character of general truths to all 
 propositions which are true in every instance that we happen 
 to know of. This is the kind of induction which is natural 
 to the mind when unaccustomed to scientific methods. The 
 tendency, which some call an instinct, and which others 
 account for by association, to infer the future from the past, 
 the known from the unknown, is simply a habit of expecting 
 that what has been found true once or several times, and 
 never yet found false, will be found true again. Whether 
 the instances are few or many, conclusive or inconclusive, 
 does not much affect the matter : these are considerations 
 which occur only on reflection ; the unprompted tendency of 
 the mind is to generalise its experience, provided this points 
 all in one direction ; provided no other experience of a con- 
 flicting 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 observ^a- 
 tion of nature by uncultivated intellects is purely passive : 
 they accept the facts which present themselves, without 
 taking the trouble of searching for more : it is a superior 
 mind only which asks itself what facts are needed to enable 
 it to come to a safe conclusion, and then looks out for these. 
 " But though we have always a propensity to generalise 
 from unvarying experience, we are not alwa3's warranted 
 in doing so. Before we can be at liberty to conclude that 
 something is universally true because we have never known 
 an instance to the contrar}', we must have reason to believe 
 that if there were in nature any instances to the contrary, 
 we should have known of them. This assurance, in the 
 great majority of cases, we cannot have, or can have only in 
 a very moderate degree. The possibility of having it is the 
 foundation on which we shall see hereafter that induction by 
 simple enumeration may in some remarkable cases amount 
 practically to proof No such assurance, however, can be 
 
84 THE THEORY OF INFERENCE 
 
 had on any of the ordinary subjects of scientific inquiry. 
 Popular notions are usually founded on induction by simple 
 enumeration ; in science it carries us but a little way. We 
 are forced to begin with it ; we must often rely on it 
 provisionally, in the absence of means of more searching 
 investigation. But, for the accurate study of nature, we 
 require a surer and a more potent instrument."-^ 
 
 In answer to this it must be maintained — in accordance 
 with the exposition of Chapter IV. — that the distinction 
 which appears to be drawn between induction by simple 
 enumeration and scientific induction, as essentially different 
 mental processes, is illusory. It must be contended, that 
 unscientific generalising from experience is, in kind, pre- 
 cisely the same mental operation as inferring a general 
 proposition by means of the method of comparison or agree- 
 ment. True it is, that in the one case the process is more 
 or less unconscious, and the mind is satisfied with such 
 instances of the phenomenon as come before it ; while in 
 the other case the process is conscious and deliberate, and 
 the mind takes pains to bring together a large variety of 
 instances. And true it is, that in the one case the mind 
 rests upon prominent circumstances which seem to be con- 
 spicuously common to the observed phenomena ; while in the 
 other case it institutes a careful comparison to ascertain what 
 circumstances are to be excluded and what retained. But 
 neither the measure of self-consciousness with which the mind 
 works, nor the extent of the field of similar instances over 
 which it ranges, nor the degree of thoroughness and accuracy 
 with which it compares the different sets of circumstances, 
 can properly be held to make any difference whatever in the 
 essential character of its action in inferring.- 
 
 1 Bk. III. ch. iii. § 2. 
 
 - Some further remarks on this subject of supposed unscientific generaUsing 
 will be found in the first section of Chapter X. 
 
MILL'S "FOUR METHODS" 85 
 
 But, having before us the general propositions, Any A is 
 the cause of a, and the others, let us see what Mill has 
 to say concerning the 'collection' of the principle. Any 
 phenomenon has a cause, from these results. 
 
 ''It deserves remark," he says in a foot-note, "that 
 these early generalisations did not, like scientific induc- 
 tions, presuppose causation. What they did presuppose, 
 was 7inifor)iiity in physical facts. But the observers were 
 as ready to presume uniformity in the co-existences of 
 facts as in the sequences. On the other hand, they never 
 thought of assuming that this uniformity was a principle 
 pervading all nature ; their generalisations did not imply 
 that there was uniformity in everything, but only that as 
 much uniformity as existed within their observation, existed 
 also beyond it. The induction, Fire burns, does not require 
 for its validity that all nature should observe uniform laws, 
 but only that there should be uniformity in one particular 
 class of natural phenomena ; the effects of fire on the senses 
 and on combustible substances. And uniformity to this 
 extent was not assumed, anterior to the experience, but 
 proved by the experience. The same observed instances 
 which proved the narrower truth, proved as much of the wider 
 one as corresponded to it. It is from losing sight of this 
 fact, and considering the law of causation in its full extent 
 as necessarily presupposed in the very earliest generalisa- 
 tions, that persons have been led into the belief that the 
 law of causation is known a priori, and is not itself a 
 conclusion from experience."^ 
 
 And in another place he writes, also in a foot-note, to 
 much the same effect. "Though it is a condition of the 
 validity of every induction that there be uniformity in the 
 course of nature, it is not a necessar}- condition that the 
 uniformity should pervade all nature. It is enough that 
 1 Bk. III. ch. xxi. § 2. 
 
86 THE THEORY OF INFERENCE 
 
 it pervades the particular class of phenomena to which the 
 induction relates. An induction concerning the motions of 
 the planets, or the properties of the magnet, would not be 
 vitiated though we were to suppose that wind and weather 
 are the sport of chance, provided it be assumed that astro- 
 nomical and magnetic phenomena are under the dominion of 
 general laws. Otherwise the early experience of mankind 
 would have rested on a very weak foundation; for in the 
 infancy of science it could not be known that all phenomena 
 are regular in their course. 
 
 " Neither would it be correct to say that every induction 
 by which we infer any truth implies the general fact of 
 uniformity as foreknozv?t, even in reference to the kind of 
 phenomena concerned. It implies, cither that this general 
 fact is already known, or that we may now know it : as the 
 conclusion, the Duke of Wellington is mortal, drawn from 
 the instances A, B, and C, implies either that we have 
 already concluded all men to be mortal, or that we are now 
 entitled to do so from the same evidence. A vast amount 
 of confusion and paralogism respecting the grounds of in- 
 duction would be dispelled by keeping in view these simple 
 considerations." ^ 
 
 The principal meaning of these passages appears to be 
 as follows. First, from the premises. A, B, C are mortal, 
 we may infer either. The Duke of Wellington is mortal, or, 
 Any man is mortal; which contention is no doubt perfectly 
 valid. Secondly, the conclusion, Any man is mortal — or 
 its equivalent, Manhood is the cause of mortality — makes us 
 acquainted for the first time with the fact, that mortality 
 has a cause or invariable antecedent ; from which position 
 we must emphatically dissent. 
 
 For the passage of the mind from the premises. A, B, C 
 are mortal, to the conclusion, Manhood is the cause of 
 1 Bk. III. ch. iii. § I. 
 
MILL'S "FOUR METHODS" 87 
 
 mortality, seems certainly to be made by means of a deductive 
 inference from the intermediate conclusion, The manhood 
 of A, B, C is the cause of their mortahty. And this con- 
 clusion, it is maintained, cannot be reached without some 
 recognition of the principles of causation and uniformity 
 in nature. Whether the mind acts consciously or uncon- 
 sciously, an essential means of arriving at the knowledge, 
 that it is the manhood of A, B, C which makes them subject 
 to death, appears to be the preliminary knowledge, that a 
 uniform cause of death exists somewhere among their attri- 
 butes or surroundings. 
 
 Since, then, it appears to be impossible for the mind to 
 pass from the premises, A, B, C are mortal, to the conclu- 
 sion, Manhood is the cause of mortality, without employing 
 the conception, The mortality of A, B, C has some common 
 or invariable antecedent, it must be steadfastly denied that 
 the proposition, Human mortality has a cause, is a truth 
 inferred by generalisation or induction, at the same time 
 with the conclusion. Manhood is the cause of mortality, or, 
 Any man is mortal. 
 
 Accordingly, if it is contended that, as the proposition. Any 
 man is mortal, is inferred, or is inferable, at the same time 
 with the proposition. The Duke of Wellington is mortal, so 
 the proposition. Any phenomenon has a cause, is inferred, 
 or is inferable, at the same time with the proposition. Human 
 mortality has a cause ; this less general proposition, again, 
 being an inference contained in the conclusion. Manhood is 
 the cause of mortality, or, Any man is mortal ; if this is 
 what Mill contends — and perhaps it is — then it must, if 
 only for the reason above stated, be entirely denied that 
 such a derivation of the law of universal causation is at all 
 possible. 
 
CHAPTER VII. 
 
 THE GREAT FALLACY IN MILL'S ''LOGIC." 
 
 I. A THOUGHTFUL student of Mill's System of Logic, 
 having been attracted by its initial promise, and led on by 
 the seeming candour and lucidity of its style, is not unlikely 
 to find himself, at the conclusion of his reading, in a state 
 of perplexity bordering on despair. Having started with 
 good hope that there will be unfolded to him a consistent 
 and intelligibl theory of inference, he may, on looking 
 back, remember or discover instances not a few of incon- 
 sistency of statement and confusion of thought. Whatever 
 information he may incidentally have gained — and it is far 
 from being denied that there is in the book much valu- 
 able information and sound discussion — he may, after long 
 pondering, be conscious that he has failed to grasp even 
 the fundamental positions which, as he supposes, it is the 
 author's intention to establish. Bearing in mind Mill's 
 assurances, that the canons of inference presented to the 
 reader will be based upon analysis of the mind's action in 
 inferring, and that all inference belongs to one universal 
 type, here spoken of as induction, it will be to him a source 
 of wondering disappointment that his view of the teaching 
 of the book is so cloudy and confused. What, he may 
 at length impatiently exclaim, after all this argument is 
 it that Mill intends his readers to understand by induc- 
 tion ? Where in his many pages is there any real attempt 
 
THE GREAT FALLACY IN MILUS "LOGIC" 89 
 
 to give a clear account of the mental process of making 
 inference ? 
 
 At the beginning of his treatise Mill makes the following 
 remarks: — "Logic has often been called the Art of Reason- 
 ing. A writer who has done more than any other person 
 to restore this study to the rank from which it had fallen in 
 the estimation of the cultivated class in our own country, has 
 adopted the above definition with an amendment; he has 
 defined Logic to be the Science, as well as the Art, of reason- 
 ing; meaning by the former term, the analysis of the mental 
 process which takes place whenever we reason, and by the 
 latter, the rules, grounded on that analysis, for conducting 
 the process correctly. There can be no doubt as to the 
 propriety of the emendation. A right understanding of the 
 mental process itself, of the conditions it depends on, and 
 the steps of which it consists, is the only basis on which a 
 system of rules, fitted for the direction of the process, can 
 possibly be founded." ^ And a little farther on he writes 
 thus: "Our object, then, will be, to attempt a correct ana- 
 lysis of the intellectual process called Reasoning or Infer- 
 ence, and of such other mental operations as are intended to 
 facilitate this : as well as, on the foundation of this analysis, 
 and pari passtc with it, to bring together or frame a set 
 of rules or canons for testing the sufiicienc}^ of any given 
 evidence to prove any given proposition."- 
 
 With regard to the first part of this initial statement and 
 this initial promise, that part which has reference to analysis 
 of mental processes, he presently goes on to say, quite 
 reasonably and justifiably: "I shall, accordingly, attempt to 
 analyse the process of inference, and the processes sub- 
 ordinate to inference, so far only as may be requisite for 
 ascertaining the difference between a correct and an incorrect 
 performance of those processes. The reason for thus limit- 
 1 Introduction, § 2. - Id., § 7. 
 
90 THE THEORY OF INFERENCE 
 
 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 our muscles were vitiated by local weak- 
 ness, or other physical defect, a knowledge of their anatomy 
 might be very necessary for effecting a cure. But we should 
 be justly liable to the criticism involved in this objection, 
 were we, in a treatise on logic, to carry the analysis of the 
 reasoning process beyond the point at which any inaccuracy 
 which may have crept into it must become visible. In 
 learning bodily exercises (to carry on the same illustration) 
 we do, and must, analyse the bodily motions so far as is 
 necessary for distinguishing those which ought to be per- 
 formed from those which ought not. To a similar extent, 
 and no further, it is necessary that the logician should ana- 
 lyse the mental processes with which logic is concerned." ^ 
 
 Now surely we are entitled, after this exordium, to expect 
 that some serious attempt will be made to explain analy- 
 tically and intelligibly the normal action of the mind in 
 making inferences. We are entitled to expect that, when 
 canons of inference are propounded, we shall find ourselves 
 addressed as students of philosophy, wishing to understand 
 the essential principles upon which they are based, and not 
 merely as learners of an art, desiring to be made acquainted 
 with useful rules for practical application. We are entitled 
 to expect that there will be an exhibition of the salient points 
 in the normal course of the mind's passage from premises to 
 conclusion, and that the connection between this course and 
 the practical rules or canons, which are offered as tests of 
 its having been correctly taken, will be made apparent. If, 
 however, we expect this, our expectation will be unsatisfied. 
 
 Again, Mill writes as follows : — " We have thus obtained 
 what we were seeking, an universal type of the reasoning 
 
 ^ Introduction, § 7. 
 
THE GREAT FALLACY IN MILL'S "LOCilC" 91 
 
 process."^ And later on, speaking with special reference to 
 Whewell's objections to his four methods, he says, " Dr. 
 Whewell's argument, if good at all, is good against all infer- 
 ences from experience. In saj^ing that no discoveries were 
 ever made by the Four Methods, he affirms that none were 
 ever made by observation and experiment ; for assuredly if 
 any were, it was by processes reducible to one or other of 
 those methods." - 
 
 With these statements before us there are two things 
 which surely we may reasonably look for. Even though we 
 may not be put in possession of the secret of the methods 
 and their canons, 3^et surely we ma}' reasonably expect to 
 find in them the two characteristics of unity and complete- 
 ness. We may reasonably expect to be satisfied, that they 
 do in truth belong to one and the same type of inference, 
 and that there is no other type, beyond them, needing to be 
 separately treated of W^e may reasonably expect that, if 
 there appear to be substantial diversities of mental process 
 within their scope, these shall be in some way harmonised ; 
 and that inferences apparently 13'ing beyond their scope 
 shall be satisfactorily shown to be within it. But if we 
 expect this, here, again, we shall meet with disappointment. 
 
 This twofold failure to satisfy expectation aroused by 
 promise and statement of the author — the failure, that is, to 
 explain the mental process of inferring, and the failure to 
 exhibit the inferences made as belonging to one universal 
 type — constitutes, together with the course of argument, which 
 renders the failure extremely difficult to detect, what may be 
 designated the great fallacy of Mill's treatise. 
 
 II. Quickly enough — it may be briefl\^ pointed out — Mill 
 
 seems to abandon his intention of putting before his readers 
 
 an analysis of the mind's action in inferring. We find him, 
 
 somewhat early in his treatise, writing thus : " An inquiry 
 
 1 Bk. II. ch. iii. § 7. - Bk. III. ch. ix. § 6. 
 
92 THE THEORY OF INFERENCE 
 
 into the nature of propositions must have one of two objects : 
 to analyse the state of mind called Belief, or to analyse what 
 is believed. All language recognises a difference between a 
 doctrine or opinion, and the fact of entertaining the opinion ; 
 between assent, and what is assented to. Logic, according 
 to the conception here formed of it, has no concern with the 
 nature of the act of judging or believing; the consideration 
 of that act, as a phenomenon of the mind, belongs to another 
 science." 1 
 
 Even if this rejection of the act of believing from the 
 domain of logic does not itself include a reversal of his 
 previous statement and promise concerning the process of 
 reasoning, the fact remains that, in presenting to us his 
 canons of induction, he seems to make no serious attempt 
 at all to exhibit them as founded upon an analysis of mental 
 action. 
 
 III. Let us now, laying aside the question of the mental 
 process of induction, and understanding by induction — 
 as, apparently, Mill would have us do — only the work 
 achieved by that process, make some inquiry into the nature 
 of this work. What is it that in induction is, somehow, 
 actually accomplished ? Whatever may be the method of 
 the mind's working, what are the materials which it employs, 
 and what the fabric which by it is constructed from them ? 
 Whatever may be the precise course that it follows, what 
 are the premises from which it sets out, and what the 
 conclusions which it eventually reaches ? What, in respect 
 of its beginning and its end, is the one universal type of 
 inference ? 
 
 To this question an answer — or, rather, answers — ma}'^ 
 be found in the following statements. 
 
 (i.) "We have thus obtained what we were seeking, an 
 universal type of the reasoning process. We find it resolv- 
 1 Bk. I. ch. V. § I. 
 
THE GREAT FALLACY IN MILL'S "LOGIC" 93 
 
 able in all cases into the following elements : Certain 
 individuals have a given attribute; an individual or indi- 
 viduals resemble the former in certain other attributes ; 
 therefore they resemble them also in the given attribute."^ 
 
 (2.) " 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. In the Method of Agreement, 
 we endeavoured to obtain instances which agreed in the 
 given circumstances but differed in every other : in the 
 present method wc require, on the contrary, two instances 
 resembling one another in every other respect, but differing 
 in the presence or absence of the phenomenon w^e wish to 
 study 
 
 " It is scarcely necessary to give examples of a logical 
 process to which we owe almost all the inductive con- 
 clusions we draw in early life. When a man is shot 
 through the heart, it is by this method we know that it was 
 the gunshot which killed him : for he was in the fulness of 
 life immediately before, all circumstances being the same, 
 except the wound."- 
 
 (3.) "All inference is from particulars to particulars: 
 General propositions are merely registers of such inferences 
 already made, and short formulas for making more."^ 
 
 (4.) " For the purposes of the present inquiry, Induction 
 may be defined, the operation of discovering and proving 
 general propositions. It is true that (as already shown) the 
 process of indirectly ascertaining individual facts is as truly 
 inductive as that by which we establish general truths. But 
 it is not a different kind of induction ; it is a form of the very 
 same process : since, on the one hand, generals are but 
 collections of particulars, definite in kind but indefinite in 
 
 1 Bk. II. ch. iii. § 7. - Bk. III. ch. viii. § i and 2. 
 
 3 Bk. II. ch. iii. § 4. 
 
94 THE THEORY OF INFERENCE 
 
 number ; and on the other hand, whenever the evidence 
 which we derive from observation of known cases justifies us 
 in drawing an inference respecting even one unknown case, 
 we should on the same evidence be justified in drawing a 
 similar inference with respect to a whole class of cases. 
 The inference either does not hold at all, or it holds in all 
 cases of a certain description ; in all cases which, in certain 
 definable respects, resemble those we have observed." ^ 
 
 (5.) " Induction, properly so called, as distinguished from 
 those mental operations, sometimes though improperly de- 
 signated by the name, which I have attempted in the pre- 
 ceding chapter to characterise, may, then, be summarily 
 defined as Generalisation from Experience. It consists in 
 inferring from some individual instances in which a pheno- 
 menon is observed to occur, that it occurs in all instances 
 of a certain class ; namely, in all which resemble the former, 
 in what are regarded as the material circumstances. 
 
 " In what way the material circumstances are to be dis- 
 tinguished from those which are immaterial, or why some 
 of the circumstances are material and others not so, we are 
 not yet ready to point out. We must first observe that 
 there is a principle implied in the very statement of what 
 Induction is ; an assumption with regard to the course of 
 nature and the order of the universe; namely, that there 
 are such things in nature as parallel cases; that what 
 happens once will, under a sufficient degree of similarity 
 of circumstances, happen again, and not only again, but as 
 often as the same circumstances recur. This, I say, is an 
 assumption involved in every case of induction. And if 
 we consult the actual course of nature, we find that the 
 assumption is warranted. The universe, so far as known 
 to us, is so constituted, that whatever is true in any one 
 case, is true in all cases of a certain description ; the only 
 1 Kk. III. ch. i. § 2. 
 
THE GREAT FALLACY IN MILL'S "LOGIC" 95 
 
 difficulty is, to find what description. This universal fact, 
 which is our warrant for all inferences from experience, 
 has been described by different philosophers in different 
 forms of language ; that the course of nature is uniform ; 
 that the universe is governed by general laws ; and the 
 like." 1 
 
 (6.) "According to this language, every well-grounded 
 inductive generalisation is either a law of nature or a result 
 of laws of nature, capable, if those laws are known, of being 
 predicted from them. And the problem of Inductive Logic 
 may be summed up in two questions : how to ascertain the 
 laws of nature ; and how, after having ascertained them, to 
 follow them into their results."- 
 
 (7.) "If these remarks are just; if the principles and 
 rules of inference are the same whether we infer general 
 propositions or individual facts ; it follows that a complete 
 logic of the sciences would be also a complete logic of 
 practical business and common life. Since there is no case 
 of legitimate inference from experience, in which the con- 
 clusion may not legitimately be a general proposition, 
 an analysis of the process by which general truths are 
 arrived at is virtually an analysis of all induction whatever. 
 Whether we are inquiring into a scientific principle or into 
 an individual fact, and whether we proceed by experiment 
 or by ratiocination, every step in the train of inferences 
 is essentially inductive, and the legitimacy of the induction 
 depends in both cases on the same conditions. 
 
 " True it is that in the case of the practical inquirer, who 
 is endeavouring to ascertain facts not for the purposes of 
 science but for those of business, such, for instance, as the 
 advocate or the judge, the chief difficulty is one in which 
 the principles of induction will aftbrd him no assistance. 
 It lies not in making his inductions, but in the selection 
 1 Bk. III. ch. iil. § I. - Bk. III. ch. iv. § i. 
 
96 THE THEORY OF INFERENCE 
 
 of them ; in choosing from among all general propositions 
 ascertained to be true, tliose which furnish marks by which 
 he may trace whether the given subject possesses or not 
 the predicate in question. In arguing a doubtful question 
 of fact before a jury, the general propositions or principles 
 to which the advocate appeals are mostly, in themselves, 
 sufficiently trite, and assented to as soon as stated : his 
 skill lies in bringing his case under those propositions or 
 principles ; in calling to mind such of the known or received 
 maxims of probability as admit of application to the case 
 in hand, and selecting from among them those best adapted 
 to his object. Success is here dependent on natural or 
 acquired sagacity, aided by knowledge of the particular 
 subject and of subjects allied with it. Invention, though 
 it can be cultivated, cannot be reduced to rule ; there is 
 no science which will enable a man to bethink himself of 
 that which will suit his purpose. . . . 
 
 " We shall fall into no error, then, if, in treating of 
 Induction, we limit our attention to the establishment of 
 general propositions. The principles and rules of Induction 
 as directed to this end, are the principles and rules of all 
 Induction ; and the logic of Science is the universal Logic, 
 applicable to all inquiries in which man can engage." ^ 
 
 (8.) " As we can ascertain whether a man was murdered 
 or died a natural death from the indications exhibited by 
 the corpse, the presence or absence of signs of struggling 
 on the ground or on the adjacent objects, the marks of 
 blood, the footsteps of the supposed murderers, and so on, 
 proceeding throughout on uniformities ascertained by a 
 perfect induction without any mixture of hj'pothesis, so if 
 we find, on and beneath the surface of our planet, masses 
 exactly similar to deposits from water, or to results of the 
 cooling of matter melted by fire, we may justly conclude that 
 1 Bk. III. ch. i. § 2. 
 
THE GREAT FALLACY IN MILL'S "LOGIC" 97 
 
 such has been their origin ; and if the effects, though similar 
 in kind, are on a far larger scale than any which are now 
 produced, we may rationally and without hypothesis con- 
 clude, eitlier that the causes existed formerly with greater 
 intensity, or that they have operated during an enormous 
 length of time."^ Let us now, in the two following sec- 
 tions, make some examination of the foregoing statements. 
 
 IV. On the discrepancy between (i) and (2), on the re- 
 ferring to one universal type both inference from a number 
 of similars and inference from two dissimilars, it is not 
 necessary to comment. The inconsistency or contradiction 
 is too apparent. On the discrepancy, however, between (3) 
 and (4), consisting in making induction mean, now an in- 
 ference to a particular conclusion, now an inference to an 
 abstract or general conclusion, some few remarks seem to 
 be called for. 
 
 Let us consider the conclusion to be drawn from the 
 premises, stated by Mill, " My father, and my father's father, 
 A, B, C, and an indefinite number of other persons, were 
 mortal."^ Let us consider it in the light of the two passages 
 now under comparison. He tells us, that general proposi- 
 tions are collections of particulars, registers of inferences 
 already made ; and he also tells us, that the same evidence 
 that justifies an inference concerning one particular justifies 
 an inference concerning a whole class. A general proposi- 
 tion, then, may be arrived at by means of a summation of 
 particular inferences; or it may be arrived at instead of a 
 particular inference from the same premises. 
 
 Now there appears to be, here and elsewhere, a confu- 
 sion between two kinds of general proposition, between an 
 abstract proposition such as, Any man is mortal, and a 
 universal proposition such as, All men are mortal. In a 
 passage connected with the statement of premises given 
 1 Bk. III. ch. xiv. § 7. = Bk. II. ch. iii. § 6. 
 
98 THE THEORY OF INFERENCE 
 
 above, and quoted at the beginning of our last chapter, 
 Mill apparently seeks to show that, when an argument — 
 ending in the conclusion, X is mortal — is expressed in 
 syllogistic form, the major premise, All men are mortal, is 
 a proposition derived from a number of particular conclu- 
 sions — such as, Socrates is mprtal — to which the original 
 premises, My father and the rest are mortal, have led. It 
 is derived from the particular conclusion, Socrates, resem- 
 bling my father and the rest, is mortal, together with all 
 possible similar conclusions supposed to be made ; summing 
 them all up in one short collective formula. 
 
 But, having thus exhibited the major premise of the 
 syllogism as a universal drawn from — and therefore of 
 course including — all similar particular propositions, he 
 proceeds to treat it as an abstract proposition, not embrac- 
 ing, but only being typical of, particular conclusions that 
 may at any time be drawn by means of it. He proceeds to 
 speak of new particular conclusions, not as being included in 
 the formula, but as being drawn from the original premises 
 according to it ; as if the formula, or major premise of the 
 syllogism, were, not, All men are mortal, but, Any man is 
 mortal. And that this is the view which he prefers to take 
 of the general proposition seems to be sufficiently clear from 
 other evidence. For instance, he remarks in a foot-note — 
 " The language of ratiocination would, I think, be brought 
 into closer agreement with the real nature of the process if 
 the general propositions employed in reasoning, instead of 
 being in the form All men are mortal, or Every man is mortal, 
 were expressed in the form Any man is mortal."^ And the 
 general propositions which he holds it to be the business of 
 induction to discover are put before us as laws of nature, 
 having presumably, as such, their proper expression in 
 abstract form. 
 
 1 Bk. II. ch. iii. § ■;. 
 
THE GREAT FALLACY IN AEILL'S "LOGIC" 99 
 
 Here, then, the question arises. Whence comes the abstract 
 proposition ? If inference is from particulars to particulars, 
 and if the general proposition is a universal one, summing 
 up particular conclusions, it may not improperly be regarded 
 as virtually contained in any particular conclusion, and so 
 belonging to the same type of inference. If, however, it 
 is an abstract proposition or formula, according to which 
 particular conclusions may be drawn, whence is it itself 
 inferred ? In the foot-note from which a sentence has just 
 been quoted Mill continues : " This mode of expression, 
 exhibiting as the type of all reasoning from experience, 
 * The men A, B, C, &c., are so and so, therefore any man 
 is so and so,' would much better manifest the true idea — 
 that inductive reasoning is always, at bottom, inference 
 from particulars to particulars, and that the whole function 
 of general propositions in reasoning is to vouch for the 
 legitimacy of such inferences." He perhaps implies by 
 this, that an abstract conclusion is but a special kind of 
 particular conclusion. But surely such a strained inter- 
 pretation of particular, as including abstract, would be 
 inconsistent with his statement, already quoted, that the 
 universal type of reasoning leads to the conclusion that an 
 individual or individuals have a given attribute. 
 
 That from the same premises the mind can and does infer 
 both particular propositions such as, Socrates is mortal, and 
 abstract propositions such as. Any man is mortal, is doubt- 
 less true. What is here contended, in opposition to Mill, is 
 that the two inferences do not belong to a single universal 
 type. It is contended that, after the mind has discovered 
 manhood to be a cause of the mortality of A, B, C, and the 
 rest, it does not pass necessarily and spontaneously to one 
 only and universal type of further conclusion ; but it starts 
 afresh in either one of two directions according to its choice, 
 following the case of Socrates, or following the case of 
 
loo THE THEORY OF INFERENCE 
 
 abstract man. It is contended that this movement cannot — if 
 only because it may be in either one of two directions — 
 properly be merged in that of the discovery of the cause of 
 the mortality of A, B, C, but requires to be treated of as a 
 separate piece of inference. The doctrine — it is thus con- 
 tended — that there is but one universal type, here breaks 
 down. For there is one process of inference from effect 
 to cause in exclusive relation to the given particulars, and 
 another process, manifestly different in kind, on to a further 
 particular or to the abstract case. 
 
 V. The thing to be commented upon in this concluding 
 section is Mill's fallacious endeavour to bring within the 
 scope of his methods and canons all inference whatsoever. 
 We have just been noticing the want of unity in the pro- 
 cesses he speaks of, and we have now to notice the absence 
 of completeness. There is a whole field of inferences which 
 his treatise does nothing, or almost nothing, to explain. 
 
 The passage numbered (5) in the above selection states 
 clearly and correctly the dependence of what he treats of as 
 induction — viz., the ascertaining laws of nature — upon the 
 principle of uniformity of nature. The assumption is made, 
 that the phenomena we deal with are, in so far as we deal 
 with them, precisely similar to others, and that they exist 
 in nature in indefinite numbers. 
 
 But, in looking at passages (6), (7), and (8), we find Mill 
 claiming for induction that it extends far beyond the field 
 of similar and indefinitely numerous phenomena. We find 
 him assuming that inductive processes include following 
 laws of nature into their results ; that received maxims of 
 probability are among the general propositions whose results 
 require to be followed ; that it is from the results of laws of 
 nature, or of maxims of probability, that the truth concern- 
 ing unique events of common life is naturally determined ; 
 that the determining the truth about complicated and unique 
 
THE GREAT EALLACV IN MILL'S "LOGIC" loi 
 
 events of human life is a process of the same character as 
 determining the truth about physical phenomena. 
 
 Now it must be most strenuously denied, first, that par- 
 ticular facts of human life, facts concrete and unique, can be 
 reached by a process essentially similar to that which estab- 
 lishes laws of nature ; and secondly, that they can be reached 
 through the instrumentality of laws of nature already ascer- 
 tained. And it may be no less strenuously denied, first, that 
 maxims of probability are commonly arrived at by the same 
 mental process as laws of nature ; and secondly, that the 
 truth concerning facts of human life is commonly determined 
 by means of such maxims. With regard to the contention, 
 that " a complete logic of the sciences would be also a com- 
 plete logic of practical business and common life," we may 
 put two kinds of question. Where, we may ask, is the 
 general truth which, as an outcome of the same premises, 
 corresponds to the particular truth, Julius Caesar was slain 
 in the Senate House at Rome ? And what possible com- 
 bination of ascertained laws of nature will lead to the con- 
 clusion, Brutus was one of his assassins ? A faint attempt 
 Mill does indeed make later on to show that concurrent 
 testimony and circumstantial evidence lead to proof through 
 the medium of approximate generalisations. But we shall 
 see, in discussing the subject of probability, how far he is 
 from establishing his position. We shall see that he quite 
 fails to show, either that the kind of argument which he in- 
 dicates is a kind of induction, or that it leads to the estab- 
 lishment of fact. 
 
 More evidence might be adduced of his elastic application 
 of the term induction. Enough, however, has been said 
 for the purpose of our argument. The point which it is here 
 desired to insist on is this : particulars manifestly more or less 
 unique are fallaciously classed with particulars that have 
 their counterparts ; and all inference from them and to them 
 
I02 THE THEORY OF INFERENCE 
 
 is quietly assumed to be virtually included in the inductive 
 process of ascertaining laws of nature. 
 
 Thus it happens, that in Mill's treatise a very large part 
 of the inference which we employ in the common affairs of 
 daily life is not merely practically disregarded, but is wrong- 
 fully deprived of its claim to be depended on. Treat the 
 phenomena of daily hfe — so he seems to say — in accordance 
 with the methods of induction set forth by me, and you 
 will make inferences upon which you may rely : if, however, 
 you draw conclusions that do not admit of being tested 
 by the canons, they are conclusions which, not being true 
 inductions, are unworthy of being implicitly received. 
 
 It is the contention of this book — in opposition to the view 
 entertained by Mill — that there is a large class of true 
 and valid inferences which cannot possibly be made after 
 the methods employed for the discovery of laws of nature. 
 It is contended that, besides induction and deduction, there 
 are two other legitimate kinds of inference, which are being 
 more or less continually employed, which lead to conclusions 
 that are often worthy of the utmost credence, and one of 
 which — illation — has great need of being explained and vin- 
 dicated. And a serious attempt will now be made, in the 
 chapters following, to exhibit the real nature of this kind 
 of inference, and to show how it is worthy of being ranked 
 with induction as a reliable process of passing from the 
 known to the unknown. 
 
CHAPTER VIII. 
 
 THE TWO FIELDS OF INVESTIGATION. 
 
 I. There are, apparently, two quite distinct ways in 
 which it is natural for the human mind to set about the 
 work of investigating at first hand the cause or the effect 
 of any phenomenon that excites its interest. By investigat- 
 ing, let it be briefly said, is here meant seeking to ascertain 
 by means of inference that which is not itself apparent 
 through the senses ; and by investigating at first hand 
 is meant seeking to ascertain by means of inference other 
 than deduction. There are pairs of phenomena — as, for 
 example, the sun shining in the heavens, and a heated 
 atmosphere surrounding us — which appear to be directly 
 apprehended as cause and effect through the instrumentality 
 of sense. And there are pairs of phenomena — as, for ex- 
 ample, the vertical position of the sun in tropical latitudes, 
 and the extremely high temperature of these latitudes — 
 which we may conclude to be causally related by means 
 of deductive inference from our own previous knowledge. 
 But besides these two ways of becoming acquainted with 
 causes and effects there appear to be two others. In 
 the vast number of cases in which sense is no direct guide 
 to the cause or effect of any phenomenon that comes before 
 us, and in which, again, we have no knowledge, enabling 
 us to make a deductive inference, of the cause or effect 
 of any similar phenomenon, there are still two ways in 
 
I04 THE THEORY OF INFERENCE 
 
 which it may be possible for the mind to proceed to the 
 discovery of a cause or an effect. Besides deduction, the 
 mind has two distinct ways of thus passing from the known 
 to the unknown ; it is able to employ, when circumstances 
 admit of it, either one of two kinds of inference, each of 
 them distinct from deduction, and yet not more distinct 
 from it than they are from one another. 
 
