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 A
 
 A NEW LOGIC
 
 THE MODERN 
 CRIMINAL SCIENCE SERIES 
 
 Eacli Volume Royal 8vo. 
 
 (I.) Modern Theories of Criminality. 
 
 By C. Bernaldo DE Quiros of Madrid. Piice 14s. net. 
 
 (H.) Criminal Psychology. 
 
 By Hans Gross, Professor of Criminal Law in the 
 University of Graz, Austria. Price 175. net. 
 
 (iii.) Crime: Its Causes and Remedies. 
 
 By Cesare Lombroso. Price i6s. net. 
 
 (iv.) The Individualization of Punishment. 
 
 By Raymond Saleilles, Professor of Comparative Law 
 in the University of Paris. Introduction by Gabriel 
 Tarde, Professor of Philosophy in the College of 
 France. Price i6s. net. 
 
 LONDON: WILLIAM HEINEMANN
 
 A NEW LOGIC 
 
 DY 
 
 CHARLES MERCIER, M.D., F.R.C.P., F.R.C.S 
 
 PHYSICIAN FOR MKNTAL DISEASES AT CHARING CROSS HOSl'ITAL ; EXAMINER IN 
 
 MENTAL DISEASES AND PSYCHOLOGY IN THE UNIVERSITY OF LONDON ; 
 
 AUTHOR OF CRIMINAL RESPONSIBILITY ; A TEXT-BOOK OF 
 
 insanity; PSYCHOLOGY, NORMAL AND MORBID 
 
 CONDUCT AND ITS DISORDERS ; CRIME 
 
 AND INSANITY, &C., &C. 
 
 ' The present system of Logic rather assists in confirming and 
 rendering inveterate the errors founded on vulgar notions, than in 
 searching after truth ; and is therefore more hurtful than useful.' 
 
 Bacon. 
 
 ' The Greek mind must have had some vital fault.' 
 
 Calverly. 
 
 ' My brethren, I beseech you, in the name of common sense, 
 to believe it possible that you may be mistaken.' 
 
 Oliver Cromwell. 
 
 LONDON: WILLIAM HEINEMANN: MCMXII 
 
 f\ ^^ Q f\ 
 

 
 « « « 
 
 Copyright London 1012 by William Heincmann
 
 
 To 
 SIR H. BRYAN DONKIN, M.A., M.D. Oxon. ; F.R.C.P., &c. 
 
 IN PLEASANT MEMORY OF THIRTY YEARS OF CLOSE FRIENDSHIP, 
 
 VARIEGATED BY MANY A STRENUOUS ARGUMENT, BEGUN, 
 
 CONTINUED, AND ENDED WITHOUT RECOURSE 
 
 TO THE SYLLOGISM
 
 I 
 
 PREFACE 
 
 <0 
 
 A BOOK on Logic by a practising physician is not calcnlated to 
 benefit its author, cither as a physician or a logician. His pro- 
 fessional brethren will look askance upon a physician who wastes, 
 N upon such a frivolous subject as Logic, time that might be 
 N devoted to increasing his knowledge of disease ; and logicians 
 't^ will regard him with the contemptuous abhorrence that is 
 \ bestowed, all the world over, by the professional upon the 
 ^N amateur. 
 
 In foro Medicines I have a valid defence, and need not throw 
 myself upon the mercy of the Court. Engaged daily in reasoning 
 on matters of vital, and more than vital importance, I find that 
 valid conclusions can be reached only by strictly departing from 
 V the methods of Traditional Logic ; and having studied the methods 
 by which I arrive at results that are, upon the whole, successful, 
 f^ I am bound by the salutary rule of my profession, to give to 
 the world the methods by which these results are attained. 
 Caadour will not allow me to ascribe the book wholly to com- 
 pliance with this beneficent rule. Upon reading the works of 
 logicians, and studying what has been said on the subject by 
 them of old time, I am moved by the same spirit that animated 
 long ago that sorry comforter of the man of Uz, when the words 
 ^ of his companions failed them. Great men, I found, are not 
 always wise, nor do men of antiquity always understand judge- 
 ment. 'Therefore I said hearken to me ; I also will show mine 
 opinion ; for I am full of matter, and the spirit within me 
 constraineth me. Behold, my belly is as wine that hath no vent ; 
 it is ready to burst like new bottles.' An enlarged knowledge of 
 physiology would ascribe the fulness to another anatomical 
 region, but broadly and generally the words express my motive. 
 
 But I have, in the Court of Medicine, a better defence than 
 this, even. It is many years since I began to preach the doctrine 
 that, in mental disorder as in bodily disorder, the study of order 

 
 viii PREFACE 
 
 is an indispensable preliminary to the study of disorder; the 
 study of the normal should always precede the study of the 
 morbid. In this I have been so far successful that the subject 
 of Psycholoj;:}- is now made a compulsory part of the curriculum 
 for every diploma in Psychiatry. This, however, is only a 
 beginning, and but stimulates me to further effort. Insanity is 
 disorder of conduct, and my next endeavour is to obtain for the 
 study of normal conduct the recognition that is now given to the 
 study of normal mind. And the Psychological aspect of mind is 
 not the only aspect of mind that is susceptible of disorder. The 
 power of reasoning logically is very often impaired in mental 
 disease ; and in this respect again, a knowledge of the normal 
 is an indispensable preliminary to a knowledge of the morbid. 
 Until we have an adequate and correct Logic, we cannot duly 
 appreciate or appraise the erroneous reasoning either of the 
 normal or the morbid mind. It was as a prolegomenon to the 
 study of Insanity that I was first moved to examine the Logic of 
 Tradition, and to substitute for it the New Logic that is here 
 propounded. 
 
 From the professional logician I can expect no mercy. I 
 have attacked his most cherished opinions, disputed his most 
 sacred dogmas, and have held up to derision his most revered 
 authorities. To him I am that most noxious of all vermin, the 
 irregular practitioner ; and I expect him to deal with me faith- 
 fully, after the manner of the orthodox to the heterodox. If 
 he would only restrict his choice of weapons to those that are in 
 the arsenal of Traditional Logic, I should rest in the complacent 
 security of a modern battleship attacked by bows and arrows ; 
 but no logician reasons syllogistically, except in the formal argu- 
 ments with which he illustrates the syllogism, and the arrows 
 that pierce me will be winged with feathers plucked from my 
 own logical tail. 
 
 Two subjects of academic study have been pursued con- 
 tinuously, as far as academic study has been continuous, from 
 the time of the great Greek philosophers of more than two 
 thousand years ago down to the time of the present generation. 
 One of these — Geometry — was taught, until yesterday, upon the 
 lines and in the words of Euclid. The other — Logic — is taught 
 to-day on the lines, and to a great extent in the words, of
 
 PREFACE ix 
 
 Aristotle, A few years ago, Euclid was formally superseded as 
 the authorised exponent of Geometry. His system was openly 
 attacked, was defended, was attacked again ; until it was formally 
 abandoned, and it is taught no more. The fate of Logic has 
 been different. Aristotle's system of Logic has never, I believe, 
 been openly attacked all along the line. It is true that, in the 
 thirteenth century, his works were proscribed and burnt by the 
 synod of Paris ; but this was owing to no destructive criticism 
 which found them fallacious. It was rather because their 
 tendency was heretical, and because they fostered the use of 
 reason, and so were subversive of authority. With this brief 
 exception, there has been no whole-hearted condemnation of 
 Aristotelian Logic ; and Aristotle is still regarded with a 
 reverence that almost savours of superstition. Aristotelian Logic 
 is still the subject of formal teaching and examination in every 
 University in the world. It still engages the learning of scholars 
 and the subtlety of dialecticians in every Western nation. It is / 
 expounded in innumerable text books, that still continue to issue 
 from the press, and run into edition after edition. But in 
 spite of its immense prestige; in spite of the professed allegiance 
 of innumerable eminent men ; in spite of its prominence in every 
 University; its position is undermined. Under the surface there 
 exists a profound dissatisfaction and distrust. Its very exponents, 
 in commending it to their readers, adopt an apologetic tone. 
 Those who have been through the mill, and have taken their 
 degrees in Arts, of which Logic is, in some Universities, an 
 important constituent, privately deride and contemn it. Its very 
 professors, though they cherish the Organon of Aristotle as a 
 sacred text, and contend that the errors and imperfections of 
 Traditional Logic, as taught in the text books, are due to their 
 departure from the pure teaching of Aristotle, yet, in so doing, 
 admit the errors and imperfections. In short, Traditional Logic 
 is now much in the position that was occupied, two hundred 
 and fifty years ago, by witchcraft. Without being formally 
 attacked, it is crumbling into ruin, and losing its hold upon the 
 minds of men. Modern Logicians, indeed, profess that they 
 disregard the old formulae, and give us a Logic that purports to 
 be new ; but it is new more by reason of lacking the clearness 
 and intelligibility of the old Logic than by any novelty of 
 doctrine. It still clings to the syllogism, and tries to put the new i
 
 X PREFACE 
 
 wine of scientific discovery into the old syllogistic bottle. The 
 exponents of Modern Logic represent, not so much the foundation 
 of a new school of Logic, as the despairing effort of the old to 
 defend the last ditch. 
 
 In these circumstances, it seems that if left alone, Aristotelian 
 Logic, and the whole fabric of Traditional Logic that is founded 
 upon it, will speedily perish ; and that it is scarcely worth while to 
 stuff a pillow into its mouth, and suffocate the dying creature; or 
 to deliver a coup de grace to one that is already moribund. It 
 seems, however, expedient to deliver a formal attack, and for 
 these reasons : — 
 
 In the first place, however few defenders Traditional Logic may 
 have in private, it yet occupies a very conspicuous and important 
 public position, to which it is, in my opinion, not entitled. It is 
 all very well to say that an attack on Traditional Logic is 
 slaying the slain, or, as one distinguished adviser put it, that it is 
 digging up a dead horse in order to flog it ; but there stares us 
 in the face the plain, indisputable fact, that Traditional Logic is 
 still a compulsory subject of study and examination for many 
 important and honourable degrees and distinctions ; and that 
 many innocent students, who have passed or failed in these 
 examinations, still believe, with pathetic confidingness, that the 
 syllogism is, as Whately called it, the Universal Principle of 
 reasoning. 
 
 In the second place, it is impossible to tell, as matters stand, 
 what the true position of Traditional Logic is, or how far those 
 who profess and call themselves logicians, are, in fact, followers 
 of Aristotle ; who is for him, and who indifferent to him ; how 
 far his hold is slipping away, and how far he still retains his 
 grip ; whether the worship of Aristotle is already extinct, or 
 whether there is still a remnant of true believers. 
 
 Lastly, my object is not solely, nor mainly, iconoclastic. I 
 propose, not merely to demolish the system of Traditional Logic, 
 but to substitute for it a new Logic, that shall supply the defects 
 and correct the errors of the old ; and it is not practicable to build 
 upon a site, until the ramshackle structure that already cumbers 
 the ground is cleared away. 
 
 For these reasons, I accompany my exposition of what I pretend 
 are the true principles of reasoning, by a running commentary of 
 criticism applied to Traditional Logic. I can scarcely suppose
 
 PREFACE xi 
 
 that anyone who is sufficiently interested in the subject to read 
 this book, will not already be acquainted with the system now in 
 vogue ; and it would not be practicable to establish my claim to 
 have formulated a new Logic, unless I compared it point by point 
 with the old. 
 
 The central doctrine of Traditional Logic is that all reasoning ai 
 is the bringing of particular cases under general rules : its insoluble 
 difficulty was to determine the way in which general rules are dis- i 
 covered. The debates of the Schools raged for centuries about 
 this subject. Three doctrines were held, and were discussed with 
 acrimony and obstinacy that sometimes terminated in bloodshed. 
 Are general rules, principles, or Universals, Universalia ante rent, 
 Univcrsalia in re, or Universalia post rem ? In other words, is the 
 Universal a noumenal Idea, having an hypostatised existence, not 
 only apart from the mind that conceives it, but antecedent to the 
 things in w-hich it is manifested ; or is it resident alone in the 
 things that manifest it ; or is it in the mind alone that conceives 
 it ? For generations these themes were debated, and on the view 
 taken of the nature of the Universal depended doctrines of the 
 most sacred and esoteric mysteries of the Church. At long 
 length, the utter barrenness of these discussions, and the proved 
 impossibility of arriving at any consensus by dialectic alone, led to 
 the Baconian reaction, which repudiated altogether the a priori 
 Universal, and so abhorred the very suggestion of such a thing, 
 that it refused to allow the legitimacy of an hypothesis even ; for 
 in hypothesis it smelt a savour of the a priori Universal. The 
 long severance of Logic from experience led to a reaction, in which 
 experience was to supersede Logic. Facts were to be collected — 
 this was the Baconian doctrine — and whatever agreements were 
 observed among facts, were to be taken for the true Universals. 
 The Baconian reaction was, in a sense, the triumph of the 
 Universalis in re. Not until more generations had passed, was it 
 discovered that agreement among facts will not be found, unless 
 expectation of agreement is taken to the facts — that the Universal 
 must first exist in the mind, before it can be found in experience. 
 This was the discovery of the Inductive School, whose apostles 
 were Herschell, Whewell, and J. S. Mill. Of course, the practice, 
 as distinct from the teaching, existed as far back as the dawn of 
 intelligence ; and was no more discovered by the prophets of 
 Induction, than grammatical speech was invented by the first
 
 xii PREFACE 
 
 grammarians ; but the Inductive School first taught the use and 
 value of hypothesis, and the function it performs in reasoning. 
 The dominance of this school was the triumph of the Universalis 
 post rem. 
 
 Of late years, a suspicion has arisen that the doctrines of the 
 Inductive School, true though they may be, do not cover the whole 
 ground. It is discerned, dimly, as I think, that there are other 
 ways, or there is another wa}-, of arriving at general rules, besides 
 that direct appeal to experience by the erection and testing of 
 hypotheses, which is the cardinal feature in the teaching of the 
 Inductive School ; moreover, there is an uneasy feeling abroad 
 that the Aristotelian scheme of Deduction does not say the last 
 word in its own department ; and this has led to the formation of 
 a fourth body of doctrine. Foreshadowed by Kant, founded by 
 Hegel, and developed by Sigwart, Lotze, Green, Bradley, Hodgson, 
 Bosanquet, and others. Modern Logic seeks to supersede both 
 Traditional and Inductive Logic. Its teachings, however, like all 
 the writings of its founder, are vague and nebulous. It expresses 
 dissatisfaction with what is, rather than a statement of what 
 should be. It is unable to emancipate itself from the tyranny of 
 the syllogism, and it fails to make itself generally intelligible. 
 When we find one of its exponents declaring that * as the 
 fundamental form of knowledge the judgement tends to overcome 
 change and to view phenomena sub specie csternitatis, and is in this 
 respect at one with Platonic "forms," ' it is evident that we are 
 here in the presence of an attempt to rehabilitate the Universalis 
 ante rem ; so strangely does the whirligig of time bring in its 
 revenges. 
 / My own position may be thus explained : — From Traditional 
 
 .' Logic I differ in every principle and in every detail. Its cardinal 
 j doctrine, that all reasoning is the subsumption of the particular 
 
 I under the Universal, was contested by Mill, who held that reason- 
 
 ing is from particular to particular, and I am not singular, therefore, 
 in disputing that ; but my quarrel with Traditional Logic is far 
 I wider and deeper than Mill's. In my opinion, its concepts of the 
 
 composition of the proposition, and of the constituent parts of the 
 proposition, are erroneous ; its doctrines of Quantity and Quality 
 are wrong ; its Immediate Inferences are but a poor few out of 
 , multitudes that may be obtained by an adequate Logic ; the few 
 
 \ Immediate Inferences it does obtain are faulty ; its doctrine of the
 
 PREFACE xiii 
 
 syllogism is artificial and mistaken ; the rules of the syllogism are 
 all wrong ; there are multitudes of Mediate Inferences that cannot 
 be reached by the syllogism ; Traditional Logic fails to distinguish 
 the argumentum in materia from the argiunentum ex poshdato, and 
 so involves itself in endless confusion ; in short, its whole system 
 is insufficient, defective, and erroneous, from beginning to end. 
 
 From the Inductive School — no one is now a pure Baconian* — 
 I differ no less profoundly. This school accepts the Deductive 
 scheme of Traditional Logic ; and in this I cannot follow it. It 
 supplements Deduction with Induction ; but its scheme of 
 Induction is, in my opinion, faulty. The Inductive logician . 
 recognises but one mode of appeal to experience — the direct appeal. 
 The indirect appeal, by which most of our arguments in materia 
 are conducted, he confuses with syllogistic reasoning, and in this 
 I hold that he is wrong. 
 
 Modern Logic I confess I do not understand. It is, by some of 
 
 its votaries, couched in a language beyond my comprehension. 
 
 They may emulate their master, Hegel, in the profundity of their 
 
 speculations : they certainly follow him in the obscurity of their 
 
 diction. When I am told that ' the fundamental activity of 
 
 thought ' is to be regarded ' as the same throughout and as always 
 
 consisting in the reproduction by a universal of a real identity, 
 
 presented in a content, of contents distinguishable from the pre-*' 
 
 sented content, which also are differences of the same universal,' 
 
 the words convey no distinct notion to my mind, and I am unable 
 
 even to discuss them. As far as I can understand it, Modern 
 
 Logic seems to me to range far beyond the realm of Logic. In 
 
 examining the nature of Judgement, Conception, and Perception, 
 
 it invades the domain of Psychology. In discussing the Infinite, 
 
 the Absolute, Abstract Quantity, and Necessity, it trenches on 
 
 Metaphysics. In treating of the nature of Law, of Causation, and 
 
 of a priori Truth, it encroaches on Philosophy. In investigating 
 
 the nature of Truth, of Knowledge, and the relation of Knowledge 
 
 to its postulates, it is in the realm of Epistemology. No doubt, 
 
 Logic touches at various points on all these subjects, as every 
 
 science touches on neighbouring sciences at various points ; but 
 
 * True at the time it was written, this is now not true. At the meeting of 
 the British Association that is bein^ held, as these proofs are being corrected, 
 the President of the Mathematical Section advocated a return to the pure 
 system of Bacon, though whether he mentioned Bacon by name, I don't 
 remember.
 
 xiv PREFACE 
 
 Logic has its proper boundaries ; and to obliterate the distinctions 
 between it and its neighbours, incurs the objurgations justly 
 applied to those who remove their neighbours' landmarks. 
 
 Nothing is said in this book of the Symbolic Logic of Boole, 
 Jevons, Venn and others. This is a kind of calculus. It rests 
 upon a confusion between the province of Logic and the province 
 of Mathematics. It is based upon the postulate, which seems to 
 mc completely erroneous, and far remote from fact, that every 
 proposition can be expressed as an equation. It is mathematics 
 gone mad. The utter illogicality of the whole scheme is put out 
 of doubt by the fact that the operations of symbolic Logic can be 
 conducted by machinery. This is materialism with a vengeance. 
 In fact, of course, all the thinking is done before the data are put 
 into the machine ; and all the machine does, and all Symbolic 
 Logic can do, is to add and subtract. Traditional Logic pretends 
 that all reasoning is inclusion in classes and exclusion from classes. 
 This is narrow enough, and shallow enough, goodness knows ; but 
 what is to be said of a Logic that reduces all reasoning to addition 
 and subtraction ? Poor as is my opinion of Traditional Logic, yet 
 if I had to choose between it and Symbolic Logic, I should plump 
 for the Logic of Tradition, which at any rate does not pretend 
 that cogwheels can reason. 
 
 In calling the system of Logic here propounded a New Logic, 
 I do not pretend that it is in every part wholly novel. Parts of it 
 have been anticipated, and parts have been adumbrated, by 
 previous writers. Mill, for instance, made the distinction between 
 the Logic of Consistency and the Logic of Truth ; Spencer 
 adumbrated the indirect appeal to experience that I call Mediate 
 Induction ; and perceived that the Aristotelian and Euclidean 
 Analogy is a reasoning process ; Hamilton adumbrated the 
 doctrine that Deduction is but the explication of what is implicit 
 in the premisses, and laid down, as others had done before him, 
 the rule that nothing may be concluded that is not in the 
 premisses ; Jevons, in his doctrine of Substitution of Similars, 
 anticipated one of the Minor Canons of Explication ; and no 
 doubt other instances of forestallment could be found. These, 
 however, are but fragments. They are details scattered here and 
 there. As an organised and coherent body of doctrine, covering 
 the whole field of reasoning, growing naturally from a single root, 
 and forming an harmonious and interdependent whole, the system
 
 PREFACE XV 
 
 here propounded is so different from all previous expositions as to 
 warrant the title I give to it, of A New Logic. 
 
 Though it is in principle new, I have of course incorporated 
 such parts of the old Logic as seemed sound ; and though my 
 system is new, I do not pretend that it is complete. Complete- 
 ness is not to be expected in a first essay, and I may adapt to it 
 an apposite exhortation of the Father of Logic with respect to his 
 first essay on another subject. ' Let this then be taken for a 
 rough sketch . . . since it is probably the right way to give first 
 the outline, and fill it in afterwards. And it would seem that any 
 man may improve and complete what is good in the sketch, and 
 that time is a good discoverer and co-operator in such matters. 
 It is thus in fact that all improvements in the various arts have 
 been brought about, for any man may fill up a deficiency ' 
 {Ethics: Book L, Chapter V.). By the time the New Logic has 
 stood two thousand years of commentary, its details may have 
 been filled in ; and then, no doubt, like its predecessor, it will 
 have had all the guts taken out of it, and will be ripe for super- 
 session by a better. 
 
 Here I must express the deep obligations under which I lie to 
 three friends who have assisted me with their criticisms. Mr. 
 Cannan, who read the first two drafts of the book, condemned it 
 unsparingly, and to his trenchant criticisms the book owes the 
 elimination of many crudities. Sir Bryan Uonkin, to whom the 
 book is dedicated, suggested a re-arrangement of the matter and 
 an important improvement in nomenclature, both of which I have 
 adopted ; and Professor Carveth Read has not only applied his 
 profound learning to the correction of sundry errors that my more 
 superficial acquaintance with the lore of Logic had allowed me to 
 fall into, but when I was taken ill suddenly, on the very day on which 
 the proofs began to issue from the press, he had the great kindness, 
 and the equally great courage, to undertake their correction for 
 me. It is difficult to express adequately a sense of obligation so 
 deep, but here I express, as well as I can, my gratitude, heaped 
 up, pressed down, and running over, for services so great and so 
 timely. 
 
 CHAS. MERCIER. 
 London, W,
 
 CONTENTS 
 
 PREFACE. 
 
 PAGE 
 
 Logic and Geometry, their similar history and dissimilar fate .... viii 
 
 The decay of Logic ix 
 
 Traditional Logic, its central doctrine. Universalia xi 
 
 Successive Schools of Logic : — the Baconian, the Inductive, the Modem, the 
 Symbolic. Differences between these and the New Logic, which is, 
 
 however, but a sketch xv 
 
 INTRODUCTION. 
 
 The Province of Logic : opinions of difierent writers i 
 
 Science and Art : their natures and relations 2 
 
 Logic is the Science and Art of the Proposition and of Reasoning ... 6 
 
 The origin of propositions — from Experience— from Hearsay — from Reasoning 8 
 
 The three processes of Reasoning, — Induction, Deduction, and Analogy . . 9 
 
 Outline of the book 13 
 
 BOOK I. 
 The Proposition. 
 
 CHAPTER I. 
 
 The Nature and Meaning of Propositions. 
 
 The function of words in reasoning 17 
 
 ' Verbal ' and ' Real " propositions, so-called 17 
 
 Insignificant, Defining, and Substantial propositions ig 
 
 Insignificant propositions : — Synonymous propositions. Unintelligible proposi- 
 tions, and Contradictions in terms 19 
 
 The Defining proposition 21 
 
 The Substantial proposition 21 
 
 The extra-mental reference of propositions 22 
 
 The Material and the Postulated propositions, the pabulum, respectively, of 
 
 Empirical and of Formal reasoning, which are again contrasted . . 24 
 
 Conclusions 28 
 
 N.L. b
 
 XVlll 
 
 CONTENTS 
 
 CHAPTER II. 
 Kinds of Propositions. 
 
 Incomplete and Complete propositions .... 
 Complete propositions : Categorical and .\nalogical . 
 Modal propositions : their exclusion from Logic is illogical 
 Modality of the Hypothetical proposition .... 
 
 The Compound proposition . 
 
 Summary- of kinds of propositions 
 
 PAGE 
 30 
 32 
 
 33 
 36 
 38 
 39 
 
 CHAPTER III. 
 
 The Constituents of Propositions. 
 
 The Aristotelian analysis of the proposition into Subject and Predicate 
 The Scholastic analysis into Subject, Copula and Predicate 
 The proposed analysis into Subject, Ratio and Object 
 Propositions in which less than three elements are expressed 
 F*ropositions in which more than three elements appear to be expressed 
 Rules for analysing propositions. Examples 
 
 40 
 40 
 42 
 43 
 
 45 
 45 
 
 CHAPTER IV. 
 
 The Ratio. 
 
 The Copula : its four meanings as declared by Logic 
 
 Assumptions of Traditional Logic with respect to the Copula 
 
 Examination and rejection of these assumptions 
 
 Relations expressible by the Ratio ........ 
 
 How Traditional Logic distorts the proposition to make it fit into the syllogism 
 Instances of unnecessary and vicious distortion of propositions . 
 
 The copula is ambiguous, and should not be used 
 
 Preliminary note on the Categories 
 
 53 
 
 54 
 55 
 56 
 57 
 58 
 64 
 65 
 
 CHAPTER V. 
 
 Terms, Their Origin and Kinds, 
 
 Quantity. 
 
 How terms are formed by the process of Syncrisis ..... 
 
 Generalisation, Classification and Abstraction 
 
 Definitions of Quality, Concrete, Attribute, Abstract, Connotation, Denotation 
 Concept, and Class .......... 
 
 Terms are divisible into Quantitative and Qualitative . . ; . 
 
 Table I. Primary Classification of Terms . 
 
 The Traditional doctrine of Quantity : its faults ..... 
 
 Quantification of the Predicate ......... 
 
 Quantification of the Object-term ........ 
 
 Hamilton's doctrine illogically rejected by logicians ..... 
 
 67 
 67 
 
 68 
 70 
 70 
 71 
 74 
 76 
 
 77
 
 CONTENTS 
 
 XIX 
 
 CHAPTER VI. 
 New Doctrine of Quantitv. 
 
 New doctrine of Quantity stated 
 
 Table II. General Scheme of Quantity 
 
 Table III. Scheme of Extensive Quantities 
 
 Extensive Quantities . 
 
 The Indesignate Quantity . 
 
 The Designate Quantity 
 
 The Distributive Quantity . 
 
 Table IV. Distributive Quantities 
 
 Uni%'ersal Distributive Quantities 
 
 The Particular Distributive . 
 
 Table V. Particular Distributive Quantities 
 
 The Forms of Quantity, Minimal, Maximal and Exact 
 
 The faults of the Traditional view of the Particular Quantity 
 
 Various meanings of ' Some ',..... 
 
 PAGE 
 
 80 
 81 
 82 
 82 
 
 83 
 
 85 
 85 
 
 86 
 
 87 
 88 
 
 89 
 90 
 
 91 
 95 
 
 CHAPTER VII. 
 
 Particular Distributive Quantities. 
 
 The Enumerative Quantity 
 
 The Indefinite Enumerative 
 
 The Semi-definite Quantity : its set of degrees 
 
 Semi-definite Enumerative Quantities 
 
 Arguments concerning this Quantity . 
 
 The Definite Enumerative Quantity . 
 
 Distinction between Logical and Arithmetical number 
 
 Proportional Quantity . ... 
 
 Indefinite Proportional Quantity 
 
 Semi-definite Proportional Quantity . 
 
 Definite Proportional Quantity . 
 
 Ordinal Quantity ..... 
 
 Indefinite Ordinal Quantity 
 
 Definite Ordinal Quantity . ... 
 
 Residual Quantity 
 
 Comparative Quantity .... 
 The Selected Quantity .... 
 The Indefinitely Selected Quantity 
 The Definitely Selected Quantity . 
 The Purposive Quantity .... 
 The Collective Quantity 
 
 98 
 
 98 
 
 99 
 100 
 102 
 103 
 103 
 105 
 105 
 105 
 106 
 108 
 108 
 108 
 log 
 III 
 112 
 "3 
 "3 
 "5 
 116 
 
 CHAPTER VIII. 
 
 The Individual. The Singular Quantity, 
 
 The Unit Individual : difficulty of defining an individual . 
 The Individual is a conceptual creation .... 
 Kinds of Individuals. Simple and Compound Units 
 
 Table VI. Kinds of Individuals 
 
 The Simple Individual ........ 
 
 120 
 121 
 1 22 
 123 
 123 
 
 6—2
 
 XX 
 
 CONTENTS 
 
 The Aggregate Individual . 
 
 The Corporate Individual . 
 
 The Uniform Individual 
 
 The Serial Individual . 
 
 The Singular Term 
 
 Table VII. Singular Terms 
 
 The Proper Name 
 
 The Definite Singular Term 
 
 The Indefinite Singular Term 
 
 The Representative Singular Term 
 
 Traditional Logic and the Singular Term 
 
 The Composite Individual . 
 
 PAGE 
 
 123 
 124 
 
 125 
 126 
 127 
 127 
 127 
 129 
 129 
 130 
 131 
 133 
 
 CHAPTER IX. 
 
 Intensive Quantity. 
 
 Table VIII. Intensive Quantities 
 
 Positive Degree 
 
 Table IX. Positive Intensive Quantities . 
 Arguments concerning Positive Degree 
 Comparative Degree ..... 
 The Indefinite Comparative 
 The Semi-definite Comparative . 
 Table X. Semi-definite Comparative Abstracts 
 Table XI. Semi-definite Comparative Attributes 
 The Definite Comparative .... 
 The Superlative Degree .... 
 The Purposive Degree .... 
 The Emphatic or Unexpected Degree 
 
 137 
 137 
 138 
 138 
 139 
 139 
 139 
 140 
 140 
 141 
 142 
 143 
 143 
 
 CHAPTER X. 
 
 Comprehensive Quantity. 
 
 Classification. 
 
 Class Quality 
 
 Class Property 
 
 Generic Quality ........ 
 
 Generic Property ....... 
 
 Individual Property and Difference, and Class Accident 
 
 Specific Difference and Accident of the Genus . 
 
 Description, Identification and Definition 
 
 Table XII. Comprehensive Quantities 
 
 The Predicables . • . 
 
 Table XIII. Terms ... 
 
 Classification or Differentiation . 
 
 The reference of Classification 
 
 The steps and requisites of Classification 
 
 144 
 
 144 
 144 
 
 145 
 145 
 145 
 145 
 146 
 146 
 
 147 
 148 
 
 150 
 151
 
 CONTENTS 
 
 XXI 
 
 PAGE 
 
 The Basis of Classification depends on the purpose in view .... 152 
 
 Dichotomy not a necessary principle .......•• i53 
 
 The nomen indefinitum . . . . . . . . • • ■ • I53 
 
 The fundamentum divisionis . . . . . . . . • • -154 
 
 The Categories .........•••• ^5^ 
 
 CHAPTER XI. 
 
 Negative Terms. 
 
 The Negative Proposition 
 Negative Terms . 
 The Privative Negative 
 The Limiting Negatives 
 The Exclusive Negative 
 The Exceptive Negative 
 Types of Negative Proposit 
 The Duplicated Negative 
 Incongruity of Terms . 
 The Excluded Middle 
 The Infinite Negative . 
 
 ons 
 
 159 
 159 
 160 
 i6i 
 162 
 
 163 
 1G4 
 166 
 166 
 1G7 
 i6g 
 
 CHAPTER XII. 
 Modes of Denial. 
 
 Pre-negative Affirmation 
 
 Modes of Denial .... 
 
 Inconsistency of Quantitative Terms 
 
 Denial of the Singular Quantity . 
 
 Denial of the Collective Quantity 
 
 Denial of the Universal Distributive 
 
 Denial of Particular Distributives 
 
 Denial of the Minimal Particular 
 
 Denial of the Maximal Particular 
 
 Denial of the Exact Particular . 
 
 The Traditional Square of Opposition 
 
 Square of Opposition of Maximal Distributives 
 
 Square of Opposition of Minimal Collectives 
 
 Square of Opposition of Maximal Collectives 
 
 Square of Opposition of Comparative Quantities 
 
 Square of Opposition of Residual Quantities 
 
 Square of Opposition of Purposive Quantities 
 
 Inconsistency of Qualitative Terms . 
 
 Singly Unlimited Qualities . 
 
 Doubly Unlimited Qualities 
 
 Singly Limited Qualities 
 
 Doubly Limited Qualities . 
 
 Ingraduate Qualities . 
 
 The Traditional Modes of Denia 
 
 Inconsistency of Ratios 
 
 their inadequacy 
 
 171 
 172 
 172 
 173 
 
 174 
 175 
 175 
 176 
 176 
 177 
 177 
 178 
 179 
 179 
 I So 
 180 
 181 
 1S2 
 182 
 182 
 
 183 
 183 
 184 
 184 
 187
 
 XX 11 
 
 CONTENTS 
 
 BOOK II. 
 
 Empirical Reasoning. 
 
 CHAPTER XIII. 
 Empirical Reasoning. 
 
 Experience is the ultimate source of all thoughts 
 Meaning of Experience ....... 
 
 Scholastic Logic ignored the appeal to experience 
 The function of Induction is to solve problems of all kinds, n 
 only .......... 
 
 The crude effort of Modern Logic to appeal to experience 
 Reference to reality is not necessarily made by a proposition 
 The Problem : its nature : examples : mode of statement . 
 The scope and definiteness of problems .... 
 
 The modes of solving problems are two only 
 
 The Direct and the Indirect appeals to Experience 
 
 The Direct appeal is often impracticable .... 
 
 ot of 
 
 Causation 
 
 PAGE 
 
 191 
 191 
 
 192 
 192 
 
 193 
 194 
 
 195 
 
 196 
 
 197 
 198 
 198 
 
 CHAPTER XIV. 
 
 The Indirect Appeal to Experience. 
 
 Method of the Indirect appeal to Experience — finding a premiss by means of a 
 
 Datum 201 
 
 The Nature of Induction 202 
 
 Differences between Induction and Syllogism 203 
 
 Differences between Induction and Deduction 204 
 
 Constancy in experience is the ground of Induction 207 
 
 The Canons of Induction ........... 210 
 
 The First Canon. Constancy in experience is the Universal of Inductive 
 
 reasoning ............. 210 
 
 The Second Canon. The Datum 216 
 
 The Terms of the Datum must be alike in respects material to the argument . 219 
 
 ' Essential ' in Logic means ' Material to the argument' 219 
 
 The Third Canon. The Identical Homologues 219 
 
 The Identical Homologues are not a middle term 220 
 
 The Fourth and Fifth Canons. The Quaesitum 220 
 
 How the Quaesitum is obtained .......... 221 
 
 The Sixth Canon : forbids unwarranted assumptions 223 
 
 Nature and conditions of Induction 224 
 
 CHAPTER XV. 
 
 Imperfect Induction. 
 
 Induction may be imperfect without being fallacious 225 
 
 Four imperfections are possible .......... 225 
 
 1. No Datum may be obtainable, the problem cannot then be solved . 226 
 
 2. The Datum may yield no premiss, and again the problem cannot be 
 
 solved 227
 
 CONTENTS xxiii 
 
 PAGE 
 
 3. The Datum may be approximate only, and the conclusion of the Induction 
 
 is an Hypothesis ........... 228 
 
 4. The Premiss may not be constant in experience ; the conclusion is 
 
 then a Conjecture ........... 232 
 
 Imperfect Induction is wrongly called Analogy by logicians .... 234 
 
 Essential likeness, means likeness for the purpose of the argument . . . 236 
 
 Criticisms anticipated and answered 239 
 
 BOOK III. 
 
 Inference or Deduction. 
 
 The Method of Explication. 
 
 CHAPTER XVI. 
 
 Implication and the Laws of Thought. 
 
 Immediate Inference is the explication of what is implied in Simple Pro- 
 positions ............. 245 
 
 Mediate Inference is the explication of what is implied in Compound Pro- 
 positions ............. 245 
 
 An implication of a proposition is the result of contemplating from a different 
 
 point of view the relation expressed in the proposition .... 246 
 
 Otherwise, the implications of a proposition are the direct answers to questions 
 
 that are answered indirectly by the proposition ...... 247 
 
 The Laws of Thought are said to be Natural Laws ...... 249 
 
 They are said also to be behests ......... 250 
 
 Statements of the Laws of Thought ......... 251 
 
 Accepted meanings of the Laws of Thought ....... 252 
 
 Mr. Bosanquet's meaning of the first Law of Thought ..... 253 
 
 The Laws of Thought are not Laws of Thought ...... 254 
 
 They are valueless as guides to Inference ........ 255 
 
 CHAPTER XVII. 
 
 The Canons of Inference. 
 
 The Postulated proposition 
 
 The License to Postulate has but one limitation — the Self Contradictory 
 The First and Second Canons of Inference ..... 
 
 Hamilton's adumbration of this Canon 
 
 Meaning of ' Formal ' Logic ........ 
 
 Reference to reality in the postulated proposition 
 
 The Third Canon of Inference : — A postulate, once granted, must not be 
 
 drawn or ignored in the argument ...... 
 
 The Fourth Canon of Inference: — Nothing may be assumed that is not 
 
 postulate 
 
 The Fifth Canon of Inference : — When a postulate is granted, all its im 
 
 tions are granted .......... 
 
 The petitio piincipii is necessarily present in deductive reasoning 
 
 with- 
 
 n the 
 plica- 
 
 256 
 259 
 259 
 259 
 260 
 261 
 
 2G2 
 
 264 
 
 264 
 265
 
 XXIV 
 
 CONTENTS 
 
 CHAPTER XVIII. 
 
 Immediate Inference. 
 
 The Implications of Simple Propositions. 
 
 PAGE 
 
 The Canons of Explication of Simple Propositions ...... 267 
 
 The First Canon : — Every postulate implies every equivalent and included 
 
 proposition 268 
 
 The first Minor Canon : — Every postulate implies its reciprocal . . . 268 
 
 Contrast of the Reciprocal with the Converse ....... 269 
 
 Defects of the Converse ........... 270 
 
 The rules for conversion are faulty. Many propositions cannot be converted. 
 
 Some converses are nonsensical ......... 272 
 
 Conversion of the O Proposition 274 
 
 The second Minor Canon : — The Substitution of Similar Ratios . . . 275 
 
 The third Minor Canon : — The Substitution of Similar Terms .... 276 
 
 (a) Substitution by an equivalent term 276 
 
 (b) Substitution by an included term ........ 279 
 
 (c) Substitution by an implied term ........ 280 
 
 The Second Canon of Explication : — Every postulate implies everything neces- 
 sary to the postulate ........... 283 
 
 The Third Canon of Explication : — Every postulate denies and is denied by 
 
 everything inconsistent with it ........ . 285 
 
 The fourth Minor Canon : — Denial of inconsistent Ratios .... 286 
 
 The fifth Minor Canon : — Denial of inconsistent terms 286 
 
 The Obverse, its imperfections .......... 288 
 
 The sixth Minor Canon : — Denial of inconsistent implications .... 289 
 
 The Inverse, its invalidity ........... 290 
 
 The seventh Minor Canon : — Denial of inconsistent conditions .... 290 
 
 Lotze's view of Contradiction .......... 291 
 
 Table XIV. The Canons of Explication ........ 293 
 
 Examples of Arguments unknown to Traditional Logic ..... 295 
 
 CHAPTER XIX. 
 
 The Compound Proposition and its Implications. 
 
 The Compound Proposition : its varieties .... 
 The premisses of a syllogism are a Compound Proposition 
 The Canons of Explication of Compound Propositions 
 The Compound Proposition with multiple Ratio 
 
 Implications of this Proposition 
 
 Value of the Compound Proposition .... 
 
 The Syllogism and the Method of Explication compared 
 
 Compound Propositions to which the Syllogism cannot be applied 
 
 The Argument a fortiori .... 
 
 The Axioms of Mathematics 
 
 Other such arguments .... 
 
 Further limitations of the syllogism . 
 
 Bringing the middle term into the conclusion 
 
 The Method of Explication has no figures or moods 
 
 Comparison of Explication with Reduction 
 
 The Method of Explication is self-evidently valid 
 
 The Rules of the Syllogism are erroneous . 
 
 297 
 298 
 299 
 300 
 301 
 303 
 304 
 304 
 305 
 305 
 309 
 310 
 
 313 
 314 
 315 
 317 
 i^7
 
 CONTENTS XXV 
 
 CHAPTER XX. 
 Fadlts of the Rdles of the Syllogism. 
 