 Before speaking more particularly of the difference be- 
 tween these two kinds of inference — induction, already treated 
 of, and illation, about to be treated of — something must be 
 said concerning the conditions of their employment. They 
 appear to belong respectively to two distinct fields of 
 investigation. Induction, together with deduction, belongs 
 to one field ; and illation, together with delation (a kind 
 of inference not concerned with the discovery of causes 
 and effects), belongs to the other. Let us consider what 
 the two fields are. 
 
 In dealing with particular phenomena, whose causes or 
 effects we are in search of, we seem inevitably to refer them, 
 with more or less consciousness and deliberateness, to one 
 or the other of two distinct classes or collections. Every 
 effect together with its at present hidden cause, and every 
 cause together with its at present unknown effect, is re- 
 garded by us, either as constituting one of the innumerable 
 manifestations of the orderly and settled course of nature, 
 or as constituting a part of one of the innumerable groups 
 of particular events which make up the drama of human life. 
 It js looked upon, either as exemplifying and having its 
 explanation in some general law, or as occupying its own 
 particular position in the circumstances of some definite 
 time and place. Either we see in it a member of a class 
 containing other combinations of cause and effect precisely 
 similar to itself, or we treat it as a junction of compound 
 cause with compound effect which is not other than special 
 
THE TWO FIELDS OF INVESTIGATION 105 
 
 and unique. In the one case it becomes an object with us 
 to add to our store of knowledge of natural laws having 
 more than a single application ; in the other case we strive 
 to fill in or extend that mental picture of the world in which 
 we see particular incidents historically linked together as 
 causes and effects. In other words, the mind, in its inves- 
 tigation of causes and effects, conducts its inquiries at one 
 time in the field of natural law, at another time in the field 
 of history. To some persons the former kind of mental 
 activity, to others the latter, appears to be the more con- 
 genial ; but both kinds seem to be, in greater or less degree, 
 habitually engaged in and pursued by all. 
 
 Let us notice briefly a few instances of the mind's re- 
 ferring phenomena which excite its interest and curiosity to 
 one or the other of the aforesaid fields. Let us suppose a 
 person to be instituting inquiry as to the cause of (i) the 
 unhealthy appearance of some common shrub met with in a 
 walk, (2) the dark complexion of a native of India whom he 
 has seen, (3) a friend of his having been seen riding on a 
 beautiful horse, (4) some fruit being found one morning 
 lying on the ground in his orchard. Is it not sufficiently 
 clear, that in the two former cases the mind is likely to 
 betake itself, so to speak, to the field of natural law, and 
 there carry on its investigations ; while in the two latter 
 cases it will move in the field of special events linked to- 
 gether, that is, in the field of history ? The person in 
 question would naturally — so it seems — look for a cause of 
 the unhealthiness of the shrub such as might be found 
 similarly manifesting itself in other shrubs ; and for a cause 
 of the dark complexion of the Indian such as might be seen 
 to have operated similarly in the case of other natives of the 
 same country. On the other hand, he would endeavour to 
 find an explanation of his friend's being seen on the back of 
 a beautiful horse, as also of the ground of his orchard being 
 
io6 THE THEORY OF INFERENCE 
 
 strewn with fruit, in some definite group of circumstances 
 and events having elsewhere no exact counterpart. 
 
 In like manner phenomena seem to be referred by the 
 mind either to the field of natural law, or to the field of 
 history, when, instead of their causes, it is their effects that 
 are being sought. Thus to the field of natural law would 
 be assigned the causal phenomenon of treating a strawberry- 
 bed with some particular dressing, when there are other beds, 
 besides itself, that are subjected to the same treatment. 
 And to this field would belong the trying some particular 
 fly to fish for trout, when there are other anglers, besides 
 the one, also making use of it. The effect looked for, 
 whether of the dressing or of using the particular fly, is 
 an effect such as shall be apparent elsewhere than in one 
 particular bed of strawberries or in one particular angler's 
 creel. It is, in each case, an effect which shall be under- 
 stood to follow from the operation of some natural law. On 
 the other hand, it is the field of history in which the mind 
 works, when a meteorologist, having noticed the state of the 
 barometer, seeks to ascertain the effect of the causes whose 
 presence is here indicated on some particular person or some 
 particular undertaking, in whom or in which he is interested, 
 on the given day. And it is in the same field that an answer 
 must be looked for by one who would know what has been 
 the effect upon his own life of giving his son a university 
 education. The influence of the weather upon the particular 
 person or undertaking, and the attitude and relation of the 
 young man to his father, constitute more or less unique 
 phenomena, which must be regarded as special combinations 
 of effects, combinations whose exact counterparts are not to 
 be found elsewhere. 
 
 II. The two fields of investigation, although from one 
 another quite distinct, are nevertheless so far connected 
 that a relation of causation established in either of them 
 
THE TWO FIELDS OF INVESTIGATION 107 
 
 may be, in a manner, transferred to the other, and there 
 regarded as a true relation. If, on the one hand, it can be 
 said to be natural for a certain particular phenomenon to 
 have been caused by, or to have produced, another, then, 
 in a certain true though restricted sense, it is a matter of 
 history that it has been caused by, or has produced, the 
 other. And if, on the other hand, it is known as a histori- 
 cal fact that a certain particular phenomenon has proceeded 
 from, or has produced, another, then it may be affirmed to 
 be somehow in accordance with a law or laws of nature 
 tliat the one should proceed from, or should produce, the 
 other. If, for example, we discover that the unhealthy 
 appearance of a certain shrub is such as is naturally due 
 to frost, then we may pronounce it to be a historical fact 
 that at some time and in some degree frost has been 
 encountered by it. Or if we learn that it is natural for a 
 certain Indian to have a dark complexion, as being a native 
 of a tropical country, then we may also realise that it forms 
 a part of his individual history that the circumstances of 
 his birth were such as to produce some degree of darkness 
 in his skin. Again, if we should hear, as a matter of fact, 
 that certain meteorological causes were followed by weather 
 favourable or unfavourable to some particular person or 
 undertaking, we may safely say that this result was brought 
 about only in accordance with laws of nature. And if we 
 have reason to conclude that in certain given circumstances 
 the sending a young man to the university has produced 
 such and such results upon his father's life, we may be 
 satisfied that somehow it is only natural that these results 
 should be produced. 
 
 But it is only in a manner, only, that is, under certain 
 reservations or restrictions, that the mind can transfer 
 relations of causation, when it does transfer them, from 
 one field to the other. The question, what these reserva- 
 
io8 THE THEORY OF INFERENCE 
 
 tions or restrictions are, will be noticed almost immediately. 
 It may first be pointed out — this section being thus brought 
 to a close — that the field in which the mind of any indi- 
 vidual thinker more naturally and spontaneously works is 
 determined, partly by the objective character of the pheno- 
 menon whose cause or effect it desires to investigate, and 
 partly by its own subjective bent. There are, on the one 
 hand, phenomena which seem more especially to appeal to 
 the senses and understanding as resembling others ; and 
 there are, on the other hand, phenomena which seem more 
 especially to strike men as unique. Every phenomenon no 
 doubt has, in greater or in less degree, each of these two 
 characteristics ; but in some, resemblance to others is more 
 prominent than diversity, in some, diversity from others 
 is more conspicuous than resemblance. And according to 
 the characteristic which seems to prevail does the mind 
 naturally tend to fix upon the field of natural law, or upon 
 the field of history, as that in which investigation must be 
 carried on. For example, the application of a particular 
 dressing to a strawbeny-bed, supposed by no means to 
 be confined to a single experiment, is, as a cause whose 
 effect is sought, spontaneously referred by the mind to the 
 field of natural law ; while the fact of a particular person, 
 whose poor circumstances in the past are well known, being 
 seen mounted on a beautiful horse is referred, for the 
 ascertainment of the cause of this unique event, to the 
 field of history. 
 
 But there also appear to be many phenomena with regard 
 to which, since neither resemblance to nor diversity from 
 others is especially manifest, the mind is fully at liberty 
 to choose into which of the two fields it will conduct them 
 for purposes of investigation. If, for instance, a person 
 would ascertain the cause of his feeling unwell on a par- 
 ticular day, it may be open to him to enter upon the inquiry. 
 
THE TWO FIELDS OF INVESTIGATION 109 
 
 either as one that belongs to the domain of natural law, or 
 as one that concerns only his own private history. Either 
 he may look upon his uneasiness as a symptom belong- 
 ing to a class the members of which proceed each from a 
 common or similar cause ; or he may treat it as one of 
 a group of symptoms and circumstances affecting himself 
 alone, and proceeding from some common or joint cause. 
 So again, if he desires to estimate the effect upon his own 
 health of having adopted a particular regimen, either he may 
 search for some common change wrought in the physical 
 condition of himself and of others who likewise have adopted 
 it, thus carrying on his inquiry in the field of natural law; 
 or he may hope to draw a conclusion from his intimate 
 acquaintance with the special conditions of his own body^ 
 conducting his investigation in the field of history. As the 
 result of the one method of proceeding, he acquires some 
 additional knowledge of the general physiological principles 
 upon which nature works ; as the result of the other, he 
 arrives at a fuller understanding of the particular picture 
 of the human constitution which, in his own person, she 
 presents to his view. In which of the two fields the mind 
 determines to conduct such inquiries, or, in other words, 
 which of the two kinds of information it resolves to search 
 for, seems to be dependent upon its own general or tem- 
 porary subjective bent. 
 
 III. It was suggested near the beginning of this chapter, 
 that each of the two fields has its own kinds of inference. 
 And it has just been suggested in the preceding section, 
 that a relation of causation established in either field — of 
 course, by a kind of inference peculiar to that field — can 
 only be affirmed in the other under certain reservations or 
 restrictions. It will now be our purpose to consider what 
 these reservations or restrictions are. An endeavour will 
 be made to show, how a relation of causation established 
 
no THE THEORY OF INFERENCE 
 
 in the field of natural law necessarily fails to be an adequate 
 representation of any similar relation in the field of history ; 
 or, in other words, how a historical fact cannot really be 
 inferred by the mental processes that appertain to the field 
 of natural law. The converse truth — that a relation of 
 causation established in the field of history fails to be an 
 adequate representation of any similar relation in the field 
 of natural law ; or, in other words, that a law of nature 
 cannot really be inferred by the mental process that ap- 
 pertains to the field of history — it will not be necessary 
 to consider. For the main purpose of this chapter, in 
 insisting on the distinction between the two fields of in- 
 vestigation with their corresponding kinds of inference, is 
 to vindicate the claim of the latter field together with its 
 special kind of inference to equal recognition with the 
 former. While, therefore, the insufficiency of investigation 
 carried on in the field of natural law to establish causal 
 relations in the field of history must be exhibited in order 
 to this end, there is no similar ground for dwelling upon 
 the converse truth. Moreover, we are not yet in a position 
 to discuss it, since we have not yet become acquainted 
 with illation, the method of discovering causes and effects 
 in the field of history. And it may be further added, that 
 the truth in question will to some extent incidentally disclose 
 itself, as we become familiar with operations in the field of 
 history. 
 
 The essential characteristic of any phenomenon placed by 
 the mind for purposes of investigation in the field of natural 
 law is, that it has, or may have, exact counterparts of itself 
 existing elsewhere in nature. The particular B whose cause, 
 or the particular A whose effect, we purpose to ascertain is 
 at once assumed to be precisely similar to other B's, or other 
 A's. The cause of this particular B — so we argue — is a kind 
 of cause such as is assignable in common to all other B's. 
 
THE TWO FIEI.DS OF INVESTIGATION in 
 
 The actual or possible fact of the existence elsewhere of 
 others exactly like it is an essential part of our conception 
 of the phenomenon before us. It is distinctly apprehended 
 as not singular, not unique ; it is conceived of as one of a 
 famil}' or group of phenomena all of which are identically 
 alike. 
 
 Now phenomena, as they are made known to us through 
 our senses — phenomena, as we have actual experience of 
 them — do not appear to satisfy the primary condition, just 
 described, of inductive investigation in the field of natural 
 law. It would seem to be the case, that we are by no means 
 entitled to say of an}^ phenomenon, as it actually' presents 
 itself to us, that its exact counterpart does exist or can exist 
 anywhere in nature. No mouthful of food can be said, in 
 every particular of touch and taste, to be exactly similar 
 to any other ; no peal of thunder can be said, in respect 
 of every one of the conditions under which it strikes the 
 ear, to have or to have had its exact counterpart elsewhere ; 
 no human form can be said, in every circumstance of feature 
 and expression, to bear an exact resemblance to an}^ other. 
 The constituent elements which make up phenomena of any 
 given kind are, it would seem, so multitudinous, and the 
 number of possible combinations of these elements — in other 
 words, the number of conceivable phenomena of the given 
 kind — so indefinitely large, that in no case whatsoever is 
 the mind justified in pronouncing, that between any two 
 phenomena, apparently similar, the resemblance is in all 
 respects exact. 
 
 And yet, in proceeding by induction in the field of natural 
 law, the mind certainly does deal with phenomena as if it 
 were assured of exact resemblance between them and others. 
 Wherein, then, is to be found the explanation of this seem- 
 ingly irrational and futile course ? Apparently it is to be 
 found in this circumstance — that the mind has the power of 
 
112 THE THEORY OF INFERENCE 
 
 discerning and abstracting common or precisely similar 
 elements which enter into the composition of diverse phe- 
 nomena. Among the sensations felt by the palate in eat- 
 ing apples of different sorts and at different times it can 
 lay hold upon one set which is invariably present, and 
 designate this the taste of apple. In all various instances 
 of peal and crash echoing through the heavens it can detect 
 the presence of one common type of sound, which it knows 
 as thunder. Beneath all diversities of lineament it can see 
 in every face certain common attributes, which constitute 
 it the face of man, woman, or child. In some such way 
 as the chemist is able to abstract or separate the oxygen 
 of the atmosphere from the other elements, in conjunction 
 with which alone it is known to ordinary men, the mind can 
 abstract and separate for its own further use certain parts 
 of any phenomenon that appeals to it through the channels 
 of sense. And since allied phenomena, though in no case 
 themselves identically similar, must have among their con- 
 stituent elements some that are identically similar, the mind, 
 abstracting certain of these elements from one phenomenon, 
 searches for and finds in another their exact counterparts. 
 
 The phenomena, then, with which the mind deals in the 
 field of natural law are not real phenomena, but abstractions. 
 They are to a certain extent its own creations. They are 
 not the things, but only abstract portions of the things, of 
 which it becomes cognisant through the medium of sense. 
 Regarded as being themselves things, they have existence 
 for the mind alone. 
 
 IV. Again, in the case of a phenomenon dealt with by the 
 process of induction, not only must it be conceived of as 
 having actual or possible counterparts elsewhere, but also 
 it and its counterparts must be distinctly recognisable by 
 the mind. Pronouncing of any phenomenon, whose cause 
 or effect we wish to ascertain, that it bears an exact resem- 
 
THE TWO FIELDS OF INVESTIGATION 113 
 
 blance to other actual or possible phenomena, we draw, 
 deductively, the conclusion that, whatever the cause or effect 
 of the one may be, those of the others must be identically 
 similar. And we seek, by comparing or contrasting sets of 
 circumstances, to find a residuum which, being present as 
 antecedent or as consequent in all the sets in which an 
 instance of the phenomenon is wholly present, or absent 
 from all those from which an instance happens to be wholly 
 absent, shall be or shall contain the cause or the effect 
 required. 
 
 The process, it will be observed, whether conducted by 
 the method of comparison or by the method of contrast, is 
 essentially dependent upon our having such full cognisance 
 of the similar phenomena with which we deal, as to be able 
 to say of any one, either that it is wholly present among, or 
 else that it is wholly absent from, any set of circumstances of 
 which we make use. The mind, when working in the field 
 of natural law, forms an abstract image or picture of each 
 of the phenomena with which it deals ; and it is through 
 recognition of the presence, or the absence, here and there, 
 of the counterpart of such picture that inductive inference 
 is carried on. 
 
 It thus comes to pass that in another way the phenomena 
 of the field of natural law are not real phenomena. They 
 are phenomena isolated by the mind from all others, and 
 apprehended by it only in their individuality. All the par- 
 ticular circumstances which, though not forming an actual 
 part of any given effect or cause, nevertheless stand in 
 obvious relations of time and place to it, and with it appeal 
 to the mind through the senses as a compound historical event 
 — all these circumstances are ignored. Thus here again 
 it may be said that the mind is dealing, not with real pheno- 
 mena, but with abstractions. For a thing regarded only in 
 its individuality, as being just what in itself it is, and as not 
 
114 THE THEORY OF INFERENCE 
 
 V being anything else than just what in itself it is, seems in 
 truth to be but an abstraction. It seems to be to a certain 
 extent a creation of the mind, not a thing made known to 
 it by the experience of sense. Not only is it the case, that 
 we have no experience of any phenomenon devoid of touches 
 peculiar to itself, and precisely similar to some other; but 
 also it is the case, that we have no experience of any pheno- 
 menon entirely independent of its surroundings, and capable 
 of being adequately apprehended without reference to them. 
 Things, as we know them, are not complete in themselves 
 and self-contained. Individuality is but a special kind of 
 abstraction. 
 
 Phenomena being thus dealt with in the field of natural 
 law as abstract and individual, it will not be difficult to see 
 that inference by induction must be wholly insufficient to 
 establish historical conclusions. A causal relation between 
 two phenomena, transferred from the field of natural law 
 and interpretable only under the reservations or restrictions 
 above described, is not, and cannot be made to be, in any 
 full sense, a causal relation in the field of history. Even the 
 particular proposition. This A is the cause of this B, arrived 
 at by means of induction, although it has the definiteness 
 appropriate to a causal relation in the field of history, is 
 nevertheless far from expressing all that is meant by the 
 same proposition when used to signify a fact properly be- 
 longing to this field. 
 
 Let us take the two illustrations of transfer from the field 
 of natural law to the field of history given in the second 
 section. The first of these was the case of the unhealthy 
 appearance of a particular shrub being ascertained by induc- 
 tion to be due to frost. If among the antecedents of the 
 phenomenon there is known to be but the one instance of 
 frost, then we are in a position to say, Last night's frost has 
 been the cause of injury to this shrub. And we have before 
 
THE TWO FIELDS OF INVESTICxATION 115 
 
 us what is in a certain sense a fact of history. But let us 
 consider (i) what it is that we are affirming, and (2) what 
 it is that we might or should be affirming had we approached 
 the subject from another side. What we are affirming is 
 this : The abstract part of this shrub, in respect of which it 
 precisely resembles other shrubs, has suffered a certain 
 injury from that abstract part of last night's frost, in respect 
 of which it precisely resembles other frosts. But what we 
 might or should be affirming, were we to begin by regarding 
 the frost and the injury to the shrub in the field of history, 
 is something of this kind : The cold of last night, of which 
 you and I were so painfully conscious, has inflicted an injury 
 upon this shrub, which formed so conspicuous a feature in 
 our garden. In the field of history the frost and the shrub 
 are their full selves, without any abstracting or paring to 
 produce an exact resemblance between them and other 
 phenomena. And yet they are not by themselves, for a 
 material part of the conception of them is their being con- 
 nected with other phenomena by relations of time or place. 
 
 Our second illustration was that of the dark complexion 
 of a certain Indian being due to his being a native of a 
 tropical country. Here we may say that in a certain sense 
 a historical fact is expressed by the definite statement, His 
 Indian birth is the cause of his present dark complexion. 
 But, as before, there is a vast difference between the inter- 
 pretations that must be put upon the words, accordingly as 
 they are referred to the field of natural law or to the field 
 of history. In the one case the meaning is as follows : His 
 birth in a country possessing, as an abstract constituent of 
 its climate, that which makes it resemble other tropical 
 countries, is the cause of that abstract quality of complexion, 
 in respect of which he resembles other persons whom we 
 call dark. In the other case the meaning is something of 
 this kind : His being a native of that well-known British 
 
ii6 THE THEORY OF INFERENCE 
 
 dependency, India, is the cause of his having a complexion 
 which attracts so much attention when he walks through 
 the streets of our small town. 
 
 It seems, then, to be sufficiently clear that, if we are to 
 draw inferences and establish conclusions in the field of 
 history, we must have some other mode of proceeding than 
 by means of induction. Even if conceivably, by means of 
 exhaustive analysis of concrete phenomena, followed by a 
 correspondingly complete synthesis of ascertained elemen- 
 tary laws of nature, we could acquire an adequate know- 
 ledge of causal relations between concrete phenomena in the 
 field of natural law, these relations would nevertheless not 
 be those of the field of histor}^ For, though the phenomena 
 would be concrete, yet the attribute of individuality would 
 still adhere to them. 
 
CHAPTER IX. 
 
 CONTINUITY IN NATURE. 
 
 I. The making inferences, or passing from the known to 
 an apprehension of the hitherto unknown, is dependent in 
 the field of history, no less than in the field of natural law, 
 upon the mind's recognition of a certain fundamental prin- 
 ciple. Unless the mind is conscious that the new fact, 
 whatever it may be taken or may prove to be, must stand 
 in a certain relation to the old facts, it has no power of 
 forming conclusions respecting it upon the truth of which it 
 can rely. But the fundamental principle of inference, or the 
 necessary relation between new and old, is one thing in the 
 field of natural law, and another in the field of history. 
 Illation is in no way dependent upon that truth of nature 
 which we have seen to be the basis of induction, the truth, 
 namely, that there is a uniformity of relation between causes 
 and effects. But it takes its stand upon a principle which 
 may be said to be allied to it, namely, that there is a 
 continuity in the action, and in the grouping, of natural 
 causes. 
 
 What alone makes it possible for the mind to have 
 understanding of the world in which it lives, to have 
 thoughts concerning it other than those which are directly 
 due to the impressions of sense, to get behind phenomena 
 and ascertain something of what they mean, to trace con- 
 nections between them and regulate action in dependence 
 
ii8 THE THEORY OF INFERENCE 
 
 on them — what alone appears to make this possible, is the 
 conviction, the innate conviction, that there is an orderly 
 and settled design of nature, of which design phenomena, 
 as they occur, are the expression. Nothing resembling a 
 satisfactory explanation of the mind's action in making 
 itself acquainted with the ways of nature can apparently 
 be given, unless it is assumed as a primary and fundamental 
 fact, that the mind regards the universe as the embodiment 
 of order and intelligent and settled purpose. And it seems 
 to find, constituting part of the order and purpose of 
 nature, besides causation and uniformity in nature, this 
 other fundamental principle : The elemental forces of nature, 
 the first causes — whatever they may be — which give rise 
 to particular phenomena, taken as a whole, remain always 
 substantially unchanged. 
 
 This principle of continuity in nature is a necessary 
 condition of our being able to infer the future or the past. 
 That is to say, if we imagine a time when the system of 
 nature can be said to have been, or to be about to be, 
 other than it has been and is within the scope of our 
 experience, the time which we thus imagine is a time the 
 history of which, both general and particular, must be to 
 us a perfect blank. Concerning it we can make no in- 
 ferences. We know nothing of what phenomenal causes 
 may exist to produce effects, or of what effects there may 
 be that have had their origin in causes. In order to 
 making attempts to understand the world's history, we 
 must be satisfied that it is a world which, during the period 
 over which our investigation ranges, has remained and will 
 remain substantially in harmony with the teachings of our 
 experience. This does not by any means prevent due 
 recognition of development in the action and interaction of 
 elemental forces. The mind demands, not that change shall 
 be entirely absent, but that whatever change there is shall 
 
CONTINUITY IN NATURE 119 
 
 be orderly and progressive. It demands that the change 
 itself shall be the expression of settled purpose and design. 
 
 From this general principle we derive the two following 
 particular results. 
 
 1. All such phenomena as we are led to ascribe to 
 elemental forces — or, in other words, to the system of 
 nature — as their source, are phenomena which must for 
 ever remain unchanged, or must change only in the way 
 of orderly development. On the one hand, we have firm 
 assurance that such phenomena as the regular continuity 
 of successive sun-risings, and the gradual maturing of 
 animal and vegetable life, will uninterruptedly proceed. 
 On the other hand, we recognise in nature nothing catas- 
 trophic : if catastrophes there should be, it must be from 
 outside the world, which we are learning to understand, 
 that they will come upon us. 
 
 2. A phenomenon of a special kind, which we cannot do 
 otherwise than ascribe to the action of elemental forces, 
 is the manner in which causes were originally grouped. 
 According!}', the grouping of causes once established is 
 the grouping which we look upon as a continuous feature 
 of nature's order. Any cause continues, subject to the 
 operation of development, to combine with such other sets 
 of causes as it has combined with from the beginning. 
 
 Let us suppose a case of concrete L having been always 
 followed, or preceded, by concrete M or by concrete N. 
 Then we know that any new instance of L will be followed, 
 or preceded, by one of M or N. We know this, not, of 
 course, as in the field of natural law, because abstract L 
 is the cause or effect of abstract M or N, but because ab- 
 stract L is one of a group of causes which have always pro- 
 duced among them either a concrete M or a concrete N, or 
 because it is one of a group of effects which have always 
 been together preceded either by a concrete M or by a 
 
I20 THE THEORY OF INFERENCE 
 
 concrete N. If it is concrete L, as a cause, that is being 
 considered, we say that abstract L combines in nature with 
 other causes to form a group, which group is characterised 
 by having either some concrete M or some concrete N as 
 its consequent. If it is concrete L, as an efiect, that is 
 under consideration, we say that the cause of abstract L 
 combines in nature with other causes to form a group, 
 which group is always recognisable as an instance either 
 of concrete M or of concrete N. 
 
 Similarly, if it is the case that P has always been accom- 
 panied either by Q or by R, we judge that any new instance 
 of P will be accompanied either by one of Q or by one 
 of R. We judge, if they are causes, that abstract P will 
 always act in conjunction either with abstract Q or with 
 abstract R ; or, if they are effects, that the cause of abstract 
 P will in the future, on any occasion of its acting, join 
 either with the cause of abstract Q or with that of ab- 
 stract R. 
 
 This principle of continuity in nature is not only different 
 from, it is quite independent of, the principle of uniformity 
 in nature. Although it involves, of course, an apprehension 
 of the principle of causation, yet it appears in no way to 
 involve an apprehension of the important corollary just 
 mentioned; just as, for example, the conception of solar 
 light, although involving the conception of the sun, does not 
 involve the further conception of solar heat. In the argu- 
 ment that, because all observed instances of concrete L 
 have produced hitherto the effect M or N, therefore this 
 particular L must produce M or N, there is no reference 
 whatever to similar causes, and consequently no introduc- 
 tion of the principle of uniformity. The reference is not 
 to any similarity between this and other instances of ab- 
 stract L, regarded as being themselves operating causes, 
 but it is only to a similarity between them, regarded as 
 
CONTINUITY IN NATURE 121 
 
 being attached to, and lending their name to, various groups 
 of operating causes. It is not at all the abstract L — of 
 which repeated instances occur — whose effect is appre- 
 hended as M or N, but it is the groups of causes of which 
 abstract L from time to time constitutes a part. These 
 groups of causes may, for anything the argument requires, 
 be entirely different from one another — except for their 
 containing abstract L — even on occasions producing instances 
 of the same effect M, or the same effect N. The notion of 
 causation made use of seems to be no more than that of 
 certain antecedents, viz., those — whatever they ma}- be — that 
 from time to time include abstract L, producing a certain 
 limited range of observed consequents, M and N. And of 
 this notion of causation the principle of uniformity con- 
 stitutes no part. 
 
 To avoid misconception, it ma}' be well to point out — 
 though the remark has no direct bearing upon the subject 
 before us— that M and N, each sometimes following after 
 or preceding L, must of course contain a common element, 
 which is the unfaihng effect or cause of abstract L. With 
 this unfailing effect or cause the mind, when working in 
 the field of history, is not concerned. 
 
 II. Let us now devote some further attention to this 
 relation between observed antecedent and observed conse- 
 quent in the field of history. Upon it depends the possi- 
 bility of making illative inferences. In order to discover, 
 in the field of history, the exact locality of a required cause 
 or effect, it is necessary that we should be able, from past 
 experience, to mark out certain narrow limits within which 
 the search may reasonably be confined. We call to mind 
 what we know of the kinds of cause which have seemed 
 to lead to effects of a similar kind to the one before us, or 
 of the kinds of effect which have seemed to follow from 
 causes such as that we are considering. And among 
 
122 THE THEORY OF INFERENCE 
 
 possible manifestations of these kinds of cause, or these 
 kinds of effect, we search for a particular one, which shall 
 be the definite cause of the given effect, or the definite 
 effect of the given cause. If, for example, we would ascer- 
 tain under what particular circumstances a sum of money 
 has disappeared, we start with the general premise, that 
 such disappearances have taken place in one or another of 
 certain kinds of way, kinds of way with which experience 
 has rendered us more or less familiar. We have known 
 money to be stolen, let us say, or we have known it to 
 be accidentally dropped, or we have known it to be put 
 away for safety in some forgotten place. And it is among 
 these alternatives, if anywhere, that, making use of the 
 principle of continuity in nature, we expect to find the 
 solution of the present problem. Money, we say, disappears 
 sometimes through theft, sometimes through carelessness, 
 sometimes through forgotten hiding; consequently it may 
 be expected that in the present instance its disappearance 
 is owing to some manifestation of one of these three kinds 
 of cause. 
 
 A technical formula for the sort of knowledge of nature 
 that we employ is, some X is Y. This formula, understood 
 to mean, some X has as its cause or as its effect Y, 
 covers both the case of a concrete effect known to be 
 preceded by several alternative concrete causes, and the 
 case of a concrete cause known to be followed by several 
 alternative concrete effects. Some white hair is human 
 hair, is a proposition expressing results of observation in 
 the one case ; Some men have white hair, expresses results 
 of observation in the other. The former means, that some 
 white hair results from, or contains in itself the effects of, 
 attributes and conditions that are found in man ; the latter, 
 that some men produce, or contain in themselves the causes 
 of, white human hair. Neither proposition, be it observed. 
 
CONTINUITY IN NAT UTliL ^ 123 
 
 asserts a relation of causation between whiteness of hair 
 and any essential attribute of man. On the contrary, it 
 may be almost said that such a relation is implicitly denied ; 
 since, if it were supposed to exist, the emplo3'ment of the 
 word ''some" would be inappropriate. In saying. Some 
 men have white hair, we affirm that with the essential 
 attributes of manhood are sometimes conjoined other causes, 
 the effect of the whole being the concrete white hair of 
 particular persons. And tlie statement, Some white hair 
 is seen in men, is equivalent to the assertion that the causes 
 of white hair in the abstract are sometimes joined to other 
 causes and conditions, the combination being recognisable 
 as a concrete instance of humanity. 
 
 We have, then, in the premises of illative inference no 
 ascertained laws of nature, no fixed relations between 
 definite cause and definite effect ; but only the results of 
 our observation of the ways in which combinations of causes 
 exist in nature. Causes of concrete manifestations of white 
 hair, whatever these causes may be, are observed to exist 
 sometimes among the attributes and conditions of concrete 
 manhood : — humanity may exist without them, and they 
 likewise may exist elsewhere. Not a reasoned knowledge of 
 the causal ideas of nature, but some practical acquaintance 
 with her intermixture of ideas, is what we profess when in 
 the field of history we make the assertion that, some X is Y. 
 We have obtained glimpses of the sort of company" among 
 which she places, from time to time, the causes — if we are 
 seeking for causes — or causes producing the effects — if we 
 are seeking for effects — which we are anxious to discover. 
 And this kind of knowledge, limited and superficial though 
 it may seem to be, is adequate for the purpose of drawing 
 inferences by the method of illation. 
 
CHAPTER X. 
 
 DELA TION. 
 
 I. It has already been explained of the term 'delation' 
 that it is introduced into this book, partly for reasons of 
 etymology, partly because no better appears to be available. 
 It is employed to signify a kind of inference which is the 
 companion of illation in the field of history, and stands to 
 it in much the same relation as deduction to induction in 
 the field of natural law. 
 
 As deduction is a recognition of the fact that there is 
 unifonnit}- in nature, so delation is a recognition of the fact 
 that there is continuity in nature. It consists in arriving 
 at knowledge of a future or a past event by means of the 
 consideration, that the causes or forces of nature operate 
 continuously with such regularity and in such conjunctions 
 as have been manifested throughout the range of our ex- 
 perience. The exactness of the inference may, of course, 
 be to some extent impaired by allowance made for develop- 
 ment in nature. 
 
 Whatever may be the number of particular classes of 
 conclusion which the mind draws, or is entitled to draw, in 
 the light of the above general consideration, there seem to 
 be only two to which it is necessary for us to devote atten- 
 tion. They are as follows. First, a phenomenon known 
 by experience to take place, or a cause known by experience 
 to operate, after certain intervals of time may be expected 
 
DELATION 125 
 
 to take place, or to operate, always at the expiration of these 
 intervals. Secondl}^, a phenomenon known by experience 
 to be always accompanied, or followed, or preceded b}^ one 
 of several alternatives may be expected, on any recurrence 
 of it, to be accompanied, or to be followed, or to have been 
 preceded by one of these alternatives. Whatever other 
 kinds, besides these, of specific conclusion ma}- properly be 
 drawn, the mind does not seem, for practical purposes, 
 commonly to avail itself of its power of drawing them. 
 
 But here some explanatory remarks require to be made, 
 with special reference to the final section of Chapter VI. 
 If it be affirmed of the conclusion, A phenomenon hitherto 
 followed by one of several alternatives will continue to be 
 so followed, that it is one proper to be drawn, it can, 
 perhaps, scarcely be denied that the mind is equall}- entitled 
 to draw the conclusion, A phenomenon hitherto followed by 
 one invariable consequent will continue to be followed by 
 this consequent. For it seems at first sight to be a reason- 
 able view, either that the former position is derived from the 
 latter, or that the latter is derivable from the former. A 
 phenomenon followed by one of several defined alternative 
 consequents may seem to be a special case of a phenomenon 
 followed by one invariable consequent ; or a phenomenon 
 followed by one invariable consequent may seem to be a 
 special case of a phenomenon followed by one of several 
 defined alternative consequents. Is the mind, then, entitled, 
 is the mind able, to infer such conclusions as, Any man is . 
 mortal, Any bird builds a nest, by delation, in the field of 
 history ? Is it possible that Mill is partly justified in his 
 contention, that there is a rude process of generalising, by 
 simple enumeration, which is independent of a knowledge 
 of uniform causation ? Is the principle of uniformity in 
 nature, as distinct from that of causation, not essential to an 
 act of generalising- ? 
 
126 THE THEORY OF INFERENCE 
 
 The question seems to be, not so much what the mind is 
 entitled to do, as what it actually does. Is it ever the case 
 that, when it concludes one phenomenon to be invariably 
 and unconditionally followed by another, it looks upon the 
 cause of the latter, not as being contained in, but only as 
 being bound up with the former ? When we say in the 
 field of history, Some men have white hair, we affirm that 
 the cause of white hair is sometimes joined with the essen- 
 tial attributes of manhood. But when it was said, as in the 
 instance given by Mill, All swans are white, was the idea in 
 the mind of the reasoner, that the cause of white plumage 
 is an invariable addition to the nature of a swan ? Was it 
 not, rather — according to the view taken in this book — that 
 the invariable cause is contained in the swan's nature, con- 
 stituting a portion of it ? 
 
 But, however this may be, the argument against Mill is 
 unaffected. The insuperable difficulty still remains of ex- 
 tracting the principle of universal causation from the given 
 premises. It appears to be no less impossible to derive 
 the conclusion, Any phenomenon has a cause, from such 
 premises as. Any A has bound up with it the cause of B, 
 in the field of history, than it is to derive it from such 
 premises as, Any A is the cause of B, in the field of natural 
 law. 
 
 Let us now proceed to consider some particular cases of 
 delation given by Butler in the introduction to his Analogy 
 of Religion. The passage from which they are taken will 
 be quoted in a future chapter. He, it must be pointed out, 
 seems to present them as instances of very high probability 
 being practically equivalent to certainty. The view that 
 will be here taken of them is that they are real inferences — 
 inferences, that is, not of something probable, but of some- 
 thing made known — based upon a sure apprehension of 
 continuity in nature. 
 
DELATION T27 
 
 II. "The observation of the ebb and flow of the tide 
 for ages together gives us a full assurance that it w^ill 
 happen again to-morrow." Whereas one observation — so 
 runs his argument — of this phenomenon affords some sort 
 of presumption that it may recur to-morrow, continuous 
 observation gives rise to firm conviction that it will then 
 recur. He thus appears to look upon certainty as the 
 extreme upward limit of a simple probability. In this case, 
 however, we can scarcely suppose that the mind does really 
 reach, as would seem to be implied, its full assurance by 
 means of successive stages of gradually increasing proba- 
 bility. Its feeling of certainty appears to be referable to 
 a direct recognition of the continuous action of elemental 
 forces. Either we look upon the phenomena of the tides 
 as the immediate outcome of these forces ; or, if investiga- 
 tion leads us to attribute the ebb and flow to phenomenal 
 causes, we regard the regularly recurrent action of these 
 causes as a part of the settled order, of nature determined 
 by the aforesaid elemental forces. 
 
 That the certainty which we feel as to the recurrence 
 to-morrow of the tidal movements is far removed from very 
 high probability, would seem to become more fully apparent 
 when we consider how the case w^ould be, if we had 
 reason to suppose that these movements had, in the ordi- 
 nary course of nature, been at any time suspended. If 
 with our own eyes we had witnessed the phenomenon ten 
 thousand times, and but once only had marked its absence, 
 though we should still be conscious that the probability of 
 its happening to-morrow was extremely high, yet surely 
 it caimot be said that our expectation would at all amount 
 to full assurance. 
 
 III. "No man can make a question but that the sun 
 will rise to-morrow, and be seen, where it is seen at all, 
 in the figure of a circle, and not in that of a square." Of 
 
128 THE THEORY OF INFERENCE 
 
 the proposition that the sun will certainly rise to-morrow — 
 to take this first — it made be said that here also Butler 
 seems to put before us an instance of an extremely high 
 simple probability leading to an admittedly conclusive in- 
 ference. But the fact appears to be, that it is not at all 
 through considerations of probability that we attain to the 
 assured conviction that the sun will rise, but that we see, 
 either in the phenomenon of sunrise, or else in the regular 
 recurrence of the known causes of the phenomenon, an 
 essential feature of the settled order and course of nature. 
 
 Another well-known writer, Cardinal Newman, likewise 
 regards the assurance that we have of to-morrow's sun- 
 rise as dependent only on probability. " As to the sun's 
 rising to-morrow," he writes, "there was a first day of the 
 sun's rising, and therefore there may be a last." ^ This 
 remark of his, though true, is scarcely to the point. It is 
 applicable, not to our inferred knowledge of events within 
 the compass of nature's order, but to our ignorance of the 
 length, of time for which this order will endure. Inference 
 presupposes the existence and continuance of a settled order 
 of nature ; and so far as the order is contemplated as sus- 
 pended or impaired, so far the power is of course lost of 
 making inferences. 
 
 Mill also, we may go on to notice, treats the conviction 
 that the sun will rise as a conviction which, though it is 
 undistinguishable from a feeling of certainty, is nevertheless 
 only a conviction that the event is very highly probable. 
 It will be instructive to consider with some care the nature 
 of his argument. He notes, as we have done, that either 
 sunrise itself, or the phenomenal causes of sunrise, may 
 be the thing whose return we confidently expect to-morrow; 
 his treatment of the two cases being, however, essentially 
 identical. It will be sufficient for our purpose to consider 
 
 ^ Grammar of Assent, ch. viii. § i. 
 
DELATION 129 
 
 only what he says with reference to the latter. He writes 
 as follows. 
 
 " On what grounds, it may be asked, do we expect that 
 the sun will rise to-morrow ? To-morrow is be3^ond the 
 limits of time comprehended in our observations. They 
 have extended over some thousands of years past, but they 
 do not include the future. Yet we infer with confidence 
 that the sun will rise to-morrow ; and nobody doubts that 
 we are entitled to do so. Let us consider what is the 
 warrant for this confidence. 
 
 " In the example in question, we know the causes on 
 which the derivative uniformity depends. They are, the sun 
 giving out light, the earth in a state of rotation and intercept- 
 ing light. The induction which shows these to be the real 
 causes, and not merely prior effects of a common cause, being- 
 complete, the only circumstances which could defeat the deri- 
 vative law are such as would destroy or counteract one or 
 other of the combined causes. While the causes exist, and are 
 not counteracted, the effect will continue. If they exist and 
 are not counteracted to-morrow, the sun will rise to-morrow. 
 
 " Since the causes, namely, the sun and the earth, the one 
 in the state of giving out light, the other in a state of rota- 
 tion, will exist until something destroys them, all depends 
 on the probabilities of their destruction, or of their counter- 
 action. We know by observation (omitting the inferential 
 proofs of an existence for thousands of ages anterior) that 
 these phenomena have continued for (say) five thousand 
 years. Within that time there has existed no cause sufficient 
 to diminish them appreciably, nor which has counteracted 
 their effect in any appreciable degree. The chance, there- 
 fore, that the sun ma}' not rise to-morrow amounts to the 
 chance that some cause, which has not manifested itself in 
 the smallest degree during five thousand years, will exist 
 to-morrow in such intensit}^ as to destro}' the sun or the 
 
ISO THE THEORY OF INFERENCE 
 
 earth, the sun's light or the earth's rotation, or to produce 
 an immense disturbance in the effect resulting from those 
 causes. 
 
 " Now, if such a cause will exist to-morrow, or at any 
 future time, some cause, proximate or remote, of that cause 
 must exist now, and must have existed during the whole of 
 the five thousand years. If, therefore, the sun do not rise 
 to-morrow, it will be because some cause has existed, the 
 effects of which, though during five thousand years they 
 have not amounted to a perceptible quantity, will in one day 
 become overwhelming. Since this cause has not been re- 
 cognised during such an interval of time by observers 
 stationed on our earth, it must, if it be a single agent, be 
 either one whose effects develop themselves gradually and 
 very slowly, or one which existed in regions beyond our 
 observation, and is now on the point of arriving in our part of 
 the universe. Now all causes which we have experience of 
 act according to laws incompatible with the supposition that 
 their effects, after accumulating so slowly as to be imper- 
 ceptible for five thousand years, should start into immensity 
 in a single day. No mathematical law of proportion between 
 an effect and the quantity or relations of its cause could pro- 
 duce such contradictory results. The sudden development 
 of an effect of which there was no previous trace always 
 arises from the coming together of several distinct causes 
 not previously conjoined ; but if such sudden conjunction is 
 destined to take place, the causes, or t/ieh' causes, must have 
 existed during the entire five thousand years ; and their not 
 having once come together during that period shows how 
 rare that particular combination is. We have, therefore, 
 the warrant of a rigid induction for considering it probable, 
 in a degree undistinguishable from certainty, that the known 
 conditions requisite for the sun's rising will exist to-morrow." ^ 
 1 Book III. ch. xix. § 2. 
 
DELATION 131 
 
 The sure conviction entertained by all that the sun, having 
 risen day by day for ages past, will rise as usual again 
 to-morrow, is represented by Mill as an instance of what 
 he terms " the extension of derivative laws to adjacent 
 cases." His view, as described above, of the path followed 
 by the mind in its passage from the known to the unknown 
 does not appear to be in all points tenable. The argument 
 seems to be, (i) that the phenomenal causes of sunrise 
 will continue their action until they are counteracted or 
 destroyed ; (2) that, according to all experience, counter- 
 acting and destroying causes never spring up suddenly into 
 immensity by mere development ; (3) that, if such a cause 
 should at any time arise, it must be in consequence of a 
 conjunction of already existing causes ; (4) that such a 
 conjunction has not taken place within the thousands of 
 years that the world has been the object of intelligent 
 human observation ; (5) that it is probable in a very high 
 degree that such a conjunction, being thus known to be 
 extremely rare, will not occur to-morrow; (6) that the 
 recognition of this very high probability is a product of 
 induction ; (7) that the probability is so high as to be 
 undistinguishable from certainty. 
 
 With reference to the above argument, it may be remarked 
 first of all, that Mill, like ourselves, places dependence upon 
 a settled order of nature. But he does not depend upon it 
 to the same extent. He regards it, apparently, as a funda- 
 mental truth, needing no argument to prove it, that causes 
 once set going by primeval forces continue to operate 
 according to the law of their being ; and in this respect his 
 view may be said to be substantially in harmony with our 
 own. He regards it, moreover, as an accepted fact, how- 
 ever ascertained, that no other single cause will spring up 
 and suddenly arrest them. But he does not, as we do, 
 ■consider further that the law of their being admits of no 
 
132 THE THEORY OF INFERENCE 
 
 sudden change, in whatever way occasioned. He does not, 
 as we have imphcitly done, consider that the law of their 
 being is understood to involve complete immunity from 
 catastrophic disturbance, so long as the present order of 
 things, with which alone investigation is concerned, continues 
 to exist. The position he assumes is this. Regarding it as 
 possible that catastrophic disturbance may occur within the 
 present system of nature through some conjunction of causes, 
 he seeks to show that we have good ground for certainly 
 concluding that it will not occur to-morrow. It has not, he 
 says, happened once in the course of some thousands of 
 years, and is therefore an event which manifestly is extremely 
 rare. Consequently, that it will occur to-morrow, is in the 
 highest degree improbable. 
 
 What, now, is the nature and value of this reasoning ? 
 What right have we to enunciate this conclusion from the 
 premises laid down ? By what course does the mind here 
 travel from the familiar picture of the past to a vision of the 
 unknown to-morrow ? 
 
 With regard to the sun's having risen daily for five 
 thousand years, either our position is, that in all that time 
 we have known no instance to the contrary, or it is, that in 
 all that time we have known the event to recur continuously. 
 Either our view is, that a certain combination of causes, 
 destructive of sunrise, has never, so far as we are aware, 
 taken place, or it is, that such a combination is known to 
 have never taken place. In the former case, conceiving it 
 to be possible that it may at any time occur, we have no 
 sure ground, perhaps no very strong ground, for concluding 
 that it will not occur to-morrow. For we know nothing of 
 the infrequency with which causes are ordained by nature to 
 combine for the prevention of sunrise, beyond the fact that 
 during the five thousand years there is no evidence of the 
 combination having happened once. It may, on the hypo- 
 
DELATION 133 
 
 thesis we are considering, be, for anything we know to the 
 contrary, according to the design of nature that to-morrow's 
 sunrise shall not take place. It would be quite in accord- 
 ance with what we know of the rarity of its being counter- 
 acted, that the counteraction should occur for the first time 
 to-morrow. 
 
 If, however, we take our stand on the other hypothesis, 
 and consider ourselves to know positively that for five 
 thousand 3xars the phenomenon of sunrise has on no occa- 
 sion failed, then the question arises. By what right do we 
 assume it to be possible that in the present constitution of 
 things it should ever fail ? Apparently we have no rational 
 justification for making this assumption. If we know that 
 the sun has always risen, then, apparently, we know that 
 it belongs to the constitution of things that it should, as 
 usual, rise to-morrow. We infer, in accordance with our 
 apprehension of continuity in nature, either that the phe- 
 nomenon, ascribed to the action of elemental forces, will 
 re-appear after the accustomed interval of time, or that the 
 known causes upon which it is dependent will continue to 
 act as hitherto they have acted. 
 
 And now, with reference to Mill's assertion that we have 
 the warrant of a rigid induction for concluding that the sun 
 will rise to-morrow, let the question be put, Where is the 
 induction ? With reference to his statement that what the 
 induction warrants is a conclusion that is very highly pro- 
 bable, let it be asked. How can a rigid induction issue in a 
 probable conclusion ? And with reference to his contention 
 that the probability is so high as to be undistinguishable 
 from certainty, it must be maintained that expectation based, 
 if in this case it could be based, on considerations of pro- 
 bability, would not by any means amount to full assurance. 
 
 A word may be said concerning our conviction that the 
 sun will maintain, as hitherto, its circular appearance. The 
 
134 THE THEORY OF INFERENCE 
 
 shape of the sun may, it would seem, be properly regarded 
 as a phenomenon due to the action of the same combined 
 elemental forces which make it in other respects the body 
 that we know. Its shape, in fact, and the other properties 
 which we ascribe to it, constitute together one phenomenon. 
 And we look for a round sun as naturally and necessarily 
 as we look for a sun at all. 
 
 IV. "The prince who had always lived in a warm cHmate 
 naturally concluded that there was no such thing as water 
 becoming hard." In this case, again, the conclusion seems 
 to be derived from an apprehension of continuity in nature. 
 We may, perhaps, look upon it as a negative case of a 
 cause continuing to act as it has always acted. A sup- 
 posed cause, such as would make water solid, cannot have 
 existence, there being no trace of it within the limits of 
 experience. 
 
 The inference thus made involves, of course, two assump- 
 tions. It involves the assumption that the conditions affecting 
 water in one portion of the world have been thoroughly 
 observed ; and it involves the assumption that these condi- 
 tions are everywhere substantially the same. The reasoner, 
 assuming that the disposition of causes in the part of nature 
 with which he is acquainted is fully known to him, and that 
 the disposition of them in that part which has not come 
 under his observation is very similar, correctly argues that 
 water can never become solid. But these assumptions are 
 natural and proper only to an intelligence that is very im- 
 perfectly developed. With growing experience the observer, 
 while still firmly holding that the disposition of causes in 
 his own corner of the world must continue unchanged, will 
 feel the need of satisfying himself that he has sure ground 
 for knowing what this disposition is. And, while still firmly 
 holding that the disposition of causes in the world as a 
 whole must continue without change, will begin to doubt 
 
DELATION 135 
 
 whether he has sufificient ground for thinking that this 
 disposition is the same in every part. 
 
 A prince, then, with a trained and developed mind would 
 not refuse to believe that water could become solid in 
 another countr}', unless he felt assured that he had good 
 ground for holding, both that the fluidity of water in his 
 own warm climate had never once been disturbed, and 
 that the forces affecting water in a cooler climate are 
 substantially the equivalents of those affecting it in the 
 warm one. 
 
 V. "We conclude that it is supposable there may be 
 frost in England any given day in January next ; probable, 
 that there will on some day of the month ; and that there 
 is a moral certainty, that is, ground for an expectation, with- 
 out any doubt of it, in some part or other of the winter." 
 Our special concern here is with the last only of these 
 three conclusions. The others have been quoted in connec- 
 tion with it, because the passage seems clearly to indicate 
 the supposed derivation of certainty from extremely high 
 probability. 
 
 Our reason for concluding with full assurance that there 
 will be frost in England on some da}^ during the winter is 
 this : We believe the phenomenon in question to have been 
 continuous in the past. Regarding it as a certain fact that, 
 as winter has succeeded winter throughout the centuries that 
 are gone, frost has invariably made some appearance, we 
 entertain no doubt that in the coming winter it will not for 
 the first time be wholly absent. There seems to be no 
 question whatever of any probability of its appearing or not 
 appearing. There seems to be no such upward passage of 
 the mind, and scarcel}' a possibility of such a passage, as 
 it appears to be Butler's purpose to put before us ; a pas- 
 sage, that is, from the slight probability of frost on a given 
 day in January, through the great probability of frost in 
 
136 THE THEORY OF INFERENCE 
 
 the course of that month, to the certainty of frost before 
 the expiration of the winter. 
 
 Nevertheless it may be admitted that there is some plausi- 
 bility in his view. Would not, it may be objected, probability 
 gradually develop into certainty, were we to suppose the 
 mind travelling northwards from England to the Arctic 
 Regions ? and is not the alleged mental passage, from the 
 probability of frost in England on a given day in January to 
 the certainty of it in the course of the winter season, precisely 
 similar to the supposed passage, from the probability of frost 
 on a given day in Januar}^ in England to the certainty of it 
 in the Arctic Regions ? 
 
 The answer to these questions seems to be as follows. 
 First, the passage from England to the Arctic Regions is one 
 that we can without much difficulty conceive the mind as 
 undertaking ; but the passage from a given day in January, 
 through an ascending series of groups of days, to the complete 
 winter is not an operation which we can at all suppose that 
 the mind does actually engage in. Secondly, if the mind did 
 choose to make the former passage, still the feeling of a 
 certainty thus reached as the extreme limit of probability 
 would not be the same thing as the feeling of certainty which 
 attaches to delative inference. In the one case the feeling 
 would seem to be that, as frost has been known to be absent 
 from England, so it may conceivably have been, and again 
 be, absent from the Arctic Regions on the given day, though 
 experience teaches that such absence has never yet been 
 known. In the other case, that of delative inference, the 
 conviction of the presence of frost appears to be of a distinctly 
 stronger kind. For we do not seem able to conceive, or at 
 all events we do not conceive, even the possibility of its 
 absence. 
 
CHAPTER XL 
 
 ILLATION. 
 
 I. At length we enter definitely upon the important subject 
 of illation, the kind of inference employed in discovering 
 causes and effects in the field of history. The term, it may 
 be explained, has been suggested by Cardinal Newman's 
 use of the phrase " the illative sense " in an allied significa- 
 tion. His doctrine will come under consideration in the 
 following chapter. 
 
 Let us suppose that we wish to discover the cause of a 
 real phenomenon p, which presents itself to us as concrete 
 and unique, and at the same time as connected by relations 
 of time and place with other phenomena seen around us. To 
 begin the discussion by repeating all that has been said 
 in previous chapters concerning the multiplicity of causes 
 which contribute to the production of any effect would seem 
 to be unnecessary. It will be understood that the cause of 
 / which it is our object to discover is some one of the in- 
 definite number of causes to which it owes its origin. At 
 the same time it is a cause which, of all this indefinite 
 number, shall lie somewhere in such close proximity to the 
 effect, that the ascertainment of a relation of causation 
 between the two phenomena shall be felt to do some- 
 thing to explain them both. To a person seeking for the 
 cause of a present severe cold, it would generally seem 
 irrelevant to be told — what may, however, be perfectly true 
 
138 THE THEORY OF INFERENCE 
 
 — that it is in a measure due to some small imprudence 
 committed years ago, or to some motive of yesterday which 
 contributed, directly or indirectly, to his going out of doors. 
 What he is looking for is a particular cause which shall be 
 in agreement with his general conception of the kinds of 
 cause which give rise, more or less immediately and directly, 
 to influenza and catarrh, a cause in regard to which he may 
 take precautions against repetitions of it. 
 
 To have some clear conception of the different kinds of 
 cause to which effects resembling the phenomenon have 
 hitherto been due — or, in stricter language, of the different 
 kinds of concrete phenomena which have contained the 
 cause of the given kind of effect — is a necessary condition 
 of finding the required definite cause. We must, at starting, 
 be in a position to confine our inquiry within certain narrow 
 limits : illation then may enable us to find, by making 
 search within these limits, a particular cause of the pheno- 
 menon before us. We must know, for example, that some 
 p is rt, some p is b, some / is c, some / is d. That is to say, 
 we must know that instances oi p have sometimes been pre- 
 ceded by a concrete a, sometimes by a concrete b, sometimes 
 by a concrete c, sometimes by a concrete d. We then know, 
 by means of acts of delative inference, that the cause of the 
 new instance of / before us is to be found, if anywhere, 
 among instances of a^ or of b, or of c, or of d. 
 
 In tracing the cause of an effect /, there appear to be, 
 in general, three distinct steps taken by the mind. All of 
 them, however, may not be necessary on all occasions ; nor, 
 when all are taken, need they be always taken in the same 
 order. The steps are (i) that of reducing within the 
 narrowest possible limits the kinds of cause, a, b, c, d, from 
 which / may proceed; (2) that of finding a definite pheno- 
 menon, P, which might produce as its effect a manifestation 
 of one of the afore-mentioned kinds of cause, such as a or 
 
ILLATION 139 
 
 c; (3) that of formulating some definite event, A, which, 
 being a particular manifestation, say of a, shall fulfil the 
 twofold condition of being an explanation both of the known 
 effect /, whose cause is sought, and also of the definite 
 cause P, known or supposed to be in operation somewhere. 
 This formulated event A is the solution of our problem. 
 
 The first step, the reduction of the number of kinds of 
 cause amongst which search has to be made, is accomplished 
 by means of regarding/, in the first place, as a part of some 
 compound whole ; associating with it, in the second place, 
 other effects appearing in some sort of proximity to it ; and 
 assuming, in the third place, that some one common or joint 
 cause has produced them all. Let us suppose that we fix 
 upon (/ and r as being, with /, parts of one whole and pre- 
 sumably springing, with it, from one and the same concrete 
 cause. The immediate problem is then to find a common 
 kind of cause to which all may be attributed. Knowing, as 
 we do, that/ has had its origin in an a, or a d, or a. c, ov a. 
 
 d, let us suppose that we also know, by means of acts of 
 delative inference, that q has sprung from an a, or a I?, or an 
 
 e, or an y, and r from an a, or a d, or a £; or an /i. Com- 
 paring then the several sets of kinds of cause, we find that, 
 if/, q, r have all been produced by one cause, that cause 
 must belong either to the kind a or to the kind b. 
 
 The step mentioned as the second is that of looking round 
 and fixing tentatively and hypothetically upon a definite 
 cause, P, known or supposed to be at work, and ascertaining 
 that it would, according to the teaching of past experience, 
 give rise to a cause of the kind, say a or c. Two ways 
 may be indicated of satisfying ourselves that we have such 
 a cause before us. We may know, as facts, that P is in 
 operation, and that it has in the past produced results of the 
 kind a and of the kind c. Or we may know, as facts, that 
 certain other effects, x and y, exist, and that these are cap- 
 
140 THE THEORY OF INFERENCE 
 
 able of being accounted for by the existence of a supposed 
 cause, P, which would naturally produce an a if it did exist. 
 
 Having thus found, in the first step, that / has been pro- 
 duced by an a or by a b, and, in the second step, either that 
 a cause certainly exists which might very well produce an a, 
 or that a cause might very well exist which would certainly 
 produce an a^ we then, in the third step, put these two results 
 together. We conclude that P, the definite cause known or 
 supposed to exist, has produced a definite action, A, of the 
 kind a; which action we fomiulate, and accept it as the 
 required cause of /. The existence of a definite instance of 
 a, connecting together/ and P, serves to explain, in the one 
 case, /, q, r, P, in the other case, /, q, r, x, y, all of them 
 definite facts known to have occurred. And thus uniting 
 and explaining a mass of concrete phenomena A is accepted 
 by the mind — more or less confidently and more or less 
 correctly — as a new fact in the field of history. 
 
 A fact substantiated in the manner just described, by its 
 power of linking together and throwing light upon other 
 facts of which the mind already has cognisance, is a fact 
 with which it becomes acquainted by means of illative in- 
 ference. That an event or circumstance can be made to 
 present itself as a more or less obvious feature of some 
 consistent picture, or as a more or less necessary member of 
 some organic whole, is the ground on which the mind takes 
 its stand when, having previous knowledge of the remaining 
 portions of the picture or of the whole, it declares that the 
 event or circumstance wanted to complete it is a fact of 
 history. Of the cogency of the method, the necessity, that 
 is, under which the mind lies of following it to such a con- 
 clusion ; of the objective value or truth of the conclusion 
 when it is arrived at ; and of the mind's action when con- 
 tradictory conclusions seem to claim acceptance ;— of these 
 subjects, which require to be carefully considered, it will be 
 
ILLATION 141 
 
 more convenient to speak in a later chapter. It seems 
 better, instead of entering on them now, that we should 
 confine our attention to mastering the details of the simple 
 process of illation, and wait awhile before discussing further, 
 in these and other respects, the rationale of the mind's 
 action. 
 
 We have had before us the process of discovering the 
 cause of a given effect. It will perhaps be well, even at the 
 risk of tediousness, to exhibit the reverse process of in- 
 vestigating the effect of a given cause, before we concern 
 ourselves with illustrations. This question of inference by 
 the method of illation is of so much importance, that it seems 
 desirable to incur the danger of wearying somewhat the 
 general reader, rather than to give the profounder student 
 reason to complain that it has been discussed too slenderly. 
 
 We wish, let us say, to ascertain an effect in the field of 
 history of a cause A observed to be at work. As before, 
 there appear to be three main steps which it is, in general, 
 necessary for the mind to take. That which may be first 
 mentioned is the operation of reducing within narrow limits 
 the different kinds of effect, P, Q, R, which we have to regard 
 as possibly produced by the given cause. A second is the 
 observing and fixing upon a definite eifect a^ which may 
 have as its cause one of the afore-mentioned kinds of effect, 
 say P or R. The remaining one is the bringing together A 
 and a by formulating a particular manifestation, say of P, 
 which shall be at once the cause of a and the required effect 
 of A. 
 
 The operation of reducing the kinds of effect, which it is 
 needful to regard as having their origin in A, is performed 
 by associating with A other observed causes, B and C, and 
 looking for one joint effect to proceed from all. If it is 
 known that A may be followed by an effect of the kind 
 P, Q, or R ; B by one of the kind P, Q, or S ; C by one 
 
142 THE THEORY OF INFERENCE 
 
 of the kind P, Q, or T ; then we conclude that the joint 
 effect must be of the kind P or Q. 
 
 An effect of the kind P or Q, if it has real existence, 
 is in turn a cause producing a further effect. For some 
 phenomenon which may be such a further effect we proceed 
 to make search in the neighbourhood of A. Let us suppose 
 that we become acquainted with a, which may, as we know, 
 have proceeded from a P or from an R. 
 
 The mind is then in a position to take the remaining step, 
 which will consist in connecting together A and a by means 
 of some intermediate P. The hypothesis of the actual 
 existence of /, a definite instance of P, proceeding from A 
 and producing a, serves to interpret both A and a, associating 
 them, together with B and C, in one harmonious whole. 
 The mind accordingly pronounces that the required effect 
 of A is /, that special manifestation of P which has produced 
 a. The degree of confidence with which the mind makes 
 its declaration, and the degree of objective truth which 
 enters into it, are questions the discussion of which must 
 for the present be postponed. 
 
 II. Let us now, by means of examples, endeavour to 
 realise more fully the twofold method or process that has 
 been described. It will, perhaps, be more satisfactory to 
 make further use of illustrations given in a former chapter, 
 than to introduce for our present purpose others that are 
 altogether new. Let us, therefore, suppose first that we 
 have to investigate the cause to which is attributable (i) 
 a certain person's being seen riding a beautiful horse, (2) 
 a farmer's finding his orchard strewn with fruit. 
 
 The first inquiry, it may be noticed, might easily be made 
 with either one of two intentions. It might be made rela- 
 tively to a certain person's being seen riding, who had not 
 previously been known to indulge in this exercise ; or it 
 might be made relatively to his being seen on the back 
 
ILLATION 143 
 
 of a beautiful horse, although he was supposed to be a poor 
 man. The question put might be, How comes he to be 
 on horseback ? or it might be, How^ has he managed to 
 get so good a horse ? And according to the nature of the 
 question which it proposes to itself will the mind make 
 choice of suitable phenomena as auxiliar}^ to its investiga- 
 tion. Upon the view which it takes of the phenomenon 
 under consideration will depend its selection of others as 
 presumably having some causal connection with it. Thus 
 in the former case there might be associated with it such 
 facts as these : he has recently taken a house in the country ; 
 he is known to have lately consulted a doctor. In the 
 latter case we should make choice of facts of a different 
 description, as, for instance, these : he is now living in an 
 expensive house; an uncle of his who was very well off 
 has recently died. 
 
 Dealing with the phenomenon in connection with the 
 former set of facts, we argue in some such wa}^ as this. 
 This person's riding may, as we are entitled to infer from 
 our past experience of human action, be attributed, either 
 (i) to a wish to taste the enjoyment that is to be met with, 
 or (2) to a wish to improve his health, or (3) to a wish to 
 associate more closely with a friend in whose company he 
 rides. A new fact in his life, which may be hypothetically 
 supposed to be connected with the new fact of his riding, 
 as an effect proceeding from the same cause, is that he has 
 recently taken a house in the country. Now this effect 
 may be ascribed, either (i) to a wish to benefit his health, 
 or (2) to a wish to benefit the health of his famil}^, or (3) 
 to a wish to associate more closely with his friend, who is 
 also his near neighbour in the countr}-. Putting the two 
 phenomena together, as having one common or joint cause, 
 we conclude that this must be, either (i) a wish to benefit 
 his health, or (2) a wish to associate more closely with his 
 
144 THE THEORY OF INFERENCE 
 
 friend. But another fact, of the nature of a cause, now 
 offers itself to our notice, as possibly containing the ex- 
 planation of which we are in search. The person in ques- 
 tion has, we learn, lately been to a doctor for his advice. 
 This fact, regarded as a cause, might issue, either (i) in 
 a determination to lead an outdoor life for the sake of 
 health, or (2) in the adoption of some other new rule of 
 life. Accordingly, comparing the two possible kinds of 
 common cause of the observed facts of riding and living 
 much in the country with the two possible kinds of effect 
 of the observed fact of consulting a doctor, we find that 
 there is one kind of phenomenon, namel}', leading an out- 
 door life for the sake of health, which may contain among 
 its instances or manifestations both the cause of the riding 
 and the taking a house in the country and the effect of the 
 consultation. And we may formulate one definite instance 
 which will fulfil this double function. We may judge that 
 the cause of the person's being seen on horseback on the 
 given morning was his attending to the advice given by 
 the doctor on the occasion of the visit which he is known 
 to have paid. That the doctor advised him, on a known 
 occasion, to live much in the open air, and that this advice 
 was being attended toon a given morning, is a new fact 
 accepted by the mind, because it links together and explains 
 three observed facts — the person's riding, his taking a house 
 in the country, and his paying a visit to the doctor. 
 
 Were we, on the other hand, to take the latter of the 
 two suggested sets of facts, our argument might run thus. 
 This person's opportunity of riding a valuable horse may 
 arise, either (i) from its being lent to him by the wealthy 
 friend with whom he rides, or (2) from unjustifiable ex- 
 travagance, or (3) from his having come into possession of 
 a considerable sum of money. Another new fact in his 
 life, which may tentatively be regarded as springing from 
 
ILLATION 145 
 
 the same cause as this expensive manner of riding, is that 
 he is now living in a costi}' house. This latter fact may 
 be due, cither (i) to extravagance, or (2) to the possession 
 of large means, or (3) to the supposed necessities of 
 business. If, then, the two effects have in truth a common 
 or joint cause, this must be taken to be, either (i) extrava- 
 gance, or (2) the possession of large means. But that the 
 person should be in possession of large means is, let us 
 suppose, a very likely circumstance, since a rich uncle of 
 his is known to have lately died. This uncle's wealth 
 might, it is true, have gone elsewhere. But if we suppose 
 it to have been bequeathed, as it well may have been, to 
 his nephew, then we are in possession of a hypothesis 
 which further links together and explains two other facts 
 — the nephew's riding a beautiful horse and his living in 
 an expensive house. Associdting the two observed instances 
 of the nephew's contact with wealth with the acquisition 
 by some one of the uncle's property, b}' means of an inferred 
 intermediate fact — namely, the spending b}^ the nephew of 
 money inherited from the uncle — the mind has before it a 
 historical picture in which facts are consistent with one 
 another and satisfactorily explained. 
 
 The second inquiry which we proposed to make was the 
 investigating the cause of a certain farmer finding his orchard 
 strewn one morning with fruit. The cause, he may say, 
 judging from his past experience, is to be found, either (i) 
 in connection with the decay that takes place in the quiet 
 course of nature, or (2) in connection with violence of wind, 
 or (3) in connection with an act of theft. On looking round, 
 he may take note of scattered bits of broken bough, the 
 presence of which seems to negative the first of the three 
 alternatives. Let us now suppose that a boy in the village 
 is found in possession of a number of apples of which he 
 can give no satisfactory account. This fact, taken in con- 
 
146 THE THEORY OF INFERENCE 
 
 junction with the others, seems to indicate that the apples 
 h'ing on the ground have been left there by pilferers. If 
 next it should appear that the brother of this boy was 
 known to be extremely' fond of apples, and to have been 
 guilt}' on some previous occasion of stealing them, or that 
 having been ill-treated b}- the owner of the orchard he was 
 likeh' to wish to do him an injury, we have a cause — 
 namel}', a known or supposed motive of the brother — which 
 it seems reasonable to connect with the effects that have 
 been observed. There is a cause — either the boy's fondness 
 for apples and his lax morality, or his ill-treatment by the 
 farmer — which may well have led to the stealing of apples, 
 and there are circumstances — the apples and the bits of tree 
 lying on the ground, and the apples in possession of the 
 boy's brother — which ma}- well have their explanation in 
 an act of theft. Accordingl}' the inference is made, that 
 the brother of the bo}- in whose possession the apples were 
 found stole them, leaving others lying about, in consequence 
 of his known fondness for the fruit, or in consequence of 
 his supposed desire to avenge a known act of ill-usage. 
 
 III. We pass on to consider examples of the discovery 
 of an effect. And let us, as before, return to illustrations 
 that have been alread}' used. Let us endeavour to follow 
 the process of finding an effect (i) of the meteorological 
 causes whose presence is indicated by a low state of the 
 barometer on some particular morning, (2) of a certain 
 3-oung man's being sent b}- his father to the university. 
 