 PAGE 
 
 The rule of three terms is unnecessary . . . . . . . .318 
 
 The rule of three propositions is unnecessary 319 
 
 The middle term need not be distributed ........ 322 
 
 The rule of distribution of terms is inadequate ....... 323 
 
 The rule against negative premisses is erroneous 324 
 
 The rule that a negative premiss necessitates a negative conclusion, and vice 
 
 versa, is erroneous ........... 325 
 
 The rule against particular premisses is erroneous 325 
 
 Examples of valid arguments that break the rules of the syllogism . . . 326 
 
 The syllogism is a mode of Explication, and a defective mode .... 329 
 
 The petitio principii of the syllogism ......... 330 
 
 The nine radical vices of the syllogism 333 
 
 CHAPTER XXI. 
 The Conditional Proposition and its Implications. 
 
 The Conditional Proposition ; its varieties 
 
 The Disjunctive Proposition : its ambiguity . . . ... 
 
 The Implications of Conditional Propositions 
 
 Why the Antecedent may not be denied, nor the Consequent affirmed uncon 
 ditionally ............ 
 
 Why the Antecedent may not be affirmed nor the Consequent denied 
 The Hypothetical Syllogism : a confusion of the Mode of Argument 
 
 334 
 335 
 338 
 
 339 
 339 
 340 
 
 BOOK IV. 
 Analogy, &c. 
 
 CHAPTER XXII. 
 
 Analogy. 
 
 The true meaning of Analogy 3^5 
 
 Analogy compares Ratios only, and ignores the meaning of the terms of the 
 
 sub-relations ,.= 
 
 Analogy and Proportion : Quantitative Analogy 346 
 
 Discernment of likeness and unlikeness is the basis of all reasoning . . . 348 
 
 Characteristics of Analogy 340 
 
 Instances of Analogy ............ 349 
 
 Completely and incompletely expressed Analogy ...... 350 
 
 Allegory, Simile, Metaphor, and Metaphorical expressions .... 351 
 
 Suggestion in Analogy : is not Inference 351 
 
 Uses of qualitative Analogy 3r3 
 
 Uses of quantitative Analogy 353
 
 XXVI 
 
 CONTENTS 
 
 CHAPTER XXIII. 
 Composite Reasoning. 
 
 All modes of reasoning grow from one root 
 But are distinct when developed ..... 
 
 And are often used alternately in the same train of reasoning 
 Examples .......... 
 
 PAGE 
 
 357 
 358 
 358 
 358 
 
 CHAPTER XXIV. 
 
 Fallacies. 
 
 Traditional Logic does not recognise that a fallacy must be a breach of some 
 
 rule of reasoning . 
 Nor does Modern Logic 
 The Fallacies of the Sopliistici Elenchi 
 Classification of Fallacies . 
 Fallacies in dictione 
 
 Equivocation .... 
 
 Bivocation .... 
 
 Amphiboly .... 
 
 Fallacies in Punctuation . 
 
 Fallacies of Accent and Emphasis 
 
 363 
 363 
 364 
 365 
 366 
 366 
 369 
 370 
 372 
 374 
 
 CHAPTER XXV. 
 Fallacies (continued^. 
 
 Fallacies Extra Didionem 
 
 Fallacies of Confusion of the Modes of Reasoning 
 The petitio principii in the syllogism . 
 Fallacies of Empirical Reasoning 
 
 Jumping to a Conclusion 
 
 The Accident 
 
 Non idem pro eodem .... 
 
 Indiscrimination .... 
 
 The Previous Question . 
 Fallacies of Inference or Deduction . 
 
 The Contradiction in Terms . 
 
 Neglect of the Purpose of the Argument 
 
 Ignoratio Elenchi .... 
 
 Non sequitur ..... 
 Fallacies of Analogy .... 
 
 The Fallacy of Assimilating the Terms 
 
 The Fallacy of Assimilating unlike Ratios 
 
 The Fallacy of Discriminating similar Ratios 
 Paradox . ... 
 
 Enumeration of Fallacies . 
 
 377 
 377 
 379 
 381 
 382 
 
 383 
 
 384 
 386 
 
 387 
 388 
 
 389 
 389 
 391 
 392 
 399 
 
 399 
 400 
 
 400 
 
 401 
 
 401
 
 CONTENTS 
 
 xxvu 
 
 CHAPTER XXVI. 
 Faults of the Existing Systems of Logic. 
 
 Uncertainty as to the Province and Functions of Logic 
 
 Confusion of the Modes of Reasoning 
 
 Erroneous doctrine of the Import of Propositions 
 
 Neglect of the Purpose of tlie Argument . 
 
 Irrational limitations of the scope of Logic 
 
 Erroneous analysis of the Proposition 
 
 Erroneous doctrine of the Copula 
 
 Confusion of the meanings of the Copula with the kinds of Subject 
 
 Definition of the Particular so as to include the Universal 
 
 The logical doctrines of Quantity and Quality are defective to the point of 
 
 ineptitude ....... 
 
 Logic lays down no rules for the conduct of reasoning except the Laws of 
 
 Thought, the Dictum, and the Canons of the Syllogism 
 Defects of these rules .......... 
 
 Logic knows of but four forms of Immediate Inference out of hundreds 
 
 The Immediate Inference of Logic is awkward, cumbrous, inefficient, and of 
 
 limited application ..... 
 Logic knows not of analogical reasoning, nor of the reasoning of mathematics 
 
 nor does it distinguish between logical and arithmetical quantity 
 Logic recognises but few of the fallacious modes of reasoning, and does not 
 
 refer the fallacies it does recognise to the breach of any rule of reasoning 
 The fault of Modern Logic — obscurity ....... 
 
 The fate of Traditional Logic — disuse ....... 
 
 PAGE 
 
 404 
 
 404 
 
 405 
 40G 
 
 406 
 406 
 407 
 
 407 
 
 410 
 410 
 410 
 
 411 
 
 411 
 
 412 
 413 
 415 
 
 APPENDIX. 
 
 A Classification of Sciences , 
 
 417
 
 INTRODUCTION 
 
 THE PROVINCE OF LOGIC 
 
 It is scarcely too much to say that, of the innumerable writers 
 on Logic, no two are agreed on what its subject-matter is, what its 
 limits are, or even whether it is a Science or an Art. Aldrich 
 regards it as the Art of Reasoning ; Mansel, as the Science of 
 Formal Reasoning ; Whately, as the Art and Science of 
 Reasoning ; the Post Royal logicians, as the Science of the 
 operations of the understanding in the pursuit of Truth ; Hamilton, 
 as the Science of the Necessary Laws of Thought ; Mill, as the 
 Art of Correct Thinking, and the Science of the conditions of 
 Correct Thinking; Bain, as a Theoretical or abstract Science, 
 the Practical Science of Proof, and a body of Method auxiliary 
 to the search for Truth. Of recent writers on Deductive Logic, 
 Prof. Carveth Read calls it the Science of Proof; Mr. Welton, the 
 Science of the Principles that regulate valid thought ; and Dr. 
 Mellone says that it deals with the principles that regulate valid 
 thought, and on which the validity of thought depends. Logicians 
 of the Modern School do not formally define the scope or province 
 of Logic. Mr. Bosanquet does say incidentally, in his second 
 volume, that * Logic is little more than an account of the forms 
 and modes in which a universal does or does not affect the 
 differences through which it persists,' but I find no other 
 indication of the province of Logic. Logicians are not agreed 
 even about the subject-matter of Logic. Some say it is 
 concerned with Propositions ; others that it treats of Concepts ; 
 yet others that its subject is Real Existence. Some say that 
 Logic is concerned w-ith the process only of thought, and is 
 regardless of results; others that it looks to results only, and is 
 regardless of processes. 
 
 In spite of this immense diversity of opinion as to what Logic is, 
 and what it treats of, all writers on Logic include much the same 
 subjects, and all writers on Traditional Logic treat them in much 
 the same way. The latter begin with a discussion on Names 
 
 N.L. B
 
 2 A NEW LOGIC 
 
 or Terms ; consider the Proposition as the unit of Logical 
 doctrine ; pass on, after discussing the various forms of 
 propositions, to their combination in the syllogism ; deal 
 exhaustively with the modes and figures of that venerable 
 institution ; and treat, as incidental or subsidiary subjects, of 
 Classification, Definition, and Fallacies. Some logicians treat 
 of Probability and Analogy also ; others do not. Modern text 
 books add, under the name of Induction, a consideration of the 
 means of ascertaining Causation, which I regard as somewhat of 
 an intruder into the domain of Logic. Writers on what is called 
 Modern Logic do not exclude these topics, but they treat them 
 as mere incidents in an examination of the fundamental nature 
 of Judgement, Conception, Inference, and so forth, and pay but 
 little attention to the Methodology of reasoning. 
 
 To write upon a subject without ascertaining the nature or 
 extent of the subject-matter, does not appear to me a very 
 reasonable or useful course ; and before discussing logical 
 doctrines, it seems best to settle what is meant by Logic, or, at 
 any rate, what meaning is attached to it in this book. 
 
 As has been shown above, writers on Logic are not agreed on 
 whether it is a Science or an Art, or both ; and although some are 
 of one opinion, and others of another, these opinions are not 
 usually fortified by reasons ; and Mill is, I think, the only writer 
 who discusses the nature and limits of Science and Art, or the 
 differences or relations between them. My own opinion on the 
 matter is as follows. 
 
 At the root, and as the motive, of all human endeavour, are 
 two fundamental, original, and consuming desires, — the desire to 
 know, and the desire to do. Curiosity is the foundation of all 
 Science ; the desire to exercise Capacity is the origin of all the 
 Arts. As soon as Curiosity and Capacity begin to be exerted, a 
 further desire comes into play. We desire to find out, and to 
 achieve other ends ; but we desire also, to find out, and to achieve 
 these other ends, with the least expenditure of exertion ; and we 
 soon find that, by acting, we assist Curiosity to attain knowledge; 
 and by knowing, we assist Action to do things easily and well. 
 As soon as anything attracts attention, we act in order to know 
 it better. We look at it, we move towards it, we touch it, handle 
 it, perhaps listen to it, smell it, and taste it. Thus, by the Art of 
 Investigation, we assist Curiosity to attain Knowledge, and the
 
 SCIENCE AND ART 3 
 
 knowledj:^e thus gained enables us the better to utih'sc for our 
 purposes the thing thus better known. So that knowledge 
 depends much on action ; and action depends much on knowledge. 
 In practice, the two are inseparable ; it is only by analysis that 
 we are able to separate them. 
 
 Knowledge, however, is not Science until it is organised ; and 
 action is not Art until it is methodised. Organising is a mode, 
 not of knowing, but of doing ; and hence Science cannot come 
 into existence without the practice of Art. Correspondingly, in 
 order to do an act at all, we must know how to do it ; and to do 
 an elaborate act we must be assisted by that organised knowledge 
 of the way to do it, that constitutes the methodology of the Art 
 in question. Thus knowledge and action depend on each other, 
 and grow up together into Sciences and Arts. Science cannot 
 come into existence without the aid of the Arts of Investigation 
 and Organisation ; nor can Science become elaborate or extended 
 without the aid of other Arts, such as Nomenclature, Description, 
 analysis, and so forth ; all of which may be called the Arts of 
 Science. 
 
 Arts express purposes, and strive after results. To achieve these 
 purposes and attain these results, the action, of which the Art 
 consists, must be adapted to the circumstances in which it takes 
 place, and which it modifies ; and first among these circumstances 
 is the subject-matter of the Art, or the material on which the Art 
 is exercised. For action to be successful, the circumstances in 
 which it takes place must be known ; especially must the 
 properties of the subject-matter be known ; and when the Art is 
 elaborate, it cannot treat its subject-matter to the best advantage 
 unless the knowledge of this subject-matter is organised into 
 Science. The art, for instance, of making objects of steel requires 
 an organised knowledge of the properties of steel. Thus, Science be- 
 comes the more necessary to Arts, as Arts become more intricate. 
 
 But Science aids Arts in other ways than by furnishing an 
 organised knowledge of their common subject-matter. Modes of 
 action are themselves subjects of investigation ; and the knowledge 
 of them thus attained may be organised into a Science, which 
 then raises the Technique of an Art into its Methodology' ; and 
 without such an organised knowledge of technique, the more 
 elaborate arts, such as that of working in steel, cannot be 
 profitably pursued. 
 
 B 2
 
 4 A NEW LOGIC 
 
 Lastly, the products of Art, no less than the subject-matter and 
 the methods, may be investigated, and may form the subject- 
 matter of a science ; and in this way arise the sciences of 
 Archaeology, of Architecture, of flint implements, of Philology, of 
 Numismatics, and so forth. 
 
 In several ways, therefore. Science is dependent on Art ; in 
 several ways Art is served by Science. Art and Science are 
 distinct, but inseparable. They are a happily married pair ; and 
 their numerous and vigorous offspring are of both sexes — the 
 products of arts, and extensions of knowledge. If Science is 
 organised knowledge, Art is systematic action ; and neither can 
 be attained without the other. 
 
 Science and Art differ, moreover, in this : — that to science, a 
 subject-matter is necessary ; but an art can proceed without a 
 subject-matter. There can be no knowledge without something 
 known, as distinguished from the knower ; but there may be doing 
 without a product, as distinguished from the doer. 
 
 The art of dancing, for instance, is not exercised upon any 
 material; produces no change in anything but the dancer: leaves 
 no result, except in him. Most arts, however, have their subject- 
 matter, on which the skill of the doer is exercised ; which is 
 changed by his exertions ; and whose changed form remains as a 
 permanent result of the exercise of the art. 
 
 Science regards its subject matter in two aspects. It considers 
 the nature of the subject-matter, its relations and its kinds ; and 
 analyses it into its constituent parts. This may be called the 
 statical aspect. Further, Science regards its subject-matter 
 in its time-relations. It investigates the ways and stages 
 by which the subject-matter became what it is, and forecasts, 
 if possible, what it will become- It treats of the history and 
 future of its subject-matter, and thus regards it in its temporal 
 aspect. 
 
 Those arts that have a subject-matter, alter this subject-matter 
 for the purpose of attaining results, and the methodology of the 
 art shows what alterations are best for the purpose, and how they 
 can best be achieved. Methodology, therefore, treats its subject- 
 matter in its dynamical aspect. 
 
 Applying these considerations to Logic, we are now in a position 
 to decide how it stands. Is it a science or an art? If it is a science, 
 what is its subject-matter ? If it is an art, what does it do ? What
 
 THE PROVINCE OF LOGIC 5 
 
 purpose does it serve, what results does it achieve, and how does 
 it attain them ? 
 
 In all modern text books, logic is divided into two separate 
 parts — Deduction and Induction. Deductive Logic has for its 
 subject-matter the proposition. It considers the nature of 
 propositions and their kinds; it analyses propositions into their 
 constituent parts, and describes them. Deductive Logic, as 
 commonly understood, is the science of propositions. 
 
 But Deductive Logic is an art also. All the examination, 
 description, and analysis of propositions is undertaken with a 
 view to showing how syllogisms may be constructed and inferences 
 deduced. The investigation of the structure and kinds of pro- 
 positions is merely a preliminary to the Methodology of Deduction. 
 Deductive Logic, besides being the pure science of the proposition, 
 is the methodology of Deduction, and the art of drawing inferences, 
 immediate and mediate. We have seen how close are the inter- 
 connections of Art and Science, and there is nothing improper or 
 confusing, therefore, in treating of both Art and Science in the 
 same book. 
 
 Inductive Logic, as expounded in the text books, treats of the 
 methods by which causation may be ascertained ; and of little or 
 nothing else. Mill's ' Canons of Induction,' which are the 
 foundation on which all subsequent writers have built their treat- 
 ment of Induction, are canons for the discover^' of causation. 
 Inductive Logic does not treat specifically of propositions, any more 
 than Deductive Logic treats of causation. The two departments 
 are entirely distinct ; and are different in subject-matter, in purpose, 
 and in treatment. The only connection between them is that 
 Induction seeks to show how those universals are found, that are 
 necessary to the process of Deduction. Inductive Logic is the art 
 of discovering causation. 
 
 Interspersed among these topics, we find, in text books of Logic, 
 chapters on Probability, on Classification, on Definition, on Nomen- 
 clature, on the Laws of Thought, on Hypothesis, and other matters. 
 For the most part, the connection of these topics with the science 
 of the proposition and the art of propositionising on the one hand, 
 and with the discovery of causation on the other, is not made 
 clear. Probability would seem to belong to Epistemology, and 
 the Laws of Thought to Psychology. The want of a definite under- 
 standing of the nature and limits of Logic, has led, so it seems, to
 
 6 A NEW LOGIC 
 
 the inclusion in it of topics foreip^n to the subject; and the fact 
 that no two books take the topics in the same order, indicates 
 that they are rather gathered together by somewhat haphazard 
 aggregation than the result of organic growth from a single root. 
 
 Modern Logic discusses much the same topics, but discusses them 
 from a difterent point of view, and rather psychologically than 
 logicalK'. The aim of Modern Logic seems to be to dive into the 
 deepest recesses of the mind, to search out the ultimate nature of 
 the processes concerned in judgement, and to do no more. It does 
 not, as Traditional Logic does, expound a Methodology of the 
 subject, or attempt to furnish rules by which reasoning may be 
 conducted. 
 
 In common use, 'logical' means 'consistent with reason'; 
 and, in the practice of logicians, both Traditional and Modern, the 
 main aim of the Art of Logic is undoubtedly to show how reasoning 
 is, and should be, conducted. Whatever attention is given to 
 other topics, such as Nomenclature, Probability, Classification, 
 and so forth, is given to them because they are contributory or 
 ancillary to the art of reasoning. For the purpose of this book, I 
 divide Logic into two primary departments, both of which have 
 the proposition for their subject-matter. The first department of 
 Logic is the Science and Art of the proposition ; it is an investiga- 
 tion of the nature, the kinds and the components of propositions, 
 and it is the Art of propositionising, or of expressing in verbal 
 propositions the thoughts we have in our minds. The second 
 department of Logic is the Science and Art of reasoning ; it is 
 an investigation of the ways in which new propositions can be 
 constructed out of old propositions already in our possession, and 
 it is the Art of constructing propositions from these materials. 
 The first Book is devoted to the Science and Art of the proposi- 
 tion, the remaining Books to the Science and Art of reasoning, 
 and in both cases the Science and the Art are treated concurrently. 
 
 The Science of the proposition and the Art of propositionising 
 have reached, in Logic as hitherto expounded, a very rudimentary 
 stage only. I do not pretend that I have treated them exhaus- 
 tively, but I have treated them fully ; and I regard the first 
 Book, in which these topics are dealt with, as equal in import- 
 ance to all the rest. The most important effect of the study of an 
 adequate and correct Logic may be expected to be the cultivation 
 of precision of statement ; which is more important even than a
 
 VALUE OF CLEAR EXPRESSION 7 
 
 knowledge of the processes of reasoning, for it is not only a more 
 desirable end in itself, but is also an indispensable preliminary to 
 valid reasoning. Aristotle seems to have realised this when he 
 included his fallacies in dictione among fallacies. Fallacies in 
 dictione are not mistakes in reasoning ; they are mistakes in state- 
 ment — in the statements on which reasoning is founded, and 
 which enter into reasoning. The prime value of the study of an 
 adequate Logic is in the cultivation of precision in the expression 
 of thought, by which thought is not only more clearly expressed, 
 but in the process is itself clarified and made precise. It can 
 never be too emphatically or too positively asserted that slovenly 
 expression means slovenly thinking. It is nowadays assumed, 
 as a matter of course, that obscurity of diction means profundity 
 of thought, the truth being the very reverse ; and the conspicuous 
 success of a few writers, in attaining celebrity by confused and 
 unintelligible utterance, has raised confusion of utterance into a 
 cult. It is time that this bladder was pricked, and that obscurity 
 of expression should stand exposed for what it is — the unpardon- 
 able literary sin. A writer whose meaning is not immediately 
 apparent on a first reading, is either muddleheaded, and in that 
 case is not worth reading ; or he is too lazy and slovenly to put his 
 meaning clearly, and in that case is offering his reader an insult ; 
 or he is trying to obtain a cheap reputation for profundity, and is 
 then contemptible. 
 
 No nobler instrument of expression than the English language 
 has ever been devised by the mind of man, which cannot con- 
 ceive a thought that this language is incapable of expressing. 
 It is eminently plastic, and not only takes readily to its ample 
 bosom new formations that are legitimately born, but adopts, 
 with almost regrettable facility, others that are marked with 
 an ineffaceable bar sinister. He who pretends that his thoughts 
 are too profound to be expressed intelligibly in the English 
 language must not count on always finding readers sufficiently 
 gullible to accept his pretension. Sooner or later he will be 
 called upon to stand and deliver his meaning, and if his wallets 
 are found to be empty, he will have no one but himself to thank 
 for his humiliation. 
 
 A self-respecting potter does not put on the market cups and 
 saucers that are out of shape, warped in the firing, or smudged in 
 colour ; a joiner would consider himself disgraced if he offered for
 
 8 A NEW LOGIC 
 
 sale a table or a bench with gaping joints, or legs out of truth ; 
 authors alone among craftsmen hold that it is no disgrace to utter 
 wares that proclaim aloud the unskilfulness, the carelessness, the 
 ignorance, of their maker. Such authors are to be blamed ; but 
 their fault is venial beside that of him who foists upon us a stale 
 loaf of bread, and gives us to understand that it is four-year-old 
 mutton, or even manna direct from heaven. An adequate Logic 
 is an Adulteration Act, that empowers us to take samples of 
 literary wares, to test them, to analyse them, and to stamp them 
 as what they are. 
 
 The remaining Books treat of the Science and Art of Reasoning 
 in propositions; and this art is exercised in three several ways. 
 
 ' The book is on the table.' By what means may I come into 
 possession of this proposition ? There are three ways. I may see 
 the book there ; I may get my proposition direct from experience, 
 by the evidence of sense — by perception. When I perceive the 
 book on the table, a relation is established in my mind between 
 the two things, and is given direct in experience. This relation is 
 expressed in the proposition 'The book is on the table.' It is true 
 that perception is a rudimentary process of reasoning ; but it is 
 not a process of reasoning as reasoning is understood in Logic. I 
 do not ' reason the matter out.' I do not arrive at the result by 
 the rearrangement or combination of materials already present in 
 my mind. It was presented to me ready made, and all I did was 
 to adopt it. If a jug slips out of my hand, falls on the floor, and 
 is smashed, I get, direct from experience, the proposition * The 
 jug is broken.' No process of reasoning is needed, and none is 
 employed. I get my proposition direct from experience ; and this 
 is one mode of origin of propositions. It is the ultimate origin of 
 all propositions, but it is outside the realm of Logic. 
 
 Another way of obtaining propositions ready made is to get 
 them from experience second hand. I ask where the book is, and 
 I am told it is on the table. I ask where the jug is, and I am told 
 the cat broke it. In both cases a new relation is established in the 
 mind, and is expressed in a proposition; but in neither case is it 
 established by reasoning. I do not form the relation by the 
 operation of my own mental exertion : I receive it ready made 
 from without : I get it by hearsay. I may exert reasoning to 
 decide whether to accept it or not ; but if I accept it, I accept it 
 ready made, and do not myself take any part in its establishment.
 
 THE NATURE OF REASONING 9 
 
 The process of attaining it, is a process, not of reasoning, but of 
 learning, and has no place in Logic. 
 
 It is the third mode of attaining propositions from experience 
 that alone belongs to Logic. This mode is the formation or 
 establishment of new propositions, by combining, dividing or 
 otherwise altering, without fresh experience, propositions already 
 present in the mind. I can get the proposition ' The book is on 
 the table ' in this way, without seeing the book there, or being 
 told that it is there ; and there are three ways of constructing 
 propositions by the activity of the mind working on materials that 
 it already possesses. 
 
 By the first of these processes I ask myself the question * Is 
 the book on the table ? ' If I seek to answer this question by 
 searching the table, I employ the direct appeal to experience, 
 which is not, strictly speaking, among the operations of Logic. 
 But I must have some experience ad hoc to go upon. I can 
 never solve this problem by interrogating my own inner conscious- 
 ness, and combining, dividing, and altering what I find there, 
 unless what I find is the memory of some experience of the 
 relation of the book to the table. But give me some experience 
 bearing on the relation of the book to the table, and even though 
 that experience may not directly give me the proposition * The 
 book is on the table,' I may be able to arrive at this proposition 
 indirectly, by the help of remembered experiences present in my 
 mind in the form of propositions. If, for instance, I see a parcel 
 on the table, and remember that I tied the book up in that parcel, 
 then, from the combination of that experienced proposition with 
 this remembered proposition, I can get the result * The book is on 
 the table.' If I know, by experience or by hearsay, that the jug is 
 made of glass, and has been dropped on the stones ; then, com- 
 bining this proposition with another, already present in my mind, 
 that glass things break when so dropped, I can obtain, by logical 
 process, the proposition ' The jug is broken.' 
 
 In the foregoing cases, the logical process is tied to experience, 
 and reasoning in which appeal to experience is an integral factor 
 forms the most important domain of Logic. But it is not the 
 only domain. We can, if we please, cut the string that ties us to 
 the ground of experience, and soar into the air of imagination. 
 The knowledge that we gain from experience may be severed 
 from experience more or less completely. It must always remain.
 
 TO A NEW LOGIC 
 
 in a sense, bounded by the limits of experience, for we can never 
 completely transcend experience, but in this sense the limits of 
 experience are extremely elastic. Without appealing to experience 
 at all, we may take components of propositions derived, as all 
 such components must ultimately be, from experience, and treat 
 them in various wa3'S so as to form new propositions, that may 
 or may not be consistent with experience. From * men ' and 
 ' immortal ' we can, if we choose, derive the proposition * Men 
 are immortal,' which is inconsistent with experience, it is true, 
 but still is a proposition, constructed according to the rules of 
 logical art, and susceptible of being modified in many ways in 
 accordance with those rules, so as to form new propositions, such 
 as ' Men do not die,' ' Men live for ever.' Or we can take a 
 proposition and divide it into components, still without any 
 appeal to experience. ' Men are mortal ' can be divided into 
 ' Some men are mortal and the rest of men also are mortal.' 
 Here we get two propositions out of one. Or we can combine 
 two or more propositions together, still without appealing to 
 experience of their subject-matter. From ' this man is English,' 
 ' that man is English,' and ' the other man is English,' we can 
 get the single proposition 'All three of these men are English.' 
 Or we can modify the construction of a proposition, still without 
 appealing to any experience of its subject-matter, and still be 
 proceeding according to the rules of logical art, as when we 
 change ' Men are mortal ' into * Men are not immortal.' These 
 are far from exhausting the modes in which new propositions 
 may be constructed in the department of logic that ignores 
 experience. As long as we are tied to the Logic of experience, 
 we cannot reason except of the things that experience presents to 
 us; but if we choose to leave this Logic behind us, we can 
 reason of whatever things our imagination is capable of picturing, 
 and even of any words we can form. We can reason about the 
 gods and creatures of heathen mythology, about the characters 
 of fiction, about infinity, eternity, and impossible quantities, and 
 all other kinds of imaginary things. 
 
 In all these efforts of reasoning we are bound by one dominant 
 rule. There is but one limit to our power and liberty of altering, 
 combining, and dividing propositions so as to form new ones, and 
 this is that the new must be consistent with the old. We may 
 alter, combine, divide, transform, and transmogrify a proposition
 
 THREE KINDS OF REASONING ii 
 
 in any way we please, so long as we preserve the consistency of 
 the product with the original. Hence this field of Logic is 
 sometimes called the Logic of Consistency. 
 
 There is yet a third method by which new propositions are 
 constructed by the art of reasoning. Two relations may be 
 compared, and may be discerned to be like or unlike ; and this 
 likeness or unlikeness may be stated in a proposition. It is 
 evident that this method of forming propositions is, like the last, 
 independent of any appeal to experience, and so differs from the 
 first mode of reasoning. It differs also from the second mode, for 
 it makes no alteration in the propositions it compares, nor does 
 it pay any regard to their consistency or inconsistency. It looks 
 to nothing but the likeness or unlikeness of the relations they 
 express. 
 
 The first of these three modes of reasoning is Empirical 
 Reasoning, so called because an appeal to experience is an 
 integral and indispensable part of the process. It is the Logic of 
 Discovery ; of Truth ; of Fact ; of Matter. It is coterminous 
 with Induction, as Induction ought to be understood ; but the view 
 that is here taken of the mode of discovering truth by Inductive 
 reasoning, is not the same as the prevalent doctrine of Induction, 
 though it is called by the same name. The true process of Induc- 
 tion seems to me very different from that which is usually so called, 
 as is explained in the second Book, which is devoted to this mode 
 of Reasoning. 
 
 The second mode of reasoning includes the Immediate and 
 Mediate Deduction, or Inference, of Traditional Logic, and it 
 includes a great deal more. The inferences deduced in the text 
 books from simple and compound propositions, are but a small 
 fraction of those that can be deduced by proper methods, which 
 are set forth in the third Book. The Logic expounded in that 
 book is the Logic of Inference ; of Consistency ; of Proof and 
 Disproof ; of Form. Useless in the discovery of Fact ; ignoring 
 the truth or falsity of the matter of which it treats ; its value is in 
 testing Consistency ; in argument ; in explicating ; convincing ; 
 refuting. This is the field of Traditional Logic. 
 
 The third mode of reasoning is the Logic of Analogy. As con- 
 cerned with qualitative relations, it aids neither Discovery nor 
 Proof. It is concerned neither with Fact nor with Consistency. 
 Its sole value is in explaining, expounding and enforcing statements.
 
 12 A NEW LOGIC 
 
 But as applied to quantitative relations, Analogy is one of the 
 most powerful engines in the hands of man. The largest and 
 most important part of mathematical reasoning is analogical. 
 Most of the operations of algebra and of geometry, and of their 
 higher developments, are reasonings by analogy ; and the higher 
 and more abstruse calculi are founded entirely on analogy ; which 
 has been strangely neglected by logicians. The reasonings of 
 Mathematics have always been excluded from Logic, and most 
 illogically excluded ; for, if Logic purports to be the Science and 
 Art of reasoning, it must show how all reasoning is conducted, or 
 confess its own inadequacy. The ground on which mathematical 
 reasoning has been excluded from Logic is, apparently, that Logic 
 does not include mathematics; nor does it. Nor does it include 
 chemistry, or protozoology ; but a Logic that pretends to be com- 
 plete must find a place for the modes of reasoning by which the 
 chemist and the protozoologist reach their conclusions ; and so it 
 must find a place for the modes of reasoning by which the 
 mathematician reaches his conclusions. By excluding Analogical 
 Reasoning from its purview ; or rather, by its incompetence to 
 recognise Analogical reasoning, as a mode of reasoning distinct 
 from Induction and Deduction, which alone it does recognise. 
 Logic has shut out from its cognisance a large, important, and 
 fertile field of reasoning, in which some of the greatest triumphs 
 of the human intellect have been achieved. It is true that many 
 logicians mention Analogy, and describe what they call analogical 
 reasoning, but this is, in their mouths, but another name for 
 Induction; and of Analogy in its proper sense, as defined by 
 Aristotle and Euclid, they are profoundly ignorant. 
 
 In actual practice, these three modes of reasoning, or any two 
 of them, are often combined, or rather alternated, in order to 
 arrive at results ; and a chapter is given to the modes of 
 combination. 
 
 In order to reason correctly by any of these methods, certain 
 Canons, or rules, appropriate to the method, must be observed ; 
 and the Canons appropriate to each method are stated in the 
 book that investigates that method. Violation of any of these 
 Canons results in fallacious reasoning ; and fallacy cannot be 
 committed in any other way than by violating or exceeding the 
 provisions of a rule. All the fallacies are collected together, and 
 set forth in separate chapters at the close of the volume.
 
 SCHEME OF THE BOOK 13 
 
 This, then, is the scheme of the work. The first Book is 
 devoted to an examination of the Proposition ; the second to 
 Empirical Reasoning ; the third to Inference or ExpHcatory 
 Reasoning ; and the fourth treats of Analogical Reasoning, Com- 
 posite or Combined Reasoning, and Fallacies; and concludes with 
 a summary of the main errors and defects of the Logic that is 
 now in vogue.
 
 BOOK I 
 
 THE PROPOSITION
 
 CHAPTER I 
 
 THE NATURE AND MEANING OF PROPOSITIONS 
 
 The subject-matter of the science and art of Logic is the 
 proposition ; and the proposition is the verbal expression of the 
 formation or establishment of a mental relation. 
 
 Words are not necessary to reasoning, and in fact an immense 
 number, perhaps the majority of our reasonings, are conducted 
 without the use of words, even of unspoken words. Without 
 formally expressing the judgements in words, we judge that the 
 book-case is too heavy to lift ; that the tea is too hot to drink ; 
 that the cab will come if whistled for ; that the door will be opened 
 if we ring the bell ; that if we go out in the rain we shall get wet ; 
 that the wind is too strong to put up the umbrella ; that it is too 
 far to walk in the time at our disposal ; that it is dangerous to 
 cross the street till the traffic thins ; and innumerable others. But 
 reasonings on abstract subjects usually require the use of words, 
 for the abstract is embodied in the word, and until so embodied, 
 it often exists vaguely only, and but half formed in the mind. 
 And reasoning that is not expressed in words must remain for ever 
 locked up in the mind of the reasoner. Logic, as the science and 
 methodology of reasoning, must be expressed in words ; and the 
 subject-matter of Logic is, as aforesaid, the verbal expression of 
 a mental relation; that is to say, the proposition. 
 
 Logicians distinguish between what they call * verbal ' proposi- 
 tions, and what they call ' real ' propositions. The nomenclature 
 is inappropriate in several ways, for ' real ' as applied to proposi- 
 tion, is used in several senses by logicians ; and ' verbal,' as a 
 distinction between some propositions and others, is clearly a 
 misnomer, for all propositions are expressed in words, and are 
 therefore verbal. Here, therefore, at the very outset of our logical 
 studies, we meet with a striking instance, the first of very many, of 
 the inaccuracy, looseness, and ambiguity with which words, the 
 material of their craft, are used by logicians. 
 
 * Verbal propositions,' like other terms of their art, are differently 
 defined by different logicians. Some call them ' Propositions that 
 
 N.L. C
 
 i8 A NEW LOGIC 
 
 appear to convey knowledge, but in reality do not.' Others 
 define them as ' Propositions from which we learn nothing,' 
 ' Propositions only by satisfying the forms of language, not by 
 conveN'ing a knowledge of facts,' and so forth. The instances 
 usually given are * A triangle is a rectilinear figure with three 
 sides.' ' The functions of an archdeacon are archi-diaconal 
 functions.' It may be admitted that such sentences as these 
 convey little knowledge ; that we learn little from them ; that they 
 are propositions only by satisfying the forms of language, and not 
 by conveying a knowledge of facts : all this may be true, but a 
 proposition may be ' real ' in the logical sense, and yet we may 
 learn nothing from it, and it may convey no knowledge of fact ; 
 a proposition may be * verbal ' in the logical sense, and yet convey 
 new and useful information ; and, in any case, the objection to 
 ' verbal ' propositions that they convey no information, that we 
 learn nothing from them, and that they convey no knowledge of 
 facts, comes strangely from logicians, who unanimously and 
 strenuously assert that the primary and fundamental law of all 
 thought is ' Whatever is, is,' or * A thing is identical with itself.' 
 
 That ' Rain falls from above ' and * A bird has feathers ' 
 are * real ' propositions in the logical sense, no logician would 
 dispute ; yet neither of these conveys any knowledge to anyone 
 who has ever been in the rain and seen a bird. We learn nothing 
 from them ; and they convey to us no information. But they do 
 satisfy the third definition or description of the ' real ' proposition ? 
 They do convey a knowledge of fact ? Yes, these particular ' real ' 
 propositions happen to do so, but let us take another, that no 
 logician will have the hardihood to deny is 'real' — 'Julius Caesar 
 is still alive.' Does this convey knowledge of fact ? ' Oh, but,' 
 says the logician, ' I don't mean fact in the same sense that you 
 mean it.' * My good friend,' is my answer, ' when people say 
 things, they are bound by what they say, not by what they mean. 
 If you meant something different from what you said, you should 
 learn to express your meaning accurately. If you use a word in 
 a sense different from its customary use, you must define the 
 sense in which you use it, or you must suffer the consequence of 
 having its customary meaning attached to it.' 
 
 On the other hand, ' A quadruped is a four-footed animal ' 
 would be acknowledged by every logician to be, in the logical 
 sense, a ' verbal ' proposition ; and }et every child who does not
 
 INSIGNIFICANT PROPOSITIONS 19 
 
 know the meaning of ' quadruped ' learns something from this 
 proposition. To him it conveys information, and a knowledge of 
 fact. 
 
 It seems clear that to say that a triangle is a three-angled figure, 
 or that the functions of an archdeacon are archi-diaconal functions, 
 is to use propositions that are * verbal ' in quite another sense than 
 that in which ' A quadruped is a four-footed animal ' is ' verbal ' ; 
 and in my view, propositions may be classified, with respect to 
 their significance, in the following way. 
 
 A proposition may express a relation between words alone, 
 without regard to their meaning. Such propositions may be 
 termed Insignificant. 
 
 Or it may express a relation between the meanings of words as 
 words, without more reference to the things to which the words 
 refer than is inseparable from the use of the words. Such a 
 proposition may be termed Definitive, or Defining. 
 
 Or it may refer primarily, not to the words, but to the things 
 named by the words ; and is then a Substantial proposition. 
 
 Insignificant Propositions. 
 
 These are propositions in which a relation is predicated between 
 words alone, without regard to the meanings of the words. 
 Strictly speaking, such propositions are not true propositions, 
 but bastard, pseudo, or quasi-propositions, since the relation such 
 a proposition purporte to express has no answering relation in the 
 mind. Since, however, such propositions are occasionally used 
 either legitimately, with full knowledge of their emptiness ; or 
 illegitimately, without appreciation by the user that they are but 
 empty forms of words, it is necessary to include them in an 
 enumeration of propositions. Insignificant propositions are of 
 three kinds, — the Synonymous proposition, the Unintelligible 
 proposition, and the Contradiction in terms. 
 
 The Synonymous Proposition. 
 
 This forms one kind of the propositions that are called verbal 
 by logicians. It is a proposition whose terms are synonymous on 
 the face of them, such as ' The functions of an archdeacon are archi- 
 diaconal ' ; ' Opium causes sleep by means of its soporific virtue ' ; 
 * A quadruped is a four-footed animal ' ; * A brighter light implies 
 increased luminosity.' In each of these quasi-propositions, there 
 
 c 2
 
 20 A NEW LOGIC 
 
 are two verbal terms, connected by a verbal indication of relation- 
 ship ; but as each of the verbal terms expresses the same concept, 
 there are not two mental terms, but one only; and a relation 
 cannot be established with one term only. A man cannot be a 
 father who has never had a child. A thing cannot be below if 
 there is nothing above it ; nor before, if nothing comes after. 
 The Synonymous proposition resembles the fraction ^, which is 
 no fraction, or the equation i = i, which is no equation, but 
 means, after all, no more than one. 
 
 A synonymous proposition is not insignificant if it is not 
 synonymous. That is to say, a proposition which is synonymous, 
 and therefore insignificant, to one person, who knows that the terms 
 are synonymous, is significant to another person, to whom the 
 terms were not synonj'mous until they were declared to be so by 
 the very proposition in question. To a child who does not know 
 the meaning of the term quadruped, the proposition, * A quadruped 
 is a four-footed animal ' is a significant proposition, because to 
 him the terms are not synonymous until they are made so by the 
 proposition. So the dictionary meaning of any word is a significant 
 proposition when it first becomes known, and thereafter is in- 
 significant. 
 
 The Unintelligible Proposition. 
 
 In this proposition or quasi-proposition, the terms are verbally 
 different, but as one or both of them have no answering concept 
 in the mind, the proposition resembles the fraction g, or the 
 equation = 0. ' Brillig is a slithy tove ' is an unintelligible 
 proposition. It has the form and appearance of a proposition, but 
 it is a pseudo-proposition only, for its terms represent no mental 
 concepts. The form is empty. So, ' A seafaring man is a 
 matross' is, to most Englishmen, an unintelligible proposition. 
 One term is significant, but the insignificance of the object-term 
 reduces the whole proposition to insignificance. 
 
 The Unintelligible proposition is insignificant so long only as its 
 terms remain without meaning, and to those only to whom the 
 meaning of its terms are unknown. * Ponos is Kala-azar' is to 
 you, reader, if you do not happen to know the meanings of both 
 the terms, an unintelligible proposition ; but to me it is significant, 
 because I happen to know the meanings of the terms. ' Brillig is 
 a slithy tove ' is unintelligible, I expect, to both of us.
 