 In the first case, we may suppose an observer to be 
 aware that the effect of the meteorological causes indicated 
 by the barometer — whatever this effect may be — is of a kind 
 which is included sometimes in heavy falls of rain, some- 
 times in slight showers, sometimes in violent storms of wind. 
 We ma}' suppose him to examine the aspect of the sky, and 
 to be aware that the causes there indicated produce an 
 
ILLATION 147 
 
 effect — whatever it may be — which sometimes forms part 
 of weatlier that is thoroughly wet, sometimes of weather 
 in which showers are followed by intervals of sunshine, 
 sometimes of weather that is dull and close. Putting to- 
 gether the two sets of causes, as presumably about to give 
 rise to some joint effect, he may conclude, by means of acts 
 of delative inference, that this effect will be accompanied by 
 i-ain, whether much or little. He presently hears, let us 
 next suppose, that a friend of his, being on an expedition 
 in the neighbourhood covered by the causes, returned home 
 wetted to the skin. This kind of wetting he knows to be 
 an effect the cause of which — whatever it may be — is found 
 sometimes contained in exposure to heavy rain, sometimes 
 contained in a fall into the water; and he concludes, by 
 means of another act of delative inference, that his friend 
 has suffered one of these misfortunes. By adopting the 
 alternative of exposure to rain he supplies himself, not only 
 with an explanation of his friend's wetting, but also with 
 an explanation of the state of the barometer and the aspect 
 of the sky observed by him in the morning. The hypothesis, 
 that a heavy storm has resulted from the causes indicated 
 and has drenched his friend, links together the state of the 
 barometer, the aspect of the sky, and the wet condition of 
 his friend into one consistent and self-explanatory whole. 
 The observer readily assents to the conclusion, that this 
 storm of rain has taken place, in order to satisfy a twofold 
 need experienced by the mind. This is the need of con- 
 necting facts together in relations of causation, and of con- 
 necting them in relations that harmonise wnth its own 
 previous acquaintance with the groupings of causes in the 
 operations of nature. 
 
 In the second example, we have to call to mind various 
 alternative effects, more or less commonly observed, of 
 sending a young man to the university. And from among 
 
148 THE THEORY OF INFERENCE 
 
 the many sets or classes of alternatives that might possibly 
 be adduced we must make selection of one set or class, 
 according to the object and purpose with which we start the 
 investigation. Let us suppose, then, that we wish to ascer- 
 tain an effect of this kind— in what way the relation in which 
 a certain son stands to his father has been brought about 
 by the former having received a university education. We 
 have, accordingly, to place before us sucli alternative kinds 
 of effect as might make themselves apparent in intercourse 
 between son and father. Some undergraduates, we may 
 say, develop in their university career a taste for quiet study, 
 others for idleness and athletic sports, others for mixing in 
 earnest work with the throng of men. Among these kinds 
 of result we must look for a particular effect produced upon 
 our young man. Let us now suppose that he is known to 
 possess — as a cause co-operating with his university educa- 
 tion — a character and temperament such as are commonly 
 seen to lead to active brain-work in connection either with 
 books or with affairs. B}^ reason of this supposition our 
 three alternative kinds of effect or result are reduced to two. 
 If next we may be supposed to learn that the son, having 
 left the university, is living quietly at home in company with 
 a studious father, we may have here a definite circumstance 
 indicative of the effect for which we are making search. For 
 this circumstance may be taken to be a consequence either 
 of a studious habit of mind, or of an indolent desire for 
 quiet ease. If we consider that it springs from a cause of 
 the former kind, then in the definite exhibition which we 
 have before us of this kind of cause, an exhibition which will 
 also be a definite manifestation of one of the alternative 
 kinds of effect produced by the original cause, we have a 
 connecting link between these three things — the original 
 cause, the associated cause, and the observed circumstance. 
 We are thus led to conclude, that the effect of sending the 
 
ILLATION 149 
 
 young man to the university is this : he has contracted a 
 love of stud}^ which finds its gratification in the quiet life 
 which we see him leading at liome in company with liis 
 father. 
 
 IV. It will now, perhaps, be worth our while to follow 
 once more the process of illation, in order to compare it step 
 M" step with the process of induction. It will be sufficient 
 for this purpose, if we take onl}^ the case of ascertaining the 
 cause of a given effect, and if, in considering induction, we 
 look only to the method of comparison. Let us suppose 
 that the problem before us is to satisfy ourselves as to the 
 cause of a certain person being troubled with a bad cold — a 
 problem for which we may find a solution both in the field 
 of natural law and in the field of history. What w'e desire 
 to have presented to us in the field of natural law is a 
 phenomenon out of which it may not be difficult to conceive 
 the given effect proceeding ; and what we desire to see before 
 us in the field of history is a phenomenon w^iich it may not 
 be difficult to associate with the given effect in a single scene 
 of human life. 
 
 In either investigation we have to call to our aid other 
 phenomena besides the effect in question. There lies before 
 us a concrete X, compounded of abstract X and other 
 circumstances. According to the field in which our work 
 lies do we make choice of phenomena to be treated in 
 connection with this concrete X. In the one case we look 
 for phenomena which resemble it, in the other for phenomena 
 which may be regarded as parts, with it, of one whole. 
 In the one case, wishing to find a cause of abstract X, 
 regarded as part of the composite phenomenon, concrete X, 
 we collect other instances of concrete X, each of which 
 is looked upon as an envelope containing an abstract X. 
 precisely similar to the one already before us. And we 
 argue, from the principle of uniformity in nature, that the 
 
ISO THE THEORY OF INFERENCE 
 
 required cause must have its exact counterpart among the 
 antecedents of every instance thus collected. In the other 
 case, our object being to find a cause of our concrete X, 
 regarded as being itself part of a composite phenomenon 
 or collection of phenomena, we treat it in conjunction with 
 other phenomena which presumably belong to the same 
 whole. Our argument, based upon the principle of continuity 
 in nature, then is, that a causal relation or set of relations 
 connecting the phenomena in one whole must present a 
 picture entirely in harmony with other pictures of nature's 
 working already familiar to the observer. 
 
 Our choice of phenomena, it may be pointed out, does 
 not appear to be either more arbitrary or more accidental 
 in the latter case than in the former. If the number of 
 phenomena which may be taken as co-elements with concrete 
 X of some whole is indefinitely large, so also is the number 
 of those which may be pronounced to bear some resemblance 
 to it. And if we can very much reduce this latter number by 
 determining in what respect we desire to find resemblance, 
 so also we can very much reduce the former number by 
 determining the exact kind of whole of which we desire to 
 see a completed picture. In the case of a person afflicted 
 with a bad cold, there may be said to be innumerable in- 
 stances of indisposition resembling the cold in one symptom 
 or another ; but, if we look for instances of resemblance in 
 respect of what we consider to be the distinctive features of 
 a cold, the number becomes very greatly lessened. Similarly 
 the number of actions performed and sensations felt by the 
 person having the cold, which are phenomena capable of 
 being taken in conjunction with it as parts of some whole, may 
 be said to be innumerable ; but, if we look for actions and 
 sensations that have to do with health only, their number is 
 brought within comparatively narrow limits. Further, it does 
 not appear that there is necessarily any more difficulty in 
 
ILLATION 151 
 
 deciding what phenomena really form parts of the whole which 
 we desire to complete, than in deciding what phenomena are 
 really precisely similar to the one before us. We may, 
 indeed, mistakenly decide that John Smith's having had a 
 hot bath, and his observed loss of appetite, are closely 
 connected with the cold from which he suffers, and may thus 
 follow a path which leads to no satisfactory result. But so 
 also we may mistakenly decide that William Jones, whose 
 symptoms resemble in some respects those of John Smith, 
 is suffering from a cold. 
 
 Having fixed upon a limited range of phenomena as suitable 
 for the particular purpose that we have in view, we take 
 instances within this range and consider what information 
 relevant to our purpose we have, or can obtain, concerning 
 them and concerning the original phenomenon. In the field 
 of natural law we ask, What are the antecedent circum- 
 stances of these several phenomena ? For among the sets 
 of antecedents search has to be made for a kind that is 
 common to them all. In the field of history the question is, 
 What are the special kinds of phenomena which have seemed 
 to be causall}^ connected with those in question in time past ? 
 For among the sets of kinds of phenomena search has to be 
 made for a kind that is common to them all. And both the 
 antecedents in the one case, and the kinds of phenomena 
 in the other case, with which we concern ourselves, are, in 
 general, such only as stand in some near relation of time 
 or place to the phenomena under consideration. All remote 
 antecedents, and all distantly connected kinds of phenomena, 
 we pass over as having no practical bearing upon the solu- 
 tion of our problem. 
 
 If our object is to ascertain the cause of John Smith's 
 cold, regarded only as a manifestation of the abstract pheno- 
 menon, we fix upon a number of other persons likewise suf- 
 fering from cold, and we set side by side, so to speak, all the 
 
152 THE THEORY OF INFERENCE 
 
 different sets of antecedents, and search among the sets for 
 one which appears in all ; confining our attention, however, 
 to recent events that seem to have a bearing upon the health 
 of the bodily organs with which cold is connected. And it 
 may happen that we shall find that all the persons, includ- 
 ing John Smith, have lately been subjected in one way or 
 another to unwonted changes of temperature. This being 
 so, unwonted changes of temperature, we more or less con- 
 fidently conclude, are the cause of the cold from which our 
 friend is suffering. With the particular occasion of his being 
 subjected to them we have no further concern. 
 
 If, however, we seek to know a near and concrete cause 
 of a really concrete cold, we proceed in this wise. We fix 
 upon a number of other concrete phenomena presenting 
 themselves in the near neighbourhood of the cold, and 
 apparently capable of being combined with it, by causal 
 connections, in one picture harmonising with our previous 
 knowledge of the grouping of causes. We endeavour to 
 formulate some one historical event which shall be a 
 common or joint cause of the associated effects, and at the 
 same time an effect of an associated cause. Thus we take, 
 let us say, the patient's loss of appetite as an effect pre- 
 sumably proceeding from the same cause as the cold, and 
 his having had a certain hot bath as a remoter cause to 
 which this common cause may be due. The question then 
 is. Can we, consistently with what we already know of 
 nature, fix upon a circumstance or event which is at once 
 the cause of the cold and loss of appetite and the effect of 
 the hot bath ? And it may be that we find a satisfactory 
 answer to this question by arriving at the conclusion, that 
 a chill occasioned by taking the particular hot bath is the 
 required cause of the particular bad cold. 
 
 The comparison which we have made between induction 
 and illation seems to show that they are quite distinct 
 
ILLATION 153 
 
 mental processes, and yet that in some respects they bear 
 a close resemblance to one another. There is in each the 
 selecting, and invoking the aid of, a group of phenomena 
 which seem to be allied in a special way to the one under 
 consideration. There is in connection with each a preli- 
 minary drawing a conclusion or conclusions, by deduction 
 or b}^ delation, in accordance with the fundamental principle 
 of the field in which investigation is being made. There 
 is in each a search made for a kind of phenomenon which 
 shall satisfy the conditions of this conclusion. And there 
 is in each a limiting the range of search to such kinds of 
 phenomena as stand in some near relation of time or place 
 to the given effect. As formal processes of the mind, induc- 
 tion and illation appear to stand on an equal footing in 
 respect of gravity and complexity. A comparison of the 
 processes in point of certainty of conclusions drawn will 
 form a part of our concluding chapter. 
 
 Two additional remarks may now be made. The first is 
 that, as in the field of natural law a further deductive step 
 often follows after induction, so in the field of history the 
 result of illation may be carried beyond the ascertainment 
 of the particular cause of a particular effect. While in the 
 former field we can proceed from the proposition. This A is 
 B, to the conclusion. Any A is B, in the latter we can turn 
 the proposition. This A is B, into the conclusion, Some A is 
 B. That is to say, the causal connection found to exist, in 
 the field of history, between a particular A and a particular 
 B is a connection which may be usefully remembered as a 
 new premise in the event of future dealings with an A or 
 with a B. 
 
 And the second remark is this. The work of finding a 
 cause may sometimes be begun in either one of the two 
 fields, and then continued in the other. In the exhibition, 
 in Chapter IV., of the process of finding by induction the 
 
154 THE THEORY OF INFERENCE 
 
 origin of a case of poisoning, we were supposed to have 
 found a few alternatives among which the cause must 
 he. And it was remarked that, unless by means of ex- 
 periment or of the evidence of other facts we could make 
 choice among these alternatives, we must be content to 
 stop short of complete discovery. Now the evidence of 
 other facts may be evidence collected and utilised in the 
 field of history. If induction leads no farther than to the 
 conclusion that poison has been introduced into some one 
 of several articles of food, there may be facts, of which 
 illation can make use, pointing to the conclusion that 
 poison was introduced by a certain person, or on a certain 
 occasion, into a particular one of the given articles. And 
 so too, on the other hand, if by illation we should be led 
 to the conclusion that poison has been introduced into 
 some one of a number of dishes, and these dishes should 
 be variously partaken of by different persons, induction 
 might enable us to discover the one particular dish which 
 contained the poison. 
 
 V. Before concluding this discussion of illative inference, 
 the attention of the reader must be directed to the fact, 
 that in assent given to propositions on the evidence of 
 testimony we have a notable exemplification of it. This 
 point is not brought forward for the mere purpose of 
 illustrating further the method of illation, but, rather, in 
 order to emphasise the use that is actually made of it. 
 The mental process of being convinced by testimony is a 
 phenomenon which plainly needs to be accounted for, 
 and we find in the illative method the required explanation. 
 A person testifies, let us say, to the existence of some 
 object or circumstance which he professes to have seen. 
 What rational ground have we then for accepting it as true 
 that this object or circumstance has existence ? Why 
 should we place reliance (i) upon the accuracy of his 
 
ILLATION 155 
 
 perception, and (2) upon a harmony between his perception 
 and his speech ? By what course of reasoning can we 
 reach the conclusion, tliat the actual existence of the alleged 
 object or circumstance is the true explanatory cause of his 
 saying what he does ? The problem appears to be one 
 the solution of which is to be found in the field of history, 
 and not in the field of natural law. 
 
 It may, indeed, be taken to be a law of nature, that there 
 is in every man a faculty of seeing things in some measure 
 as they are. And it may, further, be taken to be a law 
 of nature, that there is in every man some disposition to 
 testify in accordance with what he supposes that he has 
 seen. But no less must it be held to be a law of nature, 
 that there is in the case of every man some liabilit}^ to 
 misinterpret what lies before him, and some disposition 
 to subordinate testimon}^ to the satisfaction of his own 
 desires. And, in the absence of knowledge of the relative 
 strength of faculties and motives, we can only say, with 
 respect to men in general, that, according to the laws of 
 nature, a person may or may not be trustworthy as an 
 observer, and may or may not be trustworthy as a reporter. 
 
 If, as no doubt we may, we choose to consider that a good 
 and prolonged education is a cause moving men strongl}^, 
 both in the direction of seeing correctly, and in the direction 
 of speaking truly, then perhaps we are entitled to hold, 
 that in the case of well-educated persons of full age there 
 is a strong tendency to report correctly the things of which 
 they speak. We may say, in the field of natural law, 
 Most well-educated persons of full age speak the truth. 
 In other words, A well-educated person of full age speaks 
 the truth, unless, as occasionally happens, some special cir- 
 cumstances prevent his doing so. 
 
 Can we now go on to formulate a law of nature setting 
 forth the circumstances in which causes arise that are 
 
156 THE THEORY OF INFERENCE 
 
 strong enough to counteract the habit of speaking truly ? 
 Is it possible to say that a well-educated person of mature 
 age is, in the absence of certain conditions, to be believed, 
 and, in the presence of these conditions, not to be believed ? 
 Surely it is utterly impossible to formulate a law of nature 
 by which our attitude towards a witness, even one well- 
 educated and of mature age, is rigidly to be guided. It 
 would, apparently, be a perfectly hopeless task to attempt 
 to classify, even in the limited case of well-educated and 
 adult persons, those who on any given occasion would speak 
 the truth, and those whose word, whether on account of 
 misapprehension or of dishonesty, is not to be credited. 
 The question, whether a given individual, who asserts that 
 he was the witness of some phenomenon, is or is not to 
 have credit given to his statements, is a question which 
 cannot possibly be solved by means of any received general 
 truths of the field of natural law. It is a question which 
 belongs essentially to the field of history. 
 
 The problem to be solved is this : A witness testifying 
 to some particular circumstance, what is the cause of his 
 so testifying ? from the fact of his testimony being such 
 as it is, what further fact are we led to infer ? And the 
 method of solving it is the method of illation. 
 
 First, his testimony, whatever it may be, is a fact which, 
 in accordance with what we already know of like concrete 
 effects, may be ascribed, either (i) to accurate observation 
 and truthful speech, or (2) to inaccurate observation and 
 truthful speech, or (3) to deliberate perversion of facts 
 observed, or (4) to exercise of imagination or invention. 
 Secondly, we may call to our aid, as effects presumably 
 springing from the same cause as the statements which he 
 makes, particulars of the manner in which he gives his 
 evidence. If he appears to speak openly and straight- 
 forwardly, we consider, either that he has no intention to 
 
II.LATIOX 157 
 
 deceive, or that he is a master of the art of" conceahng his 
 real character. If, again, he shows no undue anxiety for 
 his statements to be accepted, we judge, either that he is 
 speaking impartially, or that he is exercising some amount 
 of self-restraint. And if he impresses us as a person of 
 gravity and decorum, we consider that he is speaking, not 
 of any creations of his own, but of things belonging to the 
 domain of real life. Putting together his words and these 
 other co-existing facts, we have ground for concluding that 
 his statements are to be ascribed to his reporting truthfully 
 what he thinks that he has seen. Lastly, if we know him 
 to be a person who has some trained power of observing 
 accurately things similar to the one concerning which he 
 now gives evidence, and w^ho has a strong disposition to 
 report truthfully what he sees, we have in this power and 
 disposition a particular known cause, which it is reasonable 
 to associate with the effects before us. It is reasonable to 
 conclude, that there is a particular act of accurate observing, 
 followed by truthful speaking, which is an intermediate 
 phenomenon between the known character of the witness 
 on the one hand, and the statements heard, and particulars 
 of manner noted, on the other hand. In other words, the 
 evidence which we hear has, as we infer, its source in the 
 witness seeing an event and reporting it as it happened. 
 
 Inference from concurrent testimony is likewise made b\^ 
 the method of illation, though the process of reasoning, 
 after the first step, is somewhat different : it does not need 
 to be carried quite so far. We have before us a number 
 of witnesses, concerning whose individual veracity we make 
 no inference. Each of them, regarded separatel}', ma}^ or 
 may not be speaking truly. His statement may proceed 
 from accurate observation and truthful speech, or it may 
 proceed from a variety of other sources. The combined 
 statements are so many phenomena which we associate 
 
158 THE THEORY OF INFERENCE 
 
 together as effects presumably having a common origin. 
 The required kind of common origin we find — with an 
 assurance proportioned to the number of independent 
 witnesses, and to the supposed paucity of the causes that 
 would lead them to speak untruly — to be, truthfully re- 
 porting something which has been accurately observed. 
 And a necessary cause or condition of all being on this 
 occasion accurate observers and truthful reporters is, as we 
 at once perceive, the occurrence of the event to which they 
 unite in testifying. We conclude, accordingly, that the 
 event in question has actually happened. 
 
 Illation, then, and illation only — it is here maintained — 
 can account for our accepting facts as true on the ground 
 of their being represented to us as true by other persons ; 
 whether the testimony be that of a single witness of whose 
 veracity we become assured, or the concurrent testimony 
 of a number of persons whose individual credibility is more 
 or less undetermined. 
 
CHAPTER XII. 
 
 NEWMAN'S "GRAMMAR OF ASSENT." 
 
 I. In Newman's well-known Grm/n/iar of Assent we have 
 a serious and methodical attempt to exhibit the mind's 
 action in giving assent to undemonstrable propositions. His 
 purpose, like our own, is to vindicate, in the interest of 
 religious faith, the naturalness and reasonableness of hold- 
 ing a certain class of beliefs, beliefs which are neither the 
 immediate outcome of intuition or of the evidence of sense, 
 nor capable of being logically proved. His book thus having 
 in view the same object as ourselves, and being, as it is, 
 a treatise of acknowledged weight, it will be well that we 
 should consider carefully the nature of his argument. It 
 is desirable, in defence of the position we are taking up, 
 to claim the support of his great authority for points on 
 which we find ourselves in agreement with him ; and it is 
 desirable that, where on important points we differ or seem 
 to differ from him, some explanation of the difference should 
 be submitted to the judgment of the reader. 
 
 The position which is the groundwork of our four previous 
 chapters — that there is a class of inferred truths to which 
 logical methods are powerless to lead — forms likewise the 
 basis of Newman's argument. Let us for the moment con- 
 fine our attention to the two classes of inferred proposition 
 which the mind receives as true, reserving for later con- 
 sideration the two classes of evidence on which it acts. It 
 
i6o THE THEORY OF INFERENCE 
 
 will be readily understood that in the distinction which has 
 been drawn between inference in the field of natural law 
 and inference in the field of history there is implied a dis- 
 tinction between assent in the one field and assent in the 
 other. Inference, inductive and illative, has been taken 
 to signify a completed act of passing from the known to 
 the unknown, and so to include the final stage, which is 
 unconditional assent to the newly discovered truth. We 
 may say, then, that one part of our fundamental position 
 is, that assent means one thing in the field of natural 
 law and another thing in the field of history ; that in 
 the former field it is given to propositions about things 
 abstract and individual, and in the latter to proposi- 
 tions concerning things concrete and related to other 
 things. 
 
 This distinction, so far as it relates to a difference between 
 assent to propositions about things abstract and assent to 
 propositions concerning things concrete, is dwelt upon at some 
 length b}' Newman. He speaks of the former as notional 
 and of the latter as real assent. To real assent he also 
 assigns the term belief. On the one hand — so he lays it down 
 — we apprehend abstractions, and assent to propositions 
 about abstract notions ; on the other hand, we apprehend real 
 existences, and give our assent to propositions about concrete 
 things. His presentation of his argument is not succinct 
 enough to lend itself readily to quotation, but the follow- 
 ing passages will, perhaps, sufficiently confirm and illustrate 
 what has been said. 
 
 " There are propositions, in which one or both of the 
 terms are common nouns, as standing for what is abstract, 
 general, and non-existing, such as * Man is an animal, some 
 men are learned, an Apostle is a creation of Christianity, a 
 line is length without breadth, to err is human, to forgive 
 divine.' These I shall call notional propositions, and the 
 
NEWMAN'S "GRAMMAR OF ASSENT" i6i 
 
 apprehension with which we infer or assent to them, 
 notional. 
 
 "And there are other propositions, which are composed 
 of singular nouns, and of which the terms stand for things 
 external to us, unit and individual, as ' Philip was the father 
 of Alexander,' ' the earth goes round the sun,' ' the Apostles 
 first preached to the Jews ; ' and these I shall call real pro- 
 positions, and their apprehension real, 
 
 "There are then two kinds of apprehension or inter- 
 pretation to which propositions may be subjected, notional 
 and real. 
 
 " Next I observe, that the same proposition may admit 
 of both of these interpretations at once, having a notional 
 sense as used by one man, and a real as used by 
 another. Thus a schoolboy may perfectly apprehend, and 
 construe with spirit, the poet's words, * Dum Capitolium 
 scandet cum tacita Virgine Pontifex ; ' he has seen steep 
 hills, flights of stepsj, and processions ; he knows what en- 
 forced silence is ; also he knows all about the Pontifex 
 Maximus, and the Vestal Virgins ; he has an abstract hold 
 upon every word of the description, yet without the words 
 therefore bringing before him at all the living image which 
 they would light up in the mind of a contemporary of the 
 poet, who had seen the fact described, or of a modern historian 
 who had duly informed himself in the religious phenomena, 
 and by meditation had realised the Roman ceremonial, of the 
 age of Augustus. Again, ' Dulce et decorum est pro patria 
 mori,' is a mere common-place, a terse expression of ab- 
 stractions in the mind of the poet himself, if Philippi is to be 
 the index of his patriotism, whereas it would be the record of 
 experiences, a sovereign dogma, a grand aspiration, inflaming 
 the imagination, piercing the heart, of a Wallace or a Tell."^ 
 
 ^ A7t Essay in Aid of a Grammar of Assent, by John Henry Cardinal 
 Newman, ch. i. § 2. 
 
i62 THE THEORY OF INFERENCE 
 
 "There is a third remark suggested by the view which I 
 have been taking of real assents, viz., that they are of a 
 personal character, each individual having his own, and 
 being known by them. It is otherwise with notions; 
 notional apprehension is in itself an ordinary act of our 
 common nature. All of us have the power of abstraction, 
 and can be taught either to make or to enter into the same 
 abstractions ; and thus to co-operate in the establishment of 
 a common measure between mind and mind. And, though 
 for one and all of us to assent to the notions which we thus 
 apprehend in common, is a further step, as requiring the 
 adoption of a common stand-point of principle and judgment, 
 yet this too depends in good measure on certain logical 
 processes of thought, with which we are all familiar, and on 
 facts which we all take for granted."^ 
 
 Let us now take notice of a point, most important in its 
 bearing upon the question of the generation of real assent, in 
 which Newman's view is not in accord with ours. Though 
 he agrees with us in distinguishing between things abstract 
 and things concrete, yet he differs from us in not distinguish- 
 ing between things individual and things related to other 
 things. Except for purposes of comparison and abstraction 
 he looks upon things, whether notionally or really appre- 
 hended, as only individual. He writes as follows: — "All 
 things in the exterior world are unit and individual, and are 
 nothing else ; but the mind not only contemplates those unit 
 realities, as they exist, but has the gift, by an act of creation, 
 of bringing before it abstractions and generalisations, which 
 have no existence, no counterpart, out of it."'- "We are 
 ever grouping and discriminating, measuring and sounding, 
 framing cross classes and cross divisions, and thereby rising 
 from particulars to generals, that is, from images to notions. 
 In processes of this kind we regard things, not as they are 
 1 Ch. iv. § 2. - Ch. i. § 2. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 163 
 
 in themselves, but mainly as they stand in relation to each 
 other. We look at nothing simply for its own sake ; we 
 cannot look at any one thing without keeping our eyes on 
 a multitude of other things besides. ' Man ' is no longer 
 what he really is, an individual presented to us by our 
 senses, but as we read him in the light of those comparisons 
 and contrasts which we have made him suggest to us. He 
 is attenuated into an aspect, or relegated to his place in a 
 classification. Thus his appellation is made to suggest, not 
 the real being which he is in this or that specimen of 
 himself, but a definition." ^ 
 
 It thus comes to pass that Newman's line of demarcation 
 between notions and things, between abstractions and real 
 existences, does not quite coincide with ours. With us a 
 clothed abstraction, such as a particular specimen of manhood, 
 is still an abstraction so long as it is regarded as individual 
 and unrelated to its environment. It is still a phenomenon 
 belonging to tlie field of natural law and lying within the 
 domain of logic. It ceases to be an abstraction, and passes, 
 as a concrete thing, into the field of history, only when the 
 relations in which it stands to things around it constitute 
 part of our conception of it. Newman, however, makes the 
 criterion of abstractions and of concrete things consist, not 
 in their standing alone or being related to other things, but 
 in the degree of vividness with which they happen to be 
 realised. An object is not apprehended, in the two cases, 
 in different ways, but only with different degrees of strength. 
 The following passages may be quoted in confirmation of 
 these remarks. 
 
 " I have already given various illustrations of Real Assent ; 
 I will follow them up here by some instances of the change 
 
 of Notional Assent into Real Twenty years ago, 
 
 the Duke of Wellington wrote his celebrated letter on 
 
 1 Ch. iii. 
 
1 64 THE THEORY OF INFERENCE 
 
 the subject of the national defences. His authority gave it 
 an immediate circulation among all classes of the community ; 
 none questioned what he said, nor as if taking his words on 
 faith merely, but as intellectually recognising their truth ; 
 yet few could be said to see or feel that truth. His letter 
 lay, so to say, upon the pure intellect of the national mind, 
 and nothing for a time came of it. But eleven years after- 
 wards, after his death, the anger of the French colonels with 
 us, after the attempt upon Louis Napoleon's life, transferred 
 its facts to the charge of the imagination. Then forthwith 
 the national assent became in various ways an operative 
 principle, especially in its promotion of the volunteer move- 
 ment. The Duke, having a special eye for military matters, 
 had realised the state of things from the first ; but it took 
 a course of years to impress upon the public mind an assent 
 to his warning deeper and more energetic than the recep- 
 tion it is accustomed to give to a clever article in a news- 
 paper or a review." ^ 
 
 " It is plain what a different sense language will bear in 
 this system of intellectual notions from what it has when it 
 is the representative of things : and such a use of it is not 
 only the very foundation of all science, but may be, and is, 
 carried out in literature and in the ordinary intercourse of 
 man with man. And thus it comes to pass that individual 
 propositions about the concrete almost cease to be, and 
 are diluted or starved into abstract notions. The events 
 of history and the characters who figure in it lose their 
 individuality. States and governments, society and its 
 component parts, cities, nations, even the physical face of 
 the country, things past, and things contemporary, all that 
 fulness of meaning which I have described as accruing to 
 language from experience, now that experience is absent, 
 necessarily becomes to the multitude of men nothing but a 
 
 ^ Ch. iv. § 2. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 165 
 
 heap of notions, little more intelligible than the beauties of 
 a prospect to the short-sighted, or the music of a great 
 master to a listener who has no ear." ^ 
 
 II. Having realised the distinction drawn between the two 
 kinds of assent, or the two classes of proposition to which 
 assent is given, we pass on to the very important question 
 of the sources from which assent springs. This will lead, 
 in the present section, to some discussion of the subject of 
 inference, that is, of logical or formal inference. 
 
 Let us notice, first, that no assent is, in Newman's view, 
 involved in this kind of inference. He is at great pains to 
 exhibit the two things as essentially distinct. " Assent," 
 he says, " is unconditional ; else, it is not really represented 
 by assertion. Inference is conditional, because a conclu- 
 sion at least implies the assumption of premisses."- And, 
 commenting on statements made by Locke, he writes as 
 follows : — 
 
 " The first question which this theory leads me to con- 
 sider is, whether there is such an act of the mind as assent 
 at all. If there is, it is plain it ought to show itself un- 
 equivocally as such, as distinct from other acts. For if a 
 professed act can only be viewed as the necessary and im- 
 mediate repetition of another act, if assent is a sort of 
 reproduction and double of an act of inference, if when 
 inference determines that a proposition is somewhat, or not 
 a little, or a good deal, or very like truth, assent as its 
 natural and normal counterpart says that it z's somewhat, or 
 not a little, or a good deal, or very like truth, then I do not 
 see what we mean by saying, or why we say at all, that there 
 is any such act. It is simply superfluous, in a psychological 
 point of view, and a curiosity for subtle minds, and the 
 sooner it is got out of the way the better. When I assent, 
 I am supposed, it seems, to do precisely what I do when I 
 1 Ch. iii. - Ch. i. § i. 
 
i66 THE THEORY OF INFERENCE 
 
 infer, or rather not quite so much, but something which is 
 included in inferring ; for, while the disposition of my mind 
 towards a given proposition is identical in assent and in 
 inference, I merely drop the thought of the premisses when I 
 assent, though not of their influence on the proposition in- 
 ferred. This, then, and no more after all, is what nature 
 prescribes ; and this, and no more than this, is the con- 
 scientious use of our faculties, so to assent forsooth as to do 
 nothing else than infer. Then, I say, if this be really the 
 state of the case, if assent in no real way differs from infer- 
 ence, it is one and the same thing with it. It is another 
 name for inference, and to speak of it at all does but mislead. 
 Nor can it be fairly urged as a parallel case that an act of 
 conscious recognition, though distinct from an act of know- 
 ledge, is after all only its repetition. On the contrary, such 
 a recognition is a reflex act with its own object, viz., the act 
 of knowledge itself. As well might it be said that the hear- 
 ing of the notes of my voice is a repetition of the act of 
 singing : — it gives no plausibility then to the anomaly I am 
 combating. 
 
 " I lay it down, then, as a principle that either assent is 
 intrinsically different from inference, or the sooner we get 
 rid of the word in philosophy the better. If it be only the 
 echo of an inference, do not treat it as a substantive act ; 
 but, on the other hand, supposing it be not such an idle re- 
 petition, as I am sure it is not, — supposing the word ' assent ' 
 does hold a rightful place in language and in thought, — if it 
 does not admit of being confused with concluding and infer- 
 ring, — if the two words are used for two operations of the 
 intellect which cannot change their character, — if in matter 
 of fact they are not always found together, — if they do not 
 vary with each other, — if one is sometimes found without 
 the other, — if one is strong when the other is weak, — if 
 sometimes they seem even in conflict with each other, — then, 
 
NEWMAN'S "GRAMMAR OF ASSENT" 167 
 
 since we know perfectly well what an inference is, it comes 
 upon us to consider what, as distinct from inference, an 
 assent is, and we are, by the very fact of its being distinct, 
 advanced one step towards that account of it which I think 
 is the true one." ^ 
 
 Here Newman's view appears to be at variance with our 
 own. We may, indeed, without difficulty concede the point, 
 that assent is not merely another name for inference ; for 
 assent may no doubt be given to truths which become known 
 to us otherwise than by inference, and also may continue to 
 be given to inferred truths long after the act or process of 
 inferring them has faded from the memory. But neverthe- 
 less we must maintain that true inference includes assent, 
 being a completed passage from things known to things 
 hitherto unknown. The state or condition of being in 
 London, it may well be granted, is not the same thing as 
 travelling to London ; and yet the having completed the 
 journey involves the being in that city. In a somewhat 
 similar manner, as it seems, the passage of the mind from 
 old facts to new includes the resting in, or giving assent to, 
 those that are new. 
 
 But, secondly, let us inquire what it is that Newman 
 understands by inference. If we find that he and we, when 
 making use of the term, do not mean by it the same thing, 
 it is possible that, though there is not accordance, yet there 
 is no very notable discrepancy between the two views of 
 the relation in which assent stands to inference. It is, at 
 all events, desirable that we should be careful to examine 
 the matter from his own standpoint. 
 
 In this book logical inference has been represented as 
 consisting of induction and deduction. From such a fact as, 
 John died, taken in conjunction with other similar facts, we 
 reach the inferred conclusion, John's manhood was the cause 
 
 1 Ch. vi. § I. 
 
1 68 THE THEORY OF INFERENCE 
 
 of his death. And from this latter fact we may pass on to 
 the inferred conclusion, Any man must die, or, Richard must 
 die. But the conclusion, Richard must die, instead of being 
 drawn directly from the ascertained fact, John's manhood 
 was the cause of his death, may be drawn from it indirectly 
 by means of the general or abstract conclusion, Any man 
 must die ; the abstract conclusion being specially interpreted 
 with reference to Richard. 
 
 Now it has been maintained in the chapter on deduction, 
 that the latter part of this indirect method of reaching a new 
 particular conclusion, a part which may be presented in the 
 form of syllogism, is not inference. It is argued, with Mill, 
 that inference ceases with the abstract conclusion, and that 
 deriving the particular from the abstract is not inference, 
 but interpretation. 
 
 But Newman, as we shall see, considers that this, which 
 we deny to be inference, constitutes the main part of logical 
 or formal inference. And thus he is led to condemn, on two 
 grounds, the uncertainty of inferential conclusions. Conclu- 
 sions reached by inference — that is, by syllogism — cannot, 
 he argues, command unqualified assent owing to their un- 
 certainty. In the first place, they rest on premises which 
 are assumed, not proved ; in the second place, the application 
 of a general rule to a concrete case is liable to error. The 
 following passage is a part of what he says on the subject of 
 the syllogism. 
 
 " The first step in the inferential method is to throw the 
 question to be decided into the form of a proposition ; then 
 to throw the proof itself into propositions, the force of the 
 proof lying in the comparison of these propositions with 
 each other. When the analysis is carried out fully and put 
 into form, it becomes the Aristotelic syllogism. However, 
 an inference need not be expressed thus technically ; an 
 enthymeme fulfils the requirements of what I have called 
 
NEWMAN'S "GRAMMAR OF ASSENT" 169 
 
 Inference. So does any other form of words with the mere 
 grammatical expressions, ' for,' ' therefore,' ' supposing,' 
 'so that,' 'similarl}',' and the like. Verbal reasoning, of 
 whatever kind, as opposed to mental, is what 1 mean by 
 inference, which differs from logic onl}' inasmuch as logic is 
 its scientific form. And it will be more convenient here to 
 use the two words indiscriminately, for I shall say nothing 
 about logic which does not in its substance also apply to 
 inference. 
 
 " Logical Inference, then, being such, and its office such 
 as I have described, the question follows, how far it answers 
 the purpose for which it is used. It proposes to provide 
 both a test and a common measure of reasoning; and I think 
 it will be found partly to succeed and partly to fail ; succeed- 
 ing so far as words can in fact be found for representing the 
 countless varieties and subtleties of human thought, failing 
 on account of the fallacy of the original assumption, that 
 whatever can be thought can be adequately expressed in 
 words. 
 
 "In the first place. Inference, being conditional, is hampered 
 with other propositions besides that which is especially its 
 own, that is, with the premisses as well as the conclusion, 
 and with the rules connecting the latter with the former. 
 It views its own proper proposition in the medium of prior 
 propositions, and measures it by them. It does not hold a 
 proposition for its own sake, but as dependent upon others, 
 and those others it entertains for the sake of the conclusion. 
 Thus it is practically far more concerned with the comparison 
 of propositions, than with the propositions themselves. It 
 is obliged to regard all the propositions, with which it has to 
 do, not so much for their own sake, as for the sake of each 
 other, as regards the identity or likeness, independence or 
 dissimilarity, which has to be mutually predicated of them. 
 It follows from this, that the more simple and definite are 
 
I70 THE THEORY OF INFERENCE 
 
 the words of a proposition, and the narrower their meaning, 
 and the more that meaning in each proposition is restricted 
 to the relation which it has to the words of the other pro- 
 position compared with it, — in other words, the nearer 
 the propositions concerned in the inference approach to 
 being mental abstractions, and the less they have to do with 
 the concrete reality, and the more closely they are made to 
 express exact, intelligible, comprehensible, communicable 
 notions, and the less they stand for objective things, that is, 
 the more they are the subjects, not of real, but of notional 
 apprehension, — so much the more suitable do they become 
 for the purposes of Inference." ^ 
 
 III. Let us now, of Newman's two grounds of objection to 
 the conclusions of what he looks upon as logical or formal 
 inference, make some examination of the former, leaving the 
 latter for consideration in the following section. The one 
 bears upon the question of notional assent as well as real ; 
 the other is concerned with the question of real assent only. 
 Syllogistic conclusions cannot in general — so he seems to 
 say — be absolutely assented to, because the premises on 
 which they are based are for the most part no more than 
 assumptions. The following are his own words, which seem 
 undoubtedly intended to apply to abstract matters as well 
 as concrete. 
 
 "Inference comes short of proof in concrete matters, be- 
 cause it has not a full command over the objects to which it 
 relates, but merely assumes its premisses. In order to com- 
 plete the proof, we are thrown upon some previous syllogism 
 or syllogisms, in which the assumptions may be proved ; and 
 then, still farther back, we are thrown upon others again, 
 to prove the new assumptions of that second order of syllo- 
 gisms. Where is this process to stop ? especially since it 
 must run upon separated, divergent, and multiplied lines of 
 
 1 Ch. viii. § I. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 171 
 
 argument, the farther the investigation is carried back ? At 
 length a score of propositions present themselves, all to be 
 proved by propositions more evident than themselves, in 
 order to enable them respectively to become premisses to that 
 series of inferences which terminates in the conclusion which 
 we originally drew. But even now the difficulty is not at 
 an end ; it would be something to arrive at length at pre- 
 misses which are undeniable, however long we might be in 
 arriving at them; but in this case the long retrospection 
 lodges us at length at what are called first principles, the 
 recondite sources of all knowledge, as to which logic pro- 
 vides no common measure of minds, — which are accepted 
 by some, rejected by others, — in which, and not in the syllo- 
 gistic exhibitions, lies the whole problem of attaining to 
 truth, — and which are called self-evident by their respective 
 advocates because they are evident in no other way. One of 
 the two uses contemplated in reasoning by rule, or in verbal 
 argumentation, was, as I have said, to establish a standard 
 of truth and to supersede the ipse dixit of authority : how 
 does it fulfil this end, if it only leads us back to first prin- 
 ciples, about which there is interminable controversy ? We 
 are not able to prove by syllogism that there are any self- 
 evident propositions at all ; but supposing there are (as of 
 course I hold there are), still who can determine these by 
 logic ? Syllogism, then, though of course it has its use, still 
 does only the minutest and easiest part of the work, in the 
 investigation of truth, for when there is any difficulty, that 
 difficulty commonly lies in determining first principles, not in 
 the arrangements of proofs." ^ 
 
 Now surely this objection to the inclusion of assent in 
 inference is not capable of being sustained. Does it not 
 involve a somewhat strange assumption ? Does it not imply 
 that unconditional assent to the premises of a syllogism is 
 
 ^ Ch. viii. § I. 
 
172 THE THEORY OF INFERENCE 
 
 only given in the case of incontrovertible objective truth ? 
 Does it not say, in effect, that assent to a conclusion, de- 
 pending upon assent to a previous conclusion, will, in general, 
 partake of the uncertainty in which first principles are con- 
 fessedly involved ? But if assent is a subjective matter, if 
 for each individual there are propositions to which, though 
 they may be denied by others, he personally gives a full 
 assent — and this undoubtedly appears to be the case — how 
 does controversy concerning them affect the possibility of his 
 building upon them innumerable other propositions which he 
 looks upon as true ? Surely the mind may reason syllo- 
 gistically without the concurrence of other persons in the 
 major premise. 
 
 But if this view of Newman's should be correct, if syllo- 
 gistic conclusions are not, in general, absolutely assented to, 
 what then, we have to ask, is the immediate source of the 
 notional assent, that undoubtedly exists, to propositions that 
 are neither first principles nor entirely based upon incon- 
 trovertible first principles ? 
 
 To this obvious and important question we shall not find 
 in Newman's treatise any satisfactory reply. He does not 
 profess, indeed, to be giving much attention to notional 
 assent ; it is real assent which he is specially anxious to 
 distinguish from inference. Notional assent, while he con- 
 tends that it is different from inference, and cites examples 
 of cases in which he says that it is given, he nevertheless 
 practically treats, either as if it scarcely had existence, or 
 as if it were almost synonymous with inference. He writes 
 as follows : — 
 
 "We may call it then the normal state of Inference to 
 apprehend propositions as notions ; and we may call it the 
 normal state of Assent to apprehend propositions as things. 
 If notional apprehension is most congenial to Inference, real 
 apprehension will be the most natural concomitant on Assent. 
 
IHMnMWHHHl 
 
 NEWMANS "GRAMMAR OF ASSENT" 173 
 
 An act of Inference includes in its object the dependence of 
 its thesis upon its premisses, that is, upon a relation, which 
 is an abstraction ; but an act of Assent rests wholly on the 
 thesis as its object, and the reality of the thesis is almost a 
 condition of its unconditionality."^ "In comparison of the 
 directness and force of the apprehension, which we have 
 of an object, when our assent is to be called real, Notional 
 Assent and Inference seem to be thrown back into one and 
 the same class of intellectual acts, though the former of the 
 two is always an unconditional acceptance of a proposition, 
 and the latter is an acceptance on the condition of an accep- 
 tance of its premisses. In its notional assents as well as 
 in its inferences, the mind contemplates its own creations 
 instead of things ; in real, it is directed towards things, re- 
 presented by the impressions which they have left on the 
 imagination. These images, when assented to, have an 
 influence both on the individual and on society, which mere 
 notions cannot exert."- 
 
 IV. Newman's first objection, then, to inference as a source 
 of assent appears to be one having little or no weight, even 
 when we put his own interpretation upon the term inference. 
 Almost identifying it with syllogistic reasoning, he seems to 
 maintain that, since the propositions constituting the premises 
 are for the most part incapable of being absolutely demon- 
 strated, the conclusions drawn from them are for the most 
 part not unconditionally assented to. The second objection, 
 which applies to real assent only, is more worthy of atten- 
 tion. It is, that syllogistic reasoning deals with abstrac- 
 tions, and on this account can never lead to more than 
 probable conclusions in relation to concrete things. 
 
 In the view that we have taken of the difference in 
 character between conclusions in the field of natural law 
 and conclusions in the field of history, the difference has 
 1 Ch. iv. - Ch. iv. S 2. 
 
174 THE THEORY OF INFERENCE 
 
 been regarded as subjective no less than objective. That is 
 to say, the mind of the reasoner is supposed to be more or 
 less conscious that its inductive and deductive inferences do 
 not place it in possession of the same kind of truth about 
 things as it manages to attain to in another way. It is sup- 
 posed to recognise the limitations of these modes of reason- 
 ing, and to perceive that, so far as concrete things are dealt 
 with by them, they are dealt with only as clothed abstrac- 
 tions. It is supposed to be more or less aware that it is 
 not, and cannot be, by following logical methods, that it 
 comes to assent to propositions in the field of history. 
 Newman, however, prefers to base his depreciation of logical 
 argument, as a means to assent in concrete matters, solely 
 on objective grounds. He endeavours to show that it cannot 
 be trusted to lead to objective truth about concrete things. 
 Instead of showing that the mind of the reasoner is not, in 
 fact, led by the methods of logic to real assent, he seeks to 
 make good the position that it cannot rely upon the objective 
 truth of the conclusions to which logic points. The quality 
 of probability or uncertainty which, in his view, accompanies 
 logical conclusions in then' application to concrete things is 
 not regarded as attaching to the mental attitude of the in- 
 dividual thinker, and making this attitude something different 
 from real assent ; but it is regarded as belonging objectively 
 to the external world, and imparting such a character to 
 logical conclusions about concrete things that no wise man 
 will unconditionally accept them. 
 
 Taking him thus on his own ground, let us see what he 
 has to say in defence of the position that abstract argument 
 cannot lead to concrete truth, a position with which we are, 
 of course, substantially in full accord. Let us see how far, 
 treating the matter in relation to objective truth, he is suc- 
 cessful in upholding this thesis. It will be well to give a 
 somewhat long quotation. 
 
IIHIItllHIIii 
 
 NEWMAN'S "GRAMMAR OP^^SSE^" 175 
 
 " Science, working by itself, reaches truth in the abstract, 
 and probabihty in the concrete ; but what we aim at is truth 
 in the concrete. This is true of other inferences besides 
 mathematical. They come to no definite conclusions about 
 matters of fact, except as they are made effectual for their 
 purpose by the living intelligence which uses them. 'All 
 men have their price ; Fabricius is a man ; he has his price; ' 
 but he had not his price ; how is this ? Because he is more 
 than a universal ; because he falls under other universals ; 
 because universals are ever at war with each other ; because 
 what is called a universal is only a general ; because what is 
 only general does not lead to a necessary conclusion. Let 
 us judge him by another universal. ' Men have a conscience ; 
 Fabricius is a man ; he has a conscience.' Until we have 
 actual experience of Fabricius, we can only say, that, since 
 he is a man, perhaps he will take a bribe, and perhaps he 
 will not. ' Latet dolus in generalibus ; ' they are arbitrary 
 and fallacious, if we take them for more than broad views 
 and aspects of things, serving as our notes and indications 
 for judging of the particular, but not absolutely touching and 
 determining facts. 
 
 " Let units come first, and (so-called) universals second ; 
 let universals minister to units, not units be sacrificed to 
 universals. John, Richard, and Robert are individual things, 
 independent, incommunicable. We may find some kind of 
 common measure between them, and we may give it the 
 name of man, man as such, the typical man, the aiito- 
 antJiropos. We are justified in so doing, and in investing it 
 with general attributes, and bestowing on it what we consider 
 a definition. But we think we may go on to impose our 
 definition on the whole race, and to every member of it, to 
 the thousand Johns, Richards, and Roberts who are found 
 in it. No ; each of them is what he is, in spite of it. Not 
 any one of them is man, as such, or coincides with the auto- 
 
176 THE THEORY OF INFERENCE 
 
 anthropos. Another John is not necessarily rational, be- 
 cause ' all men are rational,' for he may be an idiot ; — nor 
 because ' man is a being of progress/ does the second 
 Richard progress, for he may be a dunce ; nor, because 
 'man is made for society,' must we therefore go on to deny 
 that the second Robert is a gipsy or a bandit, as he is found 
 to be. There is no such thing as stereotyped humanity ; it 
 must ever be a vague, bodiless idea, because the concrete 
 units from which it is formed are independent realities. 
 General laws are not inviolable truths ; much less are they 
 necessary causes. Since, as a rule, men are rational, pro- 
 gressive, and social, there is a high probability of this rule 
 being true in the case of a particular person ; but we must 
 know him to be sure of it. 
 
 " Each thing has its own nature and its own history. When 
 the nature and the history of many things are similar, we 
 say that they have the same nature ; but there is no such 
 thing as one and the same nature ; they are each of them 
 itself, not identical, but like. A law is not a fact, but a 
 notion. ' All men die ; therefore Elias has died ; ' but he 
 has not died, and did not die. He was an exception to the 
 general law of humanity ; so far, he did not come under that 
 law, but under the law (so to say) of Elias. It was the 
 peculiarity of his individuality, that he left the world without 
 dying : what right have we to subject the person of Elias to 
 the scientific notion of an abstract humanity, which we have 
 formed without asking his leave ? Why must the tyrant 
 majority create a rule for his individual history ? ' But all 
 men are mortal ; ' not so ; what is really meant by this uni- 
 versal is, that 'man as such is mortal,' that is, the abstract, 
 typical mito-anth'opos ; to this major premiss the minor, if 
 Elias is to be proved mortal, ought to be, 'Elias was the 
 abstract man;' but he was not, and could not be such, nor 
 could any one else, any more than the average man of an 
 
NEWMAN'S "GRAMMAR OF ASSENT" 177 
 
 Insurance Company is every individual man wlio insures his 
 life with it. Such a syllogism proves nothing about the 
 veritable Elias, except in the way of antecedent probability. 
 If it be said that Elias was exempted from death, not by 
 nature, but by miracle, what is this to the purpose, undeni- 
 able as it is ? Still, to have this miraculous exemption was 
 the personal prerogative of Elias. We call it miracle, be- 
 cause God ordinarily acts otherwise. He who causes men 
 in general to die, gave to Elias not to die. This miracu- 
 lous gift comes into the individuality of Elias. On this 
 individuality we must fix our thoughts, and not begin our 
 notion of him by ignoring it. He was a man, and some- 
 thing more than ' man ; ' and if we do not take this into 
 account, we fall into an initial error in our thoughts of 
 him 
 
 " Nor does any real thing admit, by any calculus of logic, 
 of being dissected into all the possible general notions which 
 it admits, nor, in consequence, of being recomposed out of 
 them ; though the attempt thus to treat it is more unpro- 
 mising in proportion to the intricacy and completeness of 
 its make. We cannot see through any one of the myriad 
 beings which make up the universe, or give the full catalogue 
 of its belongings. We are accustomed, indeed, and rightly, 
 to speak of the Creator Himself as incomprehensible; and, 
 indeed. He is so by an incommunicable attribute ; but in 
 a certain sense each of His creatures is incomprehensible to 
 us also, in the sense that no one has a perfect understanding 
 of them but He. We recognise and appropriate aspects of 
 them, and logic is useful to us in registering these aspects 
 and what they imply; but it does not give us to know even 
 one individual being. 
 
 " So much on logical argumentation ; and in thus speak- 
 ing of the syllogism, I speak of all inferential processes 
 whatever, as expressed in language (if they are such as to 
 
 M 
 
178 THE THEORY OF INFERENCE 
 
 be reducible to science), for they all require general notions, 
 as conditions of their coming to a conclusion."^ 
 
 In the above passage there appear to be contained two 
 chief grounds for affirming that a general law cannot invari- 
 ably be applied with truth to a particular case, two main 
 reasons therefore for refusing to give unconditional assent 
 to the conclusions of a syllogism. These grounds or reasons 
 are as follows. 
 
 I. Some other general law may, in practice, come into 
 contact with the one under consideration, modifying or neu- 
 tralising the result expected. Fabricius as a man, not only 
 is amenable to bribery, but also offers resistance to it. And 
 thus it may well happen that on some given occasion he will 
 not show himself corrupt. 
 
 An answer to this objection to the conclusiveness of 
 syllogistic reasoning may be made in this way. Either, it 
 may be said, the proposition constituting the major premise 
 is not the statement of an abstract or a universal truth, and 
 is therefore quite improperly made use of; or the proposi- 
 tion containing the conclusion is misinterpreted. The major 
 premise of the syllogism must properl}^ represent one of two 
 things, the actually observed universal fact. All men what- 
 soever, Fabricius included, have been found to have their 
 price, or an abstract law of nature, Any man whatsoever has 
 his price. Now if, professing to use a universal, or a law 
 of nature, we employ a proposition which expresses the 
 result only of a partial observation of existing things ; if in 
 the enumeration Fabricius himself has not been included, or 
 if there is no ascertained relation of causation between man- 
 hood and venality, then we have no ground, so far as syl- 
 logism is concerned, for coming to any definite conclusion 
 whatever about him. If, however, the major premise is a 
 true law of nature. Any man has his price, then the conclu- 
 1 Ch. viii. § I. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 179 
 
 sion, Fabricius has his price, is properly assented to. But 
 in the two propositions " having a price " must be inter- 
 preted similarly. If we demur rightly to the conclusion 
 that Fabricius is certainly corruptible, then instead of ac- 
 cepting, Any man is certainly corruptible, as a major premise, 
 we must allow no more than that, Any man is liable to yield 
 to bribery. 
 
 2. The minor premise, bringing the particular case under 
 the general law, may be improperly assumed. For every 
 individual person differs in some respect from his fellows, 
 and so may be incapable of being placed with them in any 
 given class. Elias, for instance, in the matter of liability to 
 death, was not a man like other men, and so was not subject 
 to the general law of humanity. 
 
 To this the answer seems to be twofold. First, in so far 
 as men are different the one from the other, we do not reason 
 syllogistically about them. It is not that in the sphere of 
 difference we have syllogistic conclusions which are only 
 probable ; but we have, in this sphere, no syllogistic reason- 
 ing at all. If, in saying, All men die, we mean that liability 
 to death is an attribute belonging to abstract humanity, we 
 are using as a major premise an assertion which we are only 
 justified in making in consequence of having learned that a 
 cause of death is contained in that humanity which all men 
 alike share. If it is possible for death to have its cause 
 in a part of human nature which is not common to all men, 
 then we err if we construct a syllogism having as its major 
 premise. All men die. Secondly, on the supposition of 
 our knowing that there is in abstract humanity a cause of 
 death, then syllogistic reasoning leads to the certain con- 
 clusion, that Elias, if he was in the ordinary sense of the 
 term a man, had in him a cause of death. If he was not a 
 man, we predicate nothing of him. But Elias, though a 
 man and having in him a cause of death, did not die. How 
 
i8o THE THEORY OF INFERENCE 
 
 is this to be explained ? The simple explanation is, that 
 experience teaches that together with the cause of death is 
 sometimes joined a cause which counteracts its working. 
 This teaching of experience as to the grouping of causes 
 belongs to the field of history, and in no way detracts from 
 the certainty of relation between cause and effect in the 
 field of natural law. 
 
 It may not be amiss to notice in this connection, that 
 Newman appears to have a very inadequate conception of 
 the order of nature in the domain of natural law. While 
 recognising a certain amount of invariableness in nature^ 
 he does not admit the existence of a uniform and necessary 
 relation between cause and effect. Instead of attributing 
 similar effects to precisely similar phenomenal causes, and 
 variations in them to the modifying action of concurrent 
 causes, he prefers to look upon them as owing their existence 
 to Divine Will, concerning which Will absolute uniformity 
 cannot, of course, be predicated. So much has already been 
 said in previous chapters of this book on the subject of 
 causation, that there is no need to enter here upon a dis- 
 cussion of it. It will suffice — after reminding the reader 
 that the view here taken is, that all inference is based upon 
 a conception of the order of nature, and that this conception 
 in no way interferes with the further conception of a Crea- 
 tor and Governor whose Will is itself a cause, though not 
 a phenomenal one — to quote from Newman's words. He 
 writes as follows : — 
 
 "Of these two senses of the word 'cause,' viz., that which 
 brings a thing to be, and that on which a thing under given 
 circumstances follows, the former is that of which our experi- 
 ence is the earlier and more intimate, being suggested to 
 us by our consciousness of willing and doing. The latter 
 of the two requires a discrimination and exactness of thought 
 for its apprehension, which implies special mental training ; 
 
NEWMAN'S "GRAMMAR OF ASSENT" i8i 
 
 else, how do we learn to call food the cause of refreshment, 
 but day never the cause of night, though night follows day 
 more surely than refreshment follows food ? Starting, then, 
 from experience, I consider a cause to be an effective will ; 
 and, by the doctrine of causation, I mean the notion, or first 
 principle, that all things come of effective will ; and the 
 reception or presumption of this notion is a notional assent. 
 
 " As to causation in the second sense (viz., an ordinary 
 succession of antecedents and consequents, or what is called 
 the Order of Nature), when so explained, it falls under the 
 doctrine of general laws ; and of this I proceed to make 
 mention, as another first principle or notion, derived by 
 us from experience, and accepted with what I have called a 
 presumption. By natural law I mean the fact that things 
 happen uniformly according to certain circumstances, and 
 not without them and at random : that is, that they happen 
 in an order ; and, as all things in the universe are unit and 
 individual, order implies a certain repetition, whether of things 
 or like things, or of their affections and relations. . . . 
 
 " There are philosophers who go farther, and teach, not 
 only a general, but an invariable, and inviolable, and necessary 
 uniformity in the action of the laws of nature, holding that 
 everything is the result of some law or laws, and that excep- 
 tions are impossible ; but I do not see on what ground of 
 experience or reason they take up this position. Our experi- 
 ence rather is adverse to such a doctrine, for what concrete 
 fact or phenomenon exactly repeats itself? ... It seems 
 safer then to hold that the order of nature is not necessary, 
 but general in its manifestations. . . . 
 
 " A law is not a cause, but a fact ; but when we come to 
 the question of cause, then, as I have said, we have no 
 experience of any cause but Will. If, then, I must answer 
 the question, What is to alter the order of nature ? I reply, 
 That which willed it; — That which willed it can unwill it; 
 
i82 THE THEORY OF INFERENCE 
 
 and the invariableness of law depends on the unchangeable- 
 ness of that Will." ^ 
 
 V. Newman, then, as we have seen, differs from us in his 
 view of what logical inference is, and also in his view of the 
 nature of the conclusions of syllogistic reasoning. But he 
 agrees with us in holding that logical inference does not lead 
 to assent in concrete matters. Further, agreeing with us that 
 such assent is a fact of human nature, he largely differs from 
 us, as we have now to see, in his view of the manner in 
 which it is attained. We, on the one hand, have had ex- 
 plicitly before us a process by which, as it would seem, the 
 mind travels onwards from the known to the unknown. He, 
 on the other hand, considers that the process is substantially 
 a hidden one, not capable of being set forth in words. 
 While we have sought to follow, step by step, the mind's 
 dealing with a number of results of past experience, he is 
 content, or almost content, to lay it down that the mind 
 instinctively draws its conclusions from them. 
 
 Before giving his own account of this matter, it may be 
 pointed out, that the possibility of formulating a method of 
 illative inference appears to be dependent upon our regarding 
 phenomena as other than individual. We have looked upon 
 concrete things, or things in the field of history, as related to 
 other things around them ; and in our search for causes and 
 effects we have associated phenomena together as presumably 
 forming parts of one and the same whole. Newman, how- 
 ever, looking upon concrete things as individual, is without 
 means to find an exact method, outside the domain of logic, 
 of passing from the known to the unknown. He can do no 
 more than bring together, as grounds or arguments, a number 
 of propositions, and maintain that by their instrumentality 
 the mind somehow reaches the state of assenting to a newly 
 discovered concrete truth. The following passages will 
 
 1 Ch. iv. § I. 
 
iwwwvswHwwiiiiwmiwn 
 
 NEWMAN'S "GRAMMAR OF ASSENT" 183 
 
 suffice to exhibit his view of this action of the mind, action 
 which he terms informal inference. Although in them he 
 is speaking of the state of certitude, or feeling certain, yet 
 apparently we must take it that simple assent is regarded as 
 being arrived at in a similar way. 
 
 " It is plain that formal logical sequence is not in fact the 
 method by which we are enabled to become certain of what 
 is concrete ; and it is equally plain, from what has been 
 already suggested, what the real and necessary method is. 
 It is the cumulation of probabilities, independent of each other, 
 arising out of the nature and circumstances of the particular 
 case which is under review ; probabilities too fine to avail 
 separately, too subtle and circuitous to be convertible into 
 syllogisms, too numerous and various for such conversion, 
 even were they convertible." ^ 
 
 "This I conceive to be the real method of reasoning in 
 concrete matters ; and it has these characteristics : — First, it 
 does not supersede the logical form of inference, but is one 
 and the same with it ; only it is no longer an abstraction, 
 but carried out into the realities of life, its premisses being 
 instinct with the substance and the momentum of that mass 
 of probabilities, which, acting upon each other in correction 
 and confirmation, carry it home definitely to the individual 
 case, which is its original scope. 
 
 " Next, from what has been said it is plain, that such a 
 process of reasoning is more or less implicit, and without the 
 direct and full advertence of the mind exercising it. As by 
 the use of our eyesight we recognise two brothers, yet with- 
 out being able to express what it is by which we distinguish 
 them ; as at first sight we perhaps confuse them together, 
 but, on better knowledge, we see no likeness between them 
 at all ; as it requires an artist's eye to determine what lines 
 and shades make a countenance look young or old, amiable, 
 1 Ch, viii. § 2. 
 
1 84 THE THEORY OF INFERENCE 
 
 thoughtful, angry or conceited, the principle of discrimination 
 being in each case real, but implicit ; — so is the mind unequal 
 to a complete analysis of the motives which carry it on to a 
 particular conclusion, and is swayed and determined by a 
 body of proof, which it recognises only as a body, and not 
 in its constituent parts. 
 
 "And thirdly, it is plain, that, in this investigation of the 
 method of concrete inference, we have not advanced one step 
 towards depriving inference of its conditional character; for 
 it is still as dependent on premisses as it is in its elementary 
 idea. On the contrary, we have rather added to the ob- 
 scurity of the problem ; for a syllogism is at least a demon- 
 stration, when the premisses are granted, but a cumulation 
 of probabilities, over and above their implicit character, will 
 vary both in their number and their separate estimated value, 
 according to the particular intellect which is employed upon 
 it. It follows that what to one intellect is a proof is not so to 
 another, and that the certainty of a proposition does properly 
 consist in the certitude of the mind which contemplates it. 
 And this of course may be said without prejudice to the 
 objective truth or falsehood of propositions, since it does not 
 follow that these propositions on the one hand are not true, 
 and based on right reason, and those on the other not false, 
 and based on false reason, because not all men discriminate 
 them in the same way."-^ 
 
 "On the whole, I think it is the fact that many of our 
 most obstinate and most reasonable certitudes depend on 
 proofs which are informal and personal, which baffle our 
 powers of analysis, and cannot be brought under logical rule, 
 because they cannot be submitted to logical statistics."^ 
 
 " The question arises, whether, granting that the person- 
 ality (so to speak) of the parties reasoning is an important 
 element in proving propositions in concrete matter, any 
 
 ^ Ch. viii. § 2. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 185 
 
 account can be given of the ratiocinative method in such 
 proofs, over and above that analysis into syllogism which is 
 possible in each of its steps in detail. I think there can ; 
 though I fear, lest to some minds it may appear far-fetched 
 or fanciful ; however, I will hazard this imputation. I con- 
 sider, then, that the principle of concrete reasoning is parallel 
 to the method of proof which is the foundation of modern 
 mathematical science, as contained in the celebrated lemma 
 with which Newton opens his 'Principia.' We know that 
 a regular polygon, inscribed in a circle, its sides being con- 
 tinually diminished, tends to become that circle, as its limit ; 
 but it vanishes before it has coincided with the circle, so that 
 its tendency to be the circle, though ever nearer fulfilment, 
 never in fact gets beyond a tendency. In like manner, the 
 conclusion in a real or concrete question is foreseen and pre- 
 dicted rather than actually attained ; foreseen in the number 
 and direction of accumulated premisses, which all converge 
 to it, and as the result of their combination, approach it more 
 nearly than any assignable difference, yet do not touch it 
 logically (though only not touching it), on account of the 
 nature of its subject-matter, and the delicate and implicit 
 character of at least part of the reasonings on which it depends. 
 It is by the strength, variety, or multiplicity of premisses, 
 which are onl}^ probable, not by invincible syllogisms, — by 
 objections overcome, by adverse theories neutralised, by 
 difficulties gradually clearing up, by exceptions proving the 
 rule, by unlooked-for correlations found with received truths, 
 by suspense and delay in the process issuing in triumphant 
 reactions, — by all these ways, and many others, it is that 
 the practised and experienced mind is able to make a sure 
 divination that a conclusion is inevitable, of which his lines of 
 reasoning do not actually put him in possession. This is 
 what is meant by a proposition being 'as good as proved,' 
 a conclusion as undeniable ' as if it were proved,' and by the 
 
i86 THE THEORY OF INFERENCE 
 
 reasons for it 'amounting to a proof/ for a proof is the 
 limit of converging probabilities."^ 
 
 There is here need, before we pass on to consider, in 
 another section, the question of a faculty by which we draw 
 conclusions about things concrete, of an explanatory remark. 
 We may well agree with Newman — in respect, at all events, 
 of a very large number of cases — that the mind is unequal 
 to a complete analysis of the motives which carry it on to a 
 particular conclusion. We may be quite content to admit 
 that much of the work of illative inference is performed un- 
 consciously. But at the same time we may hold that the 
 mind, whether consciously or unconsciously, reaches conclu- 
 sions by the method which has been set forth in the preced- 
 ing chapter. We may decline to admit that it is sufficient 
 explanation, even of the mind's unconscious action, to say 
 that it somehow sees the result of converging probabilities. 
 
 VI. To the mind drawing conclusions, whether by con- 
 scious or by unconscious process, in the field of history, we 
 may, if we will, apply a special name. And a term employed 
 by Newman, viz., the illative sense, would seem to be a 
 fitting expression by which to designate it. It would corre- 
 spond to the term, the sense of order, or moral sense, used 
 in ethics to signify the mind occupied in forming judgments 
 on points of conduct. The sense of order, or moral sense, 
 being a name given to reason, or the mind acting by con- 
 scious process, and perception, or the mind acting by uncon- 
 scious process, in the domain of moral judgments, the 
 expression, the illative sense, may be similarly employed to 
 designate reason and perception as they are seen in the 
 field of illative inferences. In either region — let it be ob- 
 served — perception seems to play a very considerable part 
 in the drawing of conclusions. For even if the mind should 
 have consciously before it all the different considerations 
 
 ^ Ch. viii. § 2. 
 
NEWMAN'S '-GRAMMAR OF ASSENT" 187 
 
 upon which it acts, and also the method by which it deals 
 with them, yet the task of estimating the absolute force and 
 relative value of these considerations is one that must be 
 performed to a great extent by unconscious process. To 
 a great extent it is perception only that can determine that 
 among alternative courses of conduct, or among alternative 
 solutions of an intellectual problem, this or that course is 
 the one to be followed, this or that proposition the one to 
 be assented to. And since perception may fitly enough be 
 spoken of, by way of figure, as a mental sense, there is pro- 
 priety in describing it, when employed upon questions of 
 conduct, as the moral sense, and, when employed upon illa- 
 tive inferences, as the illative sense. Nor, since reason and 
 perception are in either case commonly acting in close con- 
 junction with each other, does it seem to be at all a violent 
 straining of language to include reason, with perception, in 
 one and the same appellation. 
 
 But Newman, while apparently understanding b}^ the 
 illative sense only what has just been spoken of as percep- 
 tion, further limits the term to the mind drawing illative 
 conclusions of a special kind. The illative sense is not, with 
 him, the mind simply making illative inferences ; but it is 
 the mind making illative inferences that are objectively 
 correct. His position herein is not — be it understood — that 
 there is an outward criterion by which objective correctness 
 can be tested, and that the mind may, by reference to it, 
 be sometimes credited with having judged correctly. But it 
 is, apparently, that of every mind a certain part, large or 
 small as the case may be, has the power of determining 
 correctly objective truth, and merits therefore a distinctive 
 name. The following passages contain the substance of his 
 view. 
 