 THE DEFINING PROPOSITION 21 
 
 The Contradiction in Terms, 
 
 This is another form of meaningless proposition which should 
 be enumerated among insignificant propositions. To say that 
 matter is immaterial, or that it can be sublimated until its 
 materiality is extracted ; or that we have a subliminal conscious- 
 ness of which we are not conscious ; or that lying is a distorted 
 way of speaking the truth ; or that there is a reality that is not 
 really real, but is a sham reality ; or to speak of the contents of 
 an empty vessel ; or of an irresistible force being applied to an 
 immoveable body ; are all contradictions in terms. These quasi- 
 propositions might be compared with the mathematical expression 
 I — I, which = o. They take away with one hand what they 
 have just given with the other. Subject and Object cancel one 
 another, and leave us with nothing. 
 
 The Defining Proposition. 
 
 This is the Synonymous proposition whose terms are not known 
 to be synonymous until the proposition is stated. The Synony- 
 mous proposition of one person is therefore the Defining proposi- 
 tion of another, and the Defining proposition becomes synonymous 
 as soon as it is known. The Defining proposition is the verbal 
 proposition of logicians. It defines the meaning of a word. The 
 subject of it is a word considered as a word, and not as the name 
 of a thing ; and it is the only form of proposition in which words 
 as words, and not as names of things, can stand as Subjects. It 
 is, therefore, as we shall find hereafter, the only form of proposi- 
 tion in which the Attributive term can stand as Subject. 
 
 The Substantial Proposition. 
 
 In the great majority of propositions, the subject is not a mere 
 word, standing as a word only, and merely defined as to its mean- 
 ing by the proposition, but is a word standing as the name of a 
 thing to which the word refers. With respect to this thing two 
 questions must be answered. P'irst, what is the nature of the 
 reference that is made to it in and by the proposition ? And 
 second, what is the nature of the predication that may be made 
 with regard to it ? 
 
 The different predications that may be made of the subject of a 
 proposition when that subject is Substantial, will be considered in
 
 22 A NEW LOGIC 
 
 their proper place when we come to examine the Ratio. But this 
 is the place to consider the reference of the proposition and of its 
 terms. 
 
 Every proposition expresses in words a mental relation, and is 
 treated in Logic, not as a form of words, but as the expression of a 
 thought ; but this statement does not clear up all the difficulties 
 connected with the meaning of the proposition. Granting that 
 the proposition expresses a mental relation, we have yet to deter- 
 mine whether this is all that it expresses. Does the proposition 
 express a relation in the mind alone, and does the reference of the 
 proposition end here ; or does it not also express a relation between 
 things having an existence outside of and independent of the mind, 
 which are represented in the mental relation ? When I state the 
 proposition ' Brutus killed Caesar,' this verbal proposition expresses 
 a relation in my mind — the imagination or idea of the killing of 
 Caesar by Brutus. All will agree to this : but there is a further 
 question. When I think of the killing of Caesar by Brutus, and 
 express this thought in the proposition, am I expressing merely 
 the thought in my mind, or am I not also expressing an historical 
 fact — that a real man, who had an actual existence outside and 
 independent of my mind, and was known to other real men as 
 Brutus, did actually kill another really existing man named Caesar ? 
 So stated, the problem admits of but one answer. The proposi- 
 tion expresses, not the idea of the killing of one mental idea by 
 another, but the real killing of a real man named Cassar by a real 
 man named Brutus. The answer is prompt, decisive, and clear, 
 and is given in favour of the Realists. But there is something to 
 be said for the Conceptualists, which seems to me to be 
 insufficiently appreciated by the exponents of Modern Logic, who 
 are, to a man, uncompromising Realists. In the judgement, ' Gold 
 is yellow,' says Lotze, * the logical subject is not the idea of gold, 
 but gold . . . the one idea is not predicated of the other.' 
 ' Judgement proper,' says Mr. Bradley, ' is the act which refers an 
 ideal content, recognised as such, to a Reality beyond the act.' 
 'Judgement,' says Professor Bosanquet, 'is the reference of a 
 significant idea to a subject in Reality by means of an identity of 
 content between them.' ' Our judgements express,' says Professor 
 Minto, ' beliefs about things and relations among things in reruni 
 naiiira ,• when anyone understands them, and gives his assent to 
 them, he never stops to think of the speaker's state of mind, but
 
 REFERENCE TO REALITY 23 
 
 of what the words represent.' These doctrines must be admitted 
 to be accurate, as far as they are intelligible — and I must confess 
 some difficulty in clearly apprehending the meaning of some of 
 them — as long as the subjects of the judgement are such known 
 and admitted realities as Brutus and gold. But suppose my 
 proposition is, not ' Brutus killed Caesar,' but ' A centaur killed a 
 phoenix.' How now ? Does the proposition now refer to reality ? 
 Does it mean that a real centaur, really existing in the real world 
 that we know, really killed a real phoenix ? Mr. Bradley, if I 
 understand him aright, says that it does ; and so does 
 Mr. Bosanquet ; but as to the latter, I cannot be sure, for in 
 another place he speaks of what is really real, as distinguished 
 from sham reality. Such expressions seem to me to darken 
 counsel ; but it is clear, or I think it would be considered clear by 
 anyone but a Modern logician, that the word * real,' as applied 
 to centaurs and phoenixes, must be used in some sense very 
 different from that in which it is applied to Brutus, and Csesar, 
 and gold. 
 
 There are here two distinct and different questions, which seem 
 to me to have been confused together by logicians of the Modern 
 School. The first question is Do we understand a proposition as 
 the expression of a relation in the mind alone, or do we not under- 
 stand it as having a further reference to things outside and beyond 
 the mind ? Do we understand the proposition ' Brutus killed 
 Caesar,' or ' A centaur killed a phoenix,' to express an imaginary 
 killing of the ideas of Caesar and the phoenix by the ideas of Brutus 
 and the centaur respectively, or do we not rather represent the 
 action of killing as taking place in the world outside the mind, 
 between the agents Brutus and the centaur, and the sufferers, 
 Caesar and the phoenix ? To my mind it seems that it is the last 
 question that must be answered in the affirmative; and that 
 Professor Minto is right in saying that we never stop to think of 
 the speaker's state of mind, but think only of what the words 
 represent. 
 
 The other question is a very different one. It is this : — Is the 
 reference to externality, which is admittedly contained in every 
 proposition, necessarily a reference to the real world of experience ; 
 or may it not be to an imaginary world, existing in the mind alone, 
 but referred to as if it were real ? It seems to me that the second 
 instance, of the death of the phoenix at the hands of the centaur,
 
 24 A NEW LOGIC 
 
 conclusively answers this question in the latter sense. I do not 
 see how it is possible to contend that the centaur and the phoenix 
 are real, in any known, understood, or admissible sense of the 
 word real; and when logicians of the Modern School speak of the 
 judgement as referring a 'content,' or a 'significant idea,' to a 
 ' Reality beyond the act,' it seems to me that they are either mis- 
 taken, or they are using the term Reality in some new and special 
 sense, which unfortunately they never define, and which includes 
 unreality. The want of any definition of this, the most important 
 term in their most fundamental doctrine, renders their whole 
 system unintelligible to the uninitiated. I can scarcely suppose 
 that the exponents of Modern Logic mean, by their reference to 
 Reality, that real centaurs or real phoenixes ever really existed in 
 the real world in which we live, though the expressions used by 
 these logicians may certainly be understood to imply that this is 
 what they do mean. If by reality they mean merely that reference 
 to externality or objectivity, which I agree and maintain is inherent 
 in every proposition and in every judgement, then I respectfully 
 agree with them, and regret that they do not express themselves 
 more clearly. 
 
 In my view, the position is this: — With respect to their external 
 or objective reference, there are two distinct kinds of propo- 
 sitions ; or psrhaps more accurately, propositions are understood 
 in two different senses. There is the material proposition, that is 
 understood and accepted as referring to real existence, to fact, to 
 an external world which is the world of experience ; and these 
 propositions are the basis of Empirical or Material reasoning. 
 This is the reasoning on which Conduct is founded. This is the 
 reasoning that determines our action. This is the reasoning by 
 which we solve the problems that confront us daily, hourly, and 
 momentarily in the world of experience in which we live. This 
 is the reasoning by which truths are discovered. The unit of such 
 reasoning is the ' real ' proposition — the statement of fact, of 
 truth — and, without such propositions. Empirical reasoning cannot 
 be conducted. To attain truth, we must start from truth. To 
 reach fact, we must base our reasoning on fact. Material reason- 
 ing is based on material propositions, and, to the validity of the 
 conclusions of this mode of reasoning, the truth of its premisses 
 is vital.
 
 POSTULATION 25 
 
 But Empirical reasoning is not the only mode of reasoning. 
 Besides the vast field of material reasoning, which is based solely 
 on fact, or on what we believe to be fact, there is another field of 
 reasoning of even greater extent ; w'ith which fact is in no way 
 concerned ; whose conclusions are unaffected by the truth or falsity 
 of their premisses ; in which any appeal to reality or to expe- 
 rience is out of place and irrelevant ; in which the propositions do 
 not refer to real existence, or to the world of experience, but to 
 postulated existence, and to a world which is objectified, it is true, 
 but may be wholly imaginary. This is the Logic of Postulation, 
 of Consistency, of Form, of Proof. In this mode of reasoning, 
 the proposition is postulated for the purpose of the argument. 
 It may be true or false ; it may be true of the world of experience, 
 or it may be wildly impossible or absurd ; but it is postulated for 
 the purpose of the argument ; and, being postulated, we may 
 argue from it as if it were true, and maintain the postulate of 
 its reality or truth in spite of experience, and as long as we 
 please, so that we remain detached from experience. But the 
 argument must be conducted throughout on the understanding 
 that the propositions are postulated only. They may or may 
 not be true in fact, but if they are, their truth adds nothing 
 to the force, cogency, or validity of the argument. They 
 may be manifestly false, impossible, inconceivable even ; but their 
 falsity, impossibility, or inconceivability detracts nothing from 
 the validity of the arguments that rest upon them. They are 
 postulated for the purpose of the argument, and for this purpose, 
 postulation is sufficient. 
 
 A proposition has been defined, by a recent writer, as * the 
 verbal expression of a truth or falsity ' ; and it is added that a 
 logical proposition implies belief in the statement made, and claims 
 assent. My concept of the proposition is the direct contradictory 
 of this. In my view there is an immense class of propositions 
 that are false, and are known and understood to be false, both 
 by those who utter and those who receive them, and yet are 
 strictly within the domain of Logic. There is another immense 
 range of propositions, whose truth or falsity is unknown to 
 and disregarded by the utterer, and whose truth or falsity is 
 utterly irrelevant to the arguments into which they may enter ; 
 but yet they may be the subjects of strict, valid, and useful logical 
 reasoning.
 
 26 A NEW LOGIC 
 
 ' The earth is larger than the sun ' is a proposition having a 
 definite meaning, and capable of entering into logical argument ; 
 but it does not, to me at least, imply belief in the statement made ; 
 nor do I, in making it, claim the assent of the hearer. Yet I can 
 argue from it, and deduce perfectly valid conclusions. If the earth 
 is larger than the sun, then the sun is smaller than the earth; 
 then the relative movements of the earth and the sun cannot be 
 what they are supposed to be. These arguments are valid. They 
 are irrefragable ; but their validity does not rest on the truth of 
 the premiss. They are equally valid whether the premiss is true 
 or false. 
 
 Mill also denies that a proposition must necessarily be either 
 true or false. He says that between and beyond the true and the 
 false, there is a third possibility — the Unmeaning ; and he gives 
 as an example ' Abracadabra is a second intention.' Mill seems 
 to have thought that unmeaning propositions are not susceptible 
 of logical treatment, but if he did think so, he was mistaken. We 
 can argue as easily, and as cogently, and with as complete validity, 
 from ' Abracadabra is a second intention ' as from ' All men are 
 mortal.' If Abracadabra is a second intention — I don't say 
 whether it is or not, nor do I care, but if it is — then one second 
 intention at least is Abracadabra ; then Abracadabra is not a first 
 intention, nor a third intention ; then it is not possible to deny 
 that Abracadabra is a second intention. All these are logical 
 arguments ; all are valid ; all follow of strict logical necessity 
 from the postulate ; none of them pays any regard to the meaning 
 of the postulate, or is in any way vitiated if the meaning of the 
 postulate is unknown. 
 
 Logic must pay regard to the objective reference of the propo- 
 sitions it employs ; but it need not pay regard to their truth or 
 falsity, unless the argument is a material argument. If the 
 argument belongs to the Logic of Consistency, this Logic must 
 not pay regard to the truth of its propositions. Chalk is harmo- 
 nious ; Whatever is harmonious is black; .'. Chalk is black. This 
 argument is nonsense. It is perfectly good in form, but it is 
 nonsensical on account of its matter. A logical argument must 
 be stated in propositions, and these arc not propositions, for they 
 have no answering relations in the mind. The argument is stated, 
 however, as a material argument, and as a material argument it is 
 absurd and nonsensical ; but if stated as a formal argument, it is
 
 POSTULATION 27 
 
 perfectly sound. Chalk is not, in fact, harmonious, nor, in fact, is 
 what is harmonious black ; but we may, for the purpose of argu- 
 ment, postulate or pretend that chalk is harmonious, and that 
 what is harmonious is black ; and then, on these postulates, we 
 may build an argument of consistency that is perfectly sound. // 
 chalk is harmonious, and if what is harmonious is black, then 
 chalk is indisputably black, and the inference is unescapable and 
 irrefragable. The postulates are false, indeed ; in fact, they are 
 nonsensical ; but of this falsity and nonsensicality the Logic of 
 Consistency takes no heed. As a material argument, the reason- 
 ing is silly, and worse than silly. As an argument from postulates, 
 or a formal argument, it is perfectly sound. In the argument of 
 consistency, our postulates may be false, or nonsensical, or merely 
 symbolic. We can reason, in this Logic, as readily and as 
 validly from ' If the earth is larger than the sun,' or * If chalk is 
 harmonious,' or ' If S is M,' as from * If men are mortal.' In 
 either case, Formal Logic will show you what is implied and in- 
 volved in your postulates, what are the consequences of your 
 postulation, and to what you committed yourself when you made 
 your assumptions. If your postulates are false, that is your affair. 
 In that case, you must not act upon the conclusions that formal 
 Logic attains ; or if you do so, you do so at your peril. Formal 
 Logic is a mill that will grind whatever you give it to grind, and 
 will turn out the grist in a form different from that in which it 
 was put into the mill. If you give it sound wheat, it will grind it 
 up into wholesome flour ; but if you give it canary seed, or linseed, 
 or hemlock seed, or even flints and broken glass, it will grind 
 them all impartially into flour ; and if you are foolish enough to 
 eat the grist, the consequences are on your own head. You must 
 not blame the mill. 
 
 Some adumbration of this doctrine seems to have been present 
 in the minds of those logicians who say that every categorical 
 argument may be stated hypothetically. This is an imperfect 
 half-truth. To state an Empirical or Material argument 
 hypothetically would be destructive of its nature. Hypotheses 
 often result from Empirical reasoning, and this mode of reasoning 
 is often undertaken for the very purpose of obtaining an 
 hypothesis ; but the premiss of an Empirical argument cannot and 
 must not be hypothetical. So to state the premiss would take the 
 argument out of the range of Empirical reasoning, and remove it
 
 28 A NEW LOGIC 
 
 into the realm of reasoning from postulation. But in the Logic of 
 consistency, the argument must be stated hypothetically ; or, if 
 not actually so stated, it must be understood that the premisses 
 are, in fact, hypothetical or postulated. The hypothetical form 
 is not, as Traditional Logic supposes, a mere alternative, that may 
 be adopted or not at pleasure ; and that, if adopted, merely fails to 
 vitiate the argument. It is vital to the mode of reasoning; and, 
 if omitted, is productive of one of the worst forms of fallacy — 
 the fallacy of confusion of the mode of argument, which will be 
 described in the chapter on fallacies. 
 
 Postulation of premisses, in the Logic of Consistency, is not 
 merely a duty ; it is not only a necessity ; it is also a very valuable 
 privilege. Postulation places at our command an immense realm 
 of reasoning that, without it, would be inaccessible. It gives us 
 control of that powerful engine, the rcdnctio ad absurdum. It enables 
 us to reason about things whose real existence is not only doubtful, 
 but impossible ; not only impossible, but inconceivable. It enables 
 us to reason, not only of the Regent's canal, but of possible canals 
 in Mars ; not only of the mounting of the forty-foot telescope, but of 
 the mounting of a forty-mile telescope ; not only of the square root 
 of four, but of the square root of minus one. It enables us to 
 argue what would happen if two straight lines should enclose a 
 space ; if space were of four or of forty dimensions ; if matter 
 were imponderable, and the ether impenetrable ; of frictionless 
 machines, rigid rods, perfect circles, infinitesimal quantities, infinite 
 series, and a thousand other things that are outside, or inconsistent 
 with experience. For the purpose of argument, there is but one 
 limit to the privilege of postulation ; and, for the purpose of 
 argument, the truth or falsity of our postulates is utterly beside 
 the question, and of no account. 
 
 This discussion of the nature and meaning of the Proposition 
 has led us, therefore, to the following conclusions : — 
 
 1. A proposition is a verbal relation. 
 
 2. The verbal relation expresses a mental relation, sometimes 
 called a Judgement, more accurately called a Thought. 
 
 3. The mental relation expressed by a proposition has an 
 objective reference, or refers to a relation conceived as existing 
 outside the conceiving or judging mind. 
 
 4. The external reference of the proposited or predicated relation 
 is of two kinds : —
 
 REFERENCE OF THE PROPOSITION 29 
 
 In one, the reference is to fact. The proposition expresses a 
 relation beheved to be true of real existence in the world of 
 experience, and the validity of the argument depends on 
 the truth of the proposition. 
 
 In the other kind of reference, the objective relation expressed 
 by the proposition is postulated for the purpose of 
 argument. It is not regarded as true or false in fact, and 
 its truth or falsity is irrelevant to the argument.
 
 CHAPTER II 
 
 KINDS OF PROPOSITIONS 
 
 The kinds of propositions distinguished by logicians are 
 numerous, including the Categorical, the Inferential, and the 
 Disjunctive; the Affirmative and the Negative; the Universal 
 and the Particular ; the Discretive, the Remotive, and the 
 Exponible ; the Analytic and the Synthetic ; and several others. 
 Those who are curious in the matter may be referred to the larger 
 text books for explanations of these terms, which appear especially 
 adapted for the purposes of examinations. Here I will confine 
 myself to a less complete enumeration, believing that those who 
 are interested in the subject, and are in the habit of paying 
 attention to modes of expressing thoughts, can easily work out 
 for themselves the varieties usually described. 
 
 For logical purposes, the most important distinction between 
 different propositions is that between the Incomplete and the 
 Complete. This is a distinction new to Logic, but it is one of 
 the greatest importance. An Incomplete proposition is, as its 
 title implies, a proposition of which an element is missing. Every 
 proposition expresses a relation ; and, as we shall find further on, 
 a relation consists of three elements — two related terms, and the 
 ratio which expresses the relation between them. Any one of 
 these elements may be missing. Taking as the type the generalised 
 proposition * A is B,' there may be missing from this proposition 
 the term A, the term B, or the ratio ' is.' But if a proposition 
 necessarily contains three elements, and if from a proposition one 
 element is missing, the two remaining elements are not a 
 proposition, but two incoherent and unrelated elements ? Not 
 necessarily. We may retain the form of the proposition, even if 
 one element is missing, by introducing in its place a dummy 
 element, that may serve to keep the proposition together, as a 
 proposition, until the missing element can be supplied, and 
 substituted for the dummy. Thus, in the proposition ' A is B,' 
 the term A may be missing ; but we can keep the proposition in 
 form until the missing element can be supplied, and at the same
 
 THE PROBLEM 31 
 
 time introduce a reminder that the term is missing, and needs to 
 be suppHed, by putting in place of the missing term the relative 
 ' what.' By this means we obtain the incomplete proposition, 
 What is B. Similarly, if B is missing, we can throw the incom- 
 plete proposition into the form, A is what. These are manifestly 
 questions, and should be characterised as questions by the addition 
 of the interrogation sign ; and we then get the incomplete 
 propositions. What is B ?, A is what ?, which at once preserve the 
 form of the proposition, and remind us that the proposition is 
 incomplete and clamours for completion. If the missing element 
 is the relational link that connects the terms together in a relation, 
 we cannot thus supply a dummy for it. A what B ? is not English, 
 and though no logician is ever deterred, by the hideousness of 
 an expression, from adopting it into his scheme, it behoves 
 A New Logic to show a better way, and aspire to better things. 
 Remembering, however, that the incomplete proposition may be 
 put in the form of a question, we can, when the link of the relation 
 is missing, throw the incomplete proposition into the form * Is 
 A, B ? ' or ' What is the relation between A and B ? ' 
 
 These are ways in which the missing element of a problem may 
 be supplied by a dummy, so that the form of the proposition may 
 be preserved ; but these are not the only ways. We may substi- 
 tute for the missing element the sign of the unknown ; and may 
 express the incomplete proposition X is B ; A .y B, or A is A', 
 which are the three forms that a Problem may assume. 
 
 The incomplete proposition is, in Logic, a Problem, and should 
 be known as a problem ; and the Problem is the foundation of 
 Material or Empirical Reasoning. The whole and only function 
 of Empirical reasoning, or Induction, is to solve problems by dis- 
 covering the element in them that is missing, and substituting the 
 discovered element for the dummy element. Induction, as 
 commonly understood in logical text books, is the discovery of 
 causation, and the discovery of causation by the direct appeal to 
 experience. Induction, as I understand it, is the supply of the 
 missing element in a Problem, whatever the missing element may 
 be; and whether it refers to causation, or to any other of the 
 thousand and one relations that we may desire to discover ; and 
 whether this element is supplied by the direct or by the indirect 
 appeal to experience, the logical process is still a process of 
 Induction.
 
 32 A NEW LOGIC 
 
 The first division of Complete propositions is made according 
 to the nature of their terms. The terms of a relation may be 
 simple, or they may themselves be relations. The generalised 
 form or type of the relation with simple terms is ' A is B,' or, 
 more generally, A : B. This form of proposition we will call P. 
 Instead of bringing an indivisible term B into relation with an 
 indivisible term A, we may, however, bring into relation two 
 terms, each of which is itself a relation, as when we say ' the 
 relation between a parson and his parishioners is like the relation 
 between a shepherd and his flock ' ; or ' the relation between 
 three and six is unlike the relation between seven and twelve.' 
 The generalised form, or type, of this kind of relation is ' a : 6 is 
 like (or unlike) c : d,' or ' {a : b) is like (or unlike) (c : d),' or '{a : b) : 
 (c : d).' Let us call this form of proposition Q. 
 
 It is manifest that if, in Q, we replace the term {a : b) by A, and 
 the term (c : d) by B, we get the proposition A : B, which is 
 identical with P. P and Q are therefore identical in form in 
 material respects, and differ only in the character of their terms, 
 which are simple or indivisible in P, and in Q are themselves 
 relations. In P, the terms are indivisible wholes ; in Q, they are 
 wholes discriminable into the three elements of which every 
 relation consists. Propositions of the type P are the propositions 
 of Deductive reasoning ; those of the type Q are the propositions of 
 Analogical reasoning. We thus find that each of the three modes 
 of reasoning employs its own form of proposition. The Problem 
 is the foundation of Inductive reasoning, and is used in Induction 
 alone. It has no place in Deduction or in Analogy. Propositions 
 of the type Q are analogical propositions, or analogies, and are 
 used in Analogical reasoning only. Propositions of the type P are 
 used in Deductive reasoning, and no other form of proposition is 
 employed in Deduction. Since, however, propositions of this 
 type are utilised in Induction also, it would be misleading to call 
 them Deductive propositions. They are known in Logic as 
 Categorical propositions. 
 
 Many forms of the Categorical proposition are distinguished in 
 Traditional Logic, some of the distinctions being important both 
 in that Logic and in this; some of them important in Traditional 
 Logic only ; and some of no importance at all. 
 
 In Traditional Logic, the utmost importance is attached to the 
 division of propositions according to their Quantity, into the
 
 MODAL PROPOSITIONS 33 
 
 Universal and the Particular. In the Logic here propounded, the 
 division on this ground has no place. I do not agree that 
 quantity inheres in the proposition at all. In my view, quantity 
 resides, not in the proposition as a whole, but in its terms, and 
 may be in either term, in both, or in neither. I do not agree that 
 quantity is limited to the Universal and the Particular; I think 
 the quantities of terms are many ; but my views on quantities are 
 set forth in the subsequent chapter on that subject, and need not 
 be given here. 
 
 Another of the great divisions of propositions made by Tradi- 
 tional Logic is that according to Quality ; and as this also has a 
 chapter devoted to it, I need not consider it here. All that need 
 be said now is that I differ in toto from the doctrines of quality 
 held by Traditional Logic. 
 
 The next great division of propositions made by Traditional 
 Logic is the division into Pure propositions and Modal proposi- 
 tions. Pure propositions alone are wittingly admitted into 
 Traditional Logic. For reasons that I am utterly unable to 
 appreciate, the Modal proposition is ejected and excluded from 
 Traditional Logic, which thereby condemns itself to inefficiency 
 and practical uselessness. 
 
 The Modal proposition is that in which an assertion or denial is 
 made, not simply, but cum modo — with a qualification. Originally, 
 the mode of a proposition meant the degree of certainty with 
 which the proposition was stated. Aristotle distinguished four 
 such modes, — Necessary, Contingent, Possible, and Impossible. 
 The logicians of the Schools extended the scope of modality, until 
 it included every conceivable form of proposition with the excep- 
 tion of an insignificant remnant ; and thus reduced Logic to 
 practical impotence, and went far to bring upon it the contempt 
 that it now enjoys. Mediaeval logicians regarded every modifica- 
 tion or qualification of the copula, however insignificant, as a 
 * mode ' ; and no modal proposition is susceptible of logical 
 treatment. To such lengths was this ridiculous formality carried, 
 that even the past and future tenses of the copula were excluded, 
 as modals, from logical argument. ' Caius is not truthful,' was, 
 according to Scholastic Logic, an admissible proposition. It could 
 form the ground of Inference ; it could enter into a syllogism ; it 
 could be converted, denied, contraposited, and subjected to all 
 the operations of logical art ; but ' Ananias was a liar ' was extra- 
 
 N.I,. D
 
 34 A NEW LOGIC 
 
 logical. It could not form a ground of Inference. Nothing could 
 be inferred from it, not even the useful and elegant deduction 
 that some liar was Ananias. It could not be subjected to any of 
 the operations that logicians performed upon propositions. Such 
 absurdities go far to account for the neglect with which Tradi- 
 tional Logic is treated by practical reasoners, and for the contempt 
 into which it is fallen ; and although even Traditional Logic does 
 not now countenance such nonsense,* its scope and range are still 
 artificially, and most unnecessarily restricted. The withered hand 
 of the Schools still stretches over it, numbing and paralysing its 
 usefulness. To be admitted within the sacred precincts of Logic, 
 to form the basis of any process of logical inference, a proposition 
 must still be purged of all suspicion of ' modality.' It must be 
 either apodeictic or assertory. It must affirm that A is necessarily 
 B, or deny without qualification that A is B. If the certainty and 
 assurance of the affirmation or denial is in any way impaired or 
 qualified, the proposition is cast out and rejected, and forbidden 
 the joys of the logical heaven. Things are seldom what they seem >' 
 You cannot often catch an old bird with chaff; He will probably 
 burn his fingers; It looks very likely to rain; They are almost 
 certain to win ; — all these are extra-logical. Traditional Logic will 
 have nothing to do with them. It is incapable of treating them. 
 It rejects them as impracticable and refractory ; and can draw no 
 conclusion from them, nor admit them as the ground of any 
 inference. Yet how continually, throughout life, have we not to 
 act upon inferences drawn from uncertainties ! If we could limit 
 our conduct to the guidance of certainty, how simple, and how 
 uninteresting would life not be ? ' Probability,' says Butler, ' is 
 the guide of life ' ; and of what earthly use is Logic if it does not 
 assist us in the guidance of life ? What else is reason for ? 
 
 The exclusion of Modals is but one of the ways in which 
 Traditional Logic has whittled away its subject-matter, till all the 
 flesh and blood are taken from it, and nothing is left but dry 
 bones; but it is perhaps the most comprehensive, the most 
 important, and the most vital omission. More than any other of 
 the futilities of Traditional Logic, it reduces an important and 
 useful machine to the dimensions of a useless toy. 
 
 I assert, and assert without fear of contradiction, that we can 
 
 • This is premature. I find that one authoritative text book still main- 
 tains this doctrine.
 
 MODAL PROPOSITIONS 35 
 
 argue, and do constantly argue, and what is more, we found our 
 conduct on the arguments, on grounds of all degrees of certainty 
 and likelihood, from * A is necessarily B,' though ' A is almost 
 certainly B,' to ' A is not likely to be B,' and 'It is scarcely 
 possible that A can be B.' On reasonings from such grounds we 
 act daily in the most important affairs of life. We buy and sell, 
 work and rest, travel and remain at home, marry and are given in 
 marriage, on the faith and on the strength of reasonings founded 
 on such propositions. To every one but a logician, it is 
 undeniable and indefeasible that as long as the qualification or 
 mode runs through the argument, and appears unweakened in the 
 conclusion, it does not affect the validity of the argument in the 
 least. If he is probably travelling abroad, he is probably not at 
 home. If it is very unlikely that he can walk a mile, it is very 
 unlikely that he can walk two. If he may or may not come this 
 way, we may or may not meet him. If he can scarcely get his 
 breath, he can scarcely be expected to sing. If it is almost 
 certain that he started too late, it is almost certain that he missed 
 his train. What is wrong with these arguments ? Not logical ? I 
 know they are not. That is my grievance. That is what I 
 complain of. What is the use of a logic that cannot compass 
 such elementary inferences as these ? If it is frankly admitted 
 that Traditional Logic does not profess to be of any use or value, 
 I have no more to say, except that it is high time we had one 
 that is ; but if Traditional Logic claims, as by the mouths of some 
 of its votaries it does claim, to furnish the Universal Principle of 
 reasoning, then I say that these instances are enough to demolish 
 that claim at once and for ever. 
 
 So far from Logic excluding from its purview the Modal 
 proposition, I maintain that a competent Logic must include all 
 forms and varieties of the Modal ; and even Traditional Logic, 
 which professes to exclude the Modal, cannot get on without it ; 
 and does, in fact, admit some forms of the Modal proposition, and 
 discusses them freely, and formally, and at length, without in the 
 least recognising their true nature, or appreciating that they are, 
 in fact, Modals. 
 
 ' A cannot possibly be B ' is, in Traditional Logic, an apodeictic 
 proposition, and as such, is admissible into Logic. *A may 
 possibly be B ' is a Modal, and as such is inadmissible. * A cannot 
 under any circumstances be B ' is apodeictic, and logical. * A is 
 
 D 2
 
 36 A NEW LOGIC 
 
 under some circumstances B ' is Modal, and extra-logical. Every 
 logician will, I think, agree to these statements. If, however, 
 'A is under some circumstances B' is modal and extra-logical, 
 can it be contended that it ceases to be modal if we alter ' some 
 circumstances' to 'these circumstances'? If 'A is in some 
 circumstances B' is Modal, does it cease to be modal if it is 
 altered into ' A is in these circumstances B ' ? If in the one case, 
 the assertion made in the proposition is qualified, and made 
 cum modo, is it not qualified in the other, and made ciim modo, in 
 that other also ? I can hardly suppose that even a logician would 
 make the distinction when the two cases are thus placed before 
 him. But if we are using a Modal proposition when we say ' A 
 is under these circumstances B,' is this proposition any the less 
 modal if we particularise the circumstances, and say ' A, provided 
 it is C, is B,' or ' A, whenever C is D, is B ' ? If these are not 
 Modals, if these propositions arc not stated with a qualification, 
 and cum modo, then it seems to me that the distinction between 
 the Modal and the Pure proposition disappears, and there is no 
 longer any such thing as a Modal. 
 
 But * A, provided it is C, is B ' may be written ' If A is C, it 
 is B,' and * A, whenever C is D, is B,' may be written 'If C is D, 
 A is B,' and these are the ordinary stock examples of the 
 Hypothetical proposition, given in every text book of Traditional 
 Logic. It is not true, therefore, that Traditional Logic excludes 
 all Modal propositions from its purview. It excludes those 
 Modals that it recognises as Modals, but it freely admits others 
 that it fails to recognise. If Traditional Logic chose to say 
 that the hypothetical proposition is a Modal sufficiently distinct 
 in construction from other Modals to deserve separate treatment, 
 I should have no quarrel with it on this ground, and no objection 
 to make; but this is not what it says. It says, ' Under no cir- 
 cumstances will I admit a Modal within my sacred precincts ' 
 and then, when a Modal presents itself under a disguise so thin 
 that any one but a logician can see through it in an instant. 
 Traditional Logic welcomes the impostor with open arms. 
 
 Otherwise put, the Modal is a proposition stated cimi modo — 
 with a qualification. Very well. To what element in the 
 proposition is the qualification attached ? Which element does it 
 qualify ? It certainly does not qualify the subject. If it did, 
 'All A is B,' and 'some A is B ' would be Modal propositions;
 
 MODAL PROPOSITIONS 37 
 
 and no logician would admit this. Nor does it qualify the 
 Predicate ; for if it did, ' Some men are moderately honest,' ' All 
 cornflowers are a particular shade of blue' would be Modal 
 propositions, which no logician would contend. The qualification 
 that converts a Pure proposition into a Modal, is a qualilication of 
 the copula. This is shown by the practice of considering those 
 propositions Modal in which the copula is in the past or future 
 tense, or in the first or second person. Any qualification of the 
 copula, therefore, changes the Pure proposition into a Modal. 
 Now the protasis of a hypothetical proposition is a qualification 
 of the copula. ' A (provided C is D) is B,' is qualified in the 
 copula, and in no other element. The qualification does not 
 attach to the subject A, nor to the predicate B. It attaches to 
 the copula, and qualifies the copula ; and any qualification of the 
 copula constitutes the proposition a Modal proposition. 
 
 The Hypothetical proposition is, therefore, a Modal proposition, 
 a conclusion that must carry consternation to the votary of 
 Traditional Logic, who has fondly thought that he had excluded 
 all Modals from his scheme of logical doctrine. To the Logic 
 here expounded, the admission, not only of the Conditional pro- 
 position, but of every other Modal, is not only legitimate, but 
 also necessary. This Logic professes to treat of every mode of 
 reasoning that is employed by the mind, and to pretend that we 
 cannot, or do not, reason except on grounds of apodeictic 
 certainty ; or that reasonings from certainties are conducted in a 
 manner in any respect different from that employed in reasoning 
 from likelihood or unlikelihood; is a contention that cannot be 
 admitted until it is proved. The onus of proof lies on those who 
 make the assertion. Logicians have excluded Modal propositions 
 from their scheme without rhyme or reason ; or rather, they have 
 professed and believed that Modals were excluded from Logic, 
 and yet have admitted one form of Modal, not knowing that it is 
 a Modal ; and have arbitrarily excluded the remainder, because 
 they would not fit in to the artificial and unnatural scheme of 
 reasoning that Traditional Logic supplies. In the inductive 
 portion of their scheme, logicians tell us that when it is found 
 that an hypothesis does not cover all the facts, that hypothesis 
 must be discarded. They admit, nay, they proclaim, that their 
 hypothesis of the mode in wiiich reasoning is conducted, does not 
 cover all the facts ; but do they on that account discard their 
 
 v-f .^ae ^ V ' v_/
 
 38 A NEW LOGIC 
 
 hypothesis ? They cling to it all the more tenaciously. Incon- 
 sistency is, to other reasoners, a vice to be condemned and 
 avoided. To logicians, it is a guiding principle. 
 
 Whether the Hypothetical or Conditional proposition is or is 
 not a Modal, is of great importance to Traditional Logic. To the 
 New Logic here expounded, it does not matter at all. What does 
 matter to both schemes is that the Conditional proposition is 
 sufficiently distinct from the ordinary Categorical to demand 
 separate treatment, and to be regarded as a distinct variety. 
 
 A third variety of the Categorical proposition, sufficiently distinct 
 to require separate treatment, is the combined or Compound 
 proposition, in which two or more propositions, having a common 
 element, are combined, and expressed as one ; as ' A and B are 
 both C,' ' A has been, will be, and is B,' * A is both B and C In 
 each of these cases, more than one relation is expressed, and there 
 is more than one proposition. The first contains the two proposi- 
 tions, ' A is C and B is C ' ; the second contains three propositions, 
 ' A has been B,' * A will be B,' and ' A is B ' ; the third contains 
 the two propositions, 'A is B ' and ' A is C In each case more 
 than one proposition is expressed in what purports to be a single, 
 if a compound proposition ; and the combination is more than a 
 mere artifice of language. It corresponds with a combination of 
 the relations in the mind, through and by means of the element 
 common to both. If there is no common element, no Compound 
 proposition can be constructed. * A is B, and B is C ' is a Com- 
 pound proposition, by virtue of the common element B ; but ' A 
 is B and C is D ' is not a Compound proposition, and cannot be 
 combined into a Compound proposition. 
 
 According to the scheme of Traditional Logic, there are two 
 primary kinds of proposition, the Categorical and the Hypo- 
 thetical ; but as it is admitted by all logicians that the Categorical 
 proposition may be expressed as an hypothetical, the distinction 
 breaks down in practice ; and, for practical purposes, there are, 
 in Traditional Logic, but four kinds of proposition, distinguished 
 by variations of quantity and quality in the Categorical proposition. 
 These kinds are as follows : — 
 
 The Universal Affirmative or A proposition — All A is B. 
 The Universal Negative or E proposition — No A is B. 
 The Particular Affirmative or I proposition — Some A is B. 
 The Particular Negative or O proposition — Some A is not B.
 
 KINDS OF PROPOSITIONS 39 
 
 For this classification, I substitute, in the Logic here pro- 
 pounded, the following : — 
 
 1. The Incomplete Proposition, or Problem — What is B ? 
 
 2. The Complete proposition with unified terms, or the 
 Categorical Proposition — A is B. 
 
 3. The Complete proposition with relations for terms, or the 
 Analogical Proposition — The relation between A and B is like the 
 relation between C and D. 
 
 Each of these forms of proposition is divisible into sub-varieties, 
 some of which are important, and some unimportant. 
 
 The forms of the Problem are three, according to the element 
 that is missing : — 
 
 a. The missing element is the Subject — What is B ? 
 
 b. The missing element is the Ratio — 7s A, B ? 
 
 c. The missing element is the Object — A is what ? 
 
 The forms of the Categorical Proposition also are three : — 
 
 a. The Categorical Proper — A is B. 
 
 b. The Compound proposition — A and B are both C. 
 
 c. The Conditional proposition — A is conditionally B. 
 
 The forms of the Analogical Proposition are two, according to 
 the nature of the relation : — 
 
 a. The relation of a to 6 is like the relation of c to d. 
 
 b. The relation of a to 6 is unlike the relation of c to d. 
 Further divisions of the Problem, and of the Categorical 
 
 proposition will come into view when we consider them separately 
 and in more detail.
 
 CHAPTER III 
 
 THE CONSTITUENTS OF PROPOSITIONS 
 
 The constituents of propositions are to be discovered by 
 analysis ; and propositions may be analysed in three ways, of 
 which the way of Traditional Logic is incomparably the worst. 
 
 Aristotle analysed the proposition into Subject and Predicate; 
 or the Subject, and that which is predicated concerning the 
 Subject. According to him, the propositions Man — is mortal, 
 A — is unequal to B, were thus divided. The division is a reason- 
 able and defensible division ; but it is not well adapted to logical 
 purposes, for it does not reveal the true structure of a proposition, 
 as the expression of a relation ; nor does it lend itself readily to 
 the operations of Inference. For instance, a proposition so divided 
 cannot be reciprocated or converted. If we attempt these opera- 
 tions we get Is mortal — man, and Is unequal to B — A ; which 
 are useless and nonsensical. 
 