 " Certitude is a mental state : certainty is a quality of 
 propositions. Those propositions I call certain, which are 
 
i88 THE THEORY OF INFERENCE 
 
 such that I am certain of them. Certitude is not a passive 
 impression made upon the mind from without, by argumen- 
 tative compulsion, but in all concrete questions (nay, even 
 in abstract, for though the reasoning is abstract, the mind 
 which judges of it is concrete) it is an active recognition 
 of propositions as true, such as it is the dut}' of each indi- 
 vidual himself to exercise at the bidding of reason, and, 
 when reason forbids, to withhold. And reason never bids 
 us be certain except on an absolute proof; and such a proof 
 can never be furnished to us by the logic of words, for as 
 certitude is of the mind, so is the act of inference which 
 leads to it. Every one who reasons is his own centre ; and 
 no expedient for attaining a common measure of minds can 
 reverse this truth ; but then the question follows, is there 
 any criterion of the accuracy of an inference, such as may 
 be our warrant that certitude is rightly elicited in favour 
 of the proposition inferred, since our warrant cannot, as I 
 have said, be scientific ? I have already said that the sole 
 and final judgment on the validity of an inference in con- 
 crete matter is committed to the personal action of the ratio- 
 cinative faculty, the perfection or virtue of which I have 
 called the Illative Sense, a use of the word ' sense ' parallel 
 to our use of it in 'good sense,' 'common sense,' a 'sense of 
 beauty,' &c. ; — and I own I do not see any way to go farther 
 than this in answer to the question."^ 
 
 "This is what I have to remark concerning the Illative 
 Sense, and in explanation of its nature and claims ; and on 
 the whole, I have spoken of it in four respects, — as viewed 
 in itself, in its subject-matter, in the process it uses, and in 
 its function and scope. 
 
 " First, viewed in its exercise, it is one and the same in 
 all concrete matters, though employed in them in different 
 measures. We do not reason in one way in chemistry or 
 
 1 Ch. ix. 
 
NEWMAN'S "GRAMMAR OF ASSENT" 189 
 
 law, in another in morals or religion ; but in reasoning on 
 any subject whatever, which is concrete, we proceed, as 
 far indeed as we can, by the logic of language, but we are 
 obliged to supplement it by the more subtle and elastic logic 
 of thought ; for forms by themselves prove notliing. 
 
 " Secondly, it is in fact attached to definite subject-matters, 
 so that a given individual may possess it in one department 
 of thought, for instance, history, and not in another, for in- 
 stance, philosoph}'. 
 
 "Thirdly, in coming to its conclusion, it proceeds always 
 in the same way, by a method of reasoning, which, as I have 
 observed above, is the elementary principle of that mathema- 
 tical calculus of modern times, which has so wonderfully 
 extended the lirnits of abstract science. 
 
 " Fourthly, in no class of concrete reasonings, whether in 
 experimental science, historical research, or theology, is there 
 any ultimate test of truth and error in our inferences besides 
 the trustworthiness of the Illative Sense that gives them its 
 sanction ; just as there is no sufficient test of political 
 excellence, heroic action, or gentleman-like conduct, other 
 than the particular mental sense, be it genius, taste, sense 
 of propriety, or the moral sense, to which those subject- 
 matters are severally committed. Our duty in each of 
 these is to strengthen and perfect the special faculty which 
 is its living rule, and in every case as it comes to do our 
 best. And such also is our duty and our necessity, as 
 regards the Illative Sense." ^ 
 
 Exception must be taken to this view of Newman's of the 
 nature of the illative sense. It seems to be analogous to the 
 mistaken view, upheld by Butler, that there is in every man 
 a certain faculty, known as conscience, whose peculiar func- 
 tion it is to discern and point to objective right. The one 
 philosopher in relation to intellectual judgments in concrete 
 
 1 Ch. ix. § 2. 
 
I90 THE THEORY OF INFERENCE 
 
 matters, no less than the other in relation to moral judg- 
 ments in matters of personal conduct, seems to declare that 
 the faculty which judges correctly is something distinct from 
 the faculty which judges more or less incorrectly. And, 
 further than this, both seem to say that correctness is relative, 
 not at all to the individual nature of the person judging, but 
 only to some objective standard existing more or less out- 
 side himself. It is, apparently, as if one should maintain 
 that the palate which approves of wholesome food is a dif- 
 ferent organ from the palate which approves of food that is 
 unwholesome ; and that the wholesomeness of food depends, 
 not at all upon peculiarities of constitution of the individual 
 taster, but only upon the fully developed nature of the 
 perfect man. 
 
 VII. We must dissent, then, as we have seen, from New- 
 man's view that the illative process is altogether silent or 
 implicit. We must likewise dissent from the view, which he 
 appears to hold, that there is in man an illative sense which 
 differs from ordinary reason and perception, and takes cog- 
 nisance only of objective truth. We may, however, agree 
 in a measure with his estimate of the character of the work 
 which the illative sense performs. We may admit that it is 
 possible to describe illation as the extracting a definite con- 
 clusion from a cumulation of probabilities. 
 
 But this position requires very careful examination. Cer- 
 tainly — it may at once be said — his view of proof as a quasi- 
 mathematical limit of converging probabilities cannot be 
 accepted. In order that it may appear how far we are in 
 agreement or disagreement with him, it seems now to be 
 necessary to institute an investigation of the philosophical 
 and the mathematical meaning of probability. On other 
 grounds, too, such an investigation is at this point desir- 
 able. For, in the first place, it may help to win acceptance 
 for the doctrine of illation presented in the preceding chapter, 
 
NEWMAN'S "GRAMMAR OF ASSENT" 191 
 
 to exhibit it in its relation to the famihar kinds of argu- 
 ment commonly called probable. And, in the second place, 
 in thus exhibiting the doctrine, it is likely to be made in 
 itself at once more impressive and more clear. To the con- 
 sideration, then, of probable argumentation we may next 
 address ourselves. 
 
CHAPTER XIII. 
 PROBABLE CONCLUSIONS. 
 
 I. Bishop Butler being often referred to as speaking 
 with authority on the vakie of evidence that is only probable, 
 this chapter may not inaptly be prefaced by a leading quota- 
 tion from his writings. At the same time the passage chosen 
 will serve as a convenient basis for the discussion that lies 
 before us. In the introduction to his Analogy of Religiofi 
 he writes as follows : — 
 
 " Probable evidence is essentially distinguished from de- 
 monstrative by this, that it admits of degrees ; and of all 
 variety of them, from the highest moral certainty, to the 
 very lowest presumption. We cannot indeed say a thing 
 is probably true upon one very slight presumption for it ; 
 because, as there may be probabilities on both sides of a 
 question, there may be some against it : and though there 
 be not, yet a slight presumption does not beget that de- 
 gree of conviction, which is implied in saying a thing is 
 probably true. But that the slightest possible presumption 
 is of the nature of a probability, appears from hence, that 
 such low presumption often repeated, will amount even to 
 moral certainty. Thus a man's having observed the ebb 
 and flow of the tide to-day, affords some sort of presump- 
 tion, though the lowest imaginable, that it may happen 
 again to-morrow. But the observation of this event for so 
 many days, and months, and ages together, as it has been 
 
PROBABLE CONCLUSIONS 193 
 
 observed by mankind, gives us a full assurance that it 
 will. 
 
 "That which chiefly constitutes />rol?a/?t7z'(y is expressed 
 in the word likely, that is, like some truth or true event ; 
 like it, in itself, in its evidence, in some more or fewer of 
 its circumstances. For when we determine a thing to be 
 probably true, suppose that an event has or will come to 
 pass, it is from the mind remarking in it a likeness to 
 some other event, which we have observed has come to 
 pass. And this observation forms, in numberless dail}^ 
 instances, a presumption, opinion, or full conviction, that 
 such an event has or will come to pass ; according as the 
 observation is, that the like event has sometimes, most 
 commonly, or always, so far as our observation reaches, 
 come to pass at like distances of time, or place, or upon 
 like occasions. Hence arises the belief, that a child, if it 
 lives twenty years, will grow up to the stature and strength 
 of a man ; that food will contribute to the preservation of 
 its life, and the want of it for such a number of days be 
 its certain destruction. So, likewise, the rule and measure 
 of our hopes and fears concerning the success of our pur- 
 suits ; our expectations that others will act so and so in 
 such circumstances ; and our judgment that such actions 
 proceed from such principles ; — all these rely upon our 
 having observed the like to what we hope, fear, expect, 
 judge; I say, upon our having observed the like, either 
 with respect to others or ourselves. And thus, whereas 
 the prince, who had always lived in a warm climate, 
 naturally concluded in the way of analogy, that there 
 was no such thing as water becoming hard, because he 
 had always observed it to be fluid and yielding : we, on 
 the contrary, from analogy, conclude, that there is no pre- 
 sumption at all against this ; that it is supposable there 
 may be frost in England any given day in January next ; 
 
194 THE THEORY OF INFERENCE 
 
 probable, that there will on some day of the month ; 
 and that there is a moral certainty, that is, ground for an 
 expectation, without any doubt of it, in some part or other 
 of the winter. 
 
 " Probable evidence, in its very nature, affords but an 
 imperfect kind of information, and is to be considered as 
 relative only to beings of limited capacities. For nothing 
 which is the possible object of knowledge, whether past, 
 present, or future, can be probable to an Infinite Intelligence ; 
 since it cannot but be discerned absolutely, as it is in itself, 
 certainly true, or certainly false. But, to us, probability is 
 the very guide of life. 
 
 " From these things it follows, that in questions of diffi- 
 culty, or such as are thought so, where more satisfactory 
 evidence cannot be had, or is not seen, if the result of 
 examination be, that there appears, upon the whole, any 
 the lowest presumption on one side, and none on the 
 other, or a greater presumption on one side, though in the 
 lowest degree greater, this determines the question, even 
 in matters of speculation ; and, in matters of practice, will 
 lay us under an absolute and formal obligation, in point 
 of prudence and of interest, to act upon that presumption, 
 or low probability, though it be so low as to leave the 
 mind in very great doubt which is the truth. For surely 
 a man is as really bound in prudence to do what upon 
 the whole appears, according to the best of his judgment, 
 to be for his happiness, as what he certainly knows to 
 be so. Nay, further, in questions of great consequence, a 
 reasonable man will think it concerns him to remark lower 
 presumptions and probabilities than these ; such as amount 
 to no more than showing one side of a question to be as 
 supposable and credible as the other; nay, such as but 
 amount to much less even than this. For numberless in- 
 stances might be mentioned respecting the common pur- 
 
PROBABI-E CONCLUSIONS 195 
 
 suits of life, where a man would be thought, in a literal 
 sense, distracted, wlio would not act, and with great 
 application too, not only upon an even chance, but upon 
 much less, and where the probability or chance was greatly 
 against his succeeding. 
 
 "It is not m}^ design to inquire further into the nature, 
 the foundation, and measure of probability ; or whence 
 it proceeds, that likeness should beget that presumption, 
 opinion, and full conviction, which the human mind is 
 formed to receive from it, and which it does necessarily 
 produce in every one ; or to guard against the errors to 
 which reasoning from analogy is liable. This belongs to 
 the subject of logic, and is a part of that subject which has 
 not yet been thoroughly considered. Indeed, I shall not 
 take upon me to say, how far the extent, compass, and 
 force of analogical reasoning, can be reduced to general 
 heads or rules, and the whole be formed into a system. 
 But though so little in this way has been attempted by 
 those who have treated of our intellectual powers, and the 
 exercise of them, this does not hinder but that we may 
 be, as we unquestionably are, assured, that analogy is of 
 weight, in various degrees, towards determining our judg- 
 ment, and our practice. Nor does it in any wise cease to 
 be of weight in those cases, because persons, either given 
 to dispute, or who require things to be stated with greater 
 exactness than our faculties appear to admit of in practical 
 matters, may find other cases, in which it is not easy to 
 say, whether it be, or be not, of any weight ; or instances 
 of seeming analogies, which are really of none. It is 
 enough to the present purpose to observe, that this general 
 way of arguing is evidently natural, just, and conclusive. 
 For there is no man can make a question but that the 
 sun will rise to-morrow, and be seen, where it is seen at 
 all, in the figure of a circle, and not in that of a square." 
 
196 THE THEORY OF INFERENCE 
 
 It will be well to begin the consideration of the foregoing" 
 passage, and so to enter upon the subject of probabilit}^, by 
 determining a specific sense in which the terms ' probable ' 
 and ' probability ' shall be used. It seems highly desirable 
 that both of them should be employed to signify the same 
 kind or degree of uncertainty, and that this kind or degree 
 should remain unchanged. Butler, it will be observed, uses 
 the expressions somewhat loosely. When, for instance, he 
 says that probable evidence admits of all variety of degrees, 
 he evidently means by ' probable ' the possessing in some 
 indefinite degree, whether small or great, a claim to be 
 received. But when immediately afterwards he remarks 
 that we cannot affirm a thing to be probably true upon 
 one very slight presumption of it, he appears to under- 
 stand ' probably ' in its popular signification of being seen 
 to have a preponderating claim. Although it cannot, per- 
 haps, be said that his argument suffers in point of clear- 
 ness from the use which he makes of the terms in question, 
 yet it will be well for us to avoid this possible source of 
 confusion. 
 
 Let us, then, agree to understand probable and probability 
 as having reference always to one and the same kind or 
 degree of uncertainty. And let this kind or degree be an 
 indefinite degree, concerning which all that need be known 
 is that it is sufficient to prevent a thing from being un- 
 feignedly assented to on the one hand, or absolutely denied 
 on the other hand. A probable truth or a probable event 
 may thus be one of which we are almost certain, or it may 
 be one of which we are almost able to deny the possibilit}^ 
 It is an alleged fact whose naturalness or possibility must 
 be admitted, but not to the exclusion of the naturalness or 
 possibility of other facts inconsistent with it. It occupies 
 a place as one among a number of alternatives. There is 
 evidence in support of it which cannot, on the one hand, 
 
PROBABLE CONCLUSIONS 197 
 
 be altogether set aside, nor, on the otlicr hand, entirely 
 extinguish the evidence adduced in favour of competing 
 facts. 
 
 Similarly the term probability, expressing evidence, may 
 be understood to signify evidence vv^hich almost amounts to 
 convincing proof, or evidence which affords no more than a 
 slight presumption in favour of the alleged circumstance. 
 The phrase, probable evidence, is thus the equivalent of the 
 term probability. Should w^e have occasion at any time to 
 speak of this evidence as large or small, strong or weak, we 
 may conveniently make use of some such expressions as, 
 highly probable or slightly probable, high probability or low 
 probability. 
 
 It may be further noticed at this point, that pro- 
 babilit}^, besides being capable of being looked upon as 
 high or low, may have a definite numerical value attached 
 to it. The principles by which its value is assessed will 
 be discussed in the chapter following. For the present 
 it will suffice to say that the numerical value of a pro- 
 bability indicates the degree of its approach to certain 
 evidence. 
 
 n. Butler, to a great extent correctl}', refers probable 
 conclusions, that is, conclusions that a fact or event is pro- 
 bable, to the recognition of likeness between a thing before 
 us and other things that have previously been objects of 
 observation. But he is at no pains to point out, that a con- 
 clusion consequent upon a recognition of likeness is not 
 necessarily a probable conclusion. On the contrary, from 
 the instances he gives, he might be taken to imply that all 
 conclusions (other than those of deduction) drawn from a 
 recognition of likeness are in a true sense probable conclu- 
 sions. He might be supposed to hold that sure or certain 
 evidence is only that which is probable in a very high degree, 
 and full conviction only another name for very strong pre- 
 
198 THE THEORY OF INFERENCE 
 
 sumption. This point we have already had occasion to notice 
 in the chapter on delation, In which some of his illustrations 
 were discussed ; and it is not necessary to say more con- 
 cerning it. Let it be our business now to consider what is 
 the nature of the mental process of concluding that an event 
 is probable. And as we have, in the chapter referred to, 
 examined some sure conclusions, so also let us examine 
 some probable conclusions, set forth in the passage that 
 has been quoted. 
 
 " A man's having observed the ebb and flow of the tide 
 to-day, affords some sort of presumption that it may happen 
 again to-morrow." The explanation of this appears to be 
 as follows. We may suppose the phenomenon in question 
 to have been brought about by some unknown combination 
 of causes ; and, supposing this, we ma}', by an act of delatlve 
 inference, conclude that a similar combination, producing a 
 repetition of the phenomenon, will certainly at some time or 
 other occur again. The combination has manifested itself 
 once as a part of the order of nature, and after some unknown 
 interval of time may be again expected. This conclusion — 
 though, perhaps, in real life we do not practically draw it — 
 seems to be a legitimate result of delatlve inference, and a 
 result which explains the probable conclusion supposed 
 by Butler to be drawn from a single observation of tidal 
 movements. 
 
 For, though we are entitled to affirm that at some 
 time or other the tide will again ebb and flow as we have 
 seen it ebb and flow to-day, yet of the date fixed by 
 nature for the recurrence of the phenomenon we know 
 nothing at all. It may be to-morrow, it may be fifty or 
 a thousand years hence. To-morrow, for anything we 
 know, is on an equality with every other day of some in- 
 definite future space of time; it is one of an indefinite 
 number of alternatives. In connection with each of the 
 
PROBABLE CONCLUSIONS 199 
 
 days there is a probability that on it the tidal movements 
 will recur. 
 
 in. " We conclude that it is supposable there may 
 be frost in England any given day in January next ; pro- 
 bable, that there will on some day of the month ; and 
 that there is a moral certainty, that is, ground for an ex- 
 pectation, without any doubt of it, in some part or other ol 
 the winter." Here we have three conclusions, the grounds 
 of which we have to seek only in the case of the first 
 two. The third has been quoted for a reason which will 
 appear. 
 
 First let it be supposed, that ice has been known to be 
 formed on a given day in January, say the ist, in some 
 previous winter. We are then able, by means of two acts 
 of delative inference, to reach the conclusion that it will 
 appear on the 1st of January in some future year. For, 
 in the first place, we may be said to recognise more or less 
 definitely and clearly, that there are climatic causes and 
 conditions in respect of which one New Year's day has 
 been in the past precisely similar to another; and these 
 we may expect to continue to operate as usual. And, in 
 the second place, the causes of ice having, as we know, 
 once combined with the causes which permanently char- 
 acterise the 1st of January, may be expected in the future 
 to combine with them again. Thus, then, we may con- 
 fidently look for frost on some future New Year's day. 
 Now next New Year's day is one of the series of alternative 
 days on which the expected combination of causes will recur. 
 Hence there is a probability, common to itself and every 
 other member of the series, that the appearance of ice will 
 take place on it. 
 
 Secondly, let the supposition be, that ice has been seen 
 on some unrecorded day of January in a former year. 
 From this circumstance we are entitled, as in the case just 
 
200 THE THEORY OF INFERENCE 
 
 noticed, to draw the conclusion, that on some undefined 
 day in January next frost is probable. For an undefined 
 day in January next is one of a number of alternative 
 days, similarly undefined, in successive Januarys, in some 
 one of which months frost may certainly be again ex- 
 pected. 
 
 With reference to this second conclusion, that frost will 
 probably — in the sense, that is, of most probably — appear 
 on some day of January next, it must further be pointed out, 
 that we have here a question, not merely of the existence of 
 a probability, but also of its degree or weight in relation to 
 other probabilities. On the one hand, the fact of ice having 
 been seen in some month of January creates a probability 
 that it will again be seen in January next. On the other 
 hand, the fact of some month of January having been 
 observed to pass without the appearance of ice creates a 
 probability that none will appear in the coming January. 
 These opposing probabilities the mind is understood, in the 
 case before us, to weigh the one against the other, concluding 
 that the balance of probability, or the resulting probability, 
 is in favour of the appearance of ice. Consideration of the 
 ground of the mind's action must be reserved for the follow- 
 ing chapter. 
 
 The reason may now be explained of introducing the 
 conclusion as to the certainty of frost in some part of the 
 winter. Being in possession of this certain knowledge, we 
 may, if we will, derive from it the probability of frost on 
 New Year's day, instead of deriving it in the way pointed 
 out. We have looked upon the ist of January in the coming 
 year as one of a number of alternative New Year's days, on 
 some one of which we know that there must be frost. But 
 equally well, if we know that there must be frost in some 
 part of the coming winter, we may regard it as one of the 
 hundred days that make up the season. 
 
PROBABLE CONCLUSIONS 201 
 
 So again, the 1st of January next is one of the thirty- 
 one ahernative da3'S on which irost may appear, if it 
 appears at all in the course of the month. Hence from 
 the probability, that frost may be looked for on some 
 undefined day, there is derivable a lesser probability, 
 that it will appear on the first day of the month in 
 question. This probability, it may be remarked, as the 
 days vanish one by one without the appearance of ice, 
 grows continually stronger in favour of each one that 
 remains. 
 
 And yet another way of deriving the probability of frost 
 on New Year's day may be mentioned. We may suppose 
 ourselves to become acquainted with all the different kinds 
 of weather by which previous New Year's days have been 
 characterised. We may have learned that the causes per- 
 manently operative on that day have combined sometimes 
 with the causes of frost, and sometimes with the causes of 
 various other kinds of weather. We are thus able to infer 
 that frost is one of the alternative kinds of weather possible 
 on the coming 1st of January. 
 
 Let it now be carefully noticed that, in whatever way 
 we derive the probability, the essential principle remains 
 the same. It is, that we have reason to know that the 
 event in question is one of a number of alternatives, 
 the occurrence of any one of which would satisfy ex- 
 pectation. 
 
 IV. "We believe that a child, if it lives twenty 3'ears, will 
 grow up to the stature and strength of a man ; that food will 
 contribute to the preservation of its life, and the want of it 
 for such a number of days be its certain destruction." Here 
 we seem to have two distinct arguments, which require to be 
 noticed separately. 
 
 The first case seems to be one, not simpl}' of probability, 
 but also of degree of probability. We have known instances 
 
202 THE THEORY OF INFERENCE 
 
 of children arriving at mature manhood after the expiration 
 of a certain number of years ; but we have likewise known 
 instances of children who have not developed in the usual 
 way. Hence, relying upon the continuity in nature of the 
 grouping of causes and conditions, we recognise a probability 
 that a particular child will attain to the strength and stature 
 of a man, and also a probability that he will not attain to 
 them. It is, apparently, a case of a concrete cause being 
 followed sometimes by one effect, and sometimes by another. 
 Childhood is, according to our experience, followed some- 
 times by developed manhood, sometimes by stunted faculties 
 and form. In the case, then, of any new child brought 
 under our notice, we have ground for concluding that there 
 is a probability of either issue. At the same time, when we 
 compare the probabilities, we find that the former outweighs 
 the latter. 
 
 The second case — the twofold conclusion concerning the 
 relation of food to life — appears to be a sure conclusion in 
 the field of natural law. It appears to be the application 
 to a particular child of an ascertained relation between 
 abstract cause and abstract effect. As such there is no 
 need to comment on it here. It gives occasion, however, 
 for pointing out another source of probable conclusions. 
 We know, in the case before us, that food is certainly a 
 cause of life : induction may be said to have thoroughly 
 established this. But we may very well suppose ourselves 
 to be in the position of having obtained by means of 
 induction some other result not quite so definite. We 
 may suppose ourselves to have ascertained, for example, 
 that the dietary of a certain person is or contains the 
 cause of his conspicuously good healtli, and yet to have 
 failed to ascertain to which of several articles of food the 
 result is due. We have, say, A B C as residual antecedents, 
 and no means of deciding between their respective claims to 
 
PROBABLE CONCLUSIONS 203 
 
 be the cause. This being so, we may say of each that it 
 is a probable cause of the effect in question. Each is one 
 of several alternatives, and the proving of any one of them 
 to be the cause would be a circumstance quite in harmony 
 with our present knowledge. 
 
CHAPTER XIV. 
 
 THEORY OF PROBABILITY. 
 
 I. The probable conclusions with which in this book we 
 are specially concerned are such as relate to the sequence of 
 concrete phenomena. Concrete A having once been known 
 to be the cause of concrete B, we are in a position to affirm a 
 probability that any new instance of A will be followed by 
 one of B, and that any new instance of B will have been 
 preceded by one of A. 
 
 These and similar probable conclusions are identical with 
 the preliminary conclusions of illative inference. To say 
 that there is a probability of this A being followed by a B, 
 is equivalent to saying that this A may be followed by a B. 
 Now there are two distinct methods by which these con- 
 clusions may be dealt with, the method of illation, and the 
 method of probability. There are two distinct ways, that 
 is, in which a number of them taken together may be made 
 to yield one derivative conclusion. And we have to make 
 it our business to inquire into the relation between, and the 
 comparative value of, these two ways or methods. We have 
 to endeavour to ascertain how far we do, or how far we 
 can — as Butler holds, as Newman holds, as Mill holds, that 
 we can and do — reach our assured convictions of truths of 
 history by regarding the class of propositions in question 
 as announcing probabilities, and somehow treating the an- 
 nouncements as probabilities are treated. What is about 
 
THEORY OF PROBABILIT\- 205 
 
 to be said on the subject of probability is said, be it 
 understood, with special reference to sequences, of concrete 
 phenomena. 
 
 When Ave infer delatively that this concrete B may have 
 been preceded, or that there is a probability of its having 
 been preceded, by concrete A, we may in the act of delation 
 make explicit references to past instances of such sequence, 
 and to the principle of continuity in nature. We may say 
 that B has been known to follow A, and that therefore it 
 would be in accordance with the settled order of nature for 
 the B before us to have an A as its antecedent. But 
 apparently it is not always, perhaps it is not commonl}^ the 
 case, that we reason thus explicitly. What we mostly seem 
 to do is to merge the three ideas which in the argument are 
 brought together — the ideas, namely, of nature's order in 
 the past, of the continuity of nature's order, and of nature's 
 order in the future — in the one idea of naturalness. The 
 sequence of A and B, with which we are acquainted^ 
 presents itself to the mind as a natural sequence, and 
 therefore as a sequence which may be looked for in the 
 future. The circumstance of a concrete B following upon 
 a concrete A, having once been noted, leaves, as it were, 
 upon the mind an impression or picture of a natural con- 
 nection between A and B. And when the explanatory 
 antecedent of any new instance of B is sought, the mind, 
 inevitably requiring to see before it something natural, 
 turns to its past experience for a list of natural ex- 
 planations. 
 
 The mind, when it thus acts delatively by implicit process, 
 does not seem to be dependent only upon its own actual 
 and definite experience for the conclusions which it draws. 
 The impression of a natural sequence between A and B may 
 apparently be due to other means. It may be to some 
 extent created or enhanced by the accepted testimony of 
 
2o6 THE THEORY OF INFERENCE 
 
 other persons, and also by experience of sequences between 
 phenomena allied to A and B. Nor must the power in this 
 direction of meditation and imagination be overlooked. 
 These supplements to, or substitutes for, actual and definite 
 experience — and there may be others — giving rise to an im- 
 pression of the naturalness of particular observed sequences, 
 give rise in corresponding measure to apprehension of the 
 naturalness or the probability of the recurrence of these 
 sequences. So far as apprehension of particular proba- 
 bihties is a real and not a merely theoretical apprehension, 
 it seems to be dependent on impressions existing in the 
 mind ; and these impressions are, perhaps, in the great 
 majority of cases partially derived from other sources than 
 actual and definite experience. The term experience, how- 
 ever, may very well be employed, for general purposes, in 
 a sense sufficiently wide to cover all these sources. 
 
 II. The twofold fact, that experience of sequences of 
 concrete phenomena leaves upon the mind impressions of 
 their naturalness, and that the mind can only expect and 
 interpret the unknown in strict accordance with its impres- 
 sions of what is natural, apparently supplies the key to the 
 mental process of comparing and measuring probabilities 
 of alternative events. We are accustomed to speak of the 
 probability of one of several probable events being higher 
 or greater than that of another. Of several alternatives, 
 any one of which will answer expectation, we select one as 
 having greater hkelihood than all the rest. We look upon 
 one event as having a priority of right to be expected, upon 
 one interpretation of a phenomenon as having a priority of 
 claim to be received as true. 
 
 Now what is the meaning of this expecting at the same 
 time, with different degrees of expectation, a number of 
 things of which we know that only one can happen, and of 
 this interpreting in a number of ways, with different degrees 
 
THEORY OF PROBABILITY 207 
 
 of confidence, an event of which, as we are well aware, only 
 one of the interpretations can be true ? Certainly the 
 answer to this question seems to be, that what we really 
 mean is this : — each of the events contemplated as happen- 
 ing, and each of the interpretations contemplated as being 
 true, accords with some more or less strong or profound 
 impression of naturalness already existing in the mind. 
 The most probable event, and the most probable interpre- 
 tation, is that which corresponds to the strongest of the 
 mental impressions which experience has created. Any 
 event, or an}' interpretation of an event, is expected, is 
 regarded as probable, only because a picture of the event 
 or interpretation, as constituting a part of the order of 
 nature, already has existence in the mind. And it is 
 according to the comparative vividness of the pictures 
 answering to the several events or several interpretations 
 that, while all of them are expected, yet the contemplation 
 of one arouses greater intensity of expectation than the 
 contemplation of another. 
 
 Probabilities, then, relating to alternative effects of a 
 given cause, or alternative causes of a given effect, may be 
 said to be ranged by the mind, or to be capable of being 
 ranged when the need arises, in order of degree ; their 
 degree depending upon the strength of an impression 
 created in the mind by past experience. Accordingly as 
 the mind perceives with more or less keenness, and feels 
 with more or less intensit}', the naturalness of a contem- 
 plated circumstance, will it mark the probability of that cir- 
 cumstance as relatively high or low. 
 
 But, besides ranging probabilities of alternative circum- 
 stances in order of degree, it is to a certain extent both 
 possible and convenient to assign numerical values to them. 
 If a mental impression depended for its strength, or a mental 
 picture for its vividness, only upon the number of separate 
 
2o8 THE THEORY OF INFERENCE 
 
 experiences, supposed to be all of the same impressiveness, 
 that have gone to create it, and if this number could in every 
 case be truly reckoned, then we should at once have the 
 means of making definite numerical comparison between one 
 probability and another. The material would be at hand for 
 assigning to every probability a value which might after- 
 wards represent its magnitude, without any explicit reference 
 to the particular alternatives with which it had been com- 
 pared. Now, although these definite and equal experiences, 
 whose number can be reckoned, are not by any means the 
 sole producers of mental pictures ; although they are supple- 
 mented by unequal and unnumbered experiences, which may 
 be shadowy and vague and scarcely present to the conscious- 
 ness ; yet they may, apparently, quite well be taken as 
 representative experiences for the purpose of exhibiting the 
 manner of the mind's dealing with them. As the mind deals, 
 or appears to deal, explicitly with the things that it can 
 explicitly count and measure, so we may not unreasonably 
 suppose that it deals implicitly with the things that can only 
 be implicitly assessed. Let us, then, assume, for the pur- 
 poses of this exposition, that impressions are created only 
 by equal and definite experiences whose numbers can be 
 reckoned. 
 
 If records, or if memor}^, should tell us that B has taken 
 place lOO times, and that on 20 occasions of its happen- 
 ing it has followed upon A, on 30 upon C, and on 50 
 upon D, then 20, 30, 50, represent respectively the num- 
 bers of elements of experience which have gone to make 
 up the impressions in our minds of A, C, and D as the 
 natural antecedents of B. And these numbers properly re- 
 present the proportionate probabilities of any new B having 
 as its explanatory antecedent an A, or a C, or a D. If, how- 
 ever — as is frequently the case — we wish to confine our 
 attention to the probability in favour of some one of the 
 
THEORY OF PROBABILITY 209 
 
 antecedents, as A, we make use of a shorter method of ex- 
 hibiting this. We designate the probability' of A by a proper 
 fraction, having as its numerator the number of instances of 
 the particular antecedent, and as its denominator the number 
 of instances of the one consequent. In saying that the pro- 
 bability in favour of A is yuq, we mean that there are in the 
 mind 20 elements of experience of B being preceded by 
 A, and 80 of its being preceded by something else, out 
 of 100 elements of experience of its happening at all. 
 
 And now at this point it will be well just to notice another 
 interpretation of the numerical value thus assigned to the 
 probability of A. Instead of taking it to express the degree 
 of natural expectation with which we look, on a given occa- 
 sion, for one of a number of alternative phenomena, we may 
 understand it as indicating the degree of frequency with 
 which we may expect this particular phenomenon to happen 
 in the future. Relying upon the continuity of nature, 
 and upon the sufficiency of our experience, we may argue 
 that, if in the past A has been the antecedent in 20 of 
 100 instances of B, the same proportion may be looked 
 for in the future. Of every 100 instances of B about to 
 happen, 20 may be expected to be preceded by A. This 
 interpretation of numerical probability has, indeed, little or 
 no direct bearing upon the subject of illation ; but never- 
 theless it is one of which practical use is made, and of which 
 some mention could scarcely be omitted here without an 
 appearance of inadequate treatment of the subject of proba- 
 bility. It does not, however, seem to be at all necessary to 
 our purpose that we should enter upon any further consi- 
 deration of the question. 
 
 III. Having seen how numerical values are assigned to 
 probabilities on a basis of experience, we may now proceed 
 to notice another principle in accordance with which they are 
 sometimes estimated. This principle is connected with our 
 
2IO THE THEORY OF INFERENCE 
 
 ignorance. Because of what we are conscious that we do not 
 know, as well as on account of what we have had experience 
 of, we compare and measure the probabilities of events. 
 
 If, instead of being able to judge from the specific experi- 
 ence of similar sequences that a new instance of an effect B 
 must have proceeded from an A, or a C, or a D, we know, 
 from other considerations, that A, C, and D are the only 
 possible antecedents, and know no more, then we attach to 
 the respective probabilities in favour of A, C, and D values 
 dependent on our ignorance. The causes that have given 
 rise to concrete B may have acted under the form of concrete 
 A, or of C, or of D. The mental picture arising from the 
 contemplation of B preceded by A is neither more nor less 
 vivid than the picture of B preceded by C or by D. Each 
 is a new picture, and fits in equally well with pre-existing 
 views of natural sequence and arrangement. Our expectation 
 of one is consequently equal to our expectation of another. 
 And if we choose to attach to our knowledge or sure expec- 
 tation, that B has as its antecedent one of the alternatives, 
 the numerical value I, the value of the probability in favour of 
 each separate alternative is necessarily ^. 
 
 Examples of this may be given as follows. A train from 
 London and a train from York arrive almost simultaneously 
 at an intermediate station. If we should presently meet a 
 traveller who must have arrived by one train or the other, and 
 if, knowing no more than this, we should have occasion to 
 consider the probability of his having come from the north, or 
 from the south, we could only attach to either probability 
 the value i. So again, if three trains leave Waterloo almost 
 simultaneously, one for Bournemouth, one for Reading, and 
 one for Ilfracombe, and we know of a certain person only 
 that he has taken a seat in one of them, our estimate of 
 the probability of his having gone to any particular one of 
 the three places must be J. Whether we have to choose 
 
THEORY OF PROBABILITY 211 
 
 between several possible causes of a given effect — as in the 
 former case — or between several possible effects of a given 
 cause — as in the latter case — we assign to the probability of 
 each possible cause, or each possible effect, as its numeri- 
 cal value, a fraction having for its numerator i, and for its 
 denominator the number of causes, or of effects, between 
 which choice has to be ignorantly made. In other words, 
 we divide the value which represents knowledge into the 
 given number of equal parts. 
 
 IV. Enough has now been said for our purpose concern- 
 ing the explicit measurement of simple probabilities. It 
 remains to point out to what a large extent the process ot 
 measurement, instead of being explicit, must really be im- 
 plicit ; and, besides being imphcit, must be subjective also. 
 
 We have assumed in our discussion that the elements of 
 experience, from which probabilities relating to any given 
 question are derived, are of equal impressiveness, and capable 
 of being counted and added together as separate units. With 
 this assumption it is possible, in the manner shown, to assign 
 numerical values to different probabilities. But without it 
 it is manifestly impossible to exhibit their relative values 
 with any accuracy, the mental impressions represented by 
 the values not being properly commensurable. And perhaps 
 it is in very few cases indeed that the assumption is justified 
 by the facts of common life. Apparently it is but very 
 seldom that our estimate of probabilities, though based on 
 experience, is dependent solely upon our knowledge of in- 
 stances that can be gauged and counted. In relation to the 
 ordinary affairs of life impressions of natural sequences of 
 concrete phenomena enter the mind from a variety of sources, 
 with varying degrees of strength or weakness, and more or 
 less consciously or unconsciously to ourselves. Besides the 
 many real experiences which can be neither gauged nor 
 counted, there are, recognition of sequences of allied pheno- 
 
212 THE THEORY OF INFERENCE 
 
 mena, the evidence of testimony, and the meditative and 
 imaginative action of the mind, all introducing or confirm- 
 ing impressions concerning which it may be generally said, 
 that the mind has no power, by any exercise of thought or 
 memory, to subject them to an exact process of measurement 
 and counting. 
 
 And yet the mind seems to be tolerably well aware of the 
 relative vividness and intensity of its own impressions. 
 Though it may be powerless to resolve them into their ele- 
 ments in order to give to them exact numerical values, yet it 
 often has little or no difficulty in deciding that one is stronger 
 or weaker than another. For practical purposes it seems 
 for the most part to be able to range the chief probabilities 
 that relate to any given event in an order of magnitude. 
 Implicitly it decides between alternatives, though it cannot 
 justify its decisions on explicit grounds. 
 
 Estimates of probabilities, besides being commonly implicit, 
 are for the most part subjective also. That is to say, they 
 vary with the individual thinker. An estimate may, indeed, 
 be implicit without being in a special sense subjective, and 
 subjective without being at all implicit. Thus, for example, 
 the children of one family, or the boys of one school, having 
 to a large extent been brought up under precisely similar 
 influences, will have a number of common views, at once 
 objective and implicitly arrived at, of the naturalness and 
 probability of sequences of events. On the other hand, an 
 individual, being aware of certain marked sequences of 
 events affecting himself in a peculiar way, may be in a posi- 
 tion to form an explicit estimate of probabilities based on a 
 personal experience which differs from that of other men. 
 
 For the most part, however, the same causes that make 
 estimates of probabilities implicit make them subjective also. 
 The real experiences that cannot be gauged or counted, and 
 the other instrumentalities, supplementary to real experiences. 
 
THEORY OF PROBABILITY 213 
 
 by which impressions are produced, operate on different minds 
 with ver}' different degrees of frequency and force. No two 
 persons can be said to have witliin them precisely the same 
 material for estimating the probabilities in connection with 
 any given event, except in the comparatively small number 
 of cases in which the same experience is, so to speak, arti- 
 ficially supplied to both ; as, for example, in questions of 
 probabilities founded on statistics. The comparative values 
 which any person attaches to probabilities, in relation to the 
 common affairs of life, are to a large extent dependent on his 
 own individualit}'. They depend upon the nature and extent 
 of his own personal experience. The valuation as a process 
 is implicit ; as a result it is more or less subjective. 
 
 V. Butler, not much caring to maintain that the evidence 
 in favour of religion amounts to more than very high pro- 
 bability, takes his stand on the sufficienc\^ of high probability 
 to determine conduct. He insists upon man's natural and 
 reasonable obligation to let his actions be governed by con- 
 siderations of what may happen. Now, although this subject 
 of acting on probabilities is in strictness beyond the scope of 
 our investigation, yet it lies so very near that the interest 
 and importance of it may perhaps be thought to warrant its 
 inclusion. Let us, then, make a short digression in order to 
 examine it. 
 
 If a person, writing to a friend, thinks him more likely 
 than not to have already left the country for his London 
 house, he will naturally post the letter to his town address. 
 Should the communication, however, have special reference 
 to some matter which can be best attended to while his friend 
 is still in the country, he may prefer to send the letter to his 
 country house. If an invalid is told that a certain course of 
 treatment \v\\l most likely improve his health, he will natur- 
 ally consent to the adoption of the treatment. Should he 
 learn, however, that the improvement, if effected, will be but 
 
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 SE-aer of ^mnirE ins lesn ^nr tscoE ie Di^srxeii. 
 
2i6 THE THEORY OF INFERENCE 
 
 The motive just described, the constraint to act naturally 
 by adapting conduct to the ways of nature, is perhaps the 
 one by which we are commonly influenced when we choose, 
 as the simple basis of action, the most probable of several 
 alternatives. Nevertheless, if we look upon things in a 
 larger way, we may find another ground for acting as we 
 do. It appears to be the case, that the systematic choosing 
 of the most probable alternative as the ground of action is 
 the means by which conduct can, in the result, be brought 
 into the greatest conformity with nature's ways. In a single 
 instance of choosing the highest probability our conduct, 
 though proper and natural as regards our motives, may 
 prove to be mistaken as regards results. We may know 
 that A is more likely to happen than C or D, and may 
 act accordingly; and yet, after all, it may be C or D that 
 happens. Our correct action may seem to end in failure. 
 
 If, however, we take a large number of instances, it seems 
 to be the case that our systematic choice of A instead of C 
 or D will be justified and rewarded by our obtaining the 
 largest number of successes which it is in our power to 
 obtain. We now look upon the probability as expressing 
 the degree of frequency with which an event may be 
 expected in the future ; and in what has just been said we 
 have the answer to our second question. To show what is 
 meant, we need not, perhaps, travel beyond a very simple 
 illustration. Let us suppose the probabilities in favour of A, 
 C, D to be respectively |, f , ^. That is to say, A is expected 
 to happen 4 times, C 3 times, and D once, in 8 occasions of B. 
 And let us suppose that action is taken on each of the 8 
 occasions without any knowledge of what happens on the 
 other 7. We shall thus assimilate the conditions of this one 
 simple case to the conditions of the congeries of different 
 cases with which, in a given space of time, we have to deal 
 in our course through life. If A is systematically chosen, a 
 
THEORY OF PROBABILITY 217 
 
 correct choice will be made on 4 occasions out of 8. And it 
 seems clear that this is the greatest number of correct choices 
 which we have any ground at all for relying upon making. If 
 our conduct is to be systematic and moral conduct, if it is to 
 be regulated by principle, and not to be the sport of pure 
 caprice, then, in dealing with probabilities that have relation 
 to the same event, the system and principle by which 
 it will be brought, as regards its results, into closer touch 
 with nature than by any others, appear to be those of 
 always acting on the probability which is numerically the 
 highest. 
 
 2. We have now to examine the complex case of choosing 
 between several probable events, as grounds of action, when 
 each has a different amount of good contingent on it. We 
 have to consider the rationale of acting, as we often do, on 
 a lower probability because associated with it is a greater 
 good. " In deliberations concerning conduct," says Butler, 
 " there is nothing which reason more requires to be taken 
 into the account, than the importance of it. For, suppose 
 it doubtful what would be the consequence of acting in this, 
 or in a contrar}' manner ; still, that taking one side could be 
 attended with little or no bad consequences, and taking the 
 other might be attended with the greatest, must appear to 
 unprejudiced reason of the highest moment towards deter- 
 mining how we are to act." ^ If, as before, the probabilities of 
 A, C, D are |, f , |, and if we suppose the gains contingent 
 on the respective events to be ;^8, £16, £2A^, the products, 
 already spoken of, are ;^4, £6, £l. We select accordingly 
 for the basis of action the second of the three alternatives. 
 But on what rational ground is it that we do so ? 
 
 It seems here to be the case that, if we were to look upon 
 our choice as an isolated act, we could plead no rational 
 justification for the course we take. In an act of choosing, 
 
 1 Analogy of Religion, Pari II. ch. vii. 
 
2i8 THE THEORY OF INFERENCE 
 
 considered by itself, we should be under moral obligation to 
 select the most probable or natural event, without reference 
 to the smallness of the gain contingent on it. No contingent 
 advantage, however great, associated with a less probable 
 event, would make it lawful for us to base our action on a 
 lower probability. If, however, our act of choice is regarded 
 as one of a series of like acts regulated by principle, then it 
 becomes proper for us to take as our guide the products of 
 probability and contingent good. For thus, apparently, we 
 put ourselves in the way of obtaining in the long-run the 
 greatest amount of good which it is in our power to make 
 reasonably sure of. By systematically choosing C as the 
 basis of action on each of the 8 occasions of the happening 
 of B, we may reckon — supposing ourselves, as before, to be 
 at the time ignorant of what happens on the other 7 — upon 
 choosing 3 times the event that does actually take place, and 
 upon gaining a sum of ^48 ; whereas by choosing A, although 
 we should make a correct choice on 4 occasions, yet our gain 
 would be but £12, and by choosing D, although whenever 
 we were right we should gain ^24, yet only once would this 
 event take place. This simple instance seems to illustrate 
 sufficiently well for the purposes of our digression the mean- 
 ing of the rule to be observed in choosing between different 
 probable events, having different degrees of advantage con- 
 tingent on them, in connection with the manifold affairs of 
 common life. So far as the acquisition of good of any kind 
 is an end of conduct, and so far as different degrees of good 
 are with different degrees of probability within our reach, it 
 is incumbent upon us on every occasion to take that course 
 which is associated with the greatest product of probability 
 and advantage ; because on the whole we may thus expect 
 to obtain the greatest total amount of good which it is in our 
 power to secure. 
 
 VI. Let us now consider, in immediate preparation for the 
 
THEORY OF PROBABILITY 219 
 
 following chapter, the question of the cumulation of proba- 
 bilities. If the happening of B makes A probable, and the 
 happening of another event E likewise makes it probable, 
 then — and the thought is one with which we are familiar — 
 when B and E arc both found to happen, the probability 
 of the happening of A is considerably enhanced. If, for 
 example, pains in the head are a not uncommon symptom 
 of influenza, and depression of spirits another symptom, we 
 are aware, in the case of both being present, that the proba- 
 bility of the illness being influenza is greater than if either 
 of them was not apparent. Our concern in this section is 
 with the enhanced probability, calculated after the ordinary 
 method of the theory of probability, of a conjectured event, 
 which may be to each of several given events an antecedent 
 or a consequent. It will, however, be sufficient to consider 
 only the case of a conjectured antecedent. 
 
 Let us suppose that, when a certain boy has had a cold, 
 it has been known 4 times out of 10 to proceed from bathing ; 
 and that, when he has hurt his foot, it has once out of 3 
 times been done in bathing. On the next occasion, then, 
 in which he has a cold the probability that he has been 
 bathing is yV ; and on the next occasion of injuring his foot 
 the probability of his having bathed is ^. If these two 
 misfortunes are seen to affect him simultaneously, the pro- 
 bability that he has been bathing is greater than j%, and 
 greater than J ; and we proceed to ascertain what its 
 numerical value is. 
 
 The full mathematical process of obtaining the required 
 fraction is as follows. The probability that the cold came 
 from bathing is yV ; that it did not come from bathing is yV J 
 that the injured foot came from bathing is J ; that it did 
 not come from bathing is -|. The probability, then, that 
 both came from bathing is uj X |r or ^*j. ; that the cold did 
 but the injured foot did not is j\ X f or /^ ; that the cold 
 
2 20 THE THEORY OF INFERENCE 
 
 did not but the injured foot did is j% X ^ or -J\j. Hence the 
 probability that one or both of the boy's misfortunes came 
 from bathing, that is, that he did bathe, is t/o + /o + /o or 
 If; a fraction greater, as was said, than 1*0, and greater 
 than ^. The probabihty, it may be added, that neither mis- 
 fortune came from bathing is yV X f or |§ ; the difference, 
 it will be observed, between unity and l^. 
 
 What, now, is the meaning of our numerical result ? It 
 is as follows. We are contemplating 30 separate occasions 
 on which the boy has had both a cold and an injured foot. 
 On 12 of these, by the supposed conditions of the problem, 
 his cold has arisen from bathing, and on 18 it has not. Out 
 of the 12, by the supposed conditions of the problem, there 
 are 4 on which the accompanying injury to the foot was 
 likewise the result of bathing, and 8 on which it was not. 
 Out of the 18, when the cold did not arise from bathing, 
 there are, by the supposed conditions of the problem, 6 on 
 which the hurt foot did thus arise, and 12 on which it did 
 not. Thus we have 4 occasions on which both mishaps 
 were caused by bathing, 8 on which the first alone, and 6 
 on which the second alone, was thus caused, and 12 on 
 which bathing did not account for either. In connection 
 with 18 out of the 30 past occasions aforesaid there was an 
 act of bathing, in connection with the remaining 12 there 
 was none. Hence the probability of his having now bathed, 
 or the degree of expectation with which we look to an act 
 of bathing as being the true explanation of one or both of 
 the new instances of misfortune that have come before us, 
 is |§. The bathing which is considered to account at the 
 same time for both the instances may be — let it be carefully 
 observed — either a single act, or two separate acts having 
 the common name. 
 
 We have now to notice two important points. The first 
 is, that in cumulating probabilities we cannot, in general, 
 
THEORY OF PROBABILITY 221 
 
 do otherwise than depart from the results of genuine experi- 
 ence, and introduce into our conclusions new elements of 
 doubt. In the above example, we started with the supposi- 
 tion that we had known 10 instances of the boy's suffering 
 from cold, in 4 of which we further knew him to have 
 bathed ; and with the supposition that we had known 3 
 instances of his suffering from an injured foot, in i of which 
 he had previously been bathing. We did not by any means 
 know him to have either a cold or an injured foot on all the 
 30 occasions assumed in the process of cumulation. Nor, 
 if we admit that he has suffered from either misfortune 30 
 times, are we justified in assuming, eitlier (i) that bathing 
 has been its origin throughout in the same proportion as 
 that of which we have cognisance, or (2) that the 30 occa- 
 sions of cold and the ^o occasions of injured foot have been 
 coincident. To what extent the result is vitiated by these 
 assumptions it is impossible to say. But certainly the con- 
 clusion cannot be taken to represent exactly a probability 
 based upon genuine experience. 
 
 The second point is as follows. It is not difficult to see 
 that, the greater the number of independent circumstances 
 brought together in evidence of an event, the higher is the 
 resultant probability in its favour. This probability may be 
 expressed as the difference between Unity and the product 
 of the several probabilities against the event. And, since 
 this product of proper fractions of course diminishes as the 
 factors increase in number, the difference aforesaid, or the 
 probability of the contemplated event, correspondingly in- 
 creases. The result in question seems thus far to be not 
 discordant with the teachings of experience : we are quite 
 accustomed to consider that, the larger the amount of in- 
 dependent evidence that can be heaped together, the more 
 nearly certain is it that the event has happened. 
 
 But now we must go on to notice that, with the increase 
 
222 THE THEORY OF INFERENCE 
 
 of evidence, the assumptions wliich are made in the mathe- 
 matical process of cumulating probabilities depart more and 
 more widely from genuine experience. There is a greater 
 quantity of separate events in respect of which we have to 
 assume, that the rate of frequency with which they occur 
 is continuously the same through periods other than those 
 of which we have experience. And we have to assume, in 
 general, a larger number of occasions on which we have 
 had experience of this greater quantity of events all happen- 
 ing together. The nearer, then, the calculated probability, 
 based on assumptions, approaches certainty, the more ex- 
 travagant are the assumptions which are a basis of the 
 calculation. 
 
 In particular, the assumption which the mind is called 
 upon to make, that, the more numerous are the separate but 
 concurrent circumstances testifying to a conjectured fact, 
 the more familiar to it is this combination of them, is so 
 violent, so contrary to all experience, that it cannot for a 
 moment be supposed that the mind, working implicitly, ever 
 makes it. It is manifestly the case in real life that, the 
 greater the number of independent circumstances noticed 
 as all happening together, the more unusual is their com- 
 bination taken to be, the less experience has the mind 
 already had of such concurrence. And since the exact 
 opposite of this truth is involved in the theory of cumulating 
 probabilities, it cannot for a moment be allowed that the 
 mathematical process is that which the mind really follows, 
 when it becomes convinced, through a multiplicity of evi- 
 dence, and by implicit action, that a very high probability 
 exists of the truth of a supposed event. Further, we ap- 
 parently have, in the consideration here adduced, strong- 
 ground for refusing to accept the view, that through a cumu- 
 lation of probabilities actually carried out by explicit pro- 
 cess assured conviction can ever be attained. 
 
CHAPTER XV. 
 PROBABILITY AND ILLATION. 
 
 I. We are now coming to what may be called the climax 
 of this treatise. It is the point at which, in the first place, 
 Mill's claim to have treated, in his exposition of induction, 
 of every kind of inference will be finall}^ disposed of. And 
 it is the point at which, in the second place, the presentment 
 of the method of illation will be substantially completed. 
 When these two purposes have been effected, though the 
 argument will still be in some respects unfinished, yet its 
 main issue will have been determined. There will still be 
 need, in another chapter, to amplify and consolidate the con- 
 siderations urged ; but practically the position will have 
 been established. The inutility of logic to lead to or ex- 
 plain the discovery of causes and effects in the field of history 
 will have been made conspicuous, and the adequacy of illa- 
 tion to do the required work will, it is hoped, have been 
 exhibited to the satisfaction of the reader. 
 
 With regard to Mill, the special point which in this chapter 
 has to be examined is his contention, already noticed in 
 Chapter VII., that concrete facts of common life are ascer- 
 tained by induction through the instrumentality of probable 
 conclusions. In his treatment — if, indeed, his comparatively 
 few remarks are worthy of the name — of probable evidence 
 as a ground of assent and guide to conduct he writes as 
 
 follows : — 
 
 223 
 
224 THE THEORY OF INFERENCE 
 
 " In our inquiries into the nature of the inductive process, 
 we must not confine our notice to such generalisations from 
 experience as profess to be universally^ true. There is a 
 class of inductive truths avowedly not universal, in which 
 it is not pretended that the predicate is always true of the 
 subject, but the value of which, as generalisations, is never- 
 theless extremely great. An important portion of the field 
 of inductive knowledge does not consist of universal truths, 
 but of approximations to such truths ; and when a conclu- 
 sion is said to rest on probable evidence, the premisses it is 
 drawn from are usually generalisations of this sort. 
 
 " As every certain inference respecting a particular case 
 implies that there is ground for a general proposition, of 
 the form, Every A is B ; so does every probable inference 
 suppose that there is ground for a proposition of the form, 
 Most A are B ; and the degree of probability of the inference 
 in an average case will depend on the proportion between 
 the number of instances existing in nature which accord 
 with the generalisation, and the number of those which 
 conflict with it."^ 
 
 " If we would succeed in action, we must judge by in- 
 dications which, though they do not generally mislead us, 
 sometimes do ; and must make up, as far as possible, for the 
 incomplete conclusiveness of any one indication, by obtain- 
 ing others to corroborate it. The principles of induction appli- 
 cable to approximate generalisation are therefore a not less 
 important subject of inquiry than the rules for the investiga- 
 tion of universal truths, and might reasonably be expected 
 to detain us almost as long, were it not that these principles 
 are mere corollaries from those which have been already 
 treated of."^ 
 
 "We know only that most A are B, not why they are 
 so, nor in what respect those which are, differ from those 
 1 Bk. III. ch. xxiii. § i. " Id. § 2. 
 
PROBABILITY AND ILLATION 225 
 
 which are not. How then did we learn that most A are B ? 
 Precisely in the manner in which we should have learnt, 
 had such happened to be the fact, that all A are B. We 
 collected a number of instances sufficient to eliminate chance, 
 and having done so, compared the number of instances in 
 the affirmative with the number in the negative. The result, 
 like other unresolved derivative laws, can be relied on solely 
 within the limits not only of place and time, but also of cir- 
 cumstance, under which its truth has been actually observed ; 
 for as we are supposed to be ignorant of the causes which 
 make the proposition true, we cannot tell in what manner 
 any new circumstance might perhaps aftect it."^ 
 
 It will be observed that in the above passages Mill recog- 
 nises two steps in the mental passage from the known to 
 the unknown in relation to the affairs of common life. The 
 first is that in which approximate generalisations, applicable 
 to new cases, are arrived at ; the second is that in which 
 the mind so combines them as to make some near approach 
 to the ascertainment of concrete truth. But what light does 
 he throw upon either of these steps or processes ? He 
 speaks of approximate generalisations, or probable evidence, 
 as examples of inductive truth, and at the same time as 
 derived from examining a number of instances sufficiently 
 large to eliminate chance. He speaks of practical conclusions 
 being based on a number of such generalisations. And he 
 speaks of the principles of induction applicable to approxi- 
 mate generalisation — referring, it may be to the derivation, it 
 may be to the employment, of approximate generalisations 
 or probable conclusions — as corollaries of others already 
 treated of. 
 
 In the case of the first step there appears to be an almost 
 entire absence of real explanation of the mind's action. With 
 regard to it we may simply put these inquiries. First, what 
 
 1 Bk. III. ch. xsiii. §4. 
 
226 THE THEORY OF INFERENCE 
 
 is meant by collecting a number of instances sufficient to 
 eliminate chance ? Secondly, whatever it is, how can it, 
 together with an act of counting, be spoken of as an example 
 of induction ? Thirdly, of what principle already treated of 
 can the principle of this process be regarded as a corollary ? 
 In the absence of clear and satisfactory answers to these 
 questions — and none such appear to be forthcoming — we are 
 surely entitled to say, that Mill fails to show that approximate 
 generalisations applicable within certain limits to new cases 
 are, as he considers them, inductive truths. 
 
 And the second step is similarl}^, and perhaps even more 
 unjustifiably, assumed to require no full consideration. His 
 treatment of it is scanty and inadequate in the extreme, 
 besides being, as will presently appear, quite erroneous. 
 Further, he makes no attempt, or no serious attempt, to 
 exhibit it as an instance of induction, or its principle as a 
 corollary of any principle already treated of The following 
 is what he has to say on "making up, as far as possible, 
 for the incomplete conclusiveness of any one indication by 
 obtaining others to corroborate it." 
 
 " From the application of a single approximate generalisa- 
 tion to individual cases, we proceed to the application of two 
 or more of them together to the same case. 
 
 "When a judgment applied to an individual instance is 
 grounded on two approximate generalisations taken in con- 
 junction, the propositions may co-operate towards the result 
 in two different ways. In the one, each proposition is 
 separately applicable to the case in hand, and our object 
 in combining them is to give to the conclusion in that 
 particular case the double probability arising from the two 
 propositions separately. This may be called joining two 
 probabilities by way of Addition ; and the result is a pro- 
 bability greater than either. The other mode is, when only 
 one of the propositions is directly applicable to the case, the 
 
PROBABILITY AND ILLATION 227 
 
 second being only applicable to it by virtue of the application 
 of the first. This is joining two probabilities by way of 
 Ratiocination or Deduction ; the resuljj of which is a less 
 probability than either. The type of the first argument is, 
 Most A arc B ; most C are B ; this thing is both an A and 
 a C ; therefore it is probably a B. The type of the second 
 is, Most A are B ; most C are A ; this is a C ; therefore it 
 is probably an A, therefore it is probably a B. The first 
 is exemplified when we prove a fact by the testimony of 
 two unconnected witnesses ; the second, when we adduce 
 only the testimony of one witness that he has heard the 
 thing asserted by another. Or again, in the first mode it 
 may be argued that the accused committed the crime because 
 he concealed himself, and because his clothes were stained 
 with blood; in the second, that he committed it because he 
 washed or destroyed his clothes, which is supposed to render 
 it probable that they were stained with blood. Instead of 
 only two links, as in these instances, we may suppose chains 
 of any length. A chain of the former kind was termed by 
 Bentham a self-corroborative chain of evidence ; the second, 
 a self-infirmative chain. 
 
 "When approximate generalisations are joined by way 
 of addition, we may deduce from the theory of probabilities 
 laid down in a former chapter, in what manner each of 
 them adds to the probability of a conclusion which has the 
 warrant of them all. 
 
 " If, on an average, two of every three A's are B's, and 
 three of every four C's are B's, the probability that some- 
 thing which is both an A and a C is a B, will be more 
 than two in three, or than three in four. Of every twelve 
 things which are A's, all except four are B's by the supposi- 
 tion ; and if the whole twelve, and consequently those four, 
 have the characters of C likewise, three of these will be B's 
 on that ground. Therefore, out of twelve which are both 
 
2 28 THE THEORY OF INFERENCE 
 
 A's and C's, eleven are B's. To state the argument in 
 another way : a thing which is both an A and a C, but 
 which is not a B, is found in only one of three sections of 
 the class A, and in only one of four sections of the class 
 C ; but this fourth of C being spread over the whole of 
 A indiscriminately, only one-third part of it (or one-twelfth 
 of the whole number) belongs to the third section of A; 
 therefore a thing which is not a B occurs only once among 
 twelve things which are both A's and C's. The argument 
 would, in the language of the doctrine of chances, be thus 
 expressed : the chance that an A is not a B is J, the chance 
 that a C is not a B is ^ ; hence if the thing be both an 
 A and a C, the chance is J of :j = yV"^ 
 
 Mill, then, having asserted that cumulation or addition of 
 probabilities is employed in certain given circumstances, and 
 having put before us an abstract sample of the process of 
 addition, apparently considers that he has done enough to 
 show how in these circumstances induction is the "logic 
 of practical business and common life." The following to 
 its close the argument commenced by cumulating probabilities 
 he commits to our own unaided efforts. He leaves us to 
 discover for ourselves, not only how the reasoning supposed 
 to be employed is an instance of induction, but also what 
 the precise course of reasoning is. To an examination of 
 this latter question let us, starting from the point at which 
 approximate generalisations or probable conclusions are 
 assumed to be applicable to the case before us, now address 
 ourselves. 
 
 II. In the first concrete instance alluded to by Mill — that 
 of proving a fact by the testimony of two independent 
 witnesses — evidently what we have first to do is to assess 
 the probability, in either case, that truth is being spoken, 
 and then combine, in the way of cumulation, the two pro- 
 1 Bk. III. ch. xxiii. § 6. 
 
PROBABILITY AND ILLATION 229 
 
 babilities. This, he imphes, will give us the probability 
 that the fact, which they agree in testifying, is true. Taking, 
 then, the letters and figures of the abstract example, if the 
 probability of A speaking truth is -|, and that of C speaking 
 truth is I, wc have H as the probability that either A, or 
 C, or both A and C are speaking truth ; or — as it might 
 at first sight appear — that the fact attested may somehow 
 be relied upon as true. 
 
 In the second instance — that of inferring the guilt of an 
 accused person — we apparently have to argue thus. Two 
 out of every three persons who conceal themselves, and 
 three out of every four whose clothes are stained with 
 blood, have committed crime. Whence the probability, that 
 a person who both conceals himself and has blood-stained 
 clothes has committed crime, is j^. 
 
 Let us now carefully and critically examine these two 
 results. 
 
 With regard to the first, we may begin by noticing the 
 important point, that in the given circumstances the calcula- 
 tion of probability is not correct. The fraction arrived at 
 is manifestly the probability that, if the two witnesses are 
 testifying each to his own fact, one or the other, or both 
 together, of the facts attested will be true. The complete 
 change of conditions occasioned by the hypothesis, that 
 their testimony is the same, is altogether overlooked or dis- 
 regarded. If both are asserting the existence of the same 
 thing, then, relatively to the existence of this thing — which 
 is the point in question — one cannot be speaking truly, while 
 the other lies. There are but two alternatives to consider, 
 namely, that both are speaking truly, and that both are 
 speaking falsely. Hence we have but one case, instead 
 of three, in which truth will be spoken. And the proba- 
 bility of this one case happening is -| x | or 1%, a pro- 
 bability, let it be observed, actually less, instead of greater, 
 
230 THE THEORY OF INFERENCE 
 
 than the probabihty of the truth of the alleged fact when 
 testified to by either A or C alone. The cumulation of 
 probabilities diminishes, instead of increasing, the proba- 
 bility that the thing declared is true. The greater the 
 number of witnesses, all asserting the same thing, the less 
 is their concurrent testimony to be accepted. 
 
 This seems perhaps to be a strange result. But in truth 
 — and herein the easy explanation lies — it is not in conse- 
 quence of the value assigned to testimony by any theory of 
 probability that things attested by one or more witnesses 
 take their place in our minds as established facts. It is not 
 really thus that we come to look upon alleged facts as satisfac- 
 torily substantiated. With regard to this point it may suffice 
 to refer the reader to the discussion of testimony at the close 
 of Chapter XL, and to quote from Mill the following passage. 
 
 " It is obvious, too, that even when the probabilities are 
 derived from observation and experiment, a very slight im- 
 provement in the data, by better observations, or by taking 
 into fuller consideration the special circumstances of the 
 case, is of more use than the most elaborate application of 
 the calculus to probabilities founded on the data hi their 
 previous state of inferiority. The neglect of this obvious 
 reflection has given rise to misapplications of the calculus of 
 probabilities which have made it the real opprobrium of 
 mathematics. It is sufficient to refer to the applications 
 made of it to the credibility of witnesses, and to the correct- 
 ness of the verdicts of juries. In regard to the first, common 
 sense would dictate that it is impossible to strike a general 
 average of the veracity, and other qualifications for true testi- 
 mony, of mankind, or of any class of them ; and even if it were 
 possible, the employment of it for such a purpose implies a 
 misapprehension of the use of averages : which serve indeed 
 to protect those whose interest is at stake against mistaking 
 the general result of large masses of instances, but are of 
 
PROBABILITY AND ILLATION 231 
 
 extremely small value as grounds of expectation in any one 
 individual instance, unless the case be one of those in which 
 the great majority of individual instances do not differ much 
 from the average. In the case of a witness, persons of 
 common sense would draw their conclusions from the degree 
 of consistency of his statements, his conduct under cross- 
 examination, and the relation of the case itself to his inte- 
 rests, his partialities, and his mental capacity, instead of 
 applying so rude a standard (even if it were capable of 
 being verified) as the ratio between the number of true 
 and the number of erroneous statements which he may be 
 supposed to make in the course of his life." ^ 
 
 Let us now take up the second of Mill's two concrete 
 instances. The probability, we find, that a person who 
 both conceals himself and has blood-stained clothes has com- 
 mitted crime is y|. This, when we look into it, is the proba- 
 bility that he is guilty of one of three things, either (i) of a 
 crime which leads him to conceal himself, or (2) of a crime 
 which is a cause of his clothes being stained with blood, or 
 (3) of two crimes, or one crime, having as their outcome 
 the joint result. But if we take — as Mill perhaps intends 
 us to take, and as in such matters we commonly do take — 
 the two incidents as mutually corroborative indications of 
 one and the same crime, the third of the alternatives just 
 mentioned is the only one with which we are concerned. 
 And the probability that the accused person is a criminal 
 in this restricted sense we find to be much less than the 
 probability that he is a criminal in the wider one. The 
 probability that he has committed either one crime, or two 
 crimes, of which both the concealment of himself and the 
 condition of his clothes are to be taken as results, is only 
 f X I or j'.7, a probability less than that of his having com- 
 mitted a crime indicated by either piece of evidence taken 
 1 Bk. III. ch. xviii. § 3. 
 
232 THE THEORY OF INFERENCE 
 
 singly. And the probability that it is one crime, and not 
 two, from which the joint results proceed, is of course 
 something smaller still. The cumulation of facts sup- 
 posed to be accounted for by one and the same crime 
 diminishes the probability of such a crime having been 
 committed. 
 
 Here again we may seem to have reached a conclusion 
 which contradicts experience. But here, as before, it may 
 be remarked that the explanation lies in the consideration 
 that it is not — at all events in any great measure — by means 
 of, or in accordance with, any theory of probability that the 
 mind attains assurance of facts through circumstantial evi- 
 dence. Apart from the futility, just exposed, of the method 
 of probability for discovering the kind of fact which will 
 account for a number of given circumstances, there is 
 another step for which it makes little or no provision. It 
 provides no means, or no regular means, of fitting a definite 
 cause to a definite effect. Let the probability that a certain 
 person is a criminal be what it may, by what manner of 
 dealing with probabilities are we to connect him, as Mill 
 would have us do, with the crime which is supposed to have 
 been committed ? There appears to be, in general, in the 
 theory of probability no way of attaching even a known 
 criminal to a known crime of precisely the same kind as 
 that which he is known to have committed. If it is certain 
 that A has recently committed murder, and if it is certain 
 that B has just been murdered, on what ground can it, in 
 general, be said to be probable that A has murdered B ? If 
 A can for any reason be fixed upon as one of a limited 
 number of possible perpetrators of the deed, then there is 
 material for drawing probable conclusions, and the mind 
 may attempt to estimate the probability of A being the 
 murderer, if it chooses to do so. But in the absence of this 
 condition, if not in its presence also, it associates criminal 
 
PROBABILITY AND ILLATION 233 
 
 with crime by means of a process for which the theory of 
 probabiHty has no place. 
 
 Let us now sum up. It is certain, we may say, that in 
 the actual working of the mind, in relation to the concrete 
 affairs of common life, a large body of circumstantial evi- 
 dence pointing together to one common fact produces a 
 strong disposition to assent to that fact. And the greater 
 the number of separate indications, the stronger is the claim 
 to acceptance of the fact indicated felt to be. And it is 
 certain, we may say, that in the cumulation of probabilities 
 by mathematical process a large body of circumstantial evi- 
 dence pointing together to one common fact leads, in the 
 first place — as was shown at the end of the preceding 
 chapter — only to results depending on assumptions such as 
 the mind cannot reasonably be supposed to make, and leads, 
 in the second place, to probabilities actually decreasing in 
 value with the increase in number of evidential circum- 
 stances. Although, therefore, mathematicians may, in esti- 
 mating the value and weight of evidence, choose to treat 
 all men and things as subjects of statistics and numerical 
 probabilities — thus producing results opposed to human ex- 
 perience — yet it must be maintained that the working of the 
 minds of ordinary men proceeds on quite different lines. 
 When the mind is looking at things naturally, increase in a 
 body of convergent evidence brings with it increase of vivid 
 reahsation, and also increase of assurance : when it is fol- 
 lowing the unreal guidance of the theory of probability, its 
 power of realising and affirming the conclusions which it 
 reaches becomes less as the evidence on which they are 
 based becomes more abundant. The theory of probability, 
 interesting though it is, and in its measure true, is quite 
 unequal to dealing witli the concrete problems of common 
 life. 
 