 It may have been this insusceptibility to conversion, of the 
 Aristotelianly divided proposition, that led the Schoolmen to 
 devise another mode of analysing the proposition ; a mode that 
 has endured to the present day, and is taught in every text book 
 of Logic, although it is manifestly, radically, and incurably vicious. 
 The logicians of the Schools detached the copula from the pre- 
 dicate, and divided the proposition into three elements, still 
 retaining for the third element the title of predicate, although, 
 as a predicate, it is destroyed by the mutilation. According to 
 the Scholastic anal}'sis, the proposition consists of Subject, 
 Copula, and Predicate ; and is in the form Man — is — mortal, 
 A — is — unequal to B. It is manifest that, in this division, the 
 so-called predicates * mortal,' and ' unequal to B,' are not predi- 
 cates at all. They do not predicate anything of their subjects. 
 A predicate is no more a predicate after its copula is torn 
 away, than a man is a man after he has been beheaded. The 
 so-called predicate predicates nothing. 'Mortal' and 'unequal 
 to B,' tell us nothing about 'man' and 'A' respectively, until the 
 copula is added to them. Not until the copula is explicitly
 
 ANALYSIS OF PROPOSITIONS 41 
 
 stated do we know even whether it is affirmative or negative. 
 Mr. Bosanquet, as an exponent of Modern Logic, speaks of the 
 copula as a fiction, and declares that the proposition consists of 
 Subject and Predicate only; but whether he understands the 
 predicate in the Aristotelian sense, as incorporating the copula, 
 and so expressing all that is predicated of the Subject, or whether 
 he uses the word in the Scholastic sense, is not clear. In another 
 place he declares that Subject, Copula, and Predicate, are all of 
 them mere fictions. To this I do not agree. The division of the 
 Aristotelian predicate into copula and pseudo-predicate, is, unfortu- 
 nately, not a fiction. It is a patent and deplorable fact. The 
 fiction is that the division is a natural or logical division ; and if 
 this is what Mr. Bosanquet means when he says that Subject, 
 Copula, and Predicate are all mere fictions, I should agree with 
 him ; but as I scarcely ever know what he does mean, I always 
 hesitate to agree or disagree. 
 
 The Scholastic analysis of the proposition, into Subject, Copula, 
 and pseudo-predicate, does not even effect that convertibility of 
 the proposition that may be conjectured to have been its purpose. 
 Mortal — is — man is no converse of Man — is — mortal ; nor is 
 Unequal to B — is — A, an intelligible converse or reciprocal of 
 A — is — unequal to B. In order to obtain an intelligible converse 
 of a proposition so divided, it must be further manipulated and 
 transmogrified, and then all we can obtain is ' Some mortal is 
 man ' and ' Something unequal to B is A,' propositions which no 
 one but a logician would ever dream of devising, and which not 
 even a logician could find any use for, outside of his text book, or 
 the examination room. If it is permissible to make the Scholastic 
 division of 'A is equal to B' into A — is — equal to B, I see no 
 reason why it may not be divided into A — is equal — to B. The 
 Scholastic division yields a converse, Equal to B — is — A, which is 
 nonsense; but it yields no reciprocal. The other division yields 
 not only a nonsensical converse, * To B is equal A,' but a 
 nonsensical reciprocal also — ' To B equals A ' — and is therefore, 
 presumably, superior. 
 
 One merit, however, the Scholastic division of the proposi- 
 tion does possess. It does indicate, erroneously and imperfectly 
 it is true, but it does indicate the structure and nature of 
 the proposition, as the expression of a relation. A relation 
 must contain three elements ; and the Scholastic division of the
 
 42 A NEW LOGIC 
 
 proposition does yield three elements, in place of the two of the 
 Aristotelian division. The two elements of the Aristotelian 
 division, do, however, correspond with a real division in the sense 
 and meaning of the proposition. The three-fold division of the 
 Schools does not correspond with any partition in the meaning. 
 
 Every relation must contain three elements. It must contain 
 two related terms, and must contain also the link that relates 
 them. Take away any one of these three elements, and the 
 relation vanishes. Master and servant are united in the relation 
 of service. Take away the master and there is neither service nor 
 servant. Take away the service, and there is neither master nor 
 servant. Take away the servant, and there is no longer master 
 or service. Slayer and slain are united by the relation of slaying. 
 Without the slayer, there is neither slaying nor slain : without 
 the slaying, there is neither slayer nor slain : without the slain, 
 there is neither slayer nor slaying. Every logician is, I suppose, 
 agreed that the proposition expresses a relation; and if it expresses 
 a relation, then it must contain the three elements of which every 
 relation consists — the two terms, and the link that binds them 
 together. 
 
 The first term, that about which the predication of the proposi- 
 tion is made, is called the Subject ; and as the name is appropriate, 
 I propose to retain it. But, for reasons already given. Predicate 
 is a very inappropriate title for the second term of the proposition ; 
 and I propose in future to call it the Object-term ; a name that 
 expresses and emphasises the fact that it is complementary to the 
 Subject, and balances the Subject in the proposition. The link 
 that binds Subject and Object in the proposition, is the relation 
 between them ; but as the name ' relation ' is often given to the 
 completed whole, consisting of Subject, link, and Object, it is 
 inappropriate to apply it to one of the parts of this whole. 
 Traditional Logic calls the link the Copula; but the Copula of 
 Traditional Logic, even when it includes, which it usually does 
 not, the whole of the link between the terms, is but one form 
 of this link, and moreover, is an ambiguous and misleading word. 
 I propose, therefore, in future, to call the link of the proposition 
 the Ratio, a name that is already given to quantitative relations, 
 and that undergoes, therefore, but little diversion in being applied, 
 in the same sense, to the qualitative relations that are the subject- 
 matter of Logic.
 
 CONSTITUENTS OF PROPOSITIONS 43 
 
 According to this mode of division, the proposition ' A is 
 unequal to B ' is analysed into the terms A and B, and the 
 Ratio of inequality that subsists between them. A is the Subject: 
 B is the Object : and the Ratio is the expression ' is unequal to.' 
 The proposition is A — is unequal to — B. The superiority of this 
 mode of division to the division of Traditional Logic, A — is — 
 unequal to B, is apparent and great. The terms ' A ' and ' B ' 
 are complementary elements in the proposition, and balance each 
 other. The terms 'A ' and ' unequal to B ' are incongruous, and 
 not in pari materia. A — is unequal to — B, admits of conversion 
 into B — is unequal to — A, a rational converse, obtained without 
 distortion or manipulation of the convertend. ' A — is — unequal 
 to B ' cannot be so converted. The one mode of division repre- 
 sents, and expresses accurately, the judgement ; which contemplates 
 A and B, and discerns inequality between them. The other 
 pretends that the thought is concerned with ' A ' and * unequal 
 to B,' and discerns between them a relation of existence. I know 
 not what may be in the minds of logicians when they form the 
 judgement ' A is unequal to B,' but I am very sure that I do not 
 myself mean that A stands in a relation of existence towards 
 ' unequal to B,' and I doubt very much whether that is the meaning 
 in the mind of anyone but a logician. 
 
 Every proposition and every judgement consists, then, according 
 to the doctrine here advanced, of Subject and Object related by 
 a certain Ratio, and then forming, with the Ratio, a Relation. 
 In many propositions, however, but two elements are apparent ; 
 and in many other Simple propositions there appear to be more 
 than three elements. It is very important in reasoning to be 
 sure that all three elements are present in any proposition we 
 use, and to be able to identify them all ; and it is not less impor- 
 tant to distinguish between propositions that are complicated, but 
 Simple in the sense that they are neither Compound nor Condi- 
 tional ; those that consist of more than one proposition expressed 
 as one ; and those which are Modal, or qualified in the Ratio. 
 Not less important is it to identify and discriminate each of the 
 elements in a proposition. None of these tasks is always easy. 
 
 In many propositions, two elements only are apparent. Babylon 
 fell; James II. abdicated ; William III. died ; It rains; The ether 
 exists. All these are good sound propositions ; each expresses a 
 definite notion, a complete thought, and therefore a relation ; and
 
 44 A NEW LOGIC 
 
 yet each appears to consist of two elements only ; and the same 
 is true of every proposition expressed by an intransitive verb. 
 Of course, if a proposition consists of Subject and Predicate 
 only, there is nothing in these propositions to explain ; but if a 
 proposition expresses a relation, it must contain the three 
 elements that are present in every relation ; and our task is to 
 find what is become of the element that, in these propositions, is 
 missing. 
 
 To say that James II. abdicated, seems, on the face of it, an 
 incomplete expression. The full sentence would be ' James II. 
 abdicated the throne ' ; and the intransitive verb seems to be, 
 and perhaps is, in this case, formed by merely omitting the Object- 
 term, and leaving it to be understood. But ' William III. died' 
 is a different case. Here, no such Object-term is missing ; and 
 the sentence is complete as it stands. If we look at the sense, 
 however, we see that the relation the proposition expresses is a 
 relation of change, or of suffering change ; and would be more 
 completely expressed by saying ' William III. changed from living 
 to dead,' or better, 'William III. underwent the experience of 
 dying.' These are not expressions to be used in ordinary dis- 
 course ; but they expand the proposition to its proper dimen- 
 sions, and reveal the whole of the three elements it does, in fact, 
 contain. 
 
 Such expressions as * The plant grew,' ' Babylon fell,' ' Carthage 
 perished,' may all be expanded in the same way; but other cases 
 are less easy. ' He walked,' ' She danced,' 'The tiger sprang,' 
 ' The snake struck ' cannot be expanded on this plan. We cannot 
 say, or it would be incorrect to say ' He underwent the experience 
 of walking'; 'She underwent the experience of dancing'; and 
 so forth. The expressions are inappropriate, translating, as they 
 do, a relation of action into a relation of passion. But we can 
 very well expand them into ' He performed the act of walking,' 
 * She performed the act of dancing,' and so forth. These express 
 the meaning accurately, and display all the three elements that 
 exist in the relation. 
 
 * It rains' may be correctly expanded into ' Rain is falling,' but 
 'The Pyramids endure' is a more difficult case. We cannot say 
 that the Pyramids perform the act of enduring, nor that they 
 undergo the experience of enduring. To get at the true relation 
 we must violate the practice of Traditional Logic, and go behind
 
 ANALYSIS OF PROPOSITIONS 45 
 
 the words, to the sense they express. The judgement is, in fact, a 
 negative judgement in an affirmative form. Its meaning is that 
 the Pyramids do not change, or at any rate do not perish. It 
 denies a relation between the Pyramids and change, or perishing. 
 
 * The ether exists ' is more difficult still. The proposition 
 expresses a relation between the ether and existence, but what 
 relation ? A relation, it seems, of existence. Here, then. Ratio 
 and Object seem to be one ; and the three elements necessary to 
 every relation appear to be reduced to two. The only way to 
 express it as a relation, with the three elements complete, is to 
 say * The ether is in a state of existence,' and this is a tautological 
 expression. But * The ether exists ' also is tautologous ; for, 
 implied in every proposition is the postulate that its subject 
 exists for the purpose of the argument. What the proposition 
 gives us is that the ether exists, not only for the purpose of the 
 argument, but over and above this purpose it has a real existence. 
 
 At the other end of the scale are propositions that evidently 
 contain their full complement of elements, and appear to contain 
 a good deal more. * It would have made my story much better 
 to have begun with telling you that at the time my mother's arms 
 were added to the Shandys', when the coach was repainted on 
 my father's marriage, it had so fallen out that the painter, whether 
 by performing all his works with his left hand, like Turpilius the 
 Roman, or Hans Holbein of Basel, — or whether it was more from 
 blunder of his head than hand — or whether, lastly, it was the 
 sinister turn which everything relating to our family was apt to 
 take, — it so fell out, however, to our reproach, that instead of the 
 bend dexter, which, since Henry the Eighth's reign, was honestly 
 our due, — a bend sinister by some of these fatalities had been 
 drawn quite across the field of the Shandy arms.' In this and 
 other long and complex propositions, how are we to distinguish 
 and separate the several elements ? The discovery is not 
 difficult if certain rules are observed, and the rules are as 
 follow : — 
 
 I. First find the Ratio. The Ratio is what the proposition 
 asserts or denies. It is what constitutes the proposition ; and 
 it is expressed by the principal verb. But the Ratio is not 
 confined to the principal verb. It may be more — much more. 
 The proposition may be modal. The postulate may be granted 
 with qualifications or conditions or consequences ; and all such
 
 46 A NEW LOGIC 
 
 modifications of the postulate are part of the Ratio. In ' He 
 took it,' the Ratio is simple, and unqualified. In * He took it 
 quickly,' the Ratio is qualified as to manner. In ' He took it at 
 once,' the Ratio is qualified as to time. In ' He took it then and 
 there,' it is qualified as to both time and place. In ' He took it 
 from your hands,' it is qualified as to circumstance. In ' He took 
 it to throw suspicion on you,' it is qualified as to motive ; in ' He 
 took it because he was greedy,' it is qualified as to cause ; and in 
 ' He took it with the result that suspicion fell on you,' it is qualified 
 as to effect ; but in every one of these cases it is the Ratio that is 
 qualified. Any expression which answers any of the questions 
 How, When, Where, In what circumstances. Owing to what 
 cause, With what motive, or With what result, the fundamental 
 relation which is asserted in the judgement existed or took place, 
 is a part of the Ratio ; and may be known by its quality, as an 
 adverb or adverbial phrase, qualifying the principal verb, which is 
 the gist of the Ratio. 
 
 2. Next find the Terms. The Subject is that part of the pro- 
 position which expresses the person or thing about which the 
 assertion or denial is primarily made. It may always be 
 discovered by asking Who ? or What ? of the Ratio. The Subject 
 is always, therefore, a substantive or a substantival phrase. To 
 find the Subject in ' He took it,' we ask, Who took it ? and the 
 answer is He. ' He ' is the Subject of the proposition. In 
 this case, the Subject is unqualified, but it may be qualified to 
 any extent. ' The man who had been born and brought up amid 
 the refinements of luxury ; who had never had a want unsupplied ; 
 who had been nourished amid the influences of religion and 
 morality, and enjoyed all the advantages of a University educa- 
 tion ; who owned land and houses, stocks and shares, wealth in 
 every form, and luxury unlimited ; stole a penny from a blind man's 
 hat.' In this proposition, the whole of the clauses preceding the 
 principal verb ' stole ' are qualifications of the Subject. 
 
 3. The Subject and the Ratio being identified, the Object is, of 
 course, the remainder of the proposition. It expresses that which 
 is asserted, by the Ratio, of the Subject— that which stands to 
 the Subject in the relation expressed by the Ratio, — and is 
 ascertained by following the Ratio by Whom ? or What ? 
 
 Now apply these rules to the sample proposition given above. 
 First find the Ratio, which is expressed by the principal verb.
 
 ANALYSIS OF PROPOSITIONS 47 
 
 What does the proposition assert ? We have not far to seek. 
 What is asserted is ' It would have made ' ; ' Would have made ' 
 is therefore the Ratio, or the principal part of the Ratio. Is the 
 Ratio qualified in any way ? Yes. A little further along we find 
 the words ' much better,' which answer the question. How would 
 it have made ? This, therefore, belongs to the Ratio, which is, in 
 full, ' Would have made much better.' 
 
 Now to find the Object. The Ratio expresses a relation of 
 making: to find the Object, we are to ask making what ? You 
 say it would have made much better. It would have made what 
 much better ? The answer is, ' My story.' This, then, is the 
 Object. We have now identified two out of the three elements ; 
 it remains only to find the Subject. This is found by asking 
 who or what of the Ratio. Who or what would have made my 
 story much better ? The answer stares us in the face. It would 
 have made my story much better. There is a whole complete 
 proposition. Then what in the world is all the rest, from 'to 
 have begun ' down to ' Shandy arms ' at the end of the sentence ? 
 If we have already found all three of the necessary elements, 
 what is all this superfluous matter ? It is the Subject, placed in 
 apposition. The proposition says. It would have made my story 
 much better. What would have made my story much better ? 
 Why, * to have begun with telling you ' all the rest of the sentence. 
 If, however, this long Subject had been placed in its natural 
 position, in front of the Ratio, it would have been necessary to 
 suspend the expectation during the whole utterance of the 
 Subject, and to keep it suspended until the Ratio was reached. 
 Few people are capable of so long a suspension without falling 
 into confusion ; and, in any case, it is an immense saving of 
 fatigue to have the necessity for such a suspension abolished. 
 Therefore the sentence is rearranged. The Subject is at first 
 represented by * It ' until we have the Ratio clear in our minds ; 
 and then, having apprehended the general relation of the elements 
 in the proposition, we have attention to spare for the long 
 elaborate qualification of the Subject that follows. 
 
 Further, we learn from this example, that the qualification of 
 the Ratio need not be immediately attached to the Ratio, but 
 may be separated from it by the interposition of the Object. 
 
 * When the scintillations of vanity betake themselves for aid 
 to the flippancy of frolicsome levity, and would question the
 
 4S A NEW LOGIC 
 
 sage conclusions of the philosopher, and the moral inculcations of 
 the divine ; they must expect to meet with that grave reproba- 
 tion, which can only be properly awarded by the asperity of 
 virtuous indignation.' In this proposition, the Ratio is manifestly 
 * must expect to meet with.' To find the Object, we ask. Must 
 expect to meet with what ? and the answer is ' that grave 
 reprobation ' &c. To find the Subject, we ask who or what 
 must expect ? and the answer is * They.' But ^\■ho are they ? 
 For an explanation we look to the previous clause, and we find 
 ' they ' refers to ' the scintillations of vanity.' The rest of this 
 clause is not, however, a qualification of the Subject. It states 
 "ti'hcn the action takes place, and is therefore a qualification of 
 the Ratio. In logical order, the proposition should run ' The 
 scintillations of vanity must, when they betake themselves &c., 
 expect to meet with ' the dire consequences predicted. 
 
 It is clear that, in this proposition, ' When ' might be replaced 
 by ' If,' and then it would be in the regular form of a conditional 
 proposition, — If A is B, it is C. We learn, therefore, that the 
 condition of a Conditional proposition is a qualification of the 
 Ratio. 
 
 * In later English, the infinitive, the imperative, and the plural 
 and first person singular of the present indicative of the derived 
 verb, have the same form as the primary noun, so that what takes 
 place seems to be not the making of a new word but the 
 using of a noun as a verb.' Reading this sentence, we come to 
 the principal verb ' have,' and, following the rules already 
 exemplified, we find that the Subject is ' the infinitive, the 
 imperative,' and the rest of it down to ' derived verb.' These 
 are what have, and these are, therefore, the Subject. The Object 
 is clearly * the same form as the primary noun ' ; for this is what 
 they have. The opening clause ' In later English ' shows in 
 what circumstances they have, and therefore is a qualification 
 of the Ratio; but what is the rest of the sentence, from * so 
 that ' down to ' verb ' ? This has the appearance of a separate 
 proposition. It has a separate and independent principal verb, 
 — * seems to be.' The whole sentence is not a simple proposition, 
 but an argument, consisting of two propositions. It could be 
 equally well expressed by 'Because the infinitive and the rest 
 of them have the same form as the primary noun, therefore what 
 takes place &c.' It could be expressed in Conditional form, —
 
 ANALYSIS OF PROPOSITIONS 49 
 
 // the infinitive &c. have the same form, then what takes place 
 &c. But we have already seen that the condition under which 
 a postulate is granted forms a qualification of the Ratio. We 
 may, therefore, regard the first proposition as a qualification of 
 the Ratio of the second, and in strict logical order the pro- 
 position would run : — The using of a noun as a verb, not the 
 making of a new word, seems (since the infinitive &c. have the 
 form of the primary noun) to be what takes place. Here the 
 Subject is in its natural place, heading the sentence ; the Ratio, 
 with the whole of its qualification, intervenes between Subject 
 and Object ; and the Object terminates the proposition. This 
 form, however, unless the proposition is skeletonised in the 
 manner just shown, would be too cumbrous, and would require 
 too long a suspension of attention during the consideration of the 
 part in brackets, to be easily intelligible in practice. 
 
 In this example, we are introduced to a new modification of 
 the proposition, which does not seem to have received attention 
 in books on Logic, — the form ' not this, but that.' This is 
 evidently a compound proposition of the form A is both B and C, 
 with the modification that one of the constituent propositions 
 is negative — A is not B, and is C. The form, ' A is not B 
 but C,' means more than this, however. It implies that the 
 hearer would have expected A to be B, and that this expectation 
 is disappointed. It implies that the statement *A is C ' is 
 paradoxical. The distinction of these nice shades of meaning 
 belongs, however, more to composition than to Logic. 
 
 In the analysis of the last sentence, we found that the 
 Subject and Object had been transposed, the order being ' what 
 takes place seems to be the using of a noun as a verb,' whereas 
 the logical order is ' the using of a noun as a verb seems to 
 be what takes place.' This is rhetorical inversion. That is to 
 say, the inversion is made in order to transfer the emphasis 
 from the Subject to the Object. The emphatic portion of the 
 proposition is the beginning, and whatever part of a proposition 
 we wish to emphasise, we may place at the opening if we choose. 
 The whole sentence opens, in the example, with ' In modern 
 English.' This is the condition that it is desired to emphasise, 
 and for this reason it is placed at the beginning ; and this 
 transfer of emphasis is one reason for the operation of conversion 
 of propositions which will be explained in the next Book. In 
 
 N.L. E
 
 50 A NEW LOGIC 
 
 spoken language, emphasis can be conveyed by inflections of the 
 voice ; and a poor attempt to convey these inflections is made, 
 in writing by underHning, and in print by italicising, the words we 
 desire to emphasise ; but these are poor and inefficient expedients. 
 The proper way to indicate emphasis, and to balance the 
 sentence, is by the arrangement of its constituent parts. When 
 the constituents are in their natural order of Subject, Ratio and 
 Object, the Subject is not much emphasised, for it is in the place 
 in which we expect to find it ; but if either of the others is 
 transferred to this place, it gains emphasis, not merely by 
 position, but by the surprise we feel at its unusual position. ' He 
 robbed me ' states, but does not emphasise, that it was he who 
 robbed me; but 'Me he robbed' states emphatically that I was 
 the person robbed ; and ' Rob me he did ' throws dominant 
 emphasis on the action of robbing. The means of conveying 
 emphasis belongs, of course, to Rhetoric rather than to Logic, 
 but it is desirable here to show one of the reasons for altering the 
 natural order of the elements in a proposition. 
 
 So far, we find that the logical analysis of propositions into their 
 three elements demands a little care, but presents no great diffi- 
 culty, and ought not to be a stumbling block to a careful person. 
 So far, however, we have been at some pains to avoid the really 
 difficult cases ; and difficulties cannot be put off for ever, and 
 should not be put off longer than is necessary to prepare against 
 them, in spite of the practice of Traditional Logic, which has 
 succeeded in evading for two thousand years some of the main 
 difficulties by which it is confronted. 
 
 The logical proposition is the grammatical sentence ; that is to 
 say, the same form of words that is regarded in grammar as a 
 sentence, is regarded in Logic as a proposition. But although the 
 form of words is the same, the different mode of contemplation 
 introduces differences into the contemplate, and the logical pro- 
 position has certain differences from the grammatical sentence 
 which need explanation. 
 
 A grammatical sentence may have more than one verb, but a 
 logical proposition cannot have more than one Ratio. When 
 Grammar presents to the consideration of Logic a sentence con- 
 taining more than one verb, how is Logic to understand the 
 sentence? The proposition 'Brutus killed Caesar' presents no 
 difficulty, and no ambiguity. There is but one possible Subject,
 
 COMPLEX PROPOSITIONS 51 
 
 but one possible Ratio, and but one possible Object-term. But 
 the sentence 'Brutus tried to kill Caesar' contains two verbs, and 
 therefore two possible Ratios. It is only one sentence, but it 
 contains two propositions; yet it is not a compound proposition, 
 for the two propositions it contains are contained, not simul- 
 taneously, but alternatively. Logic may accept the sentence as 
 meaning Brutus— tried — to kill Caesar, which is one of the 
 alternative propositions ; or may accept it as meaning Brutus 
 — tried to kill — Caesar, which is the other alternative. Logic has 
 the right to make its selection between these alternatives ; and 
 more. Logic is not only possessed of the right, but charged with 
 the duty of selecting ; and until the selection is made. Logic is 
 debarred from accepting the sentence as a proposition. The 
 intention in the mind of the proposer may have been to assert 
 either what it was that Brutus tried to do, or whom it was that 
 Brutus tried to kill. In the one case, the verb ' to kill ' belongs to 
 the Object-term ; in the other case, it belongs to the Ratio. It 
 may belong to either, at discretion ; but it cannot belong to both 
 at once. 
 
 A grammatical sentence may have more than one Object, but a 
 logical proposition cannot have more than one Object. In 
 Grammar, 'She gave him beans' has two Objects, — the direct 
 Object, ' beans,' what she gave ; and the indirect Object, him, to 
 whom she gave them. The Logical proposition, however, which 
 expresses a relation, cannot have more than the three elements 
 common to all relations, and cannot, therefore, have two Object- 
 terms simultaneously. But as it may have more than one alter- 
 native Ratio, so it may have more than one alternative Object, 
 and Logic may regard the proposition ' She — gave him — beans ' 
 as stating what it was she gave him, or may accept the proposition 
 as meaning ' She — gave beans to — him,' that is to say, as stating 
 to whom the beans were given. Logic may select either alternative 
 for the purpose in view ; but Logic may not read into the sentence 
 both propositions simultaneously. It is bound to make its selection, 
 and until the selection is made, we have before us no logical pro- 
 position, but only a grammatical sentence. 
 
 It is evident that with more than one alternative Ratio, and 
 more than one alternative Object, the possible alternative proposi- 
 tions that may be contained in a grammatical sentence may 
 become quite numerous, and it may become an academic exercise 
 
 E 2
 
 52 A NEW LOGIC 
 
 requiring some ingenuity to state all the possible logical propositions 
 that are contained in such a sentence as * He tried to persuade 
 some of them to seek to prevail upon the others to attempt to 
 scale the cliff.' The prospect of devising such elaborate traps to 
 catch the unwary ought to go far towards consoling professional 
 logicians for the loss of the flat-traps constituted by the Figures 
 and Moods of the Syllogism.
 
 CHAPTER IV 
 
 THE RATIO 
 
 By this title is denominated the link that binds the two terms 
 together in the relation. We have seen that in Scholastic 
 Logic, the link was the third person of the present tense of the 
 indicative mood of the verb ' to be,' and that no other link was 
 admissible. * S is P ' was the only admissible form of proposition. 
 * S was P ' and ' S will be P ' were as much outside the realm of 
 Logic as ' S is probably P ' or * S may be P for anything I know 
 to the contrary.' Some logicians now formally permit a relaxation 
 of these absurd restrictions, and all logicians relax them in 
 practice; but nothing in logical doctrine is more settled than that 
 the copula must be some person in some tense of the indicative 
 mood of the verb 'to be'; and, in Logic, the meaning of the 
 copula is as follows : — 
 
 The Copula expresses either inclusion in a class or attribution 
 of a quality (or their negations). 
 
 The Copula never expresses anything but inclusion, attribution, 
 or their negations. 
 
 Which of these meanings it expresses in any given case, is 
 doubtful ; but 
 
 It ought always to be understood as expressing attribution, 
 not inclusion ; and 
 
 In fact it alwa}'S is understood to express inclusion, and not 
 attribution. 
 
 According to Traditional Logic, the proposition * A is B ' — for 
 instance, ' Logicians are mistaken," — may have any one of four, 
 and cannot have any but one of these four meanings. It may 
 mean : — 
 
 1. Members of the class of logicians arc included in the class 
 of mistaken persons. 
 
 2. Members of the class of logicians possess the attribute of being 
 mistaken. 
 
 3. Persons possessing the qualities of logicians are included in 
 the class of mistaken persons.
 
 54 A NEW LOGIC 
 
 4. Persons possessing the qualities of logicians ^oss^ss the attribute 
 of being mistaken. 
 
 These are the meanings the proposition may express. According 
 to the precepts of most logicians, it ought to be understood always 
 in the second sense. According to the practice of all, it is always 
 understood in the first. 
 
 Though these are respectively the accepted doctrine and the 
 universal practice of logicians, it is not quite correct to say that the 
 possibility that other relations can be conceived by the mind, and 
 expressed in propositions, has been completely ignored by 
 Traditional Logic. Mill admitted that the proposition may 
 express any of the five relations of Existence, Coexistence, 
 Sequence, Causation, and Resemblance ; and sixty years ago, 
 Martineau pointed out that there are other relations that are not 
 attributive, and cannot without much artificial manipulation be 
 put into a form that expresses attribution. Moreover, most text 
 books give a corner of a page to the mention of such relations as 
 * A is before B,' ' George L succeeded Anne,' ' England is north 
 of Spain,' and a few others. Even Martineau, however, adds 
 relations of time and space only, and whatever other relations are 
 allowed by logicians, such as those of father and child, king and 
 subject, master and servant, are considered with reference to their 
 terms only ; are assumed to be the expressible only in terms ; and 
 are ignored when propositions are treated of. It is assumed that 
 these relations can be conveyed only by appropriate terms, and 
 cannot be conveyed by the Copula. 
 
 Of late 3-ears, still further latitude has crept into the interpre- 
 tation of the copula. It may, according to some logicians, 
 express coexists with, coinhcres with, is like, is identical with, and 
 may have certain other meanings. But though these interpretations 
 are formally allowed, they have no leavening influence on logical 
 doctrine or practice. They exercise no influence on the 
 interpretation of the syllogism ; they are allowed grudgingly, and 
 not by all logicians. 
 
 For all practical purposes, the doctrine of the Copula as 
 applied by Traditional Logic, is as follows : — 
 
 1. The only relations conceivable by the mind are class 
 inclusion and attribution. 
 
 2. If there are any other mental relations, they can be reduced 
 to, or expressed as, those of class inclusion or attribution.
 
 THE COPULA 55 
 
 3. Whatever other relations, if any, are concei\able, must be 
 reduced to either class-inclusion or attribution before they can 
 enter into argument, from the basis of reasoning, or the ground 
 of inference. 
 
 4. The relations of class-inclusion and attribution are expressed 
 by the copula, and cannot be properly or logically expressed in 
 any other way. 
 
 5. These two relations alone can be expressed by the copula. 
 
 6. One of them, but not both, is expressed in every proposition. 
 I do not say that these doctrines are explicitly stated in any 
 
 book on Traditional Logic ; but I aflirm that they are implied in 
 the manner in which propositions are understood and treated in 
 the text books ; and that, unless it is assumed that these are the 
 doctrines applicable to the Copula, the whole treatment of propo- 
 sitions by logicians is unintelligible. It is necessary, therefore, 
 to examine the validity of these doctrines. 
 
 I. Are relations of class-inclusion and attribution the only 
 relations that can be conceived by the mind ? The question 
 carries its own answer. ' Relations can be conceived by the mind ' 
 itself expresses a relation of conception between relations on the 
 one hand, and the mind on the other. Relations may be a class ; 
 but the mind is certainly not a class ; nor is it, nor is it in this 
 proposition affirmed to be, an attribute of relations ; nor does the 
 proposition declare that relations are included in the class of 
 mental things, or that the mind is attributed to relations. 
 
 If logicians do not recognise any relation other than these two, 
 grammarians have recognised others. Mental states and mental 
 processes are expressed in words, and words have originated in 
 response to the need that has been felt for expressing mental 
 states and processes. We may be sure, therefore, that the 
 different kinds of words are a safe guide to the different kinds of 
 mental states and processes. What class of words express 
 relations ? Verbs. Verbs express relations ; and every sort and 
 kind of relation is expressed by a verb. Hence there is di prima 
 facie likelihood that, if there are different kinds of verbs, they will 
 express different kinds of mental relation.s. Are there different 
 kinds of verbs ? Grammarians say there are. They say there 
 are three kinds of verbs, expressing, respectively, relations of 
 Being, of Doing, and of Suffering ; or Existence, Action, and 
 Passion. For the purposes of Grammar, these are doubtless
 
 56 A NEW LOGIC 
 
 enough ; but Logic demands a recognition of other relations, not 
 all of which can be reduced to any of these three, or brought 
 under them. 
 
 The fundamental relation of Logic, as of Psycholog3', the 
 relation on which all reasoning depends, and out of which all 
 reasoning develops, is the primary relation of Likeness, which, 
 with its complement, Unlikeness, is the foundation of all thought. 
 Materially, existence precedes likeness, for things must exist 
 before they can be compared ; but mentally, likeness precedes 
 existence, for things cannot be known as existing, except by their 
 likeness and unlikeness to other things. 
 
 Appreciation of likeness and unlikeness gives us knowledge and 
 discrimination of things as existing, and of the respects in vvliich 
 they are alike and unlike, and thus we come to know of Existence 
 and of the relation of Substance to Attribute, 
 
 The processes of mind are in their nature serial, and therefore 
 temporal ; and unlikeness in series gives us the relation of 
 Change, as well as of Sequence, or Time. 
 
 Experiences of our own activity, together with the changes that 
 accompany it, give us, in well-known ways, knowledge of the 
 relations of Space, of Action, of Passion, and of Causation. 
 Finally, in a way that will be explained hereafter in treating of the 
 origin of terms, we attain the conception of classes, with the 
 corresponding relations of Inclusion and Exclusion. Thus the 
 several kinds of relations that may subsist between terms, and are 
 predicable of them are 
 
 Likeness and Unlikeness. 
 Existence and Change. 
 Attribution and Non-attribution. 
 Action, Passion, and Causation. 
 Temporal and Spatial relations. 
 Class-inclusion and Class-exclusion. 
 
 Of these twelve classes of predicable relations, and of the infinite 
 multitude contained under them. Logic recognises four only, 
 viz: — Attribution, Class-inclusion, and their negatives. It is 
 indisputable and manifest, and needs no insistence, argument, or 
 proof, mat the mind can and does entertain, and can and does 
 express in words, relations of all these orders. Logic denies that
 
 ERRONEOUS DOCTRINE OF THE COPULA 57 
 
 we can express in propositions, or modify by argument, any 
 relation whatever but those of attribution and class-inclusion ; and 
 whatever other relation a proposition may purport to express, must, 
 so Logic asserts, be reduced to one of these before any inference 
 can be deduced from it. 
 
 The reason of this strange contention, manifestly untrue as it is, 
 
 is utterly incomprehensible until we remember that the relation of 
 
 class-inclusion is the relation on which the syllogism rests, and 
 
 with which alone the syllogism is competent to deal. Without the 
 
 relation of class-inclusion, there can be no syllogism ; and as the 
 
 syllogism is the only mode of reasoning known to Traditional 
 
 Logic, this Logic, without the relation of class-inclusion, is a fish 
 
 with its fins and tail chopped off. It cannot move. But this 
 
 explanation takes no account of the relation of attribution, which 
 
 is very different from class-inclusion, and is admitted into 
 
 Traditional Logic ? If Logic admits the relation of attribution, it 
 
 does not restrict itself to class-inclusion, and my account of its 
 
 narrowness is exaggerated. The answer is that though Logic 
 
 professes to admit attribution as a possible relation, yet this 
 
 relation is not in fact admitted by Logic into argument. Every 
 
 'attributive' term admitted into Logic is instantly invested with 
 
 'distributed' or 'undistributed' quantity, which means that it is 
 
 instantly turned into a class, or part of a class. Once admit that 
 
 any other relation than class-inclusion exists, or at least, that any 
 
 other relation can be reasoned about, and the whole time-honoured 
 
 structure of Traditional Logic comes crashing to the ground. Is 
 
 it any wonder that Logicians guard the meaning of the copula so 
 
 carefully, and restrict it so narrowly ? 
 
 Unless we keep in view the necessity that Traditional Logic is 
 under of bolstering up the syllogism, the restrictions, and 
 artificialities, and futilities of this Logic are unintelligible. Why 
 should we be allowed to argue from the proposition ' Caesar 
 possesses ambition,' and forbidden to argue from the proposition 
 ' Caesar possesses land ' ? Why should we be forbidden to argue 
 from ' Caesar possesses land ' and allowed to argue from ' Caesar is a 
 landowner ' ? Why should we be permitted to draw from ' Caesar 
 is a landowner ' the astonishing inference that ' some landowner is 
 Caesar,' and be forbidden to draw, from the proposition ' Caesar 
 possesses land,' the very natural and obvious inference ' Some land 
 is possessed by Czesar' ? Simply and solely because the one set
 
 5S A NEW LOGIC 
 
 of propositions can enter into the syllogism, while the other can 
 not. But for the necessity of bolstering up the syllogism, the 
 logical doctrine of the copula could not stand for an hour. In fact 
 it has stood for hundreds of years. 
 
 Not being infatuated with the syllogism ; not regarding it as a 
 necessary, or even a very useful, mode of reasoning ; I am free to 
 admit into propositions all the relations that the mind can conceive 
 and that words can express. My view is that relations are expressed 
 by verbs ; that a proposition may contain any verb ; and that any pro- 
 position, no matter what verb it contains, no matter what relation 
 it expresses, can as well form the basis of argument, and the 
 ground of valid inference, as the proposition with the copula. To 
 reduce the proposition to ' logical form ' by twisting it about and 
 garbling its meaning until it can be expressed by the copula, seems 
 to me like loading oneself with fetters as a preparation for march- 
 ing. It appears to me that arguments as valid can be formed from 
 * Logicians make mistakes ' as from ' Logicians are mistaken.' 
 
 Thus, the first three questions are answered in the negative. 
 Relations of class-inclusion and attribution are not the only 
 relations conceivable. That abundance of other relations are con- 
 ceivable is proved by the abundance of verbs that have been 
 devised in order to express them. Relations of class-inclusion and 
 attribution are not the only relations that can be expressed in 
 words, for we can use any verb we please to form a proposition. 
 These two are not the only relations that can form the subject of 
 argument, for we find it is as easy to argue from one relation as 
 from another. There is no need, therefore, except the need of 
 dry-nursing the syllogism, to express relations in the form that 
 alone is regarded by Traditional Logic as the legitimate form. 
 Reduction to this form is an unnecessary exercise of perverted 
 ingenuity. It cannot often be done without garbling the meaning 
 of the proposition ; it may result in linguistic monstrosities from 
 which the mind revolts ; and it effectually deters practical reasoners 
 from seeking the aid or adopting the formulae of logic, since they 
 cannot do so without distorting the propositions concerned into 
 forms that are difficult to reach, and are abhorrent to common 
 sense when attained. 
 
 To keep on perfectly safe ground, I will not make any translation 
 of my own, but will take an example from a popular text book. 
 ' Democracy ends in despotism.' To reduce this to logical form,
 
 LOGICAL FORM OF THE PROPOSITION 59 
 
 so that it can enter into logical argument, and perhaps attain the 
 supreme distinction of a place in the syllogism, it must be translated 
 into ' all democratic governments are things ending in despotism.' 
 We will pass the cumbrous and inelegant form of the paraphrase, 
 since Logic is not bound to consider elegance; but we cannot pass 
 that it materially alters the sense of the original. The two pro- 
 positions do not mean the same thing. Not only the Ratio, but 
 the terms are altered. ' Democracy ' is not the same as ' All 
 democratic governments.' * Ends in despotism ' has not the same 
 meaning as 'are things ending in despotism.' * Democracy ' is as 
 different from ' all democratic governments ' as the abstract is 
 different from the concrete. The original asserts something of 
 Democracy, — of a form of government — of an abstract. The 
 logical substitute affirms something else of all democratic govern- 
 ments, — of a group of concrete things. The original asserts what 
 Democracy oids in, or becomes. It affirms a relation of Change. 
 The substitute asserts what democratic governments are. It 
 affirms a relation of Existence. The two things are as different 
 as existing and changing. The original asserts the ending of 
 democracy in despotism — an abstract. The substitute asserts that 
 all democratic governments are things ending in despotism — concrete 
 things that are clearly different from the state in which they end. 
 Would the ingenious logician who made this substitution be 
 satisfied to exchange a contract, giving him the right to receive 
 ' value ' for a thing, for a contract giving him the right to receive ' a 
 valuable thing ' in lieu of it ? Would he be content to exchange 
 an obligation that 'value' is due from him into an obligation that 
 'All valuable things' are due from him? The original answers the 
 question What does democracy end in ? The substitute answers 
 the question What are democratic governments ? The first is a 
 prophecy : the second is a definition or a description. 
 
 And this translation into a cumbrous, awkward proposition, 
 having a different meaning, is not in the least necessary to enable 
 the proposition to enter into an argument. It is necessary, indeed, 
 to make it express class-inclusion, and thus to fit it for entrance 
 into the syllogism ; and on this I shall have something to say 
 when the syllogism comes under review ; but it is not in the least 
 necessary for the purpose of reasoning. If Democracy ends in 
 despotism, then Despotism terminates democracy. The conversion 
 is manifestly sound and valid. It commends itself to the reason
 
 6o A NEW LOGIC 
 
 just as completely, just as effectually, just as conclusively as 'some 
 things ending in despotism are democratic governments ' follows 
 from 'All democratic governments are things ending in despotism.' 
 If, indeed, the mind could conceive no relation other than those of 
 class-inclusion and attribution, there would be some reason for 
 retaining the copula with its restricted meaning ; but in that case, 
 no proposition expressing any other meaning would ever have come 
 into existence ; there would be no other verbs, and no reduction to 
 logical form would be needed. But in fact, the mind does con- 
 stantly form relations of all orders — likeness and unlikeness, 
 existence and change, sequence, causation, action, passion and the 
 rest ; and is as competent to draw inferences from any one as from 
 any other. If democracy ends in despotism ; then it does not 
 end in freedom ; then despotism terminates democracy ; then 
 democracy ends in autocracy ; then democracy leads to despotism 
 and autocracy ; then democracy has a termination ; it does not 
 last indefinitely ; and so forth, and so on. These arguments are 
 manifestly valid. They commend themselves to the reason. 
 Supposing the premiss to be true, we could safely found our 
 conduct on them ; and if arguments conduct us to this result, 
 what more do we want ? The answer of Traditional Logic would 
 probably be somewhat as follows : — ' These arguments may be 
 sound ; but they have this inherent vice, that not being in syllogistic 
 form, they cannot be tested. We cannot be sure that there may 
 not be lurking somewhere an undistributed middle, or an illicit 
 major or minor.' This objection may be left over until we come to 
 the consideration of the syllogism. At present we are dealing with 
 the copula only; and we are arrived at this conclusion — that the 
 relation of sequence cannot be correctly expressed by means of 
 the copula. 
 