 And not alone for the twofold reason just described is the 
 
234 THE THEORY OF INFERENCE 
 
 inadequateness of the theory of probability to be condemned. 
 It is to be condemned also for the reason that, however high 
 may be the probability that a particular effect of a certain 
 kind has been produced, and that a particular cause of a 
 corresponding kind has operated, it provides Jn general no 
 means of connecting the particular cause with the particular 
 effect. Thus it fails, in general, to lead even to low pro- 
 babilities of definite concrete truths. 
 
 III. Let it now be our business to observe, how that which 
 has been set forth in this book as the process of illation is free 
 from the defects that have just been spoken of. Let it be 
 our business to observe, how that which has been presented 
 as the course which the mind naturally and commonly pursues 
 in discovering concrete causes and effects is a course which 
 avoids the insuperable difficulties of the method of probability. 
 We have to notice, in the first place, how the mind, starting 
 with probable conclusions concerning circumstances that have 
 come before it, so deals with them that it gathers vividness 
 of realisation and firmness of assurance from their increasing 
 number. And we have to notice, in the second place, how 
 it contrives to bridge the gap between an ascertained or 
 conjectured cause and an ascertained or conjectured effect. 
 It will simplify the discussion if we consider only the method 
 of finding causes of effects : that of finding effects of causes 
 is in principle the same. 
 
 In illation, then, having a number of concomitant effects 
 before us, we do not make any attempt to calculate the degree 
 in which it would accord with our experience for them all to 
 be the effects of a certain set of causes acting, singly or con- 
 jointly, under a common name. We do not, that is, search 
 for a kind of cause known by experience to be a probable 
 antecedent of each effect, and, having found one, calculate 
 the probability of all the effects having proceeded indepen- 
 dently each from a cause of this common kind. To do this is 
 
PROBABILITY AND ILLATION 235 
 
 the method of probability, which, whatever other uses it may 
 have, is of Httle or no value in tracing the concrete causes of 
 concrete effects. But, associating together the concomitant 
 effects, we provisionally assume that they are the products of 
 one common cause — not, be it observed, of causes having a 
 common name, but of one and the same compound cause. We 
 then proceed to ascertain by reference to experience what kind 
 of thing this common cause must be. Having before us the 
 probable or alternative antecedents of each of the effects, we 
 eliminate all antecedents that are not common to all the 
 effects, and we conclude that those which remain are each of 
 them alternative kinds of concrete cause of the whole bod}^ of 
 effects. Let us, for example, take Mill's instance of a person 
 concealing himself and having blood-stained clothes. A man's 
 concealing himself has crime, and other things which we may 
 speak of as ABC, as its alternative antecedents. The con- 
 dition of his clothes has crime, and ADE. Assuming, then, 
 that the two circumstances proceed from some common 
 cause, we find that this must be, either crime or A ; these 
 being the only two common kinds of alternative or probable 
 antecedent. 
 
 Now if we fix our attention upon one of the alternative 
 kinds of cause, say crime, it seems tolerably evident that — at 
 all events, in general — the larger the number of separate 
 effects of which it is taken to be an explanatory^ cause, the 
 more lively will be our realisation of it as accounting for them. 
 A person who hides himself and has blood-stained clothes 
 may be a person who has committed a murderous assault. 
 He has marks of the murderer about him ; but they are at 
 the same time marks which we could without much difficulty 
 associate also with innocent proceedings. But a person who, 
 besides having these marks, should be found to have mysteri- 
 ously absented himself from home, to have returned with 
 valuable articles in his possession, and to carry on his person 
 
236 THE THEORY OF INFERENCE 
 
 traces of a struggle, would stand out somewhat conspicuously 
 from other men as having been engaged in an unlawful deed. 
 The multiplicity of convergent details would create an impres- 
 sion of a murderous attack, which it would be comparatively 
 hard to banish from the mind. A number of effects assumed 
 to proceed from the same source, and then found to be har- 
 moniously explicable by some kind of common cause, found to 
 be mutually dependent and explanatory parts of one composite 
 whole, present a picture which, up to the point of its becoming 
 substantially complete, is rendered vivid in proportion as the 
 number of contributory effects is great. In the method of 
 probability — as we have seen — that a number of concurrent 
 effects should all have their origin in certain causes acting 
 under a common name, is a conjectured event which, from 
 want of experience of instances of similar concurrence, the 
 mind cannot be properly said to realise and expect. But in 
 the method of illation that a number of concurrent effects 
 should all proceed from one explanatory cause, is a con- 
 jectured event which, owing to the picture of a composite 
 whole consistently and harmoniously built up, impresses 
 itself on the mind as one deserving of careful and attentive 
 thought. 
 
 Our next point is the enhancement of assurance occasioned 
 by an increased multiplicity of effects. It will at once be 
 obvious that, in general, the greater the number of inde- 
 pendent effects all proceeding from one compound cause, 
 the fewer are the alternative kinds of cause from which they 
 can all alike proceed. With the introduction of new effects 
 or circumstances, claiming to spring from the same cause as 
 those already under observation, some of the common ante- 
 cedents already ascertained will, in general, have to be 
 eliminated. And thus, up to the point of the elimination 
 of all but one, the number of alternative kinds of cause 
 becomes continuously less, and our limits of choice con- 
 
PROBABILITY AND ILLATION 237 
 
 tinuously restricted. And if, by introducing new effects, 
 we can succeed in eliminating all but one, then the mind is 
 tolerably well assured that it has found in this one the kind 
 of cause which contains the true explanation of the com- 
 bined effects. 
 
 We pass on to the second main question, that, namel}', 
 of bridging the gap between an ascertained or conjectured 
 kind of effect and an ascertained or conjectured kind of cause. 
 Let us suppose ourselves to be more or less convinced that 
 A has committed a murderous assault, and that B has met 
 with a violent death. The method of probability has, in 
 general, no way of bringing these two conclusions into con- 
 nection with each other, so as to make it probable, in any 
 practical sense of the terrn, that A is the murderer of B. 
 In illation, however, the mind can assume provisionally that 
 the two ascertained or conjectured kinds of fact are causally 
 related, and upon finding a hypothetical definite fact — not 
 discordant with other known facts — which may represent 
 at once the act of A and the fate of B, can give its assent to 
 this fact as true. The provisional assumption is justified 
 by some observed contiguity between A and B, or between 
 the two sets of circumstances that have established, con- 
 jecturally or certainly, the nature of the act of the one and 
 of the fate of the other. And its assent to the specific pro- 
 position, that A has murdered B, is justified by the causal 
 explanation afforded by this inferred definite fact of the two 
 sets of convergent circumstances. 
 
 We have yet to consider the important questions of the 
 value of the assent thus given, and of the perception by 
 the mind of alternative solutions of a given problem. But 
 these we may reserve for another chapter, concluding for the 
 present with a brief general description of the nature of the 
 assent of illative inference. The assent of illative inference 
 is assent given to a proposition which satisfies and sets 
 
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240 THE THEORY OF INFERENCE 
 
 cannot be otherwise. We may admit that it is a sound 
 position, and we may accept the following words as a correct 
 description of it : — " The language in common use, when 
 concrete conclusions are in question, implies the presence 
 of this personal element in the proof of them. We are con- 
 sidered to feel, rather than to see, its cogency; and we 
 decide, not that the conclusion must be, but that it cannot 
 be otherwise. We say, that we do not see our way to doubt 
 it, that it is impossible to doubt, that we are bound to believe 
 it, that we should be idiots if we did not beheve." ^ What 
 we have to do is to inquire, on what ground it is that we 
 thus shrink and recoil from the negative of the conclusion 
 which offers itself to us for assent, and whether it is a 
 ground which the theory of probability can be said to 
 recognise. 
 
 Often, of course, it will be the case that the mind discerns 
 alternative solutions of the same problem. In the first 
 place, starting with one or two phenomena of which it seeks 
 to ascertain the cause, it may be led to different conclusions 
 by tentatively associating with them, as concurrent effects, 
 different groups of neighbouring phenomena. In the second 
 place, starting with some definite group of associated pheno- 
 mena, it may find more than one common kind of cause from 
 which all might have proceeded. And in the third place, 
 starting with some one kind of cause as having produced 
 them all, it may find more than one definite operating cause 
 whose effect this kind of cause may be taken to be. There 
 is thus, it will be seen, in illative inference regarded broadly, 
 abundant room for diversities of conclusion respecting the 
 definite concrete origin of this or that concrete effect ; and 
 it may well be that some of the conclusions are mutually 
 inconsistent. 
 
 When alternative solutions are thus present to the mind, 
 ^ Ch. viii. § 2. 
 
ASSENT AND BELIEF***=SSi;i^3S.**^ 241 
 
 judgment as to their absolute truth or falsity is of course 
 suspended. Assent may be given to each and all as con- 
 clusions which are probably true, but here assent must stop. 
 No apparent explanation of the phenomenon or phenomena 
 in question can be rejected as untrue; and none, in the 
 presence of satisfactory alternatives, can be accepted as the 
 true one. Suspense of judgment, however, does not involve 
 paralysis of action. For one alternative conclusion may 
 appear to the mind more probable than all others. It may 
 be felt to explain more facts, or to explain facts in closer 
 accordance with past experience, and thus be one on which, 
 no less than if it were without competitors, action can reason- 
 ably and properly be grounded. 
 
 And if, as may often be the case, no more than one ex- 
 planation is present to the mind, and yet the mind is con- 
 scious that some other may exist, judgment must, appar- 
 ently, still be kept suspended. An inferred event, offering 
 itself as a sufficient explanation of observed phenomena, 
 only because no other has yet been found, is an event of 
 which, in strictness, it is but the ver}^ high probability that 
 is inferred. 
 
 Of assent proper — assent to the one conclusion which 
 explains all, or nearly all, the phenomena needing explana- 
 tion — there seem to be three forms, or three stages, between 
 which we may distinguish. 
 
 First, we have assent to a conclusion which the mind, 
 consciously or unconsciousl}^, assumes to be the only one 
 that has any claim to be considered. Here the mind 
 simply takes, as it were, the new fact made known to it 
 by inference, and sets it in the place into which it fits in 
 the orderly picture of the world which is in process of con- 
 struction. It is a fact which is accepted as true and re- 
 ceived into the mind because, while it is itself in substantial 
 harmony with the impressions of experience, other scattered 
 
 Q 
 
242 THE THEORY OF INFERENCE 
 
 images of outside things — the things which are the evidential 
 facts on which assent is based — are seen to be capable of 
 being ranged around it, and by its instrumentality made, 
 together with it, orderly and intelligible parts of the grow- 
 ing representation. If this is at all a correct description 
 of the mental operation of simple assent, it is plain that the 
 operation is quite unconnected with estimates and calcula- 
 tions of probability. 
 
 Secondly, assent may be explicitly given to a conclusion 
 on the ground that it, and it alone, affords the explanation 
 that is required. This event — so the argument runs — must 
 be true, because there certainly is no other event, in any 
 degree probable, to dispute its claim. Now here, it may 
 with reference to Newman's view be to some extent admitted, 
 there is a semblance of assent being based upon the limit of 
 probability. The quantities, says Newton, in effect, in his 
 lemma, must be ultimately equal, they cannot be otherwise 
 than equal, because, by hypothesis, there is no room for any 
 finite quantity to come between them. And with some 
 similarity of reasoning we may say, in the case of assent, 
 that the probability of this event must be equivalent to 
 certainty, that we cannot conclude otherwise than that it is 
 true, since there is, by hypothesis, no other probability to 
 detract from its numerical value. If in illation it were indeed 
 the case, that probability develops into certainty with the 
 gradual disappearance of competing probabilities, then assent 
 would, apparently, be given in the form, The conclusion 
 cannot be otherwise. But the converse of this does not 
 follow. It does not follow that the one conclusion to which, 
 for some reason, assent is obviously restricted — and which 
 therefore cannot become other than it is — is in any way 
 connected with considerations of probability. 
 
 But thirdly, the words, The conclusion cannot be other- 
 wise, may have a different meaning from that just pointed 
 
ASSENT AND BELIEF 243 
 
 out. This, while it is the meaning which Newman really 
 attaches to them, is a meaning quite foreign to the argu- 
 ment of Newton's lemma. If a person, having assented 
 to a proposition on the explicit ground of there being no 
 alternative proposition demanding to be considered, should 
 interrogate himself, or be interrogated, as to why, even so, 
 he feels called upon to give assent, he could, apparently, 
 only make answer to the effect, that with all the evidence 
 that has been brought forward in its favour it cannot be 
 otherwise than true. And the real meaning of such an 
 answer appears to be as follows. A healthil}^ active mind 
 ardently seeks for explanations of phenomena that come 
 before it. It has an eager desire to ascertain causes of 
 effects and effects of causes, and a keen interest in learn- 
 ing how cause is linked with cause and effect associated 
 with effect in the field of history. It is continually em- 
 ployed in ranging facts in orderly sequence and connection, 
 and building up for itself a harmonious and consistent 
 repfesentation of the external world. And thus, to find 
 a causal explanation of a multitude of hitherto unex- 
 plained phenomena, is for it a satisfaction which it feels 
 it to be most natural that it should have, most unnatural 
 that it should let go. Having found an explanation, it 
 clings to it, and maintains that it is certainly such as can 
 be accepted, that it is certainly true, because a multitude 
 of facts, w'hich by means of it will be reduced to order, 
 must otherwise remain a more or less chaotic and unintel- 
 ligible mass. 
 
 II. It will now be well, in continuation of the comparison 
 already instituted between illation and induction, to consider 
 the nature of inductive assent, and then compare the two 
 assents together. This, moreover, will afford the needed 
 occasion for examining the value of the assent given in 
 illation. 
 
244 THE THEORY OF INFERENCE 
 
 Inductive inference leads, as we know, to a conclusion 
 of the following kind : ABC, being antecedents common 
 to all observed instances of a, and never found on occa- 
 sions when a is observed to be absent, contain among them 
 the cause of a. To reach this conclusion the mind has, 
 besides the necessary deductive act, done two things. It 
 has withdrawn its attention from all antecedents which 
 appear to it too remote from a to contain a really ex- 
 planatory cause ; and it has by a process of comparison 
 and contrast reduced the number of the antecedents re- 
 maining which can by possibility be a cause. Assent to 
 the conclusion means, then, that the mind is satisfied, that 
 the proper range of search has been truly judged, and 
 that the work of comparison and contrast has been per- 
 formed with accuracy. While the latter point is one of 
 mere observation, the former appears to be connected 
 with the mind's innate conception of causation and its 
 eagerness to find explanatory causes. A cause such as 
 the mind really apprehends and cares to know of as an 
 explanatory cause is one that is to be found in some sort 
 of proximity to the effect. And the mind assents to the 
 conclusion that the very limited collection of phenomena, 
 ABC, contains the cause of a, partly because it has an 
 innate conviction that the explanatory cause, existing and 
 required, is not among the remote antecedents which have 
 been left unnoticed. 
 
 Let us now make comparison between the two different 
 kinds of assent. There appear to be three points in respect 
 of which we may compare them. First, we may compare 
 them in respect of their subjective value, by which is meant 
 the degree of certitude present in each in the mind of the 
 individual thinker. Secondly, we may compare them in 
 respect of their demonstrative value, or the cogency of 
 the arguments producing them to move to assent the mind 
 
ASSENT AND BELIEF 245 
 
 of any other person before whom they may be laid. Thirdl}', 
 we may compare tliem in respect of their objective value, 
 an expression here used to signif\^ the nearness of the 
 inferred conclusion to actual truth and fact. 
 
 I. The certitude of illation, if we choose it in its highest 
 form, appears to be a certitude that of two alternative re- 
 presentations of a multitude of circumstances, one of them 
 orderly and intelligible, the other meaningless and chaotic, 
 it is the former that must be true, and the latter that must 
 be false. If this is so, it is scarcely too much to say, 
 that the mind, in its recoil from confusion and disorder in 
 the external world, clings to an explanation, which substitutes 
 a scene of intelligible order, no less closely than it clings to 
 axiomatic truths. Of course there are lower degrees of 
 illative assent of which this can in no wise be truly said. 
 But apparently, in extreme cases, the assurance with which 
 the mind assents to concrete truths in the field of history 
 may be no less intense than the confidence with which it 
 makes deductions in the field of natural law. 
 
 The certitude of induction — if we set aside that of the 
 initial deductive step, and that of the subsequent process of 
 comparison and contrast — appears to be a certitude that an 
 explanatory cause is to be found in some kind of proximity 
 to the effect such as the mind has recognised. It is a 
 certitude that the required cause need not be looked for 
 among the body of antecedents which has been set aside as 
 being in one wa}- or another too remote. This certitude is 
 presumably in some sort of inverse ratio to tlie magnitude 
 of the bod}^ thus set aside. The fewer the antecedents 
 that are rejected, and the more that are retained for purposes 
 of comparison and contrast, the more reason has the mind 
 to be satisfied that it has the cause enclosed in the ante- 
 cedents remaining uneliminated. But at the same time these 
 remaining antecedents will, in general, be more in number 
 
246 THE THEORY OF INFERENCE 
 
 than if a greater quantity had originally been set aside ; so 
 that the locality of the required cause is less perfectly 
 defined. In induction, then, it appears to be generally the 
 case that, when certitude that the cause is contained in 
 ABC, &c., is ver}^ great, the practical value of the inference 
 is comparatively small ; and when the practical value may 
 be great, the certitude that it is so cannot be estimated at a 
 high degree. On the whole, it may perhaps be said, that 
 certitude in the case of inductive inferences actually made, 
 whether or not it is for the most part less than that of 
 illative inferences, never reaches the point which this latter 
 is sometimes enabled to attain. 
 
 2. An illative inference is not, like a deductive infer- 
 ence, transferable from one person to another. It does not, 
 merely by means of an able exhibition of the argument, 
 become a common mental possession. The conclusion 
 arrived at by any individual thinker does not depend only 
 upon the facts before him, and the degree of carefulness 
 and acumen with which the evidence is collated. It depends 
 in great measure also upon his own personalit}'. The in- 
 terpretation of facts must be in accordance with experience ; 
 and the experience of one man is far from tallying in all 
 points w^th that of another. Two persons, having before 
 them precisely the same bod}- of facts from which to judge, 
 and with anxious care discussing the evidence point by 
 point, may be quite unable to agree upon the true interpre- 
 tation of it. In so far as particular experiences in relation 
 to the matter in hand are common to both, each will follow 
 the line of investigation taken by the other; but in so far 
 as experiences are different, each will diverge from the 
 other's path. 
 
 But though illative inference thus seems to have, on the 
 whole, little direct demonstrative value, yet indirectly it may 
 do much to compel the assent of other persons. For the 
 
ASSENT AND BELIEF 247 
 
 bare circumstance, that a particular conclusion has been 
 arrived at by an individual whose insight and judgment are 
 relied on, is to no small extent regarded by others as a 
 warrant for accepting it as true. And if we find a number 
 of persons, of perspicacity and sound judgment, uniting in 
 testifying their assent to one and the same conclusion from 
 the facts before them, then we ourselves, by an act of 
 illative inference from the several acts of testimony, may 
 not unreasonably conclude it to be true that the circum- 
 stance, which they unitedly infer, is indeed a circumstance 
 that has actually happened. The hypothesis of its being 
 a veritable fact may reasonably be looked upon as the only 
 hypothesis which affords a satisfactory explanation of the 
 several inferences that it is a fact. This act of illation per- 
 formed by us is, it may be remarked, precisely the same in 
 character as the act which would lead us to assent to the 
 united testimony of a number of witnesses who, instead of 
 having severally inferred the fact, should depose each to his 
 own actual knowledge of it. 
 
 The demonstrative value of induction, though inferior to 
 that of deduction, must be held to rank above that of illation. 
 We may perhaps assume, that one person can surely carry 
 another with him through the process of elimination by 
 comparison and contrast ; but we cannot equally take it for 
 granted, that one can bring another to take the same view 
 as himself as to the body of phenomena that may be 
 summarily set aside. The line of demarcation between the 
 antecedents among which a cause is to be sought, and those 
 which there is no need to take into consideration, will not 
 be drawn, by the consent of all inquirers, in exactly the 
 same place, even when they have precisely the same body 
 of antecedents before them. But nevertheless there will, in 
 general, be no very great divergence of opinion. Moreover, 
 as in the case of illation, so in the case of induction, the 
 
248 THE THEORY OF INFERENCE 
 
 view taken by investigators of known judgment and pene- 
 tration may, as being their view, commend itself for adoption 
 to other persons. 
 
 3. What sort of guarantee is there, we have now to 
 inquire, of the conclusions drawn, whether by illation or by 
 induction, being in accordance with actual fact ? Of course 
 a large proportion of the inferences actually made in common 
 life are, from an objective point of view, quite unreliable, 
 li in illation persons are apt to 'jump at conclusions,' so in 
 connection with induction it is common enough to ' make 
 hasty generalisations.' In both the fields of investigation 
 inferences are often drawn, which serve only the purpose 
 of giving temporary satisfaction to a mind eager to under- 
 stand the phenomena around it, and which in the light of 
 subsequent experience, or on more careful consideration of 
 the facts already known, have to be renounced or greatly 
 modified. But let us suppose a conclusion drawn in the 
 field of history, and another drawn in the field of natural 
 law, from ample evidence and by a person of trained in- 
 telligence, and assented to by him with full conviction. 
 What means have we then of assessing the proximity of 
 these conclusions to objective truth ? 
 
 With regard to an illative inference, it seems to be the case 
 that it must be true only if it is drawn in that part of the 
 field of history to which the experience of the inquirer be- 
 longs. We may perhaps take it for certain, that the grouping 
 of causes, if not absolutely continuous in an}^ one corner of 
 the world at any one period of time, is yet so continuous 
 that entire reliance may be placed upon an inference drawn, 
 under strict conditions, concerning an event in that corner 
 and at that period by one who has experience of them. But 
 we do not seem entitled to ascribe the same certainty to 
 inferences concerning events in other corners or at other 
 periods. A wise man, however, when drawing inferences. 
 
ASSENT AND BELIEF 249 
 
 will recognise this; he will bear in mind that in many 
 respects the regular grouping of causes varies according to 
 place and time ; and he will be careful not to give uncon- 
 ditional assent to a conclusion, unless he is assured that with 
 regard to the matter in question his own experience may 
 properly be taken, so far as it has been taken, to be a suffi- 
 cient guide. This being so, if a person, at once broad- 
 minded and intelligent, should entertain a deliberate and firm 
 conviction that a particular historical incident is true, we 
 may perhaps take it to be the case, that the fact cannot be 
 otherwise than he understands it to be. 
 
 In inductive inference the truth of the conclusion depends 
 upon the inquirer not having rejected as irrelevant all the 
 antecedents which contain a cause. An acute and cautious 
 person may, perhaps, be fully depended upon not to make 
 such a mistake as this. We seem to be possessed of so 
 much insight into the kind of proximity that exists between 
 cause and effect, that a person of trained intelligence is 
 practically secure against regarding as an impossible seat for 
 an explanatory cause the whole body of phenomena in which 
 the causes of a given effect really have their abode. If, 
 therefore, a person, at once intelligent and cautious, should 
 deliberately hold that certain residual phenomena, ABC, 
 contain among them the cause of a, it may perhaps be con- 
 sidered that his conviction represents an objective truth. 
 
 III. The view here taken of the function of induction does 
 not accord with that of Mill. He claims for his four methods 
 that they, and they alone, are methods of proof. Only by 
 following one of them can causes and effects with certainty 
 be discovered. He writes as follows : " Dr. Whewell's theory 
 of the logic of science would be very perfect if it did not pass 
 over altogether the question of Proof But in my appre- 
 hension there is such a thing as proof, and inductions differ 
 altogether from descriptions in their relation to that element. 
 
250 THE THEORY OF INFERENCE 
 
 Induction is proof; it is inferring something unobserved from 
 something observed : it requires therefore an appropriate 
 test of proof; and to provide that test is the special purpose 
 of inductive logic." ^ " If discoveries are ever made by obser- 
 vation and experiment without Deduction, the four methods 
 are methods of discovery : but even if they were not methods 
 of discovery, it would not be the less true that they are the 
 sole methods of Proof; and in that character, even the results 
 of deduction are amenable to them. The great generalisa- 
 tions which begin as Hypotheses must end by being proved, 
 and are in reality (as will be shown hereafter) proved, by 
 the Four Methods. Now it is with Proof, as such, that 
 Logic is principally concerned."- 
 
 It seems a curious thing — or rather it might seem a curious 
 thing, if it were not in keeping with other deficiencies in his 
 treatise — that he makes no formal and serious attempt even 
 to discuss the evidential value of testimony. Much less does 
 he exhibit conditions under which testimony is equivalent to 
 proof. If, then, we may suppose that logic does indeed 
 direct an individual investigator to the ascertainment and 
 proof of laws of nature, on what are persons, to whom it is 
 impossible to follow him in his researches, to ground their 
 assent to the laws which he professes to have discovered ? 
 Mill can hardly mean that a true fact or law ought not to be 
 assented to by any one who has omitted to verify it for him- 
 self by means of the four methods. And yet, if he does not 
 mean this, he altogether neglects to provide the necessary 
 test of what he must be supposed to acknowledge as a pos- 
 sibly valid kind of evidence. 
 
 Let us now — without re-opening the general question of 
 
 the nature and worth of the four methods — notice two points, 
 
 namely, the kind of proof to which we are led by the method 
 
 of agreement, and the kind to which we are led by the 
 
 1 Bk. III. ch. ii. § 5. " Bk. III. ch. ix. § 6. 
 
ASSENT AND BELIEF 251 
 
 method of difference. Concerning the former Mill writes as 
 follows : — 
 
 " Suppose that, by a comparison of cases of the effect, we 
 have found an antecedent which appears to be, and perhaps 
 is, invariably connected with it : we have not yet proved 
 that antecedent to be the cause until we have reversed the 
 process and produced the effect by means of that antecedent. 
 If we can produce the antecedent artificially, and if, when 
 we do so, the effect follows, the induction is complete ; that 
 antecedent is the cause of that consequent. But we have 
 then added the evidence of experiment to that of simple 
 observation. Until we have done so, we had only proved 
 invariable antecedence within the limits of experience, but 
 not unconditional antecedence or causation. Until it had 
 been shown by the actual production of the antecedent under 
 known circumstances, and the occurrence thereupon of the 
 consequent, that the antecedent was really the condition on 
 which it depended ; the uniformity of succession which was 
 proved to exist between them might, for aught we knew, be 
 (like the succession of day and night) not a case of causation 
 at all ; both antecedent and consequent might be successive 
 stages of the effect of an ulterior cause. Observation, in 
 short, without experiment (supposing no aid from deduction) 
 can ascertain sequences and co- existences, but cannot prove 
 causation." ^ 
 
 Thus he apparently holds that the proof of a phenomenon, 
 towards or to which we have been led by the method of 
 agreement, being the real cause of an effect is this — that by 
 experiment we can actually perceive that it produces the 
 effect. If this is so, it must be objected, that the test of 
 proof is not provided by logic. Surely it does not need 
 logic to authorise us to accept the evidence of our senses. 
 
 Concerning the application of the method of difference he 
 1 Bk. III. ch. vii. § 4. 
 
252 THE THEORY OF INFERENCE 
 
 writes thus : " It is inherent in the peculiar character of the 
 Method of Difference that the nature of the combinations 
 which it requires is much more strictly defined than in the 
 Method of Agreement. The two instances which are to be 
 compared with one another must be exactly similar in all cir- 
 cumstances except the one which we are attempting to investi- 
 gate: they must be in the relation of ABC and BC, or oi abc 
 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 learn at 
 once, from the commonest experience, that most of the co- 
 existent phenomena of the universe may be either present or 
 absent without affecting the given phenomenon ; or, if pre- 
 sent, 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 such circumstances as are not already known to be indif- 
 ferent; it is very seldom that nature affords two instances, 
 of which we can be assured that they stand in this precise 
 relation to one another. In the spontaneous operations of 
 nature there is generally such complication and such obscurity, 
 they are mostly either on so overwhelmingly large or on so in- 
 accessibly 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 exactl}'^ alike in any two cases, that a spontaneous 
 experiment, of the kind required by the Method of Difference, 
 is commonly not to be found. When, on the contrary, we 
 obtain a phenomenon by an artificial experiment, a pair of 
 instances such as the method requires is obtained almost as 
 a matter of course, provided the process does not last a long 
 time. A certain state of surrounding circumstances existed 
 before we commenced the experiment ; this is BC. We 
 then introduce A ; say, for instance, by merely bringing an 
 
ASSENT AND BELIEF 253 
 
 object from another part of the room, before there has been 
 time for any change in the other elements. It is, in short 
 (as M. Comte observes), the very nature of an experiment to 
 introduce into the pre-existing state of circumstances a change 
 perfectly definite. We choose a previous state of things with 
 which we are well acquainted, so that no unforeseen altera- 
 tion in that state is likely to pass unobserved; and into this 
 we introduce, as rapidly as possible, the phenomenon which 
 we wish to study ; so that in general we are entitled to feel 
 complete assurance that the pre-existing state, and the state 
 which we have produced, differ in nothing except the presence 
 or absence of that phenomenon. If a bird is taken from a 
 cage, and instantly plunged into carbonic acid gas, the ex- 
 perimentalist may be fully assured (at all events after one 
 or two repetitions) that no circumstance capable of causing 
 suffocation had super\^ened 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 b}'^ the means employed to 
 produce the change. The possibility, however, of this last 
 supposition generally admits of being conclusively tested by 
 other experiments. It thus appears tliat in the study of the 
 various kinds of phenomena which we can, by our voluntary 
 agency, modify or control, we can in general satisfy the 
 requisitions of the Method of Difference ; but that by the 
 spontaneous operations of nature those requisitions are 
 seldom fulfilled." ^ 
 
 With regard to this it must be objected, that here again 
 the proof is connected, not with logic, but with sensation. 
 If it is indeed by the method of difference that we prove the 
 death of the bird to be due to immersion in carbonic acid gas, 
 then we must have two sets of effects — namely, the bird, and 
 1 Bk. III. ch. viii. § 3. 
 
254 THE THEORY OF INFERENCE 
 
 the bird with the added fact of death — and two correspond- 
 ing sets of antecedents — namely, X, and X with the added 
 fact of immersion in gas. Now let it be granted, that in con- 
 sequence of legitimately neglecting as immaterial a number 
 of antecedents, and of perceiving that the others remain the 
 same before and after the experiment, we have the condition 
 as to the two sets of antecedents rigidly fulfilled. Let there 
 be no question, that is, that immersion in carbonic acid gas 
 is a separable cause of some effect. It has then to be con- 
 sidered, how we become aware that it is the death of the bird 
 of which it is the cause. Is the dead bird precisely the same 
 thing as the living bird together with the added fact of death ? 
 Surel}^ the only ground on which we can affirm this is, that 
 no change in the condition of the bird is apparent to our 
 senses except the addition of the phenomenon of death. But 
 this, apparently, is equivalent to saying, that we know by 
 means of sensation that immersion in gas has death as its 
 effect, oris the cause of death. Hence it appears that Mill's 
 method of difference, with its two cases and its sure conclu- 
 sion from them, is not really a method of inference at all. 
 What it professes to do is, in fact, accompHshed directly 
 through the instrumentality of sensation. 
 
 IV. It remains to say a few words on the subject of assent 
 in relation to belief. A proposition assented to is not neces- 
 sarily a proposition believed. That is to say, we seem able 
 to distinguish between two attitudes of the assenting mind 
 towards an inferred truth in respect of a subsequent relation 
 to exist between them. The act of assent may be regarded 
 by the mind as a purely intellectual act ; or it may be an act 
 which is felt to carry with it consequences, immediate or re- 
 mote, in the sphere of conduct. A fact merely assented to 
 is a fact which is seen to harmonise with some group of 
 images previously existing in the mind ; a fact believed is 
 one which is received as a member of the central body of 
 
ASSENT AND BELIEF 255 
 
 coherent representations of the world in accordance with 
 which conduct has to be determined. 
 
 This distinction being drawn between assent and behef, 
 three remarks seem to be called for. 
 
 1. It will to a great extent depend upon the form in which 
 assent finds its natural expression, whether or not it may be 
 considered as rising to the dignity of belief. A simple ap- 
 prehension and admission, that this thing or that is a true 
 fact of history or of natural law, does not seem to be, in 
 general, a mental act with which we should feel strongly 
 called upon to make our subsequent conduct harmonise ; or 
 which, in the case of other persons, we should look to as 
 affording a reliable indication of their behaviour. If, how- 
 ever, we ourselves, or other persons, assert that this thing 
 or that cannot in reason be supposed to be otherwise than 
 it is alleged to be, then we are conscious that conduct will be 
 expected not to be inconsistent with this conviction. A thing 
 concerning which we are able to express ourselves thus 
 strongly is a thing which we believe, suffering it to exercise 
 a real influence upon our actions. 
 
 2. Apparently it is a possible and a not unusual thing for 
 the mind to entertain at the same time two contrary opinions, 
 if it has merely assented to them. They may harmonise 
 sufficiently well, each with its own group of facts, for the 
 mind, not thinking deeply, to be able to admit the truth of 
 both. If, however, their truth is subjected to a severer test, 
 if the mind seeks to introduce them both into the inner 
 circle of more or less permanent beliefs, their contrariety 
 is likely to be discovered. The constant searching among 
 these beliefs for uniform guidance as to what is natural in 
 conduct — which searching is, apparently, a part of our moral 
 life — will necessarily do much to reduce them to a state of 
 consistent order. 
 
 3. Whether or not the will is at all concerned in a simple 
 
256 THE THEORY OF INFERENCE 
 
 act of assent, there seems to be little doubt that both it and 
 motives — desires, that is, and currents of constraint — have 
 often much to do with assent becoming, or not becoming, full 
 belief. The will, acting on behalf of itself and the system of 
 motives, appears to have some distinct power of controlling 
 the movements of the mind, and determining whether or not 
 it shall consider fully the evidence before it, and whether or 
 not it shall consider it impartially. It is sufficient here to 
 call attention to this seeming fact of mental life : there is no 
 occasion to dilate upon it. 
 
 THE END. 
 
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