 Nor can a relation of action be so expressed. ' Brutus killed 
 Csesar.' According to the precepts and practice of logicians, this 
 must be reduced to logical form, and then becomes ' Brutus was a 
 person who killed Casar.' Again the sense and meaning of the 
 proposition are seriously altered. The original expresses a rela- 
 tion of action. The substitute expresses a relation or mode of 
 existence. The one asserts what Brutus did to Caesar, the other 
 asserts what kind of a person Brutus was. The meanings are 
 widely different, and cannot, by any artifice, be identified. The 
 Subjects alone are the same. The Ratios and Object-terms are
 
 MEANING OF THE COPULA 6i 
 
 widely different. The one proposition answers the three questions 
 — What did Brutus do to Caesar? Who killed Caesar? and 
 Whom did Brutus kill ? The other does not answer either 
 question directly, but answers instead the question What sort of a 
 person was Brutus ? 
 
 The third assumption of Traditional Logic is that if any other 
 relations than class-inclusion and attribution, are conceivable, such 
 relations must be reduced to those of class-inclusion or attribu- 
 tion before they can enter into argument. The onus of proving 
 such an assertion is on those who make it ; and it is easily refuted 
 by adducing an instance to the contrary. Such instances are 
 abundant in the experience of everyday life. If John went out, 
 it is a safe inference that he did not remain at home ; if he 
 gave away his dinner, he did not eat it himself; if he lost money, 
 he became poorer; if he lost his temper, he did something 
 foolish ; if he drank too much, he became intoxicated ; if the 
 bank breaks, it will ruin many people ; if the tide rises high 
 enough, the ship will float. So far from the copula being necessary 
 for argument, the vast majority of arguments are carried on in 
 propositions from which the copula is absent. 
 
 The fourth assumption of Traditional Logic is that relations 
 of class-inclusion and attribution can be expressed in no other 
 way than by the copula. An assumption more manifestly false 
 was never made. The copula, so far from being the only way, is 
 not even the correct way of expressing these relations. The 
 copula is an abbreviation. It is an approximate expression. It is 
 an inefficient substitute for the proper expression. It is ambiguous. 
 Not even a logician can tell, when he meets with the copula, 
 whether it expresses class-inclusion, or attribution, or something 
 else. On his own showing, it may mean either class-inclusion or 
 attribution ; and many pages of text books on logic are filled with 
 discussions as to which meaning is to be read into it. But it is 
 easy to express either relation without ambiguity, and with 
 certainty. If, by ' Camels are ruminants,' I mean ' Camels are 
 included in the class of ruminants,' what is easier than to say 
 so in those words ? If I mean * Camels possess the faculty or 
 quality of rumination,' what is easier than so to express my mean- 
 ing ? Why, if I have a definite meaning, should I be compelled 
 to adopt a form of expression which leaves my meaning in 
 doubt, and be prohibited from expressing it in a form which leaves
 
 62 A NEW LOGIC 
 
 no room for doubt ? Approximate expressions, ambiguous expres- 
 sions, slipshod expressions, are frequent enough in the spoken 
 communications, even of educated and careful persons, in the 
 hurr)- and worry of daily life ; and are then pardonable. In 
 deliberate compositions, written down and sent to press, corrected 
 in the proof, and revised with the care that is inspired by respect 
 for the reader and regard for the reputation of the writer, they are 
 excusable with difficulty ; but what is to be said of the practice of 
 choosing an ambiguous expression, as the very foundation of 
 reasoning, in works on Logic ? 
 
 Nor is the confusion between class-inclusion and attribution 
 the only ambiguity that lurks in the copula. Traditional logic 
 makes no discrimination between the verb 'to be ' as an inde- 
 pendent verb, and the same verb as an auxiliary. ' The calf 
 will be slaughtered ' is in the form of the conventional logical 
 proposition, with subject, copula, and predicate, all complete. But 
 it has not the meaning of the conventional logical proposition. 
 It means neither that the calf will be included in slaughtered 
 animals, nor that the calf will have the attribute of having been 
 slaughtered. It means that the calf will undergo the experience 
 of being slaughtered. It means that slaughter is what will happen 
 to the calf. The proposition has the same form as * The calf will 
 be dead,' but the meaning of the verb is totally different. In the 
 last proposition, the verb ' will be ' is the copula, and expresses 
 the state of existence in which the calf will be. In ' The calf will 
 be slaughtered,' the verb 'will be' is auxiliary to ' slaughtered,' 
 and expresses, not existence in the future, but passion, or being 
 acted on, or undergoing. The meanings are as distinct as exis- 
 tence and suffering, and yet, in every text book on Logic that has 
 ever been written in English, they are confused. 
 
 The fifth assumption of Traditional Logic with respect to the 
 copula is that no relation can be expressed by it except those of 
 class-inclusion and attribution. One additional meaning has just 
 been given, and this is not the only one. The copula, in its strict 
 meaning, expresses existence, not solely existence in a class. There 
 are many modes of existence besides existence in or out of a class, 
 and all these may be expressed by the copula. When it is asserted 
 that Britons never shall be slaves, what is meant is not that they 
 shall never be included in the class of slaves, nor that they 
 shall never have the attributes of slaves. No one who ever made
 
 MEANLNG OF THE COPULA 63 
 
 the declaration ever had in his mind any thought of classes or 
 attributes. What he has in his mind, what he intends to convey, 
 and what he is understood by every one of his hearers to convey, is 
 that Britons shall never stand in the relation of slavery towards a 
 tyrant or a despot. If I hear that they were all drowned, I do not 
 understand that they were all included in the class of the drowned, 
 or that they all possessed the attribute of drownedness. What I 
 understand, and what my informant meant me to understand, is 
 that they all underwent the experience of drowning. When I say 
 * mules are barren,' I do, indeed, predicate of mules the attribute 
 of barrenness ; but when I say ' a mule is the product of an ass 
 and a mare,' I do not assert that it is included in the class of things 
 produced by an ass and a mare, nor assert of it the attribute of 
 being so produced. What I mean, and what I am understood by 
 everyone but a logician to mean, is to assert a relation of parent- 
 hood. That, I say, is the parentage of a mule. 
 
 Lastly, it is assumed by Traditional Logic that every proposition 
 expresses either class-inclusion or attribution, but not both. I meet 
 this assumption with five different negatives. In the first place, 
 as already shown, the copula need not express either class-inclusion 
 or attribution. In the second, multitudes of other relations 
 besides class-inclusion and attribution are expressed in proposi- 
 tions. In the third, a proposition may express class-inclusion and 
 attribution alternately. In the fourth, it may express them simul- 
 taneously ; and in the fifth, the universal practice of Traditional 
 Logic itself is to understand the proposition as expressing class- 
 inclusion alone, and to reject attribution altogether. 
 
 When it is said * Logicians are mistaken,' what is meant ? What 
 is the relation that the proposition asserts, conveys, and expresses ? 
 The four meanings that logicians read into it have already been 
 given. It may mean that all persons in the class of logicians have 
 the attribute of being mistaken, or that they are included in the 
 class of mistaken persons ; or it may mean the same of persons 
 having the attributes of logicians. These are what logicians say 
 it may mean, but what does it actually convey ? I assert that it 
 may mean logicians both in intention and in extension ; that it 
 may mean the class of persons who have the attributes of 
 logicians. In any given case, the utterer or the receiver may be 
 thinking more in intention than in extension, or vice versa ; but in 
 that case he should express himself without ambiguity. He should
 
 64 A NEW LOGIC 
 
 say, in the one case, ' the class of logicians ' and in the other 
 ' men having the qualities of logicians.' If he means the Object 
 in extension, he should be careful so to express himself by saying 
 ' mistaken persons.' 
 
 But the exponents of Traditional Logic, though they pay lip- 
 ser\-ice to the intensive meaning of the proposition, do not, in 
 practice, allow that a term is ever to be understood in intention. 
 So long as they are discussing the import of propositions, they 
 allow and assert that a proposition may be and ought to be under- 
 stood attributively, but the moment the last page of the chapter 
 on import is turned, they seem to obliterate the assertion from 
 their minds, and never refer to it again. According to traditional 
 Logic, the Subject should usually be understood in intention, the 
 Predicate in extension. The Subject is a thing, or class of things, 
 the Predicate an attribute of the Subject. Yet, when they convert 
 a proposition, they invariably drop the intensive character of the 
 Predicate, and regard it solely in extension. In vain shall we 
 search the books to find * Logicians are inconsistent ' converted 
 into ' Inconsistence is a quality of logicians.' It is always con- 
 verted into ' Some inconsistent persons are logicians.' The reason 
 for this strange volte-face is evident enough. Syllogistic reasoning 
 is reasoning about class-inclusion, and nothing else; and unless 
 a proposition expresses class-inclusion, it cannot enter into a 
 syllogism. Since the syllogism is the only form of reasoning, it 
 follows that no proposition can enter into reasoning unless it 
 expresses class-inclusion. 
 
 In contradistinction to Traditional Logic, I assert, and have 
 given reasons to show, that a proposition may express any relation 
 whatever ; that relations are expressed by verbs ; that any pro- 
 position containing any verb whatever can be reasoned from, and 
 argued about, as readily as any other ; that the copula is an 
 ambiguous form of expression, which should be employed as 
 seldom as possible; that, so far from every proposition being 
 translated into one containing the verb ' to be,' every proposition 
 containing this verb should, if possible, be translated into a more 
 accurate form ; that, so far from ever>' proposition being trans- 
 latable into one containing the copula, none, except those express- 
 ing existence, can be so translated without pervertmg its meaning ; 
 while, contrarily, most propositions containing the copula can be 
 expressed more accurately by some other verb.
 
 THE RATIO 65 
 
 If the Ratio must be the verb * to be ' ; and if the verb 'to be ' 
 in a proposition is always the copula ; and if, in construing a 
 proposition, we are to look always at the verbal form and never at 
 the sense, then observe the consequence in the proposition ' He 
 is certain to fall.' This has the form of the conventional logical 
 proposition, with Subject, Copula and Predicate all complete. 
 He — is — certain to fall. That is the construction according to 
 Traditional Logic. But what is the sense the proposition 
 expresses ? Does it predicate certainty of him ? Manifestly it 
 does not. The relation expressed is not one of certainty, but one 
 of happening. The correct construction is. He — will certainly — 
 fall, or, in strict logical correctness. He — will certainly undergo — 
 the experience of falling. It is a modal proposition ; and, if 
 Traditional Logic were consistent, would be inadmissible on this 
 account, but as the mode is apodeictic, it would be allowed to 
 come in, though not in the form that expresses accurately what is 
 in the mind of the proposer. The converse, in Traditional Logic, 
 is 'A person who is certain to fall is he,' which, as Pepys says, is 
 a pretty strange expression. In common sense, the converse is, 
 ' Falling is the experience he is certain to undergo,' or * Falling is 
 what will certainly happen to him.' 
 
 Such being, in my view, the nature of the Ratio, the question 
 presents itself. What are the relations that the Ratio may express? 
 This question asks, in effect. What can be predicated of a Subject, 
 or What are the Predicables ? It also asks What are the Categories ? 
 for these also are predicable of a Subject. It is true that logicians 
 regard the Categories or Predicaments as possible terms, and the 
 Predicables as possible Predicates ; but as the predicate is, in 
 Logic, a term, it is difficult to understand what the distinction is 
 that Logic makes between them. The discussion as to what 
 Aristotle's purpose may have been in enumerating the Categories, 
 and what value is to be attached to them, has been a favourite 
 battle ground for logicians, and a volume might easily be filled 
 with an account of these discussions. They remind me irresistibly 
 of the controversy that raged between the Big-endians and the 
 Little-endians ; and the questions at issue seem to me equally 
 important. What the soldier said is not evidence ; and what 
 Aristotle had in his mind when he formulated his scheme of 
 Categories really does not matter to anyone who does not regard 
 Aristotle as an inspired writer, whose lightest words are to be 
 
 N.L. F
 
 66 A NEW LOGIC 
 
 treasured as precious possessions, and whose opinions are to be 
 received with unquestioning reverence. At first sight, the Aristo- 
 teHan Categories appear to be a hodge-podge of irrelevant and 
 disconnected words, thrown together anyhow ; but on examination 
 it is found that they relate to the various parts or constituents of 
 the proposition, and are best left over, therefore, until these 
 constituents have all been examined.
 
 CHAPTER V 
 
 terms, their origin and kinds 
 Quantity 
 
 The proposition expresses a relation, and in every relation there 
 are two related thin^^s. These things, between which the relation 
 exists, are called the terms of the relation. The proposition 
 expresses the formation, in and by the mind, of a relation; and 
 the verbal terms of a proposition express mental terms, which are 
 images, ideas, or concepts, all of which may be included in the 
 term thoughts. When we inquire into the origin of terms, we are 
 inquiring, therefore, into the origin of thoughts. 
 
 All thoughts are derived from experience. They may be 
 derived directly and immediately, and are then images of things 
 and events that have been presented to sense ; or they may be 
 derived indirectly or mediately from experience, by the operation 
 of the mind upon the images derived directly from experience. 
 This mental operation consists in discerning likeness and unlike- 
 ness between things, in combining or associating in the mind 
 what are discerned to be alike, and in separating in the mind 
 what are discerned to be different. This is the primitive process 
 of thought, and to this process all thoughts, that are not mere 
 images, are due. 
 
 When chalk, foam, snow, certain flowers, certain clouds, and 
 certain other things, are successively contemplated, they are 
 discerned to be all alike in a certain respect. A fundamental 
 capacity of the mind enables us to combine, or associate together 
 in the mind, all the things that we discern to be alike in any 
 respect. This capacity is called Generalisation. A fundamental 
 capacity of the mind enables us to set apart in the mind the group 
 of things thus generalised by the discernment of their likeness in 
 one respect, and to discern that they are different in some other 
 respect from other things. This capacity is called Differentiation 
 Division, or Classification. A fundamental capacity of the mind 
 enables us to contemplate the respect in which things are alike or 
 
 F 2
 
 68 A NEW LOGIC 
 
 different, separately from the things themselves. This capacity is 
 called Abstraction. 
 
 I have distinguished these as different capacities of the mind, 
 but thev are not different processes. They are different aspects 
 of one process. In the same mental act in which we discern that 
 things are like one another, we discern that they are unlike other 
 things, and we discern the respects in which they are like one 
 another and unlike other things. The whole process I call 
 Syncrisis, and this account of Syncrisis affords us an introduction 
 to many of the fundamental terms of Logic, and an explanation 
 of them. 
 
 The respect in which things are discerned to be alike or different 
 is called a Quality of those things. 
 
 Things which possess qualities are called Concrete things, or 
 Coucretes. 
 
 A quality may be contemplated as inherent in, or manifested by, 
 a concrete: it is then abstractible from the concrete, but not 
 abstracted. Such qualities are called Attributive qualities or 
 Attributes— e.g., a white horse. 
 
 A quality may, however, be contemplated apart from the things 
 in which it inheres or by which it is manifested. It is then called 
 an Abstracted or Abstract quality, or an Abstract — e.g., whiteness, 
 hardness. 
 
 An abstract quality has qualities of its own, abstractible from 
 it — e.g., moderate hardness, excessive hardness. Contemplated with 
 respect to these qualities of its own, a quality is a Concrete 
 Quality. 
 
 The same quality is, therefore, abstract with respect to the 
 concrete from which it is abstracted, and concrete with respect to 
 the qualities it possesses. These qualities may be discerned in it 
 while it is still abstractible, and not completely abstracted ; so that 
 an Attribute as well as an Abstract quality may be concrete. 
 Concreteness is, therefore, not necessarily opposed to abstractness. 
 It is complementary to abstractness, but not inconsistent with 
 abstractness. The true opposite or contradictory of Abstract is 
 not Concrete, but Attributive. The true opposite of Concrete is 
 Qualitative. 
 
 The quality in respect of which several concretes arc alike is 
 called a Common quality of those concretes. A quality that is 
 possessed by some concretes and not by others is a Proper quality
 
 DEFINITIONS OF LOGICAL TERMS 69 
 
 of those by which it is possessed. The same quahty that is 
 common to some concretes, regarded as Hke one another in 
 respect of its possession, is proper to those same concretes, 
 regarded as different from other concretes that have it not. 
 
 An attribute may inhere in more than one concrete ; and a 
 concrete may possess more than one attribute. 
 
 The attributes of a concrete, taken together, form the Connotation 
 of the concrete. 
 
 The concretes that possess an attribute form the Denotation of 
 that attribute. 
 
 The same name that is given to a group of attributes found 
 together in a concrete is given to the concrete or concretes in 
 which that group of attributes is found. The group of attributes 
 forms the Connotation of the name ; the concrete, or group of 
 concretes, forms the Denotation of the name. 
 
 When a group of attributes, with the concretes that possess 
 them, are contemplated together, but the attributes or connotation 
 are more prominent in the mind, the connotation and denotation 
 together form a General Idea or Concept of the concretes. 
 
 When a group of concretes with their common attributes are 
 contemplated together, and the denotation is more prominent in 
 the mind, the denotation and connotation together are called 
 a Class. 
 
 The process of Syncrisis places us in possession, therefore, of 
 several kinds of terms, in addition to the individual images 
 and ideas from which all other kinds of terms are derived. It 
 places us in possession of Concretes, of Concepts, of Classes, and 
 of Qualities, and of several classes of qualities. 
 
 Since, as we have seen, qualities may be concrete, and may be 
 gathered into classes ; since both concretes and classes possess 
 qualities inherent in them ; since classes are themselves necessarily 
 concretes ; and since each class is in some sort an individual ; it 
 seems that these several kinds of terms are so inextricably 
 blended, that no absolute distinctions can be drawn between 
 them ; and that, in treating them as terms, we must treat them in 
 the mass, and cannot usefully distinguish one from another. 
 Such a view would, however, be erroneous. It is true that 
 concretes may be concrete qualities, and that classes may be 
 classes of qualities; it is true that qualities may be concrete, 
 and may be grouped into classes; but, as we have found, and
 
 70 A NEW LOGIC 
 
 as we shall find af:^ain and again, logical differences depend on the 
 different ways in which the subject-matter is contemplated by the 
 mind; and the several kinds of terms may be disentangled from 
 one another and disposed in distinct classes, if we rightly con- 
 template them. When we speak or think of an individual, we 
 are contemplating the subject of thought from its quantitative 
 aspect alone ; and thus contemplated, it does not matter whether 
 the individual is a concrete or a quality ; and if it is a quality, it 
 does not matter whether it is an attribute or an abstract. We 
 regard it purely quantitatively, and quantitatively it is an 
 individual. Similarly, when we speak or think of a class, we 
 contemplate the subject of thought in its quantitative aspect 
 only. We contemplate the class as quantitative, that is to say 
 as made up of a group of concrete individuals ; and thus contem- 
 plated, it is evident that classes and individuals may be associated 
 together as Quantitative Terms. 
 
 A quality may, as we have found, be a concrete ; but when it is 
 viewed or contemplated as a concrete, it is no longer regarded 
 qualitatively. It is regarded as itself possessing qualities, and 
 therefore as a concrete individual or class. It is regarded 
 quantitatively, and not qualitatively, and falls into the class of 
 quantitative terms. But when a quality is contemplated with 
 respect to the concretes in which it inheres, or from which it has 
 been abstracted, then it is regarded qualitatively ; and, so 
 regarded, qualities, whether attributive or abstract, from a class 
 of terms quite distinct from that which includes them when they 
 are regarded quantitatively. 
 
 The two primordial kinds of terms are, therefore, the Quantita- 
 tive and the Qualitative ; and, while Quantitative terms are 
 divisible into Individuals and Classes, Qualitative terms are 
 divided into Abstracts and Attributes. These, then, are the 
 primary classes of terms that we are to consider in detail. 
 
 TABLE I. 
 Primary Classification of Terms. 
 
 Terms 
 
 ^ ^. ^. i Individuals. 
 Quantitative 
 
 I V-'Id.bbCo. 
 
 ( Abstracts. 
 
 Qualitative , *,, •, , 
 '^ ( Attributes.
 
 LOGICAL QUANTITY 71 
 
 The Traditional doctrine of quantity is not only miserably 
 defective, but is also in such inextricable confusion that it 
 is difficult to give any intelligible account of it. The following 
 statements are authorised by a leading text book ; all of them 
 are corroborated by other text books, and all but one by every 
 text book that I have been able to consult. 
 
 In the examination and description of terms, quantity is not 
 mentioned ; nevertheless, terms are divided into Singular and 
 General, and General terms into Collective and Distributive. 
 
 Quantity means, in Logic, the quantity of propositions, as 
 Universal or Particular. The logical doctrine of quantity does 
 not apply to terms, which cannot be either Universal or 
 Particular ; at any rate, neither the Universal term nor the 
 Particular term is ever mentioned in Logic. Nevertheless, 
 every term must be either distributed or undistributed ; which 
 means that it is viewed quantitatively, and must possess one 
 of these two quantities. 
 
 The quantities known to Traditional Logic are two only, viz : 
 — the Universal, the Particular, the Distributed, the Undistributed, 
 the Singular, the General, the Distributive, the Collective, and the 
 Indesignate. 
 
 The predicate of a proposition is never quantified : it is always, 
 however, of either distributed or undistributed quantity. 
 
 Universal propositions are those in which the predicate 
 explicitly refers to the whole of the subject. 
 
 Particular propositions are those in which the predicate does 
 not refer to the whole of the subject. 
 
 There is no proposition in which the predicate does not refer 
 to the whole of the subject. This rule is not to be found in any 
 book on Logic. It is, however, indisputably true. 
 
 How logicians reconcile in^ their own minds these several 
 statements, is no business of mine. Whether they forget, when 
 they come to one page, what they have said on a previous page ; 
 or whether the Universal quantity is the same as the Distributed 
 quantity, and the Particular the same as the Undistributed ; or 
 whether they are respectively sometimes the same and sometimes 
 different ; or whether the Singular and General quantities are, irv 
 the estimation of Logic, not quantities ; or whether Logic does 
 not know what quantity is ; or whether Distributive quantity is or 
 is not the same as Distributed quantity ; or whether logicians are
 
 72 A NEW LOGIC 
 
 unable to count up to more than two ; I do not know, and It is no 
 business of mine to determine. These subtle questions must be 
 left to the acumen of logicians themselves ; but there is one matter 
 on which I am clear, and that is that in no circumstances whatever 
 does the predicate of a proposition refer to part only of the subject 
 of that proposition. The subject of a proposition may, indeed, be 
 but a small part of an individual or of a class, but however small 
 a part it may be, the predicate refers to the whole of that part. If 
 I say that a ten-millionth of a grain of radium is a recognisable 
 quantity, or that one of the innumerable host of stars is brighter 
 than the rest, or that one of the countless grains of sand on the 
 sea-shore is blown into my eye, the predication refers not to part 
 of the one-millionth, very small part though it is of a very small 
 part ; nor to part of the star or part of the grain of sand, one only 
 though each is of an incalculable multitude. The predicate refers 
 in each case to the whole of the subject, small part of a whole 
 though that subject is. What logicians mean when they say that 
 a Particular proposition is one in which the predicate does 
 not refer to the whole of the subject, is, no doubt, that the 
 subject of a Particular proposition is part of a class ; and this, 
 though not universally true, is at any rate sometimes true ; but 
 this is not what they say, or what most of them say, and what they 
 do say is never true. According to their definition, there is no 
 such thing as a Particular proposition. 
 
 Another distinction between Universal and Particular pro- 
 positions is said to be that, while the subject of the Universal 
 is understood in its whole denotation, the denotation of the 
 subject of the Particular proposition is left indefinite. According 
 to this distinction, * Some of the men were killed ' is a particular 
 proposition, and to this logicians would, I suppose, agree. But 
 according to this distinction, ' Twenty-two of the men were 
 killed ' is a Universal proposition ; yet ' twenty-two of them ' is 
 certainly part of a class, so that the proposition is Particular 
 according to one definition of Particular, and not Particular — 
 in fact Universal — according to another definition. No doubt, 
 if twenty-two of them were killed, all of the twenty-two were 
 killed, and in this sense, the proposition is Universal ; and no 
 doubt if twenty-two of them were killed, it is not specifically 
 asserted that more than twenty-two of them were not killed, and 
 logicians may claim that this renders the numbers indefinite,
 
 LOGICAL QUANTITY 73 
 
 and determines decisively that the proposition is Particular; but if 
 logicians make this claim, they are confusing definiteness with 
 exactness, which are very different things. For my own part, 
 I am unable to decide, on the principles of Traditional Logic, 
 whether 'Twenty-two of them were killed' is, in that Logic, a 
 Universal or a Particular proposition ; and I shall be very much 
 surprised if logicians give a unanimous answer to the question. 
 Fortunately for themselves, however, logicians are always ready 
 with a short way to deal with difficulties. If any example, found in 
 experience, of a Ratio, a term, a quantity, a mode of argument, or 
 anything else, will not fit in with the scheme of Traditional Logic, 
 out that example has to go. Such a Ratio, such a term, such a 
 quantity, such a mode of argument, is * not logical.' It doesn't 
 count. We are reminded of little Curran's offer to his gigantic 
 antagonist who complained of the unfairness of a duel between 
 them. Curran offered to chalk out a figure of his own size on the 
 body of his huge adversary, and to agree that every bullet that hit 
 outside the chalk marks should not count. It is little consolation 
 to a reasoner, whose arguments have been smashed, shattered and 
 pulverised, to be told that the crushing retort of his adversary is 
 outside the scheme of Traditional Logic. The Austrian generals 
 who were defeated by Napoleon proved to their own satisfaction 
 that Napoleon's methods were not warranted by the rules of war. 
 The demonstration was irrefragable, but it did not alter the 
 results of the campaigns. What were altered were the rules 
 of war. 
 
 The doctrine of Traditional Logic, that quantity inheres in the 
 proposition, seems to me fundamentally erroneous. In my view, 
 quantity resides in the terms alone, and the proposition as a whole 
 can no more be Universal or Particular than it can be white or 
 soft. A proposition expresses the formation in the mind of a 
 relation ; and though, with some straining of the meaning of 
 words, a relation may be said to be Universal or Particular, the 
 formation of a relation cannot possibly be either. If there is a 
 relation that subsists between all things, that relation may properly 
 be termed Universal ; and in this sense the relations of space and 
 time are approximately Universal. They are universal in the 
 material universe. And relations, such as likeness and unlikeness, 
 that exist between certain things only, may be termed Particular 
 relations. But the formation of a relation, cannot be either 
 
 n 
 
 1
 
 74 A NEW LOGIC 
 
 Universal or Particular ; and it is the formation of a relation that 
 is expressed by a proposition. 
 
 Traditional Logic, as now taught, denies utterly that the 
 Predicate is quantihed ; and abjures, abhors, and repudiates the 
 Haniiltonian doctrine of the quantitication of the Predicate, as 
 utterly heretical and damnable. Nevertheless, Traditional Logic 
 still teaches, by the mouths of those very logicians who pour 
 contempt upon the Haniiltonian doctrine, that the predicate of 
 every proposition must be either distributed or undistributed. Of 
 the four forms of propositions that alone exist, E and O distribute 
 their predicates, A and I leave the predicate undistributed. In no 
 proposition is the predicate quantified, but in every proposition 
 the predicate possesses either distributed or undistributed quantity. 
 That is the doctrine taught by every logician at the present time. 
 How the two portions of the doctrine are reconciled is no business 
 of mine, I am thankful to say, for, not having been brought up in 
 Traditional Logic, I find some difficulty in reconciling flat 
 contradictories. 
 
 In my view, we ma}- or may not quantify the predicate, or 
 rather, the Object-term, of a proposition ; and if we do choose to 
 quantify the Object-term, we must apply to it a quantity that is 
 applicable to it, and not one that is inapplicable. There is one 
 mode of quantity — the Extensive — that is applicable to quantitative 
 terms alone, and cannot rightfully be applied to qualitative 
 terms. There is another mode of quantity — the Intensive — that 
 is applicable to qualitative terms only, and cannot rightfully be 
 applied to quantitative terms. Traditional Logic does not 
 explicitly or formally deny these doctrines, but its practice is 
 completely inconsistent with them, and we may therefore take it 
 that if Traditional Logic did know of them, it would deny 
 them. 
 
 As already shown. Traditional Logic, though it formally and 
 verbally denies that the predicate is quantified, yet declares that 
 the predicate always possesses quantity. It declares moreover 
 that the predicate is always, or ought always, to be understood 
 as a qualitative term ; and that, being a qualitative term, it must 
 be invested with extensive quantity, of which qualitative terms are 
 not susceptible. I say that in ' All gold is heavy,' the predicate 
 ' heavy ' is to be understood qualitatively, that is to say, as a 
 quality belonging to gold ; and so far Logic agrees. But I say
 
 LOGICAL QUANTITY 75 
 
 further, that ' heavy ' cannot be every heavy, or a few heavy, or 
 many heavy, or half heavy, or have any other numerical quantity 
 attached to it. As a quality, it is susceptible of intensive quantity 
 only. It may be very heavy, or moderately heavy, or rather 
 heavy, or extremely heavy. This Logic does not admit, or at least 
 does not declare ; for no mention of intensive quantity is to be 
 found in books on Logic. On the contrary. Logic declares that 
 ' heavy ' in the given proposition, does possess extensive quantity, 
 for it is undistributed, and an undistributed term ' refers to a 
 portion of a class ' and ' leaves the extent of the denotation 
 absolutely indefinite.' The sole aim, purpose, and meaning of 
 conferring distributive quantity upon a term is to enable us, or 
 disenable us, to include some other term within it. Logicians are 
 compelled, by their doctrine that all reasoning is inclusion in 
 classes or exclusion from classes, to make every term a class. 
 They do not seem able to appreciate the difference between a 
 quantitative term and a qualitative term, or to recognise that any 
 change has taken place when the term ' heavy ' is altered into 
 * heavy things.' 
 
 But although logicians are forced by their erroneous doctrine of 
 reasoning to pretend that every qualitative term is quantitative, 
 and expresses a class or part of a class, it seems never to have 
 occurred to any logician, from the days of Aristotle down to this 
 present time of writing, that the predicate or Object-term of a 
 proposition may explicitly express a class or part of a class. That 
 All men are mortal is a proposition that every logician can under- 
 stand, appreciate, and admit within the precincts of Logic ; but 
 that Mortality can be an attribute of all men, is beyond the utmost 
 range of his imagination. 
 
 The teaching of every logician is that the subject is to be under- 
 stood in Extension, the Predicate in Intension. The practice of 
 every logician is to understand both in Extension. ' " All men are 
 mortal," ' say logicians, ' means Every man has the attribute of 
 mortality ; and therefore we will always take it to mean Every man 
 belongs to the class of mortal beings. " No man is perfect " means 
 No man possesses the attribute of perfection ; and therefore we 
 will always take it to mean No man is included in the class of 
 perfect beings.' 
 
 The sole justification — no, that is wrong; there can be no 
 justification for the constant infraction of a rule that is laid down
 
 76 A NEW LOGIC 
 
 as universally applicable. The sole foundation for this strange 
 doctrine of the quantification of the predicate, which logicians 
 formally repudiate and universally adopt, is the fancied necessity 
 of finding means to convert the proposition according to the 
 conventional rule. Unless we understand ' All men are mortal ' to 
 mean ' All men are included in the class of mortals,' we cannot 
 get the logical converse, ' Some mortals are men,' and without 
 this converse, the Moods of the Syllogism must go by the 
 board. 
 
 In my view, the signs of quantity, whether of Extensive or 
 Intensive quantity, can as readily be affixed to the Object-term as 
 to the Subject-term, and are, in the actual reasonings of daily 
 life, as often affixed to the one as to the other. Either Extensive 
 or Intensive quantity may be expressed in the Subject alone, in the 
 Object alone, or in both, or in neither. 
 
 Extensive Quantity. 
 
 Subject alone quantified — All men are liars. 
 
 Object alone quantified — Lying is common to all men. 
 
 Neither term quantified — Cloven-footed mammals are rumi- 
 nants. 
 
 Both terms quantified — One volunteer is worth twenty pressed 
 
 men. 
 
 Intensive Quantity. 
 
 Subject alone quantified — Gross ignorance is deplorable. 
 
 Object alone quantified — Lying is very shameful. 
 
 Neither term quantified — Patience is virtuous. 
 
 Both terms quantified — Intense hunger is very demoralising. 
 
 All of these variations of quantity except the first, would, I 
 suppose, be rejected by logicians as 'not logical,' but, as I owe 
 no allegiance to Traditional Logic, I accept them all, and 
 have no difficulty in arguing and drawing conclusions from them. 
 If Lying is common to all men, then All men are liars. If 
 Cloven-footed mammals are ruminants, then we may expect any 
 cloven-footed mammal to ruminate. If One volunteer is worth 
 twenty pressed men, he is worth more than ten pressed men. 
 If Gross ignorance is deplorable, we should not encourage it. 
 If Lying is very shameful, it is not to be commended. If
 
 HAMILTON'S QUANTIFICATION tj 
 
 Patience is virtuous, it is virtuous to be patient. If Intense 
 hunger is very demoralising, starving them is not the best way 
 to cultivate bravery in troops. These arguments are no more 
 difficult to construct than they are easy to refute ; but none of 
 them can be reached by any method known to Traditional Logic 
 as I understand it. 
 
 If the distribution or non-distribution of the predicate is as 
 important, nay, as necessary, in our estimation of propositions, 
 as Traditional Logic asserts, then it is not justified in rejecting 
 Hamilton's scheme of quantification of the predicate, which, 
 however, all logicians do reject. Hamilton's quantification merely 
 carries to its logical conclusion that quantification of the predi- 
 cate which all logicians admit and proclaim. It merely states 
 explicitly that which they assert is implicit in the proposition. 
 Hamilton says in effect, * It is admitted that in every proposi- 
 tion the predicate is either distributed or it is not. It is admitted 
 that this quantification is not explicit in the proposition, but 
 must be inferred from the quality of the proposition. It would 
 be much more satisfactory to state the quantity of the predicate 
 openly and explicitly ; and this I do. When the quantities of 
 the predicate are thus formally displayed, it is found that the 
 quantification in vogue is imperfect. My scheme brings to light 
 quantities that have lain unsuspected. Logic declares that " All 
 A is B" means, of necessity, "all A constitutes a part only 
 of the class B." But this does not exhaust the possibilities. 
 All A may constitute the whole of the class B ; and it is not 
 justifiable to make an assumption that may be inaccurate. 
 Moreover, not only is the assumption, that all A is some B, not 
 necessarily true, but when it happens that All A is all B, we 
 can obtain, by so stating it, a more precise and correct conclusion 
 than we can by limiting our statement to All A is some B.' 
 
 It seems to me that this reasoning is irrefutable. If quantifica- 
 tion, in the logical sense of * distribution ' does reside in the 
 predicate ; if the predicate may be either * distributed ' or 
 * undistributed ' ; and if the * distribution ' or ' non-distribution ' of 
 the predicate is as important as Traditional Logic says it is ; 
 then it seems to me beyond the pale of discussion that it is 
 desirable to state openly on the face of the proposition whether 
 or not the predicate is distributed, and not to leave the distribution 
 to be inferred from the quality of the proposition.
 
 yS A NEW LOGIC 
 
 Hamilton's scheme, as far as it relates to the affirmative 
 propositions, A and I, of Traditional Logic, is as follows : — 
 
 1. The Toto-total— All A is all B. 
 
 2. The Toto-partial — All A is some B. 
 
 3. The Parti-total — Some A is all B. 
 
 4. The Parti-partial — Some A is some B, 
 
 and there is a corresponding series of negatives. 
 
 Now, it cannot be denied, that if the proposition does in fact 
 state the inclusion of the Subject in a class, or its exclusion from 
 a class, these alternatives are possible, and do give us more insight 
 into the meaning of the proposition,— do state more clearly the 
 relation of predicate to Subject — than the mere statement All A 
 (or some A) is B. Logicians find, however, that when the negative 
 series is examined, it leads to self-contradiction and absurdities ; 
 and for this reason they reject the Hamiltonian scheme of 
 quantification of the predicate. They do not recognise, however, 
 that that scheme is a strictly logical extension and application of 
 their own doctrine ; and that if it is rejected, their own doctrine 
 must go with it. If an hypothesis, when strictly applied, leads to 
 absurdity and self-contradiction, the logical conclusion is that the 
 hypothesis is erroneous. No Logic but Traditional Logic would 
 allow us, in such a case, to retain the hypothesis with respect to 
 the cases it covers, and reject it with respect to the cases it does 
 not cover. The Ptolemaic hypothesis of crystal spheres accounts 
 perfectly for the movements of the fixed stars ; but when applied 
 to the movements of the planets and comets, it breaks down, and 
 is found inefficient. Would astronomers, then, be justified in 
 retaining it in the case of the stars, and rejecting it as far as the 
 planets and comets are concerned ? No practical reasoner w^ould 
 countenance such a proceeding for a moment ; but this is what 
 Logicians do with respect to the quantification of the predicate. 
 
 Consideration of other propositions also destroys the scheme of 
 quantity enunciated by Traditional Logic. * Caesar was killed by 
 Brutus.' Neither the Subject nor the Predicate is a class, and 
 neither, therefore, can very well be considered * distributed.' By 
 some logicians, the proposition is regarded as a Universal, since 
 the Predicate refers to the whole of the Subject ; but in the first 
 place, as already shown, in every particular proposition, the 
 Predicate refers to the whole of the Subject ; and in the second.
 
 ABSURDITY OF LOGICAL QUANTITY 79 
 
 it is incongruous and anomalous to speak of the whole of Caesar 
 being killed. We do not think of Csesar, in this connection, as a 
 whole composed of parts. We think of him as an individual ; and 
 if we think of Caesar as a whole, we do not, unless we are logicians, 
 think of killed-by- Brutus as a class or as an attribute. The proposi- 
 tion certainly does not express, as Traditional Logic asserts that 
 it does, that Caesar was one of the class of persons killed by Brutus. 
 It expresses, not the inclusion of Caesar in a class, but that Casar 
 underwent an experience — that he, as patient, suffered an experience 
 at the hands of the agent, Brutus. Some logicians, recognising 
 these difficulties, relegate the singular proposition to a separate 
 class, that is neither Universal nor Particular ; but then the logical 
 scheme of quantity falls to the ground. 
 
 My view is that quantity is not vital in reasoning. In Traditional 
 Logic, in which all reasoning consists in inclusion in classes, or 
 exclusion from classes, quantity is, of course, of paramount import- 
 ance ; but to a Logic which looks at reasoning by and large, and 
 reasons of relations of all orders, of which the relations of class 
 inclusion and exclusion form but a small minority, quantity is of 
 less importance. 
 
 But if quantity is to be admitted into reasoning at all, it must 
 be admitted freely, and in all its kinds, and degrees, and varieties. 
 To admit the two quantities, All and Some, and to exclude all 
 other quantities, every one of which is quite as important as these, 
 and quite as frequently employed in argument, is monstrous, and 
 cannot be allowed. Nothing but the blind infatuation with which 
 logicians regard the syllogism, would render such a course possible; 
 and it speaks loudly for the strength and depth of this infatuation, 
 that the multitude of quantities other than All and Some should 
 have been ostracised by Logic for so many generations. The time 
 is come, however, to break down this absurd restriction.
 
 CHAPTER VI 
 
 NEW DOCTRINE OF QUANTITY 
 
 My view of quantities is as follows : — 
 
 Terms, whether quantitative or qualitative, maybe contemplated 
 intrinsically, that is to say, without regard to any term of the other 
 kind ; and thus regarded, are susceptible of quantity ; the quantity 
 of quantitative terms being different in kind from the quantity of 
 qualitative terms. 
 
 Or terms of either kind may be contemplated in association 
 with a term of the other kind, as follows : — 
 
 Quantitative terms may be contemplated with respect to the 
 qualities they possess; and, thus contemplated, become susceptible 
 of classification. 
 
 Qualitative terms, on the other hand, may be contemplated with 
 respect to the concretes they qualify ; and, thus contemplated, they 
 form the means of classification. 
 
 It follows that our task is first to investigate the quantity of 
 quantitative terms, then the quantity of qualitative terms, and then 
 to investigate the means of classification, and the process of 
 classification. 
 
 Quantitative terms are either individuals or classes, each of 
 which has its characteristic intrinsic quantity, but both these kinds 
 of quantity have the common character of extensity, and the two 
 may be considered together as Extensive quantities. 
 
 Qualitative terms are either abstracts or attributes, each of which, 
 again, has its characteristic intrinsic quantity, but both kinds of 
 quantity have the common character of intensity or degree, and 
 the two may be considered together as Intensive or Graduate 
 quantities. 
 
 Extensive quantity is, then, of two kinds, one of which is 
 applicable to individuals only, while they are regarded as individuals, 
 and are not compared, or grouped, or contrasted, or associated, 
 with other individuals. Thus regarded, an individual is susceptible 
 of contemplation as a whole composed of parts, and we may con-
 
 SCHEME OF QUANTITY 8i 
 
 centrate our attention on the whole, or on a part, or on whole and 
 part in association, or on parts associated together. When con- 
 templated as a whole, without regard to its parts, a thing is an 
 individual, or unit, and its quantity is Singular ; when contem- 
 plated with respect to its parts it is a Composite individual, and 
 is susceptible of a quantity that is no longer Singular, but that for 
 want of a better name I call Massive quantity. 
 
 The other kind of Extensive quantity is applicable to individuals, 
 contemplated, not singly, but with respect to other individuals, 
 associated together in one or more classes. Such Extensive 
 quantity is Numerical quantity. 
 
 Intensive quantity also is of two kinds, according as it is 
 applicable to Abstract or to Attributive quality. Abstract quality 
 is in a sense absolute — in the sense, that is, that abstract quality is 
 absolved from its connection with any concrete but itself, and is 
 contemplated alone. Attributive quality, on the other hand, is 
 always related to the concrete by which it is manifested, and there- 
 fore may be termed relative. It must be admitted, however, that 
 absolute and relative, in this connection, mean little, if anything 
 more than abstract and attributive. 
 
 The complete scheme of quantity will therefore be as follows : — 
 
 TABLE II. 
 
 Scheme of Quantity. 
 
 The Quantitative term refers to indi- Kind of Quantity. 
 
 viduals — Extensive. 
 
 Singly, and contemplated ... ... Singular. 
 
 As not composite ... ... ... Unit. 
 
 As wholes composed of parts ... Massive. 
 
 Grouped in classes, and ... ... Class. 
 
 Unspecified as to Discrimination Indesignate. 
 
 Specified as taken ... ... ... Designate. 
 
 Indiscriminately ... ... Collective. 
 
 Discriminately ... ... ... Distributive. 
 
 The Qualitative term refers to quali- 
 ties — 
 
 Regarded as to their degree in Intensive. 
 
 Abstracts Absolute degree. 
 
 Attributes Relative degree. 
 
 n.l. a
 
 82 
 
 A NEW LOGIC 
 
 Qualities, regarded with respect to the 
 concretes they quaHfy are 
 
 Either ... 
 
 Or 
 
 Individuals regarded with respect to 
 the qualities they manifest, con- 
 stitute 
 
 Either ... 
 
 Or 
 
 Or 
 
 Comprehensive. 
 Common. 
 Proper. 
 
 A Class of individuals. 
 A Class of classes. 
 Classes within a class. 
 
 This is the proper logical order, but Traditional Logic gives such 
 enormous preponderance to the Distributive quantity, that in order 
 to bring my scheme into comparison and contrast with that of 
 Traditional Logic, it will be desirable to bow myself in the House 
 of Rimmon, and rearrange the Extensive quantities so as to take 
 the Distributive before the Singular and the Collective. The order 
 in which these quantities will be taken is therefore as follows : — 
 
 TABLE III. 
 
 Extensive Quantities 
 
 The Quantitative term refers to indi- 
 viduals — 
 Grouped in classes and 
 
 Unspecified as to discrimination... 
 Specified as to discrimination and 
 taken — 
 Discriminately ... 
 Indiscriminately 
 Singly and contemplated as 
 Wholes composed of parts 
 Individuals without regard to com- 
 position ... 
 
 Quantity. 
 Extensive. 
 Class. 
 
 Indesignate. 
 Designate. 
 
 Distributive. 
 Collective. 
 Singular. 
 Massive. 
 
 Unit. 
 
 Extensive quantities refer to individual things, either singly, 
 or aggregated into classes by the possession of some common 
 quality. The class is of course conceptual ; that is to say, 
 when we speak of things being grouped, or associated, or 
 aggregated, together in classes, we do not mean that the things 
 are grouped or associated together in physical propinquity ;
 
 INDESIGNATE QUANTITY 83 
 
 we mean that they are regarded or contemplated together by 
 the mhid, as ahke in some respect. Similarly, all logical quanti- 
 ties are conceptual. They are aspects of things. They are ways 
 of looking at things ; and, as the same thing may be looked at 
 from different aspects and contemplated with respect to different 
 qualities, so it may have different quantities, according to the 
 mode of contemplation. 
 
 When we contemplate individual things as grouped together in 
 classes, we may contemplate them in two ways as thus grouped. 
 We may contemplate them in the class discriminately, or one 
 by one, preserving their separateness from one another, and 
 saying what we have to say of them of each and every indvidual 
 in the class. Thus contemplated, they are contemplated dis- 
 tributively, and the quantity is the Distributive Extensive. But 
 we may contemplate them otherwise. We may contemplate 
 them indiscriminately, without distinguishing one from another, 
 or keeping them separate in thought ; and then whatever predi- 
 cation is made about them is made of all taken together in 
 bulk or in the mass, and is not true of each and every one. 
 Thus contemplated, the individuals are contemplated collec- 
 tively, and the quantity is the Collective Extensive. In ' Every 
 one of the books is a first edition ' the Subject term is Dis- 
 tributive. In * All the books together cost £300 ' the Subject 
 term is Collective. 
 
 The Indesignate Quantity. 
 
 An indesignate quantity is, strictly speaking, no quantity. In 
 many propositions no quantity is designated, either in the Subject 
 or in the Object term ; and, as Traditional Logic cannot con- 
 struct an argument with unquantified propositions, such propo- 
 sitions have always been to it a stumbling block. In such 
 propositions as ' The weather is fine,' ' Beauty is skin deep,' 
 * The falling out of faithful friends renewing is of love,' there is no 
 quantity in either term. This being so, what can Traditional 
 Logic do, since it cannot construct an argument with an 
 unquantified proposition ? The obvious expedient, and one 
 that is adopted by many cautious logicians, is to refuse to such 
 propositions any place in Logic. Such logicians arc wise in 
 their own generation, for they evade an insuperable difficulty. 
 That the price paid for this relief is such a narrowing and 
 
 G 2
 
 84 A NEW LOGIC 
 
 restriction of the province of Logic as reduces it to inefficiency 
 in a large field of reasoning, is a consideration that has never 
 troubled logicians. Indeed, there is no reason why it should 
 trouble them in this case ; for, when all Modals are excluded ; 
 when all propositions not expressed by the copula are excluded ; 
 and when all quantities but All and Some are excluded ; the 
 diminution, by the exclusion of the Indesignate out of the 
 attenuated remnant that is left, is really of little consequence. 
 When a man's arms and legs have been amputated, it makes little 
 difference to him to lose one of his ears ; and the difficulty of 
 bringing the Indesignate proposition into the scheme of Tra- 
 ditional Logic is so great, that those logicians are wisest who 
 exclude this proposition altogether. 
 
 Other logicians, however, admit it ; and the difficulty of 
 deciding whether it is Universal or Particular is neatly sur- 
 mounted, by some logicians making it Particular, and others 
 making it Universal. A third class declare that it is Universal 
 in some cases and Particular in others ; while a fourth decide 
 that the indesignate quantity results from carelessness on the 
 part of the proposer, who might have investigated and declared 
 the quantity of the indesignate Subject, but failed to do so. 
 
 In my view, the Indesignate term is neither Universal nor 
 Particular, but Indesignate. It remains indesignate until its 
 quantity is designated, and it is just as capable of entering 
 into arguments and of forming the basis of sound and valid 
 conclusions as are propositions that are specifically and definitely 
 quantified. If I say 'The poor are discontented' or 'Traditional 
 Logic is unduly restricted,' my statement must go for what it is 
 worth ; and any conclusion I may draw from it must be as 
 indesignate in quantity as the premiss from which I started ; but 
 as long as it remains indesignate throughout the argument, and 
 appears indesignate in the conclusion, the argument and the 
 conclusion are, as far as quantity is concerned, perfectly sound ; 
 and it is just as easy, just as logical, just as permissible, to 
 argue from an indesignate, as from a definitely quantified 
 proposition. 
 
 The poor are always with us ; 
 The poor are discontented ; 
 . • . The discontented are always with us.
 
 DESIGNATE QUANTITY 85 
 
 Beans are indigestible ; 
 She gave him beans ; 
 . • . She gave him what is indigestible. 
 
 These are perfectly valid arguments. In the second the 
 Predicate, and in the first both the Subject and Predicate of the 
 conclusion arc indesignate ; and in both arguments the middle 
 term is indesignate in both premisses. Yet the arguments are 
 valid, and why ? Because the term which is indesignate in the 
 premiss remains indesignate in the conclusion. The Indesignate 
 term is neither Universal nor Particular. It is, and it remains 
 throughout the argument, Indesignate. 
 
 The Designate Quantity. 
 
 If a Class term is preceded by a sign of quantity, it becomes 
 a Designate term, for the sign designates the quantity that is to 
 be attached to the term. As already stated. Designate terms are 
 of two kinds. Distributive and Collective, the Distributive 
 referring discriminately and separately to every member of the 
 class, and the Collective term referring indiscriminately to all the 
 members of the class taken together in the lump. In either case, 
 the class designated by the sign of quantity may be regarded as a 
 whole, without reference to any larger class of which it is a part; 
 or it may be regarded as part of a larger class. In the first case, 
 the quantity is called universal ; in the second, it is called 
 particular. Thus far, the statements made are true of both the 
 Distributive and the Collective terms, but from this point they 
 must be considered separately. 
 
 The Distributive Quantity. 
 
 This is practically the only quantity treated of by Traditional 
 Logic. It is true that most logicians mention the Collective 
 term, and point out the difference between it and the Distributive. 
 It is true that, in modern times, logicians have admitted the 
 Singular quantity as a possible subject of predication and argu- 
 ment. It is true that, under the name of the Substantial 
 term, a logician here and there has shown that he is aware of 
 the Uniform quantity ; but beyond a bare mention, or a very 
 perfunctory description, these quantities receive no consideration or
 
 86 
 
 A NEW LOGIC 
 
 examination at the hands of logicians. No logician known to me 
 recognises that the Collective quantity as well as the Distributive 
 is divisible into the Universal and the Particular ; no logician of 
 recent times discusses the nature of the Individual, or is aware of 
 more than two kinds of Individual. Every logician confuses the 
 Aggregate individual with the Collective class, and both with the 
 Uniform individual ; and no logician has ever yet recognised that 
 there is an Intensive quantity as well as a Numerical quantity; nor 
 has any logician regarded the Comprehensive quantity as one of 
 the quantities of terms, or relegated it to its proper place in Logic. 
 To all intents and purposes, the logical scheme of quantity is 
 limited to the Distributive quantity alone. 
 
 Nor docs the irrational limitation of the logical scheme of 
 quantity end here. Logic divides the Distributive quantity into 
 the Universal and the Particular, and then sits down contentedly 
 in the belief that the last word has been said, and that no further 
 division is required. It does not appear to have dawned upon 
 the minds of logicians that any further division is possible or 
 practicable, or that there are, in fact, any other quantities of terms 
 than the bare Universal and the bare Particular; or any other 
 signs of quantity than All and Some. Of the three varieties of 
 the Universal it knows but one; of the innumerable classes, sub- 
 classes, varieties and sub-varieties of the Particular quantity, 
 Traditional Logic knows not one. 
 
 The following is the skeleton Table of Distributive quantities : 
 
 TABLE IV. 
 Distributive Quantities. 
 
 Reference of Term. 
 
 The Distributive term refers to all 
 the individuals in a class dis 
 
 Sign. 
 
 Quantity. 
 
 w 
 
 criminately, or one by one. 
 
 and 
 
 
 J^IOLIIL/ULIV*^. 
 
 regards the class as 
 
 J 
 
 
 
 A whole, and refers to the 
 
 
 
 individuals 
 
 • • • 
 
 All 
 
 Universal. 
 
 Simultaneously 
 
 
 Every 
 
 Simultaneous 
 
 In turn 
 
 • ■ • 
 
 Each 
 
 Successive. 
 
 At random ... 
 
 . • • 
 
 Any 
 
 Alternate. 
 
 Part of a larger class 
 
 
 Some 
 
 Particular.
 
 UNIVERSAL DISTRIBUTIVE QUANTITY 87 
 
 The Universal Distributive. 
 
 When all the individuals in a class, regarded as a whole class, 
 are referred to discriminately, or one by one, the quantity is the 
 Universal Distributive, and the sign of this quantity is All. The 
 Universal Distributive quantity is, however, itself a class, and 
 includes three separate individuals, as follows : — 
 
 The Simultaneous Universal quantity is characterised by the 
 sign Every. This is the Universal of Traditional Logic, and the 
 only Universal known to that body of doctrine. When Traditional 
 Logic uses the sign All, it means Every one, and has not, until 
 lately, recognised that ' All ' includes three different meanings. 
 The Universal Distributive term refers to all the individuals in a 
 class taken discriminately, or one by one ; but things can be taken 
 one by one in different ways. If two things are on the table, we may 
 take one in each hand simultaneously, and then we take every one 
 of them. If there were fifty things on the table, and we were 
 Briareus, we could lift them all, simultaneously and separately, 
 and then we should lift every one of them ; and the universal 
 lifting is the Universal of Traditional Logic. Or without lifting 
 them, we may contemplate them simultaneously, and make the 
 same predication simultaneously of each separate one, and still we 
 contemplate and speak of every one. 
 
 But there is another way of taking them one by one, besides 
 taking them simultaneously. We may lift them one by one in 
 turn, taking them one after the other until all are lifted ; or we 
 may contemplate or speak of them one by one in turn, going on 
 until all have been thus contemplated or predicated of ; and in 
 this case we deal with each one. By Each we mean one by one 
 in turn until all have been taken. If we take each, we may not arrest 
 the process until the tale is complete : we must go on to the end. 
 Any predication made about each is not true unless it includes all . 
 
 But a predication made about every individual of a class is true 
 of any one of them taken at random ; and vice versa, what is true 
 of any one of them, is true, as far as the class likeness extends, of 
 any other, and of every other. If we select one, as we must if we 
 take them in turn, then we are not entitled, until we have selected 
 every other one, to predicate of all what is predicable of that 
 selected one ; because the very fact that it was selected raises a 
 presumption that it was in some respect different from the rest.
 
 SS A NEW LOGIC 
 
 But if we take one at random, the very fact that it is so taken 
 indicates the absence of any difference between it and the rest, and 
 what is predicable of one taken at random is predicable, as far as 
 the claps Hkeness extends, of every other. Hence Any one, though 
 it refers ostensibly to an individual only, is in practice a sign of 
 the Universal. This, which we may call the Alternative Universal, 
 is very closely akin to the Representative Individual. ' Any pen 
 is useful ' has very nearly the same meaning as * A pen is a useful 
 thing.' It has not quite the same meaning, however, as will be 
 shown when we examine the Representative Individual. 
 
 These, then, are the three varieties of the Universal quantity; but 
 though they are here explained in detail in connection with the Dis- 
 tributive quantity, it must be clearly understood that the Universal 
 is not restricted to the Distributive quantity, but is common to it 
 with the Collective quantity and the Unified Individual. The 
 Collective quantity, however, has but one form of Universal. 
 
 The Particular Distributive. 
 
 If Traditional Logic lumps together not merely the three varieties 
 of the Distributive Universal, but the Collective and some forms 
 of the Individual ; if it makes no distinction between things so 
 different as the Aggregate and the Corporate Individuals; if it is 
 blind to Intensive quantity and deaf to Indesignate quantity, we 
 need not be surprised that it fails to distinguish some of the 
 varieties of the particular Distributive, for the characterisation of 
 some of them is subtle and elusive ; but that Logic should fail 
 to distinguish or acknowledge any variety whatever of the 
 Particular, except, in a halting way, one additional meaning of 
 ' Some,' is really portentous, and calls to mind Dr. Johnson's 
 saying with respect to Thomas Sheridan. * Sherry is dull, Sir, 
 naturally dull ; but he must have taken great pains to become 
 what we see him. Such an excess of stupidity is not in nature.' 
 Logicians are blind to the obvious, naturally blind ; but they must 
 have taken great pains not to see some at least of the varieties of 
 the Particular. Such an excess of unobservation is not in nature. 
 
 A Particular Distributive term refers discriminately to the indi- 
 viduals in a class ; but the class is regarded, not as a whole, but 
 as part of a larger and including class. Now, in examining the 
 Universal term, we have already found that the individuals compos- 
 ing a class may, when contemplated discriminately, or one by one,
 
 PARTICULAR DISTRIBUTIVE QUANTITY 89 
 
 be contemplated simultaneously, or successively, or alternately ; 
 and this is equally true whether the class they compose is or is not 
 part of a larger class. But when the individuals compose a class 
 within a larger class, the double composition offers us more ways 
 of contemplating them than when they are regarded as forming a 
 primary class only. The individuals composing the subordinate 
 class, or sub-class, may be grouped together in the mind, and con- 
 templated either with respect to the larger or including class, or 
 with respect to other sub-classes within that including class. 
 
 Every quantity has its appropriate sign, which, when prefixed to a 
 term, determines the quantity of the term ; and every such sign is 
 the answer to a question that may be put with respect to the quantity 
 of the term. The following Table gives a fairly complete list of 
 the Particular Distributive quantities, together with a specimen 
 sign of each. 
 
 TABLE V. 
 
 Particular Distributive Quantities. 
 
 Reference of Term. 
 The Particular Distributive term 
 refers discriminately to all the 
 individuals in a class, regarded 
 as part of a larger class, and 
 contemplates them 
 Simultaneously 
 
 As to their number .. 
 As to their proportion 
 to the whole 
 Successively as to their 
 
 order 
 Alternatively 
 
 with respect to the 
 
 whole 
 with respect to other 
 
 parts 
 with respect to one 
 another 
 
 Indefinitely ... 
 Definitely 
 with respect to the 
 purpose in hand ... 
 
 Quantity. Specimen Sign. 
 
 ij^iiuuiciaiivc 
 
 Proportional 
 
 Most. 
 
 Ordinal 
 
 The first. 
 
 Residual 
 
 The rest. 
 
 Comparative 
 
 More. 
 
 Selective 
 
 
 Indefinite 
 
 Certain. 
 
 Demonstrative 
 
 This. 
 
 Purposive 
 
 Enough.
 
 go A NEW LOGIC 
 
 Each of these quantities is a class, and includes several distinct 
 sub-classes ; and most of the sub-classes are again divisible into 
 varieties and sub-varieties, of which the individual members are, 
 in manv cases, indefinitely numerous. The Enumerative, the 
 Proportional, the Ordinal, the Comparative, and the Indefinite 
 Selective, have each their Indefinite, Semi-definite, and Definite 
 sub-classes. The Residual quantity is divisible into the Universal 
 Residual, and the Particular Residual ; and has as many varieties 
 of these as has the whole class. The Demonstrative quantity is 
 divisible into Appropriative and Repudiative, and each of these 
 into Singular and Plural ; and the Purposive quantity is divisible 
 into the Suitable and the Unsuitable, the latter being again sub- 
 divided. The total number of Particular quantities is therefore 
 indefinitely multitudinous. 
 
 The weary student will be disquieted to learn that the varieties 
 enumerated above by no means exhaust all the recognisable and 
 distinguishable varieties of the Particular Distributive quantity. 
 Ever}- particular quantity is further susceptible of three Forms, in 
 addition to the unqualified, vague or Indesignate form that alone 
 has hitherto been referred to. The three additional Forms are 
 the Minimal, the Maximal, and the Exact. 
 
 The Minimal form of a quantity fixes that quantity as a 
 minimum, below which the quantity does not extend, but fixes no 
 maximum, and leaves it uncertain whether the part referred to in 
 the term, does or does not extend beyond the minimum, and even 
 to the whole class. The signs of the minimum are ' not less than ' 
 and 'at least,' and the indefinite ' Some at least' fixes a minimum, 
 in this case an indefinite minimum, to the quantity to which the 
 term refers, but leaves the maximum in doubt, and lets it be 
 understood that the quantity may, for aught it expresses, extend 
 to the whole class. 
 
 The Maximal form of a quantity has the opposite effect. It 
 fixes as a maximum the quantity referred to by the term, but 
 leaves the minimum uncertain. It gives us the assurance that the 
 quantity is not more than is expressed by the term, but gives us 
 no assurance that it is as many, or even that there are any at all. 
 The sign of the maximum is ' Only,' or ' Not more than,' to which 
 it may be necessary, in some cases, for the sake of greater pre- 
 cision, to add 'If any.' The indefinite 'Some only if any' 
 positively fixes the maximum at some, and assures us that it is
 
 ABSURD RESTRICTIONS OF LOGIC 91 
 
 not all; but it fixes no minimum, and the 'Some' may be an 
 inappreciably small number, or even none at all. 
 
 The Exact form of a quantity fixes both the maximum and the 
 minimum, and assures us, first, that the quantity does not extend 
 to all, nor to any more than the quantity' expressed, and second, 
 that the whole of the quantity expressed is certainly within the 
 reference of the term, which, therefore, does not, as the maximal 
 form does, or may, express a vanishing quantity. The indefinite 
 quantity cannot be expressed in its exact form by any sign less 
 cumbrous than 'Some certainly, but some only,' or 'Some only, 
 but certainly some'; in other quantities, however, it admits of 
 much neater expression, and there are several forms of quantity 
 in which the quantity itself and its form can be expressed in a 
 single word. 
 
 Out of the three primary kinds of quantity enumerated in 
 Table II., p. 81, Traditional Logic selects the Extensive, and 
 explicitly or implicitly declares that we can reason of no other. 
 Out of the two kinds of Extensive quantity, Logic selects one, the 
 Class-quantity, and, though Logic does not now declare that we 
 can reason of no other, there was a time when it did make this 
 declaration, and it now gives no more attention to the Singular 
 quantity than is barely decent. Out of the two kinds of Class- 
 quantity, Logic selects one, the Designate, and proclaims its 
 inability to reason of the other. Out of two kinds of Designate 
 quantity, Logic selects one, the Distributive, and though it goes 
 so far as to admit the existence of the other. Logic does not allow 
 that this other, the Collective quantit}', is susceptible of sub- 
 ordinate quantities. The two primar}' kinds of Distributive 
 quantity, the Universal and the Particular, are, indeed, dis- 
 tinguished by Logic, but here its discrimination ends, or almost 
 ends. Of the three kinds of Universals, Logic uses but one, 
 though it is aware of the existence of the other two ; and of the 
 eight classes of Particular Distributive quantities, each with its 
 sub-classes and varieties. Logic knows nothing at all. 
 
 Logic selects one form of one variety of one kind of the 
 Particular quantity, and explicitly excludes another form of this 
 variety; while of all other kinds, with their varieties and forms, 
 incalculably numerous though they are. Logic is profoundly 
 ignorant. It never recognises their existence, and apparently has 
 never realised or imagined that they do or can exist. Out of
 
 92 A NEW LOGIC 
 
 them all, Logic selects the Minimal Indefinite Enumerative, and 
 declares that this is the only Particular quantity of which we do 
 or can reason. It would be nearer the mark to say that it is the 
 quantity of which we reason least often. It is clear that if we are 
 to restrict our statements and reasonings to All and Some, we 
 must divest these statements and reasonings of all precision and 
 definiteness, and can reach none but vague conclusions. That the 
 reasonings of Logic are but vague must be apparent to everyone 
 who has ever opened a book on the subject. The first thing 
 with respect to these reasonings that strikes a new comer is that 
 they seem to have so little practical application ; and when he 
 seeks the reason for this detachment and aloofness from practical 
 affairs, he finds it in the indefiniteness of the Particular quantity 
 that alone is used. In the practical statements and reasonings of 
 daily life, we do not restrict our dealings to ' Some.' We never 
 do and never ought to employ this quantity if it is possible to use 
 one more definite. In our household and family affairs, in 
 business and professions, in Parliament, in the pulpit, in the shop, 
 the factory, the mine, and the railway, in work and in play, we 
 never, if we can help it, use the indefinite ' Some.' What sort of 
 a world would it be, how much business could be transacted, how 
 many things could be done, if assertion and reasoning were 
 limited to All and Some ? * A house to let, with some rooms in it, 
 some distance from some town in some county, rent some pounds 
 per annum, fare from London some money, distance some miles. 
 The trains run sometimes, and the journey takes some time.' 
 ' Please sell me some shares in some stocks and buy me some 
 shares in some other stocks. My address is some number in some 
 street in some town.' ' He is sure to be elected, for though 
 some voters are pledged to vote for his adversary, some have 
 promised to vote for him.' * I am not in your debt, for though it 
 is true that I owed you some money last week, I paid you 
 yesterday all I had.' ' Since some people live to fifty, and some 
 live to a hundred, it is evident that the same number of people 
 live to a hundred as live to fifty.' No ? Do you doubt ? Well, 
 you may perhaps have reason, but Logic has no terms to express 
 differences of quantity more precise than that between All and 
 Some, and therefore in matters of such extreme exactitude it 
 would be unfair to expect guidance from Logic. ' An excursion 
 train will start for some place next week, at some time in the
 
 ABSURDITY OF LOGICAL QUANTITY 93 
 
 day, and the return fare will be some shillings.' ' Ample provision 
 has been made for the party, for some people are coming and 
 some food has been provided.' Are these the modes of statement 
 and reasoning that are in use ? 
 
 * And slimy things did crawl with legs 
 Upon the slimy sea.' 
 
 Do we understand Some slimy things, or All slimy things ? and 
 did they crawl with Some legs, or with All legs ? and if with 
 Some, did they necessarily crawl with some-at-least-and-perhaps-all 
 legs ? 
 
 ' From that hour he never put pen to paper.' Some pen or all 
 pens ? Some paper, or some at least, it may be all paper ? 
 
 Let us try how the General Confession looks in logical terms: — 
 
 * We have erred and strayed from some, it may be all, of thy 
 
 * ways, like some, it may be all, lost sheep. We have followed 
 
 * too much some or all the devices and some or all the desires of 
 
 * our own hearts. We have offended against some, it may be all, 
 ' of thy holy laws. We have left undone some, it may be all, of 
 ' those things that we ought to have done, and we have done 
 
 * some, it may be all, of those things that we ought not to have 
 
 * done. And there is no health in us. But thou, O Lord, have 
 
 * mercy upon some and perhaps all of us,' &c. These are the 
 terms in which we ought to express ourselves if we follow strict 
 logical form. 
 
 But Logic is not content with excluding from its purview all 
 Particular distributives except the indefinite Some. We have 
 seen that there are three forms of Some — the miminal form, Some 
 at least ; the maximal form, Some only ; and the exact form, 
 Some certainly, but not all, or Some at least, but some only. To 
 these may possibly be added a fourth, viz. : — * Some, but I do not 
 say whether some at least or some only.' Of these three and 
 possibly four, Logic selects the first, drives the second out of 
 its precincts, and does not recognise the existence of the third. 
 Why Logic should take to its bosom ' Some at least,' pitch 
 
 * Some only ' neck and crop out of the house, and wilfully shut its 
 eyes to the exact * Some,' it is difficult to conjecture. Logicians 
 make it a grave charge against Sir William Hamilton, that he has 
 polluted the virgin purity of the logical Some, by befouling it with 
 the hateful meaning Some only; but for the exclusion of the
 
 94 A NEW LOGIC 
 
 maximal Some only, Logic gives neither rhyme nor reason. And 
 there is no reason for it. There can be no reason. ' Some only ' 
 is a quantity as useful, as accurate, as frequently employed, as 
 capable of entering into statement and reasoning, as * Some at 
 least,' and its exclusion from Logic is utterly unwarrantable. 
 
 If Some were drowned. Logic declares that all may have been 
 drowned, and will not admit the possibility that some must have 
 been saved ; nor will it allow us to count on the probability that 
 some may have been saved, for this is a modal, and modals are 
 excluded from Logic. I aver, on the contrary, that if some only 
 were drowned — a possibility that Traditional Logic will not 
 admit — then it is certain that some were not drowned ; and the 
 anxiety of us, who are not logicians, as to the fate of Some at 
 least of the party, is relieved ; but logicians must still remain in 
 anxious uncertainty. We, who are not logicians, know that, if 
 logicians recognise some modes of argument only, and some 
 Particular quantities only, it is certain that there are other modes 
 of argument and other Particular quantities that logicians are not 
 aware of; but logicians themselves are precluded by their own 
 rules from drawing this inference, or making this admission. They 
 claim that as they are acquainted with Some modes of argument 
 and Some particular quantities, and as Some has, in Logic, but the 
 one meaning of ' Some, it may be all,' the modes of argument and 
 the quantities with which they are acquainted may be all there 
 are. We know better, but we cannot convince a logician of his 
 error, for to him every Some is potentially All. 
 
 If Some aquatic animals at least are fish. 
 And Fish are the only animals that have true fins, 
 then Logic permits and compels us * to draw the conclusion that 
 
 Some aquatic animals at least have true fins ; — 
 and leaves us groping in the dark as to the rest of aquatic animals. 
 But if Some aquatic animals only are fish, 
 And Fish are the only animals that possess true fins, 
 then common sense allows and compels us to conclude that 
 Some aquatic animals do not possess true fins. 
 
 • I am ashamed to say that not until too late did I recognise that this is 
 not a logical argument at all. The predicate of the major is explicitly quantified, 
 and though the predicate of every proposition must be quantified, it must be 
 quantified sub rosd, and must not brazenly avow its quantification. Conse- 
 quently, the major not being a logical proposition, the argument is not a
 
 VARIOUS MEANINGS OF 'SOME' 95 
 
 This conclusion Logic forbids us to draw. Such an argument, 
 such a conchision, is illicit, illogical, illegitimate, and impossible. 
 Why? 
 
 If logicians know of some particular quantities only, then they 
 do not know all particular quantities ; then there are some 
 particular quantities of which they are ignorant ; then their 
 knowledge of particular quantities is imperfect, it is defective : 
 and then there are quantities of which they do not know. These 
 are all valid inferences from the premiss, but logicians are happily 
 ignorant of them, and doubly ignorant ; for, in the first place, the 
 premiss is inadmissible into Logic, and, in the second, the con- 
 clusions are arrived at by a process unknown to Traditional Logic. 
 They are Immediate Inferences, but none of them is a converse, 
 an obverse, a contra-positive, or an inverse. 
 
 If one particular quantity only is to be chosen to represent 
 them all, the indefinite Some is the best that could be chosen, for 
 it may be made, with little difficulty, to cover nearly all the rest. 
 Many, a few, a very few, one, two, most, few of, three more, 
 twice as many, the rest, the others, the first, the last, certain, 
 this, those, enough, too many, and so forth, may all be included 
 under Some ; but apart altogether from these more definite 
 interpretations, bare indefinite ' Some ' is susceptible of twenty or 
 thirty different meanings, as against the two that are recognised 
 and the one that is used by Logic. 
 
 * Some ' may mean an indefinite and unselected number taken 
 distributively ; or it may mean an indefinite but selected number 
 taken distributively ; or it may mean an indefinite unselected 
 number taken collectively; or an indefinite selected number taken 
 collectively ; or it may mean an indefinite proportion, either 
 selected or unselected, and in either case taken distributively or 
 collectively ; or it may mean an indefinite ordinal number, 
 selected or unselected, and taken distributively or undis- 
 tributively ; and in any case it may mean the particular Some 
 minimally, maximally, exactly, or vaguely, that is, without 
 specifying whether it is minimal, maximal, or exact. 
 
 logical argument. I can only plead in extenuation that the limits of Traditional 
 Logic are so extremely narrow, that a mere amateur cannot be expected to 
 make a bull's-eye at every shot. So few valid arguments are ' logical,' that 
 one really ought to recognise that the more cogent an argument, the stronger 
 the presumption that it is ' not logical.'
 
 96 A NEW LOGIC 
 
 The exclusion from Traditional Logic of all these meanings, 
 except one, of the indefinite Some, and of all the semi-definite and 
 definite varieties of the particular quantity, in both the distributive 
 and the collective quantities, and in all the three or four forms of 
 this quantity, is not, however, as important as it seems at first 
 sight ; for already, by excluding Modals, and all Ratios except the 
 copula, Traditional Logic had so narrowed the field of its 
 operations as to deprive itself of almost all practical usefulness ; 
 and the addition of one more unnecessary restriction makes no 
 important difference. Logicians declare that they can make no 
 reference to any part of a class without assuming that that part 
 may be the whole. Well, if their minds are so constituted that 
 this is true of them, I have no more to say, except that they 
 must not seek to impose the same restrictions upon others, 
 whose minds are more capacious. The restrictions of Traditional 
 Logic are so surprising, and are so discrepant from common 
 experience, that if it should declare that it can entertain no 
 argument, and accept no conclusion, unless the premisses are 
 written in red ink, or in black letter, I should accept the state- 
 ment without a murmur, as true of logicians themselves, as 
 long as they are engaged in reasonings that they are pleased 
 to call logical ; but I should not accept it, any more than I 
 accept the exclusion of Modals, of Ratios other than ' is ' or of 
 Particular quantities other than ' Some at least,' as true of 
 myself, or of reasoners in general, or of logicians themselves, 
 apart from their books. 
 
 The exclusion from Logic of all the semi-definite and definite 
 Particular quantities, of all exact and maximal forms of quantity, 
 of the Residual and Purposive quantities, not only deprives such 
 reasonings as Logic can effect, of all precision, and therefore, in 
 most cases, of all practical usefulness, but it also shuts out from 
 Traditional Logic an immense range of arguments that are in 
 constant use, but that this Logic cannot compass, for want of 
 terms in which to express them. When these subordinate 
 varieties of the Particular quantity are admitted into argument, 
 it is found that the methods and principles of reasoning, as 
 formulated by Traditional Logic, are not only defective, but also 
 very erroneous. The rules of the Syllogism are applicable to 
 deductive reasoning so long only as that reasoning is confined 
 to the minimal indefinite distributive quantity. As soon as
 
 THE PROPOSITION 97 
 
 other quantities are admitted into statement and argument, 
 every one of the Canons of the Syllogism is found to be false, 
 and the Square of Opposition is blown to pieces. It will 
 be necessary, therefore, even at the cost of some tedium, to 
 examine in detail each of the Particular quantities that has been 
 enumerated. 
 
 N.L. H
 
 CHAPTER VII 
 
 particular distributive quantities 
 The Enumerative Quantity. 
 
 When a term refers discriminately to all the individuals in a 
 class, regarded as part of a larger class, and contemplates them 
 simultaneously with respect to their number, the quantity is 
 Enumerative, and answers the question, How many ? 
 
 The Enumerative quantity may be Indefinite, Semi-definite, or 
 Definite. 
 
 The Indefinite Enumerative. — The sign of this quantity is Some, 
 which includes, not only the * Some at least it may be all ' of 
 Traditional Logic, but also ' Some only, it may be none,' and * Some 
 certainly, but not all.' Of these, the minimal form, ' Some at 
 least,' is sufficiently explained in the text books, and the exact 
 form, * Some only, but some certainly,' has been examined on a 
 previous page. It remains to consider the maximal form, ' Some 
 only, and perhaps none.' This maximal indefinite is not very 
 often used, though the maximal semi-definite and definite, * Few 
 if any,' and ' Not more than so many,' frequently occur in 
 reasoning. The maximal quantity is an uncertain quantity. It 
 may or may not exist ; and as its existence is uncertain, it may 
 lead to an uncertain conclusion. It is excluded from Traditional 
 Logic, therefore, on the double ground, that it is not * Some at 
 least ' and that the proposition into which it enters may be Modal. 
 Its exclusion from Traditional Logic need not, however, hinder us 
 from employing it in statement and in reasoning. If Some only 
 and perhaps none were drowned, then it is certain that some, and 
 possible that all, may have been saved. If some only and perhaps 
 none of the messengers arrived, some at least, and perhaps all, 
 stopped or were diverted on the way, and all the messages were 
 not delivered. If some only and perhaps none of the eggs hatch 
 out, some at least and perhaps all will be addled ; certainly some 
 will not hatch out ; there will be fewer chickens than eggs ; the 
 whole clutch may be a failure ; and the money paid for it will
 
 ENUMERATIVE QUANTITY 99 
 
 be partly or wholly wasted. What is the matter with these 
 inferences ? 
 
 If There were some only and perhaps no days on which he 
 played truant, 
 And He was never punished unless he played truant, 
 Then He was not punished every day. 
 
 If Some only and perhaps no logicians appreciate the defects 
 of their Logic, 
 And The defects of Traditional Logic are numerous and glaring, 
 Then Logicians as a class must be blind. 
 
 The Indefinite Enumerative quantity may qualify not the 
 Subject-term only, but the Object-term, either instead of or 
 together with the Subject-term. Vegetarianism is adopted by some 
 men. Some rats were caught in some of the traps. This form of 
 proposition is unknown to Traditional Logic, but the statements 
 thus made are valid ; and valid arguments may be deduced from 
 them. If vegetarianism is adopted by some men only, it is not 
 adopted by all men. If some of the rats only were caught in some 
 of the traps, all the rats were not caught in those traps ; and if 
 some rats were caught in some only of the traps, there were other 
 traps in which no rats were caught. 
 
 If Vegetarianism is adopted by some men, 
 And Vegetarianism is a faulty diet. 
 Then A faulty diet is adopted by some men. 
 
 If Some rats were caught in some of the traps, 
 And All the traps were baited with cheese, 
 Then Some rats were caught in traps baited with cheese. 
 
 The Semi-definite Quantity. — Before entering on the 
 examination of the Semi-definite Enumerative, it is neces- 
 sary to consider certain features that are common to all 
 semi-definite quantities. The first of these is the Emphatic or 
 Unexpected form, the sign of which is * Such ' or * So.' ' Such 
 a great many,' * So many,' ' Such a few,' * So few.' The mean- 
 ing conveyed by the addition of this qualification of the semi- 
 definite is that the quantity is unexpected. It surprises us that 
 there should be so many or so few as we find. 
 
 H 2
 
 100 A NEW LOGIC 
 
 The next modification is more important. Every semi-definite, 
 like every other quantity, exists in three forms, the minimal, maxi- 
 mal, and exact. These have already been described; but in addition 
 to differences of form, and differences of emphasis, there is a third 
 way in which semi-definite quantities may be classified. They may 
 be referred to a certain standard or medium, and may be arranged 
 in sets, according as they reach, exceed, or fall short of this 
 standard. Moreover, the excess above the standard may be 
 moderate or great, and the defect below it ma}'' be moderate or 
 great, and this gives us a set of five degrees of semi-definite 
 quantity, to one of which every such quantity may be referred. 
 The degrees may be made more numerous than this, but five are 
 enough for most purposes. This set of degrees applies to every 
 semi-definite quantity, whether Enumerative, Proportional, Com- 
 parative, Ordinal or Selective. Omitting intermediate and exces- 
 sive degrees, the degrees of semi-definite quantity include : — 
 
 The Maximative. 
 The Magnative. 
 The Medium. 
 The Parvative. 
 The Minimative. 
 
 Combining these degrees with the forms already discovered, and 
 omitting the Indcsignate form, we arrive at the following table: — 
 
 Semi-definite Enumerative Quantities. 
 
 Minimal. Maximal. Exact. 
 
 Maximative ... 
 
 A great many 
 
 — 
 
 
 Very many. 
 
 Magnative 
 
 (A) many 
 
 — 
 
 
 Many. 
 
 Medium 
 
 A good many 
 
 
 
 A good many. 
 
 Parvative 
 
 A few at least 
 
 Few 
 
 
 A few. 
 
 Minimative 
 
 
 Very 
 
 few 
 
 A very few. 
 
 'A great many ' is a minimal form, though, like other terms, it 
 is often misused. It means certainly a large number, and possibly 
 all. * A great many men are honest ' states that certainly a large 
 number of men are honest, and for aught we know, all may be. 
 ' There are a great many people on the cricket ground ' is an 
 incorrect expression, for we know that the large number there are 
 not all the people there arc. The quantity referred to is an exact,
 
 SEMI-DEFINITE ENUMERATIVES loi 
 
 though not a completely definite quantity. It means a large num- 
 ber certainly, but not all. It means a large number, no less and 
 no more ; and the proper sign of the exact semi-definite is not * a 
 great many ' but ' very many.' * A great many specimens were 
 damaged ' leaves in doubt whether all the specimens were or were 
 not damaged. * Very many specimens were damaged ' clears up 
 this doubt, and assures us that there were a very few that were not 
 damaged. 
 
 The proper magnative minimal of this quantity is * A many,' 
 which meant * certainly many, and perhaps all '; but ' A many ' is 
 unfortunately become a vulgarism, and its ostracism from polite 
 speech deprives us of the means of expressing a useful distinction. 
 
 No maximative or magnative quantity can be maximal. When 
 we speak of a great many or of very many, or of many, we never 
 make the reservation ' Perhaps none.' This reservation is con- 
 fined to quantities less than the medium. 
 
 The sign of the medium semi-definite is ' A good many.' It may 
 be minimal or exact, but can scarcely be maximal. We can scarcely 
 have occasion to speak of ' A good many only, and perhaps 
 none.' 
 
 The parvative is the only degree that runs through all the forms, 
 and the minimal form is a little incongruous, and is seldom 
 employed. * A few at least, and it may be all ' is not often used or 
 implied. In practice, the two forms are the maximal, ' Few,' mean- 
 ing * Few only, and perhaps none,' and the exact ' A Few ' meaning 
 ' A few, neither more nor less.' If we do desire to express the 
 minimal form, the addition of the article, which invests the 
 quantity with positive character, and fixes it as ' certainly a few,' 
 is not enough. We must add * at least,' which effectually adds the 
 meaning ' perhaps more or even all.' ' A few men at least are 
 honest ' leaves it possible that all men may be honest. * Few men 
 are honest ' denies that all are, and leaves it possible that there 
 may be no honest men. * A few men are honest ' declares that 
 certainly a few, but not more than a few men are honest. 
 
 The sign of the minimative Enumerative is *Ver}' few'; and it is 
 evident that this quantity can have no minimal form. 'A few at 
 least, it may be all ' is a possible, though not a very frequently used 
 quantity : but ' A very few at least, it may be all ' is not a possible 
 quantity. The addition of the ampliative, ' Very,' at once fixes a 
 maximal limit to the quantity, and prevents its encroachment
 
 102 A NEW LOGIC 
 
 upwards, just as, at the other end of the scale, the addition of the 
 ampHative to Many fixes a minimal limit. ' Very few ' shouts ' not 
 many,' says ' few only,' and whispers ' perhaps none.' In this, as 
 in the other cases, the addition of the article at once invests the 
 quantity with positive character, minimises it, and is equivalent to 
 the addition of ' certainl}'.' ' Very few ' may mean * perhaps none,' 
 but ' A very few ' means * Certainly some, but a very small num- 
 ber,' and is therefore exact in form. 
 
 The degrees that have been enumerated are not all the degrees 
 there are. Beyond ' A great many,' there are * A very great many,' 
 ' An enormous number,' and so on ; between * A good many ' and 
 ' A few ' there are * A good few ' ; and below * A very few ' are * A 
 very few indeed,' ' Extremely few,' and so on. 
 
 It is unnecessary to insist upon the frequency with which the 
 semi-definite Enumerative quantities enter into statement and 
 argument. That is at once apparent to everyone ; but it is desir- 
 able to point out and insist that there are many arguments for the 
 construction of which the semi-definite enumeratives are necessary 
 — arguments that cannot be effected except by means of these quan- 
 tities, and arguments that lead to conclusions utterly inaccessible to 
 Traditional Logic. The following illustrate a few types of these 
 arguments : — 
 
 If there are a great many books in the British Museum, then they 
 must occupy a great deal of room, and it would take a very long 
 time to read them all. If very few modes of argument are known 
 to Traditional Logic, it does not know of many. If it is profitable 
 to keep a hen when it lays a few eggs, it will certainly be profitable 
 to keep it when it lays many. If a good many people go out for 
 wool, and come home shorn, this unpleasant experience happens 
 to more than a few people, and more than a few leave their wool 
 behind them, and come home without it. 
 
 If Many are called, 
 And Few are chosen. 
 Then More arc called than are chosen ; 
 And Some who are called are not chosen, and some are both 
 called and chosen. 
 
 If There's many a slip twix't the cup and the lip. 
 And Every such slip is a disappointment. 
 Then There are many disappointments in life.
 
 DEFINITE ENUMERATIVES 103 
 
 If Many overladen ships go to sea, 
 And Few ships are lost at sea, 
 Then Some overladen ships reach port in safety ; 
 And Overloading does not necessarily result in the loss of the 
 ship. 
 
 If Few birds are incapable of flying, 
 And Few of these birds are destitute of wings. 
 Then Very few birds are destitute of wings. 
 
 If There are very many particular quantities, 
 And Logic knows of very few particular quantities, 
 Then There are many particular quantities of which Logic is 
 ignorant. 
 
 In the last example, it is the object-term that is semi-definitely 
 quantified ; yet the argument is valid. 
 
 The Definite Ennmerative quantity is a cardinal number. Tradi- 
 tional Logic always assumes, though the text books do not 
 definitely state, that Logic has nothing to do with the cardinal 
 numbers, which are supposed to be susceptible of mathematical 
 reasoning only, and to be outside the province of Logic. This doc- 
 trine, if it be a doctrine, is doubly erroneous. It is erroneous in sup- 
 posing that numerical quantities are excluded from Logic, and it is 
 erroneous in supposing that mathematical reasoning is distinct from 
 Logical reasoning, and is not included in it. Still, although Logic 
 is mistaken in supposing that its powers do not enable it to reason 
 of numerical quantities, the numerical quantities of which Logic 
 reasons are not the same as those employed in the reasonings of 
 mathematics. Arithmetical numbers are doubly limited. They 
 are exact in form. Logical numbers, unless formally stated to be 
 so, are not limited, either minimally or maximally. In Arithmetic, 
 three, or thirty, or three hundred, means that number exactly, neither 
 more nor less. No excess or deficiency is permitted, for if any 
 were allowed, the operations of Arithmetic would be impossible. 
 We could not satisfactorily add two and three together, or subtract 
 two from three, if the two might be more or less than two, and the 
 three less or more than three ; but in Logic, the statement that two 
 men entered a house does not preclude the possibility that three men 
 entered it, and necessarily implies that one man entered it. In 
 Logic, a number means that number at least, or that number only ;
 
 104 A NEW LOGIC 
 
 and if that number only, it may be that number exactly, or not more 
 than that number. Since Mathematics cannot, except under very 
 limited and rigidly defined conditions, reason of inexact numbers, 
 such as more than seven, or fewer than five, it follows, if numerical 
 reasonings are excluded from Logic, that there is a field of reason- 
 ing that is neither Mathematical nor Logical. Where do such 
 arguments belong ? They belong to the New Logic here pro- 
 pounded. 
 
 If two men left the house, and three men entered it, Arithmetic 
 assures us that the number of men in the house was augmented by 
 one ; and in so concluding, Arithmetic is reasoning according to its 
 lights, and within its limitations. Granting the assumptions of 
 Arithmetic, that two and three mean, respectively, two and three 
 exactly, neither less nor more, Arithmetic is justified in coming 
 to this conclusion. But such a conclusion would be wholly 
 unwarranted in Logic. Before Logic would be justified in con- 
 cluding that the number of men in the house was augmented 
 by one, or was augmented at all. Logic must know whether 
 the two men who left the house were two at least or two only, 
 and whether the three who entered it were three only or three at 
 least. 
 
 If ten men entered the house and two men left it, Arithmetic 
 assures us that eight remained indoors. But if ten men only 
 entered and two at least departed, Logic is not justified in con- 
 cluding that any at all remained. The two at least may be the 
 whole ten. 
 
 If ten men at least entered the house, and eight men only left it, 
 then Logic can tell us that two men at least remained in the 
 house, a conclusion that is within the scope of Arithmetic also ; 
 but Logic can conclude further, that more men entered the house 
 than left it, and this conclusion is beyond the capacity of 
 Arithmetic. 
 
 If ten men at least entered the house, and not more than three 
 left it, Logic can derive the conclusion that seven at least 
 remained ; but Arithmetic knows no such number as ' not more 
 than three,' and can derive no conclusion from these premisses. 
 If not more than ten men entered, and seven at least departed, 
 Arithmetic can arrive at no result, but Logic can tell us that there 
 remained in the house not more than three, and perhaps none 
 at all.
 
 PROPORTIONAL QUANTITY 
 
 105 
 
 The Proportional Quantity. 
 
 When the individuals in a class, regarded as part of a larger 
 class, are contemplated discriminately with respect to their pro- 
 portion to the whole of the larger class, the quantity thus 
 contemplated is the Proportional quantity, which may be an 
 indefinite, a semi-definite, or a definite proportion of the whole. 
 
 The Indefinite Proportional. — This quantity, as well as the Indefi- 
 nite Numerical, is signified by Some, and it is another disadvantage 
 of this multiguous adjective that its enumerative meaning is not 
 clearly distinguished from its meaning as a proportion of a class. 
 It is true that it does not greatly matter, when ' some ' is used, 
 whether the ' some ' is understood as enumerative or proportional, 
 but it does matter that the constant use of ' some ' in both senses 
 tends to confuse the two quantities, to obscure the differences 
 between them, and to lead to the employment of more definite 
 signs ambiguously. Generally, ' some ' simpliciter is enumerative. 
 The proportional indefinite is signified by ' Some of the.' ' Some 
 men are honest ' means that an uncertain number of the whole 
 class of men are honest. * Some of the men ' are honest means 
 that an uncertain proportion of the men in a certain class are 
 honest. The distinction is not made in Traditional Logic. 
 
 The Semi-definite Proportional. — This is subject to the same forms 
 and the same set of degrees as other semi-definite quantities. 
 
 Semi-definite Proportional Quantities. 
 
 
 Minimal. 
 
 Maximal. 
 
 Exact. 
 
 Maximative 
 
 .. Nearly all 
 
 
 Nearly, but not 
 quite all. 
 
 Magnative 
 
 .. Most 
 
 
 Most. 
 
 Medium 
 
 .. A moiety 
 
 
 A moiety. 
 
 Parvative 
 
 .. A few of 
 
 Few of 
 
 A few of. 
 
 Minimative 
 
 
 Scarcely an> 
 
 / A very few of. 
 
 It is scarcely necessary to go through these quantities and show 
 that they answer generally to the description implied by their 
 places in the table. The reader who has followed me thus far can 
 do that for himself. The Proportional Par\'ative is, in its minimal 
 form, 'A few of,' in its maximal form, 'Few of.' *A few of 
 means ' certainly a small, and perhaps a large proportion, and it 
 maybe the whole.' 'Few of means *A .small proportion only,
 
 io6 A NEW LOGIC 
 
 and perhaps none' Commonly, the possibility of 'Few of 
 vanishing into none is emphasised by adding * if any,' but this is 
 not necessary. ' Few of is already maximal. 
 
 The use of the proportional quantity enables us to conduct 
 many arguments and reach many conclusions that are unattainable 
 by Traditional Logic. If most men are honest, not only are all 
 men not dishonest, but honest men arc in the majority, and out- 
 number dishonest men. If nearly all were drowned, it follows that 
 a few of them only, in fact scarcely any, were saved ; and if nearly, 
 but not quite all, were drowned, then a very few of them were 
 certainly saved. 
 
 If Nearly all people can reason, 
 And Scarcely anyone learns logic. 
 It follows that Most people reason without learning Logic; 
 And Ability to reason does not depend on 
 knowl edge of Logic. 
 
 If Most of those in the pit were miners, 
 And Nearly all those in the pit were killed. 
 Then Certainly some, and probably most, of the 
 killed were miners. 
 
 If Most of the speakers were teetotallers, 
 And Most of them were sensible. 
 Then There were some sensible teetotallers. 
 
 The Definite Proportion is, of course, a fraction. It is a half, 
 two thirds, three fourths, or some other numerical proportion. 
 Logic, of course, excludes such quantities, on the ground that, 
 lying within the domain of Mathematics, they are necessarily 
 outside the realm of Logic ; but in examining Enumerative 
 quantities, we found that the boundaries of Logic and Mathematics 
 are not rigidly marked by the exclusion and inclusion of definite 
 numerical quantities. An argument concerned with exact definite 
 numerical quantities, that is with figures, whether integers or 
 fractions, exactly limited in both directions, and with nothing else, 
 is an arithmetical argument ; but many arguments contain 
 indefinite proportional as well as definite proportional quantities, 
 and many contain inexact as well as exact proportions ; and such 
 mixed arguments belong to Logic, just as those which contain a 
 mixture of definite and indefinite integers belong to Logic. I
 
 PROPORTIONAL QUANTITY 107 
 
 aver that if two thirds of the company at least were drunk, then, 
 according to the New Logic here propounded, not half of them 
 were sober. Traditional Logic, in order to reach this conclusion 
 from this premiss, must call in the aid of a Mathematician ; and 
 the Mathematician is entitled to say ' Mind your own business. 
 " Not half" is not a mathematical quantity. The argument is not 
 arithmetical, but logical. See ye to it, for I will be no judge of 
 such matters.' 
 
 In Arithmetic, two thirds, three fourths, nineteen twentieths, 
 and so forth, are exact fractions of an integer ; in Logic, they are 
 classes, each containing some definite proportion, that may be 
 exact or inexact, of a larger class. In Arithmetic, each fraction is 
 an exact form, and no maximal or minimal form is known : but in 
 Logic, two thirds may be two thirds exactly ; or it may be two 
 thirds at least, and perhaps all ; or it may be two thirds only, and 
 perhaps less or none. If at least two thirds of the company were 
 drunk, Arithmetic cannot tell us what proportion were sober ; but 
 Logic can conclude without difficulty that not more than one third 
 were sober, and that not half of them were sober. If not more 
 than one third were sober. Arithmetic cannot tell us what propor- 
 tion were drunk, but Logic concludes without difficulty, that not 
 only more than half, but at least two-thirds of them were drunk, 
 The Definite Proportional quantity is, therefore, in strict propriety, 
 a logical quantity ; and Logic is very incomplete without it. 
 
 If Two thirds of the company were drunk ; 
 And Not half of those who were drunk were 
 able to stand, 
 Then The New Logic can reach the conclusion, unattainable 
 either by Arithmetic or by Traditional Logic, that 
 
 At least a third of the company were 
 unable to stand. 
 
 If The ship carries two thirds only of the 
 number she is licensed for, 
 And Nearly half of these will land at the next 
 port, 
 Then There will be plenty of room on board for 
 more, 
 And At the next port she can take in nearly 
 twice as many as will land.
 
 io8 A NEW LOGIC 
 
 These are not arithmetical arguments. ' Not half,' ' at least a 
 third," ' nearly a half,' and ' plenty,' are not arithmetical quantities, 
 and Arithmetic would rightly exclude the arguments from her 
 domain. Traditional Logic is incapable of effecting them, and 
 would shirk them on to Arithmetic if it could. Failing this 
 effort, the only consistent course open to Traditional Logic is to 
 deny that they are arguments at all. It would probably content 
 itself, however, by saying that they are * not logical,' and would 
 then feel that its duty was done. 
 
 The Ordinal Quantity. 
 
 When we contemplate parts of classes in succession, with 
 respect to the order in which they present themselves, or in which 
 we choose to take them, the quantity is Ordinal, and, like the 
 other quantities that we have examined, may be definite, semi- 
 definite, or indefinite. It will be noted that the order is always 
 definite ; it is the quantity that varies in definition. 
 
 The Indefinite Ordinal quantity is signified by * the Former,' * the 
 Latter.' It indicates the position in order of the individuals, but 
 does not indicate their number ; nor does it indicate with precision 
 the ordinal position. It indicates the position with respect to one 
 other part only of the class, not to every other part. 
 
 The Semi-definite Ordinal term is characterised by an ordinal 
 number followed by the sign of a semi-definite quantity, which is 
 almost always few — the first few, the last few. We do not speak 
 of the first many, though there is no reason why we should not. 
 
 The Definite Ordinal is an ordinal number — the first, the 
 second, etc. It does not specify an individual except by his 
 position in the class, for the same individual may successively 
 occupy more than one position, and the same position may be 
 occupied successively by different individuals ; but it indicates 
 with precision the individual that for the time being occupies that 
 place. 
 
 Predications and arguments with respect to Ordinal quantities 
 arc not infrequent ; they cannot be expressed without the use of 
 this quantity, and therefore Traditional Logic, which has not 
 discovered the quantity, is incompetent to deal with them. If 
 the first comer is first served, he is not put off until others are 
 served, he is not served second, or last ; he has the largest choice ; 
 he has the opportunity of getting first away; he does not have to
 
 ORDINAL QUANTITY 109 
 
 wait so long as others; the second comer is not first served. If 
 it is the last straw that breaks the camel's back, it is not the first 
 straw, nor the second, that produces this disaster; a single straw 
 will not break a camel's back ; if the last straw is not added, the 
 camel's back will not be broken. 
 
 If Order is Heaven's first law ; 
 And The first law of Nature is self-preservation ; 
 Then Heaven and Nature are different things ; 
 And The first law of Heaven is not the first law 
 of Nature. 
 
 If The last thing a logician considers is 
 
 consistency, 
 And Consistency is the first thing a logician 
 
 ought to consider. 
 Then Logicians take things in the wrong order. 
 
 The Residual Quantity. 
 
 When any part of a class is removed, set aside, selected, or 
 distinguished in any way, the rest of the class outside of the 
 distinguished part, regarded alternatively, forms a quantity of a 
 special kind, which may be called the Residual quantity. As has 
 already been pointed out, the Residual quantity is not divisible, 
 as the quantities are that we have examined hitherto, into 
 Indefinite, Semi-definite, and Definite quantities. When a portion 
 of a class is removed, the residue is itself a class, and is susceptible 
 of all the quantities, including even the residual, that could be 
 attached to the whole class ; and thus it is primarily divisible, 
 not into Indefinite, Semi-definite, and Definite Residual, but into 
 Universal Residual and Particular Residual. 
 
 The general sign of the Universal is All, which includes the 
 three Universal quantities already examined; and correspondingly, 
 we may predicate and reason of All the rest ; of every one, each 
 one, and any of the rest. 
 
 The general sign of the Particular quantity of the whole class 
 is Some, but the general sign of the Residual Particular is Others; 
 and there are as many classes, sub-classes and varieties of the 
 Particular Residual as of the common Particular quantity. 
 
 Every Particular quantity has its complement in a Residuum,
 
 no A NEW LOGIC 
 
 which remains undistinguished when the Particular is selected out 
 of the class ; but in the majority of cases, we do not take the 
 residuum into account. It has already been shown that we 
 possess the power of concentrating our contemplation on any 
 aspect of a subject before us, and neglecting the rest ; and when 
 we select or distinguish a part of a class, we commonly ignore the 
 remainder. But there are occasions on which the recognition and 
 use of the Residual quantity are of the utmost service, and enable 
 us to reach conclusions that would be utterly unattainable with- 
 out it. 
 
 Every Particular quantity may of course leave its residuum ; but 
 it would seem that no Universal quantity can leave a residuum. 
 If all are taken, there can be none left. This is true if all 
 are taken simultaneously ; but if all are taken in succession or 
 alternately, there is at any rate a temporary residuum. If each 
 man in turn takes a step forward, the rest remain for the time 
 stationary ; and though any stick may be taken out of a bundle, 
 the rest may be left in it. 
 
 The Minimal Particular may or may not leave a residue, 
 according as it does or does not extend to all ; and one of the 
 virtues of the residual quantity is that it settles decisively the 
 form of the otherwise formless Some. If some men desire money, 
 the some may, for aught that appears in the statement, be all 
 there are : but if some men desire money and others do not, the 
 some is fixed at its maximal form, and cannot be some, perhaps 
 all. 
 
 Many arguments require the residual quantity for their statement, 
 and cannot be effected without it. It differs from the quantities 
 hitherto examined in that it must be preceded by a proposition 
 containing some other quantity, to which it is residual, and there- 
 fore every argument containing the residual must be stated in the 
 form of a compound proposition, and must be of the nature of 
 what is called, in Traditional Logic, Mediate Inference. If some 
 men desire money and others do not, then the desire for money 
 is not universal among men ; and with respect to the desire for 
 money, men are divided. If two or three men were drowned, and 
 the rest were saved, then neither were all drowned nor all saved ; 
 then all were saved but two or three ; then very few were drowned ; 
 then some at least were saved, and some only were drowned ; and 
 then, moreover, the fate of all was not the same.
 
 COMPARATIVE QUANTITY iii 
 
 The Residual may be preceded by more than one other quantity, 
 and argument may be founded on a compound proposition of 
 many members, containing many quantities. If some of the balls 
 were red, others were blue, four were green, twice as many were 
 black, certain of them were yellow, more were purple, and the 
 rest crimson, then it is an irrefragable conclusion that none of 
 them was white. 
 
 None of these reasonings can be conducted by any method 
 known to Traditional Logic. 
 
 Three children sliding on the ice, 
 
 All on a summer's day ; 
 As it fell out, they all fell in ; 
 
 The rest, they ran away. 
 
 Traditional Logic, which knows not the Residual quantity, is 
 incapable of examining this statement, and cannot tell us whether 
 it is valid or not. 
 
 The Comparative Quantity. 
 
 When the individuals in a class are contemplated discriminately, 
 as part of a larger class, and alternatively with respect to other 
 parts of the larger class, the comparison with the other part or 
 parts results in the formation of the Comparative quantity, and 
 the comparison may be indefinite, semi-definite, or definite, and 
 the resulting quantity shares the degree of definition. The result 
 of the comparison must be that the respective numbers are 
 adjudged to be alike or different, and if different, the number in 
 the class that is the chief object of attention, is adjudged to be 
 more or less than that in the other. Thus the comparative 
 quantities are primarily three, and, when the comparison is 
 indefinite, are More, Fewer, and About as Many. 
 
 Without being completely definite, the comparison may be 
 more definite than this. 
 
 On comparing these two lines of dots, it is at once apparent 
 that the lower line contains two more dots than the upper. It 
 is quite unnecessary to count each series, or to know how
 
 112 A NEW LOGIC 
 
 many dots in all each series contains. The excess of one, and 
 the defect of the other, can be stated definitely, without the 
 totals being definitely stated ; and thus the signs of the Semi- 
 definite Comparative are So many more, So many fewer, and As 
 many. 
 
 The Definite Coviparative is a multiple or sub-multiple. It is 
 Twice as many, Two thirds as many. Half as many again, and so 
 forth. 
 
 It seems incredible that Traditional Logic should have ignored 
 the Comparative quantity, so frequently is it employed, so valuable 
 are its uses, and so impossible is it to reach, without its aid, 
 conclusions of the utmost practical importance. 
 
 If more money is put into the bank than is taken out of it, the 
 balance will increase. If more money is withdrawn than is paid 
 in, the balance will be diminished. If more geese than swans now 
 live, more fools than wise, then the geese outnumber the swans, 
 and the wise are rarer than fools. If more people were thrust into 
 the Black Hole at Calcutta than the air would support, it was 
 inevitable that some of them should die. If there are fewer teats 
 than there are little pigs, one little pig must go without. If there 
 are three more people than there are seats, then three people 
 cannot sit down unless they share a seat with some one else. If 
 there are twice as many carts as horses, at least half the carts 
 must go unhorsed. 
 
 If There are more geese than swans, 
 And There are twice as many ducks as geese, 
 Then There are many more ducks than swans. 
 
 If ' The true bug had been organised with only two antennae, 
 And The humbug in the copperplate would have them twice 
 
 as many,' 
 Then The copperplate engraving was erroneous. 
 
 The Selected Quantity. 
 
 As its name implies, the Selective term selects a certain 
 individual or certain individuals out of a class, and the individuals 
 selected may be definite or less than definite in two senses. 
 They may be indefinitely selected, and indefinite, semi-definite, 
 or definite in number ; or they may be definitely selected, and 
 indefinite, semi-definite, or definite in number.
 
 SELECTED QUANTITY 113 
 
 The Indefinitely Selected Quantity is characterised by the sign 
 'Certain,' and Certain, standing alone, is a completely indefinite 
 enumerative, and means some individuals selected out of a class, 
 but neither indicates the individuals nor mentions their number. 
 We may, however, select a proportion of a class, and indicate our 
 selection by the sign * A certain proportion,' and we may select a 
 number out of the residue or a proportion of the residue, and signify 
 our selection by * Certain others,' or ' A certain proportion of the 
 others.' These are all indefinitely selected indefinite quantities. 
 
 But the Indefinitely Selected quantity, whether Enumerative, 
 Proportional, or Residual, may be semi-definite with respect to 
 the number of individuals it indicates ; and then is characterised 
 by the signs, ' Certain few,' ' A certain few,' of the whole, or the 
 rest, as the case may be. 
 
 Or this quantity may be completely definite as to the number 
 or proportion selected, though this selection remains indefinite. 
 The sign is then, ' A certain ' as in ' A certain one,' ' A certain 
 three,' ' A certain half or ' quarter.' 
 
 The individuals may be definitely selected and may or may not 
 be definite in number or proportion. The signs of definite 
 selection are This, These, That, Those. This, These, apply to 
 a selected number or proportion near at hand or appropriated ; 
 That and Those apply to a selected number or proportion at a 
 distance or repudiated. 
 
 * A certain man drew a bow at a venture,' selects one man out 
 of the army, and places the bow in his hand. It was not any 
 man in the army who drew the bow, it was a selected man ; but 
 beyond the fact that it was not any man taken at random, he is 
 not identified. He may have been this man or that ; he may 
 have been the first in the army or the last, or in any intermediate 
 position. He is not identified, but he is identifiable. 
 
 Swans sing before they die ; 'twere no bad thing 
 Did certain people die before they sing. 
 
 This selects, but does not identify, the people in question. 
 They may be these people or those ; they may be the first people 
 you meet, or the last that you wish to meet ; they may, for 
 aught we are told, be you and me, reader ; they may be but two 
 in number, or they may be all the people in the world except 
 Madame Albani ; but they are selected as possessing some 
 
 N.L. I
 
 TT4 A NEW LOGIC 
 
 quality, and, though not identified, are identifiable, provided we 
 know their distinctive quality. 
 
 This and These, That and Those, not only select, but identify 
 the individuals they characterise ; and not only do they identify 
 the individuals, but they indicate also the proximity or otherwise 
 of those individuals to ourselves, or our attitude, as appropriative 
 or repudiative, towards them. 
 
 The Selective quantity is not free from the complication of 
 'forms.' Any Selective quantity may be Minimal, Maximal, or 
 Exact. 'Certain,' 'A certain proportion' and 'Certain others* 
 may be at least, only, or exactly ; and similarly, the definitely 
 selected or Demonstrative quantity may be This or These only. 
 That or Those at least, or exactl3^ 
 
 Many predications, and therefore many arguments, can be con- 
 ducted by means of the Selective quantity only ; and many others 
 by the Demonstrative quantity only. If certain people only 
 should die before they sing, then other people should not die 
 before they sing, and it is not true that any one taken at random 
 ought to die before he sings. Moreover, it follows that certain 
 other people should sing before they die. 
 
 If A certain man went from Jerusalem to Jericho ; 
 And The way from Jerusalem to Jericho was infested with 
 thieves ; 
 Then That man ran a risk of being robbed. 
 
 If He lectured to certain students ; 
 And Those students were attentive ; 
 Then Those students may have benefited. 
 
 If this little pig went to market, then there was a little pig who 
 went to market ; it was not that little pig who went to market ; 
 and this little pig did not stay at home. If this is the house that 
 Jack built, it is not the barn that Jack built ; it is not the house 
 that Tom built ; nor is that the house that Jack built. If there is 
 no way but this, there is no other way. If that is the way the 
 money goes, then we know in what way the money goes, and in 
 what ways it does not go. 
 
 If This is our portion, 
 
 And Our lot is this ; 
 
 Then Our portion and our lot are the same thing, 
 
 And That portion and that lot are not ours.
 
 PURPOSIVE QUANTITY 115 
 
 If Any book that treats of Logic is uninteresting, 
 And This book treats of Logic ; 
 Then This book is uninteresting. 
 
 All of these arguments are beyond the range of Traditional 
 Logic, and ultra vires of it. 
 
 The Purposive Quantity. 
 
 The last quantity on our long list is the Purposive. In using 
 this quantity, we regard the individuals with respect to the 
 suitability or unsuitability of their number to the purpose in 
 hand ; and if it is unsuitable, as unsuitable by excess or by defect. 
 The Suitable quantity has its minimal and exact forms, but the 
 Unsuitable are known in the exact form only. We cannot say too 
 many only, or too many at least, or too few only, or too few at 
 least, or if we do, such expressions are meaningless ; but we can 
 say of a number that it is enough at least, or enough only, if by 
 only we mean just enough, for though a certain quantity may 
 be suitable to the purpose, the purpose may perhaps not be 
 defeated if we have more than enough. There can be no maximal 
 suitable quantity, however, for if there are less than enough there 
 are not enough. We see, therefore, that there is a clear 
 difference between more than enough and too many. More than 
 enough is excessive, but does not defeat the purpose in hand. 
 If there are more than enough stamps for all the letters, the 
 letters can still all be stamped ; but if there are too many plants 
 for the pots, all the plants cannot be potted, and if there are too 
 many letters for the stamps, all the letters cannot be stamped. 
 
 If the number is unsuitable, it may be deficient or excessive 
 by an enumerative, a proportional, or a selective quantity, and the 
 excessive or defective quantity may be definite, semi-definite, or 
 indefinite. It may be one too many, or many too few, or more 
 than enough ; it may be too many by half, or deficient by a third ; 
 it may be this one too many, or that, or those, or may be 
 defective by a certain few. 
 
 As with other quantities, the Purposive has its own field of 
 reasoning, and enters into predications and arguments that cannot 
 be conducted without its aid. If there are enough glasses to go 
 round, no one need go without a glass, and every one can have a 
 glass to himself. If there are not enough glasses to go round, 
 
 I 2
 
 ii6 A NEW LOGIC 
 
 some one must go without, or share with some one else. If he is 
 one too many, he is not wanted ; he would be better away ; there 
 are enough without him. If too many cooks spoil the broth, it is 
 a disadvantage to have too many cooks. If the Universal and 
 Particular quantities of Traditional Logic are too few for the 
 expression of all our thoughts, we must employ additional 
 quantities or leave some of our thoughts unexpressed. If the 
 number of quantities enumerated here is too many to be easily 
 remembered, it will need an effort to commit them to memory, 
 but it does not follow that they are more than enough to express 
 our thoughts. 
 
 If Too many cooks spoil the broth, 
 And Broth spoilt means meat wasted ; 
 Then Too many cooks are a cause of waste. 
 
 If Enough is as good as a feast, 
 And A feast is more than enough ; 
 Then Enough is as good as more than enough. 
 
 The Collective Quantity. 
 
 If the reader will turn back to the Table III. on p. 82 he will 
 be able to see how far our researches into quantity have extended. 
 We have examined none but Extensive quantities, and of the two 
 classes of these, we have examined part only of the Class- 
 quantity, namely, the Indesignate, and the Distributive variety of 
 the Designate. When we have examined the Collective quantity 
 we shall have completed the consideration of the Class-quantities, 
 and may turn to the examination of the Singular. 
 
 The Collective term is recognised by Traditional Logic, and is 
 by it distinguished from the Distributive term, but the notion that 
 Traditional Logic has of the Collective quantity is sadly defective, 
 and is, in some respects, completely erroneous. 
 
 The Collective term is briefly referred to in that chapter in 
 books on Logic that treats of terms, but when propositions are 
 considered, the Collective term is completely ignored, and no 
 logician entertains the possibility that a term in a proposition 
 can be Collective, or if it can, that its quantity can be other 
 than Universal. The Collective Particular is unknown to Logic, 
 and the whole logical scheme of quantity is based on the
 
 COLLECTIVE QUANTITY 117 
 
 assumption that there is no quantity but the Distributive, for, if 
 the Collective quantity is admitted, that necessary part of logical 
 doctrine, the Square of Opposition, is broken up, disorganised, 
 and dispersed, as will be shown in a subsequent chapter. 
 
 The same name is often applied to the Collective Class as to the 
 Compound Individual, and Logic never distinguishes between them. 
 Indeed, most text books adduce Compound Individuals, such as a 
 regiment, a library, a committee, as examples of the Collective 
 Class. Yet the distinction between them is plain and manifest. 
 The Compound individual term refers to a number of individuals, 
 aggregated or incorporated together into a single thing. The 
 Collective term refers to, it may be, the very same individuals, 
 collected into a class in which they are not discriminated from 
 one another. The test is simple. If one or more of the 
 constituent individuals of the compound individual is withdrawn 
 or ejected, the integrity of the individual is not impaired. In spite 
 of the loss, it remains an individual, and any predication made of 
 it as an individual is still true. But if any one or more of the 
 constituent individuals of a collective class is withdrawn, that 
 collective class is destroyed, and any predication made of it before 
 the mutilation is no longer true, or may be no longer true. The 
 House of Commons is a compound individual, and though the full 
 House consists of some 670 members, yet if only forty are 
 present, it is still the House of Commons. But all the members 
 of the House of Commons, as a collective class, number 670, and 
 if even one is withdrawn, or dies, or accepts the Chiltern 
 Hundreds, the House of Commons no longer numbers 670. If 
 only 40 members of the House of Commons are present, the 
 House, as a compound individual, can pass a Bill, or vote money, 
 or adjourn ; but if even one member is absent, the House of 
 Commons, as a collective class, no longer occupies as many seats, 
 needs as much standing room, or consumes as much food and 
 drink. If half or two thirds of the men in the regiment are absent 
 on leave, or sick, or killed in action, the regiment, as a compound 
 individual, still exists ; but if all the men in the regiment, as a 
 collective class, outnumber all the men in another regiment, or 
 are sufficient to line the street, or occupy so many berths in the 
 transport, then if only one man is withdrawn, these predications 
 may all be falsified. If several cups and saucers are broken, the 
 tea set, as a compound individual, still exists, and is still a product
 
 ii8 A NEW LOGIC 
 
 of the Worcester factory ; but if one is broken, the set no longer, 
 as a collective class, consists of thirty pieces. 
 
 Traditional Logic recognises the Collective Universal, and, in 
 the chapter on Terms, every text book of Logic distinguishes the 
 Collective Universal from the Distributive Universal ; but it does 
 not appear to have dawned upon the mind of any logician that 
 the Collective is susceptible of any quantity but the Universal. 
 In fact, however, the Collective may be Particular, and there 
 are as many varieties and as many degrees of the Collective as 
 there are of the Distributive Quantity, and every statement and 
 argument made of the one can be paralleled by a statement or 
 argument made of the other. The only Distributive quantities 
 that have no parallels in the Collective series, are the subordinate 
 Universals. Every, Each, and Any, refer discriminately, not 
 indiscriminately, to all the individuals in a class, and are therefore 
 excluded from Collective quantities. 
 
 The sign of the Collective quantity is the definite article, 
 following the common sign of quantity ; but though the Collective 
 cannot be accurately conveyed without the use of the definite 
 article, this article is not characteristic of the Collective, but may 
 be used for the Distributive also. * All the men in the regiment 
 took part in the charge,' does not convey all the men collectively : 
 it means every man taken discriminately. But 'All the men in 
 the regiment were only just enough to man the rampart ' does 
 mean all the men collectively. The test by which we distinguish 
 between the Collective and the Distributive ' All the ' is our 
 ability or inability to substitute ' Every ' for ' All.' If we can 
 make the substitution without destroying or altering the meaning, 
 the quantity is Distributive ; if not, it is Collective. The only 
 way to designate the Collective quantity without possibility of 
 mistake, is to add to the term the words ' taken together.' 
 
 It is unnecessary to go through again all the Particular 
 quantities that have been enumerated in the previous chapter, and 
 to show that each of them may be understood in a Collective as 
 well as in a Distributive sense ; but it is expedient to show^ by 
 examples that the Collective quantity is just as susceptible of 
 inference and argument as the Distributive; a fact of which 
 Traditional Logic does not seem to be aware. 
 
 If the whole library fetched ^^3000, then no one book in the 
 library can have fetched as much as this ; then neither a few, nor
 
 COLLECTIVE QUANTITY 119 
 
 very many, nor a half, nor a third of the books, nor the rest of the 
 books after some were sold, nor certain of them, nor this nor that 
 selected set of volumes, can have fetched more, nor even as 
 much as ;i^300o. If ^^50 was given for most of the books, and 
 -^1000 for all of them, then they were very unequal in value. If 
 they were all of about the same value, and £50 was enough to give 
 for two thirds of them, it was too much to give for the remainder. 
 All these arguments are beyond the competence of Traditional 
 Logic.
 
 CHAPTER VIII 
 
 THE INDIVIDUAL. THE SINGULAR QUANTITY 
 
 Reference to the scheme of Quantity on p. Si will show that 
 individuals may be contemplated in two ways. They may be 
 contemplated primarily as wholes, and if contemplated as 
 composed of parts, the composition is a secondary consideration, 
 and is used only to distinguish them, as wholes, from other wholes, 
 differently constituted. Or they may be contemplated primarily 
 as composed of parts, so that the contrast of part and whole, or 
 of part and part, is the main purpose of the contemplation. In 
 the first case, the individual is dealt with in thought as a unit, and 
 is never divided. In the second case, it is dealt with in thought as 
 a composite, or quasi-class, the difference between the individual, so 
 regarded, and the class, being that, while the constituents of the 
 class are individuals, and are therefore necessarily discrete, the 
 constituents of the Composite individual are parts, and need not 
 be discrete. 
 
 The Individual. 
 
 The first difficulty that confronts us in this part of our task is 
 to determine what is meant by an individual. To the uninitiated 
 the task may seem easy enough, but biologists know that 
 nothing is more difficult. A tree is usually regarded as an 
 individual, as strictly distinct as an individual man. But the 
 roots of a tree may contain buds — buds which are parts of the 
 root, and therefore parts of the tree. These buds may grow 
 into suckers, which are but buds more developed, and must 
 still, therefore, be considered parts of the tree, though they 
 grow at a distance from the tree, and to anyone who does not 
 know of the underground connection, appear to be individuals, 
 as distinct as the tree itself. The root may be severed between 
 the tree and the sucker, and the sucker taken up and trans- 
 planted into the next parish or into a distant county, where it
 
 THE INDIVIDUAL 121 
 
 may grow into a tree as large as its parent. Does it become 
 by this severance a separate individual, or does it still remain 
 a part of the tree, the two trees making up a single individual ? 
 Suppose that the connecting root, instead of being cut, withers 
 away, and in the course of years perishes and destroys the con- 
 nection, at what moment does the one individual become two ? 
 That the flowers are part of the tree, and that the tree with its 
 flowers are, from one point of view, a single individual, few 
 would dispute; and if this is so with the tree in flower, it is 
 equally so with the tree in fruit. Yet each fruit may be severed 
 without impairing the individuality of the tree, and may grow into 
 a separate individual. 
 
 An animal may be cut in two, and each half is then an individual 
 half, but is not an individual animal. But suppose, as happens 
 with some simple animals, that the head part grows a tail, and 
 the tail part grows a head, are there then two individuals, or is 
 there only one ? and if there are two, at what moment did the 
 two halves cease to be parts of an individual, and become separate 
 individuals ? 
 
 The old problems of the sorites and the calvities provide us with 
 similar puzzles. A heap of stones is an individual thing. If w^e 
 take one stone away, the heap still remains an individual. We may 
 go on taking away one stone after another till none is left. At 
 what stage does the heap cease to be a heap ? does the individual 
 cease to be an individual ? 
 
 Again, a human monster may consist of two heads and torsos, 
 the latter fused together at the pelvis, and terminating in one 
 pair of legs. Is it one individual, or two ? 
 
 The solution of these problems is to be found in regarding an 
 individual as constituted by the way in which things are contem- 
 plated by the mind. The individual, like the class, is a conceptual 
 creation, existing in the mind alone ; corresponding, indeed, with 
 observed facts, but itself conceptual, and not * real.' When we 
 experience the colour blue, we intuitively think of the colour as 
 resident in the extra-mental blue thing that we see. Not until we 
 study the psychological aspect of vision do we discover that the 
 colour is not in the blue thing, but in the mind alone; and that 
 although the colour corresponds with some quality in the seen 
 object, yet the quality in the object is not colour, but something 
 that gives rise to the colour in our minds. Similarly, individuality
 
 122 A NEW LOGIC 
 
 is a mental concept. It is in the mind alone ; and though it corre- 
 sponds with some quality in the individual thing, the quality in 
 the thing that arouses in us the concept of individuality, is not 
 individuality, but something else. Although the individual is a 
 mental creation, its mental origin and existence do not prevent us 
 from dividing individuals into kinds, any more than the purely 
 mental existence of colour prevents us from dividing colours into 
 kinds — red, blue, &c. 
 
 Thus regarded, individuals are susceptible of arrangement into 
 kinds, primarily according as they are or are not divisible into 
 parts. Some individuals, such as colour, likeness, &c., though 
 they may be divided into kinds, cannot be divided into parts. 
 Though we may divide colour into red, green, and blue, this 
 is a division of colour, not into parts but into kinds. Red 
 and green and blue are not parts of colour, but kinds of colour. 
 Hence the first classification of individuals is into those that 
 are indivisible into parts, and those that are divisible into parts, 
 the former being Qualitative Units, and the latter Quantitative 
 Units. 
 
 Every Quantitative Unit is divisible into parts, and such units 
 are of two kinds, according as the parts coexist, or follow one 
 another in time. The former may be called Coexistent Units, the 
 latter Serial Units. 
 
 Coexistent Units are divisible into kinds according as the parts 
 of which they are constituted are or are not contemplated with 
 respect to their continuity or discontinuity. 
 
 If they are so contemplated, the parts are either continuous, in 
 which case the individual is a Simple Unit, or they are discon- 
 tinuous or discrete, in which case the individual joins the Serial 
 Individual in the class of Compound Units. 
 
 The parts of the Compound Coexistent Unit may be alike or 
 unlike. If they are alike, the individual is an Aggregate Unit ; if 
 they are unlike, it is a Corporate Unit. 
 
 If, however, the continuity or discontinuity of the parts of the 
 individual is not taken into consideration, the individual is a 
 Uniform Individual or Unit. 
 
 Thus we arrive at a complete classification of individuals, which 
 runs as follows : —
 
 KINDS OF INDIVIDUALS 123 
 
 TABLE VI. 
 Kinds of Lndividuals. 
 
 Individuals are either 
 
 Indivisible Qualitative Units. 
 
 Divisible into parts that are ... Quantitative Units. 
 
 Coexistent ... ... ... ... Coexistent Units. 
 
 and regarded as 
 
 Continuous ... ... ... Simple Units. 
 
 Discrete ... ... ... Compound Units. 
 
 and alike ... ... ... Aggregate Units 
 
 and unlike ... ... ... Corporate Units. 
 
 and not regarded as continuous 
 
 or discrete ... ... ... Uniform Units. 
 
 Successive ... ... ... ... Serial Units. 
 
 When an individual is divisible into parts that are coexistent 
 and continuous, it is a Simple Unit, or Simple Individual, and it 
 matters not whether the parts are like or unlike. A man, a ship, a 
 country, a machine, a road, a table, a house — each of these is a 
 material unit whose parts are unlike, and each is a simple indi- 
 vidual. A piece of gold, a pint of water, a cubic foot of oxygen, 
 are simple individuals or units whose parts are alike. The parts of 
 a piece of wood may or may not be considered to be alike ; it 
 depends on the purpose in view ; but in any case, it is a simple 
 individual or unit. 
 
 When an individual is made up of parts that are discrete, the 
 parts may be alike or unlike. If the parts are alike, it is an 
 Aggregate unit individual, such as a crowd of men, a ream of 
 paper, a fleet of ships, a street of houses, a bushel of corn, a layer 
 of dust, a pair of boots. The Aggregate individual is always, in 
 books on Logic, confused with the Corporate Individual, and with 
 the Collective Class ; and usually all are confused with the 
 Uniform Individual, though this last is sometimes distinguished 
 as the Substantial term. These things are all quite discriminable 
 and distinct. There is some excuse for confusing the Aggregate 
 with the Corporate Individual, for the same group of things may 
 constitute either the one or the other, according to the manner in 
 which we contemplate them ; but the distinction between the 
 Uniform Individual and the Collective Class is much more easily
 
 124 A NEW LOGIC 
 
 made, and the confusion between them is therefore the less 
 excusable. 
 
 The parts of the Aggregate Individual are alike, and it is this 
 alikeness that enables us to unify them into an Individual. They 
 need not be closely alike. It is enough if they have such a like- 
 ness that we can unify them. A mob is still an aggregate individual, 
 if we choose so to contemplate it, though it consists of men, 
 women, and children. A fleet is still an aggregate individual, if we 
 choose so to contemplate it, even though it consists of many 
 different kinds and sizes of ships. A street of houses is still an 
 aggregate individual, even though it consists of residential houses, 
 shops, banks, warehouses, and so forth. The parts of the Collective 
 class also may be closely alike or may be different inter se, but 
 they must have enough likeness to one another to enable us to 
 group them together in a class. The very same collection of 
 individuals may be an aggregate individual or a collective class, 
 according as we contemplate it ; but this does not constitute 
 the aggregate individual and the collective class the same 
 thing, for, as already explained, both the individual and the class 
 are purely conceptual ; and if we contemplate a thing or a number 
 of things in any particular way, we cannot simultaneously contem- 
 plate them in a different way. We may successively contemplate a 
 collection of men first as a mob, which is an aggregate individual, 
 and still remains an individual though half its members dis- 
 perse ; or we may contemplate it as a collective class, capable 
 of overcoming the police opposed to it, and now destroyed, as that 
 collective class, if half its members disperse ; but we cannot con- 
 template it simultaneously as both an individual and a collective 
 class. 
 
 When the parts of a Compound Individual are not only discrete, 
 but so dissimilar that we cannot, by their likeness alone, unify 
 them into an individual, or if the unification is not in fact effected 
 by their likeness, then the individual is not an aggregate, but 
 a Corporate individual. But if the parts of an individual cannot 
 be unified by their similarity to one another, how are they to be 
 unified ? What is the basis of the unification ? It is to be found 
 in their devotion to a common purpose. A regiment, an army, a 
 college, a university, a hive of bees, a Venetian blind, a railway, a 
 table laid for dinner, a furnished house, are all Corporate 
 Individuals. They are all signified by the indefinite article. They
 
 KINDS OF INDIVIDUALS 125 
 
 arc all spoken of and thought of as individuals ; and the parts of 
 each arc unified by their devotion to a common purpose. An army 
 consists, not only of men of different ranks, but of horses, guns, 
 wagons, ammunition, pontoons, and stores, all discrete, and all 
 unlike, but all unified into a single individual army by devotion to 
 the common purpose of fighting. A Venetian blind consists of slats, 
 tapes, and cords, all discrete and all unlike ; but all devoted to the 
 same purpose of shading the window. A hive of bees consists not 
 only of the bees, but of the cavity in which they are contained, 
 of the comb, the honey, the eggs, the grubs, and the propolis, all 
 different, and most discrete, but all unified by devotion to the 
 common purpose of continuing the race of bees. A railway con- 
 sists of the permanent way, the stations, the bridges and tunnels, 
 the staff, the directorate, the shareholders, the capital, and so forth ; 
 all unified by devotion to the common purpose of transport. 
 
 The same individual may, in many cases, be Aggregate or 
 Corporate, according to the way in which it is regarded. Regarded 
 as a collection of ships, all alike in their character as ships, a 
 navy is an Aggregate Individual. Regarded as a collection of 
 different kinds of ships — battleships, cruisers, torpedo boats, 
 repairing ships, and so forth, all devoted to the common purpose 
 of fighting at sea — a navy is a Corporate Individual. Regarded 
 as composed of sixty ships, the same navy is a Collective Class ; 
 and regarded as composed of none but English ships, it is a 
 Distributive Class. Regarded as marching together disorderly 
 through the streets of Paris, a number of men and women con- 
 stitute a mob — an Aggregate Individual. Regarded as intent on 
 taking the Bastile, they constitute a Corporate Individual. 
 Regarded as numerous enough to take the Bastile, they constitute 
 a Collective Class ; and regarded as every one wearing the tri- 
 coloured cockade, they constitute a Distributive Class. The mode 
 of contemplation determines the constitution of the concept. 
 
 When a number of things are so contemplated that we disregard 
 their continuity or discreteness, and look solely to the qualities in 
 which they are alike, or rather, to their alikeness in certain 
 qualities, without paying regard to whether they are continuous 
 or not, then we constitute those things a Uniform Individual. 
 When, for instance, we contemplate successively specimens of 
 water, gold, air, or other alike material units, and consider the 
 alikeness between the several specimens of each, without regarding
 
 126 A NEW LOGIC 
 
 whether or not the specimens are continuous or discontinuous, 
 then we form concepts of water, gold, air, and so forth, as 
 Uniform Individuals. 
 
 The Uniform Individual, in as far as it is recognised at all by 
 Traditional Logic, is confused with the Class. 
 
 Lastly, the parts of an individual may not be coexistent. They 
 may follow one another in succession, constituting together a 
 Serial Individual, or Series. It would need no insistence or 
 argument to show that we may regard a series as a single 
 individual, were it not that Traditional Logic is altogether ignorant 
 of it. We constantly think and speak, however, of a revolution, 
 a journey, an election, which are series of events ; of a melody, 
 which is a series of sounds ; of a disease, which is a series of 
 bodily changes ; of a process of manufacture, which is a series of 
 manipulations ; of a lecture, which is a series of spoken words; of 
 a din, which is a series of noises ; of the growth of a tree, which 
 is a series of changes ; of the flight of a bird, which is a series of 
 movements ; of the evolution of man, which again is a series of 
 changes ; and we speak and think of each of these series as an 
 individual thing, or unit. The simplest series, and the one of 
 which we most frequently think and speak, is the numerical 
 series. When we speak of three, or of three hundred, we mean 
 every number up to and including three, or three hundred, as 
 the case may be. We indicate the series by its final number, 
 but when we speak of three hundred we do not mean the 
 three hundredth alone, but all the previous numbers in the series 
 also. 
 
 There are certain serial individuals that are complex, con- 
 sisting of a series of parts, each part being composed of coexisting 
 parts. Thus a shower of rain is a serial individual, composed of 
 drops falling in succession, but the succession is so rapid that 
 many drops are, in fact, falling at the same time ; and the con- 
 struction of a battleship is a serial individual, composed of a 
 succession of processes, or rather of many successions of processes, 
 proceeding simultaneously, and devoted to the same purpose. 
 Some serial individuals, such as a journey, or the emptying of a 
 measure of corn, have a delinite beginning and end; while in 
 others, such as a rebellion, or a reformation in religion, or a 
 disease, the beginning and end are more or less arbitrary ; but it 
 is unnecessary here to pursue these nice distinctions.
 
 SINGULAR QUANTITY 127 
 
 The Singular Term. 
 
 The Singular Term is not the same as the Individual thing. 
 The Individual thing is conceptual. It is a mental concept, 
 corresponding, more or less accurately, with its external reference. 
 The Singular Term is the name we apply to the concept, the 
 means whereby we are able to express it, and reason about it in 
 words. For the purpose of expression and reasoning, the same 
 kind of Singular term may be applied indifferently to any kind of 
 unit individual ; and thus it is necessary to classify Singular terms 
 on a plan different from that which applies to individual things. 
 The reference of the Singular term is not to a simple or com- 
 pound individual as such, but to a specified individual, a definite 
 individual, an indefinite, or a representative individual. The 
 scheme of Singular terms is therefore on very different lines from 
 the scheme of individual things, and is as follows : — 
 
 TABLE VII. 
 
 Singular Terms. 
 
 Quantity. Sign. 
 
 The Singular Term refers to 
 
 A specified individual... The Specific Singular ... A proper 
 
 name. 
 A definite individual ... The Definite Singular ... The. 
 An indefinite individual The Indefinite Singular ... A. 
 A representative indi- 
 vidual ... ... The Representative Singu- 
 
 13.1 ••• ••• ••• /\« 
 
 The Specific Singular term is the Proper name, and may 
 specify an abstract unit, as blueness, or hardness ; or a simple 
 unit, as John Jones, Helvellyn, The Saucy Arethusa, Carfax ; or 
 an aggregate individual, as The House of Commons, the Cabinet, 
 Stonehenge, The Needles; or a corporate individual, as The 
 Devil's Own, Trinity House, Parliament, The Louvre ; or a 
 uniform individual, as gold, water, dust, soot ; or a serial 
 individual, as Measles, The Messiah, the Reformation, the 
 Restoration, twenty. 
 
 The Proper Name specifies a certain individual as an individual, 
 and not formally or explicitly as a member of a class. In this it
 
 128 A NEW LOGIC 
 
 differs from the Singular Demonstrative or Selective quantity, 
 which also specifies a certain individual, but specifies it as a 
 certain member of a class. When a member of a class is specified 
 as such, the mention of the class carries with it the common 
 qualities that form the concept, and combine the individuals 
 into a class. The class quahties need not be mentioned, but the 
 name of the class implies their presence in every individual 
 bearing that name. When we speak of this man or that man, it 
 is pretty plainly intimated, though it is not stated in so many 
 words, that we mean this or that individual having the qualities 
 common to the class of men. But when we specify an individual 
 by a proper name, without mentioning the class to which he 
 belongs, do we thereby convey any qualities that he possesses ? 
 Some logicians say we do not. Proper names, they say, are not 
 connotative, that is to say, they convey no implication of any 
 qualities in the thing named. This seems to me a complete 
 misunderstanding. The proper name either has a meaning, or it 
 has none. If it has a meaning to any one who uses or hears it, 
 it specifies a certain individual ; it points out a denotation ; it 
 indicates a certain thing; and if that thing is known to us, it is 
 known by its qualities. If it is not known to us, either the proper 
 name connotes to us some qualities, or it is to us not a proper 
 name, but a meaningless word. A name must be the name of 
 something, or it is not a name. To call a name a meaningless 
 mark, or an arbitrary and unmeaning sign, is a misnomer. A 
 mark or a sign does not, in this connection, mean an ink mark on 
 paper, or a written sign, or even a public-house sign. A mark is 
 a mark of something ; a sign is a sign of something ; or the one is 
 not a mark, nor is the other a sign. And a thing is known by its 
 qualities, and by its qualities alone. Any name, or mark, or sign, 
 of any thing, must convey the qualities of that thing, or it is 
 neither name, mark, nor sign. I say that Ponos is Kala-azar, and 
 if you know the qualities of Ponos and Kala-azar, these are to 
 you proper names ; but if you do not happen to know any of the 
 qualities of Ponos or Kala-azar, and cannot therefore relegate 
 them to a class, then these words are to you not names, but 
 meaningless sounds or characters. When any one speaks to me 
 of John Jones, the name conveys to me, not only all the common 
 qualities of men, but also the additional common qualities of 
 Welshmen. If you tell me that the John Jones of which you
 
 THE DEFINITE SINGULAR 129 
 
 speak is the name, not of a man, but of a goat, or a leek, or a 
 rarebit, you do not thereby aboHsh the connotation, you merely 
 change it. If you tell me that it is not the name of a man, but 
 is the name of something else, you refuse to say what, then you do 
 not abolish the connotation, you merely reduce it to the connota- 
 tion of individual thing. If you empty the name of even this 
 connotation, then it is no longer a name at all ; it is flatus vocis. 
 
 The Definite Singular term is indicated by the definite article. 
 It is true that certain proper names have the definite article 
 attached to them, as the Dreadnought, the Cabinet, the Reforma- 
 tion ; but in these cases the proper name is the residue of a 
 Definite Singular name, that has become proper by the omission 
 of the name of the class to which the definite individual belongs. 
 The Dreadnought is the ship Dreadnought ; the Cabinet is the 
 Cabinet Council ; the Reformation is the Reformation of religion 
 in the sixteenth century. The fact that the definite Singular 
 term can become a proper name by the omission of the class name 
 seems to me to show conclusively that there is no such wide 
 difference between them as some logicians contend. 
 
 The definite article marks its subject as expressed in denotation 
 — less strictly in denotation than the proper name marks its 
 subject, but more strictly in denotation than the Definite 
 Selective marks its subject. As there can be no denotation 
 without connotation, each of these terms is connotative in some 
 degree ; but the degree is degree in explicitness, not degree in 
 amplitude. ' Big Ben ' specifics a certain individual clock, and 
 part of the connotation of the term is the situation of the clock 
 at Westminster. * The Westminster clock ' denotes the same 
 individual as is denoted by Big Ben ; but ' the Westminster clock ' 
 denotes the individual less explicitly, because there may be more 
 than one clock at Westminster, and connotes more explicitly the 
 situation at Westminster, and the horological properties of the 
 individual it refers to or denotes. Since, however, the individual 
 denoted by the two terms is the same individual, it must have the 
 same connotation, however it is denoted. The difference between 
 the two terms is that the one connotes all the qualities implicitly, 
 while the other connotes some of them explicitly. 
 
 The next kind of Singular term is the Indefinite Singular, 
 which is characterised by the indefinite article. The Indefinite 
 Singular term refers to one unspecified indefinite member of a 
 
 N.L. K
 
 130 A NEW LOGIC 
 
 class ; as a man, a quality, a mob, a college, a disease ; but this is 
 not the only term that thus refers to one member of a class. The 
 Alternative Distributive term, characterised by the adjective 'any,' 
 also refers to an unspecified and indefinite member of a class, but 
 * a man ' does not mean the same as * any man.' * A man called 
 while )-ou were out' cannot be replaced by 'Any man called 
 while you were out.' What, then, is the difference between the 
 Indefinite Singular and the Alternative Distributive? The 
 difference is this : the Indefinite Individual, e.g., ' a man,' is 
 an unchosen member of a class, determined, beyond alternative, 
 by circumstances. The Alternative Distributive, e.g., ' any man,' 
 is one member chosen out of the rest — any other of which might 
 have been alternatively chosen — and therefore not determined 
 by circumstances. In other words, the Indefinite Individual 
 is determined by circumstances, the Alternative Distributive is 
 determined by the choice of the proposer. 
 
 The Indefinite Individual is characterised by the indefinite 
 article; but this is not the only individual characterised by the 
 indefinite article. The indefinite article characterises also the 
 Representative Individual. When we say ' a man is a biped 
 mammal' or *a man is a responsible being,' the term *a man' 
 has not the same meaning as it has in ' a man called while you 
 were out.' In the last case * a man ' means a determinate indi- 
 I vidual man, whose identity cannot be altered; but when we say 
 ' a man is a responsible being ' w-e are using * a man ' very much 
 in the sense of ' any man.' We mean not a determinate individual, 
 but a representative individual. We take a man — any man — as 
 the representative of men in general, and whatever is predicated 
 of a representative man is predicated of men generally. 
 
 Yet the Representative Individual, ' a man,' has precisely the 
 same form as the Indefinite Individual, 'a man.' How then are 
 we to know when the term is being used in the one sense, and 
 when it is being used in the other ? Very simply and very easily. 
 \\'henever the indefinite article characterises a term in an attribu- 
 tive or a defining proposition, the term marks a Representative 
 individual ; in every other case, it marks an Indefinite individual. 
 ' A man is a responsible being,' * A regiment is made up of soldiers,' 
 ' A mob is liable to panic,' ' An attack of plague is very dangerous,' 
 ' Responsibility is part of the nature of a man,' * Privates and 
 officers go to the composition of a regiment,' ' Panic may at any
 
 THE SINGULAR QUANTITY 131 
 
 time attack a mob ' — in all these cases, the term characterised by 
 the indefinite article is a Representative individual, and in every 
 case the proposition is attributive or defining. But when we say 
 ' A man called while you were out,' ' A regiment marched forty 
 miles in a day,' ' A mob sacked the Tuileries,' * The bale fell on a 
 man,' * The artillery destroyed a regiment,' * Walworth confronted 
 a mob,' we are using substantive propositions ; and in these pro- 
 positions every term characterised by the indefinite article is an 
 Indefinite individual. 
 
 Mediceval Logic did not recognise or admit the Singular term, 
 and thereby tacitly declared that there can be no reasoning about 
 individual things, and even that no statement can be made about 
 an individual thing, a declaration that is evidently self-contradic- 
 tory. The mere inconsistency of a logical doctrine with common 
 sense or plain fact has never deterred logicians from maintaining 
 it ; but one would have supposed that a self-contradictory doctrine 
 would have given them some hesitation or uneasiness. Logic 
 began by assuming that the only mode of reasoning is by the 
 inclusion of things in classes, and the exclusion of things from 
 classes. If it had been content with this limitation, its reasonings 
 would have been few enough, and of little enough value ; but 
 Logic was not content with this limitation. Logicians have 
 always been possessed by a passion to exclude from the realm of 
 Logic as much as they possibly could ; and in view of the imper- 
 fection and limitation of their method, the desire was possibly 
 wise. Not only do they assume and declare that there can be no 
 reasoning about anything that is not certain, as if one of the 
 main aims of reasoning were not to render that certain which is 
 uncertain ; not only do they declare that there can be no reasoning 
 except about classes and parts of classes, which is contrary to 
 universal experience ; but they positively assert that there is no 
 part of a class but the indefinite part, or, at least, that no definite 
 part of a class can be reasoned of. Confronted with the existence 
 of individuals, which are neither classes nor indefinite parts of a 
 class. Logic was nonplussed, and took the simple course of 
 ignoring their existence. Logic in fact forestalled the methods 
 of Christian Science. When it came upon an inconvenient fact, 
 that it knew not how to account for or to deal with. Logic adopted 
 the simple course of ignoring that fact, and pretending that it 
 did not exist. Of recent years, Logic has, indeed, admitted 
 
 K 2
 
 132 A NEW LOGIC 
 
 Singular terms into its system, but when they were admitted, 
 Logic knew not what to do with them, nor where to place them. 
 On its own showing, there are, and in reasoning there can be, no 
 quantities but two — the class and the indefinite part of the class, 
 — and to which of these two is the individual to be allocated ? 
 It would seem that an individual cannot be a class, for the very 
 nature of a class is to consist of more than one individual ; and 
 though an individual may be, and in fact always is, a part of some 
 class or other, yet it is not an indefinite part. It is an extremely 
 definite and restricted part. Confronted with this difficulty, 
 different logicians have solved it in different ways. Some call 
 the individual a third variety of term, which of course it is, 
 distinct from both the class and the indefinite part of a class ; 
 but this distinction holds good so long only as terms are being 
 considered. \\'hen they come to propositions, these very 
 logicians forget all about the individual term, and declare that 
 propositions must be particular or universal, and can be nothing 
 else. Other logicians declare, consistently, that the singular pro- 
 position must be either particular or universal, and after some 
 hesitation they usually plump for his universality, for, they 
 say, when it is affirmed that Taffy is a Welshman, the affirma- 
 tion refers to the whole of Taffy, and not to an indefinite part of 
 him. Whatever Taffy's moral deficiencies may be, he has at 
 least the satisfaction of knowing that, in the eye of Logic, he is 
 not an individual nor an indefinite part of a class, but a whole 
 class all to himself. 
 
 Either the Subject-term, the Object-term, or both, may be 
 singular, and may be any kind of individual, expressed in any 
 kind of singular term ; and arguments may be conducted as well 
 about predication concerning individuals as about any other 
 subjects. If Angus McNab is a presbyterian, he is not a Roman 
 Catholic. If Pillicock sits on Pillicock's hill, he does not stand in 
 Pillicock's valley. If the King is in his counting-house, we know 
 where to find him ; and if the maid is in the garden, she is not at 
 the back door flirting with the baker. If St. Paul's was designed 
 by Wren, then Wren designed St. Paul's, and Inigo Jones did not. 
 If the King was in the counting-house, counting out his money, he 
 was not in the parlour eating bread and honey; nor was he 
 compromising his royal rank by flirting with the maid in the 
 garden.
 
 THE COMPOSITE INDIVIDUAL 133 
 
 If St. Paul's is the only English cathedral in the classic style, 
 And Wren designed St. Paul's, 
 Then Wren designed the only English cathedral in the classic 
 style. 
 
 If The maid was in the garden, 
 And The maid was hanging out the shirt. 
 Then The shirt was in the garden. 
 
 That none of these arguments is a syllogism, or can, without 
 the use of unnatural violence, be distorted into a syllogism, leaves 
 me cold. It is enough for me that they are all completely valid, 
 although the terms are all singular, and refer to individuals. 
 
 The Composite Individual. 
 
 The careful reader will have no difficulty in keeping in mind the 
 distinction between the Composite Individual and the Compound 
 Individual. The Compound individual is, indeed, regarded as 
 composed of parts, but his parts are not separately contemplated, 
 nor are they contemplated at all, except for the purpose of deter- 
 mining what kind of a unit individual he is. The parts are not 
 distinguished from one another, nor are they contrasted or compared 
 in any way with the whole of which they are parts. Their 
 function is purely definitive, and when we have determined, by 
 reference to the parts, what kind of an individual we are dealing 
 with, we may drop them out of sight, and refer to them no more. 
 But in dealing with the Composite individual, we never lose sight 
 of the parts. They cannot be disregarded for a moment. It is 
 the contemplation of the parts that renders the individual compo- 
 site, and if the parts are neglected, the composite individual reverts 
 to the unit. 
 
 As already stated, the Composite Individual is a quasi-class, in 
 which the place of the constituent individuals of the class is taken 
 by the constituent parts of the whole. So close is the resemblance, 
 that logicians have not detected any difference between the 
 composite individual and the class, and constantly give, as class 
 arguments, arguments about parts and wholes of composite 
 individuals. Every distributive quantity, whether Universal or 
 Particular, that is applicable to the individuals in a class, is 
 applicable to the parts of a whole also ; and not only are parts of
 
 134 A NEW LOGIC 
 
 a whole susceptible of distributive quantity, but they are sus- 
 ceptible of collective quantity also. Nor does the parallel end 
 here, for it is no more necessary that the quantity of the parts of 
 a whole should be designated, than for the quantity of the 
 individuals in a class. We can think, speak, predicate, and argue 
 as readily, as intelligibly, and as validly, of gold, and of water, 
 and of Logic, as we can of the rich or of the poor, or of definitions. 
 
 As logicians are in fact familiar with the composite individual, 
 though they are here for the first time presented with it as a 
 discriminated thing, and as they frequently state arguments about 
 it under the mistaken belief that they are arguing about classes, 
 there is no need to insist upon the fact that it can be the subject 
 of statement and argument. It may be useful, however, to parallel 
 some of our instances of class arguments that are out of the reach 
 of Traditional Logic, by others of massive quantity that are out of 
 its reach. 
 
 If part only of the machine is rusty, part at least remains 
 bright, and the whole of it is not rusty. If every part is greasy, 
 you cannot touch any part of it without soiling your hands. If 
 a man cannot lift the w'hole of it, it does not follow that he 
 cannot lift it in parts (this last argument employs the Particular 
 Collective Massive quantity). If a great part at least of the 
 embankment w^as washed away, the damage must have been 
 extensive. If a small part only was damaged, it should not cost 
 much to repair it. If nearly all the beer was drunk, there was not 
 much left ; but if a very little only was gone, the greater part 
 remained. If he gave away most of his property, and he had 
 very little to begin with, he left himself very poor. If he omitted 
 the last part of his sermon, and the peroration was the best part of 
 the sermon, he omitted the best part. If part of it only was 
 written, and that not the best part, he must have preached the 
 best part extempore. If more water flows out of the tank than 
 flows into it, the tank will in time become empty; and if more 
 flows in than flows out, the tank will in time overflow. If there 
 is not enough wine to go round, and you want every one to 
 have some, you had better get some more. If there has been 
 too much rain to do the plants good, and they have not been 
 sheltered, they will suffer in health. None of these arguments can 
 be compassed by the methods of Traditional Logic, for each 
 contains a quantity that Traditional Logic does not admit ; and
 
 VICIOUS LOGICAL PRACTICE 135 
 
 though Traditional Logic could, no doubt, violate its own principles 
 and construct quasi-syllogisms that would appear to prove the 
 conclusions, the arguments so constructed would in no case 
 represent the actual course of thought by which the conclusions 
 were in practice reached. Anyone who is not blinded by familiarity 
 with Traditional Logic will see that these conclusions are reached 
 intuitively from the premisses given, and that a circuitous route 
 through a syllogism or quasi-syllogism docs not represent the 
 mental process actually employed. Nothing is easier than to fake 
 a syllogism that purports to show the process of an argument. 
 We have only to garble the premiss so as to bring it into ' logical 
 form,' then to pretend that the argument is an enthymeme, and to 
 invent a premiss to suit the purpose, and we have the argument 
 expressed in a syllogism. The facts that such a mode of argu- 
 ment is utterly artificial and unreal ; that it is utterly foreign to 
 the course of thought actually pursued in reaching the conclusion ; 
 and that no one outside of Bedlam or a book on Logic would ever 
 argue in such a way ; do not deter logicians from this deplorable 
 practice.
 
 CHAPTER IX 
 
 INTENSIVE QUANTITY 
 
 In the foregoing chapters, the varieties of quantity that can be 
 attached to Quantitative terms have been enumerated and examined, 
 and the meanings of their signs discriminated and identified. It 
 now remains to examine the quantities of Quahtative terms, and 
 although Quahtative terms are susceptible of two kinds of 
 quantity, — the Intensive and the Comprehensive, — as against the 
 one Extensive quantity of Quantitative terms, the reader will be 
 relieved to know that the Intensive and the Comprehensive 
 quantities together are far less numerous than the Extensive. 
 
 Intensive quantity is quantity of degree, and is applicable both 
 to abstracts and to attributes. The degrees of both kinds of 
 qualities are the same, but the signs of intensity that are applicable 
 to the one are not applicable to the other ; so that there are two 
 parallel ranges of signs, the one range applicable to Abstract 
 qualities, the other to Attributes. Unlike the signs of Extensive 
 quantities, those of Intensive quantity are not always the same for 
 the same quantity. Corresponding quantities, even of qualities 
 belonging to the same series, that is, to the Abstract or to the 
 Attributive series, are not always indicated by the same sign. A 
 thing may be of small or great size, but it cannot be of small or 
 great whiteness or definition. It may be bitter cold, but it cannot 
 be bitter hot or bitter long. A thing may be intensely heavy, but 
 not intensely light, nor do we speak of intense weight. It may be 
 light or dark green, but not light or dark savoury. Nevertheless, 
 though the signs are not the same, the degrees correspond, and we 
 may always find a sign that will correspond in degree with that 
 of the sign applied to another quality. 
 
 There are many qualities that are not themselves susceptible of 
 degree. They may be present or absent, but if present, can be 
 present in their fulness only, and not in graduated degrees. A 
 thing is either perfect or imperfect ; there are no degrees of 
 perfection. It may be full or it may be empty, but there are no 
 degrees of emptiness or fulness, properly speaking. It may be
 
 INTENSIVE QUANTITY 
 
 137 
 
 rigid, or straight, or circular, but there are no degrees of rigidity or 
 straightncss or circularity. If it falls short of any of these 
 qualities by the shadow of a shade, the quality is, in truth, 
 altogether absent. 
 
 But though there cannot be degrees of such qualities themselves, 
 there can be all degrees of approximation to them. A thing 
 cannot be partly perfect, or rather perfect, or considerably perfect, 
 or very perfect ; but it can be nearly perfect or far from perfect. It 
 cannot be intensely full, or most full, or very full, or straight, or 
 circular ; but it can be very nearly, or far from, or approximately, 
 or not nearly, full, or straight, or circular. 
 
 The different varieties of Quality will be further examined in the 
 chapter on Negation, to which the reader is referred. 
 
 These preliminaries being settled, we may set forth the several 
 classes of Intensive quantity, in both the Abstract and the 
 Attributive series, as follows : — 
 
 TABLE VIII. 
 
 Intensive Quantities. 
 
 Specimen Signs. 
 Abstract. Attributive. 
 
 Reference of Term. 
 The intensive term refers 
 to the degree of a quality 
 compared with 
 Its degree in 
 
 Other things gene- 
 rally 
 One or more things 
 indiscriminated as 
 to intensity 
 More than one thing 
 
 as 
 
 Quantity. 
 
 Degree. 
 
 Positive. 
 
 Moderate. Rather. 
 
 Comparative. More. More. 
 
 Superlative. 
 
 discriminated 
 
 to intensity 
 The purpose in hand Purposive. 
 Expectation ... ... Emphatic. 
 
 Greatest. 
 
 Enough. 
 
 Such. 
 
 Most. 
 
 — Enough. 
 
 So. 
 
 Positive Degree. 
 Since Intensive quantity is the same as Degree, we might 
 anticipate that it would present the same set of degrees as 
 have already been found to obtain in the Semi-definite Extensive
 
 13S A NEW LOGIC 
 
 quantities ; and this we find to be the case. The Medium 
 intensity is signified in the Abstract quahtative term by ' Some ' 
 or ' Moderate,' and in the Attributive by ' Rather.' From 
 this medium, as a central plane, intensity varies upwards towards 
 a maximum, and downwards towards a minimum, and thus we 
 get the set of five or more degrees that have already been 
 enumerated. Moreover, Intensive quantities exhibit the same 
 three forms of Mimimal, Maximal, and Exact quantity that we 
 have found to pertain to Extensive quantities. If we keep the 
 forms in mind, however, it will not be necessary to encumber the 
 page by setting them forth in full, and we may take the following 
 set as comprising 
 
 TABLE IX. 
 Positive Intensive Quantities. 
 
 A bstract. A ttribtitive. 
 
 Maximative Intense. Intensely. 
 
 Magnative ... ... Considerable. Very. 
 
 Medium ... ... ... Moderate. Rather. 
 
 Parvative ... Slight. Slightly. 
 
 Minimative Very slight. Very slightly. 
 
 Statements and arguments containing the Positive Intensive 
 quantity, and inexpressible without it, are frequent enough. They 
 are, of course, outside of Traditional Logic, which knows not the 
 quantity. 
 
 If the cancer is very small, it is still in an operable stage ; if it is 
 very large, operation may not be practicable. If the sentence was 
 just, no exception can be taken to it, but if it was very unjust, it 
 ought not to have been passed, and it would be very wrong to 
 carry it out. If there is some slight difficulty about it, it cannot 
 be done with complete ease, but if the difficulty is very slight, it 
 may be neglected. If his fate is rather hard, he is not very much 
 to be envied. If the stain on the wall is very slight, it does not 
 very much matter. If the wall is ver>^ slightly out of plumb, it is 
 not very insecure. 
 
 If His nose is ver>' red. 
 And He drinks very hard. 
 Then There may be a connection between the two 
 things.
 
 COMPARATIVE DEGREE 139 
 
 If Little good can come of it, 
 And Much harm may result from it ; 
 Then It is better left alone. 
 
 If it was a very good song, and very well sung, it must have been 
 well worth hearing. If they both started from scratch, and one 
 ran very fast, but the other won the match, the winner must have 
 run very fast indeed. If the tide was very high yesterday and 
 only rather high to-day, it was higher yesterday than to-day. 
 
 Comparative Degree. 
 
 The Comparative Intensive term refers to the intensity of a 
 quality in one thing, compared with its intensity in another thing, 
 or in other things regarded indiscriminately as possessing the 
 quality in the same degree. If the other things are regarded 
 discriminately, as possessing the quality in different degrees, the 
 degree is not Comparative, but Superlative. 
 
 Comparative Degrees are three, — the Medium, the Excessive, 
 and the Defective ; and moreover, each of these may be Indefinite, 
 Semi-definite, or Definite. 
 
 The Indefinite Comparative. 
 
 The sign of the Medium Indefinite Comparative is ' About as,' 
 which suffices for the Attributive quality, but for the Abstract needs 
 the addition of ' the same.' * About as hard,' ' about as near,' 
 'about as just,' 'about as definite,' are Attributives in this 
 quantity ; but to express the Abstract, we must add ' About 
 the same hardness,' 'about the same nearness,' 'about the same 
 justice,' 'about the same definiteness.' 
 
 The sign of Excess in the Indefinite Comparative is, for 
 Attributes, ' more,' or the addition of the syllable -er. More 
 hard, harder; more near, nearer; more just, juster; more definite. 
 In the last, and many other cases, the addition of the syllable is 
 inelegant, and is not often employed. For the Abstract, the sign 
 of indefinite excess is more, greater, more intense, or some equiva- 
 lent. More or greater or more intense hardness ; more or greater 
 justice ; more or greater nearness ; more intense heat or cold. 
 
 The sign of Defect in the Indefinite Comparative is, for both 
 Attributes and Abstract qualities, ' less.' Less near, less hard, 
 less just ; less nearness, less hardness, less justice. 
 
 The Semi-definite Comparative. — This intensive quantity, as
 
 140 A NEW LOGIC 
 
 applied to Abstracts, exhibits the Exact form only ; but as 
 applicable to Attributes it exists in all the three forms that we 
 have found to belong to semi-definite extensive quantity, viz : — 
 the minimal and the maximal, as well as the exact. 
 
 The semi-definite degrees as pertaining to Abstract quality are 
 
 TABLE X. 
 
 Semi-definite Comparative Abstracts. 
 
 Maximative ... ... ... Much more intense. 
 
 Magnative ... ... ... More intense. 
 
 Medium ... ... ... As intense. 
 
 Parvative ... ... ... Less intense. 
 
 Minimative .., ... ... Much less intense. 
 
 As pertaining to Attributive quality, they are 
 
 TABLE XL 
 
 Semi-definite Comparative Attributes. 
 
 Minimal. Maximal. Exact. 
 
 Maximative Very much more. Not very much more. Very much 
 
 more. 
 Magnative.. Much more. Not much more. Much more. 
 
 Medium ... Quite as. Only as. As. 
 
 Par\-ative.., — Not quite as. Nearly as. 
 
 Minimative — Not nearly as. Much less. 
 
 It does not need much explanation to show that these degrees 
 of intensity have generally the meanings implied by their places 
 in the table. If one thing is very much harder, or softer, or 
 more definite, than another or others, a downward or minimal 
 limit is imposed on the degree of the one, by the degree possessed 
 by that other, plus the interval between the two degrees that is 
 expressed by the sign of quantity ' very much more.' But no 
 upward limit is imposed, and the very much more may be any 
 degree more. * Much more ' hard or soft or definite fixes a lower 
 minimal limit, but fixes no maximal limit. 'Quite as' hard or 
 swift or definite has the force of * at least as,' and still shows the 
 absence of any upward limit. 
 
 All the maximal degrees fix, by their very terms, an upward limit
 
 COMPARATIVE DEGREE 141 
 
 of intensity beyond whicli the degree does not extend, but fix no 
 inferior limit. It may seem that 'not very much more' has a down- 
 ward Hmit in the medium quantity, and must be at least as intense 
 as that of the quality with which it is compared ; but this is not 
 necessarily so. If this is not very much harder than that, it may not 
 be harder at all ; it may not be as hard. ' Only as ' hard means 
 
 * not more ' hard than, and clearly fixes a maximal limit only. 
 
 * As hard as that ' would seem to be not only exact, but definite, 
 but it is not quite definite. It leaves a little margin for inaccuracy, 
 especially in the direction of excess. * As hard ' is more definite 
 than 'About as hard,' but it is less definite than * Exactly as hard.' 
 
 The Definite Comparative is, in the medium degree, expressed by 
 
 * Exactly as ' ; in the excessive degree by a multiple ; and in the 
 defective degree by a submultiple. Twice as hard, as penetrating, 
 as loud, as bright ; or, in the Abstract quality, twice the hardness, 
 the penetration, the loudness, the brightness. Similarly on the 
 defective side, half as hard, half as bright ; half the hardness, half 
 the brightness. Definite comparatives, other than the medium, 
 have their minimal, maximal, and exact forms, indicated by the 
 additions of at least, not more than, and exactly — at least half as 
 bright ; not more than twice as hard ; exactly three times as great. 
 
 Statement and argument would be very much hampered, and 
 very imperfect, if the Comparative degrees were excluded from 
 Logic. If it is about as hard, it is not very much harder nor very 
 much softer. If there is much more cogency in the arguments for 
 it than against it, it is difficult not to agree with it. If the 
 sapphire is not quite as hard as the diamond, it will not scratch 
 the diamond. If fifty thousand pannier loads of Devils, with 
 their tails chopped off by their rumps, could not have made a 
 more diabolical scream than Tristram Shandy on a certain occasion, 
 he must have screamed very diabolically. If more haste is less 
 speed, it is wise to act with the least possible haste when we are in 
 a hurry. If it is more blessed to give than to receive, those who 
 wish to be blessed had better devote themselves to giving rather 
 than to receiving. If the sun is much hotter than the earth, and 
 Sirius is a good deal hotter than the sun, Sirius mustbe ver}' much 
 hotter than the earth. If darkness covereth the land, and gross 
 darkness the people, then both the land and the people are in the 
 dark, and the darkness of the land may not be so gross as that 
 which covers the people. If Bill Adams was a very much greater
 
 142 A NEW LOGIC 
 
 general than Wellington, and Wellington was a greater general 
 than Marmont, Bill Adams must have been a far greater general 
 than Marmont. These modes of reasoning are, of course, beyond 
 the reach of Traditional Logic. 
 
 Superlative Degree. 
 
 The Superlative term refers to the intensity of a quality of one 
 thing compared with its intensity in two or more other things 
 regarded discriminately. Its sign is * most,' ' least,' or some other 
 superlative adjective. With respect to the degrees of quality in the 
 other things with which comparison is made, the superlative 
 degree is always at the end of the scale. It may, however, be at 
 either end, the maximal or the minimal ; and in either case it may 
 differ from the other examples of the quality by various degrees. It 
 may be the most or the least by a little, or by much, or by a great 
 deal, or a very great deal. Since the other things with which 
 comparison of quality is made differ, ex hypothesi, in degree among 
 themselves, the Superlative cannot be definite. It can be by far 
 the largest, but it cannot be the largest by twice. It can be by 
 \evy far the least definite, but it cannot be the least definite by a 
 tenth. The Superlative is susceptible, therefore, of only two 
 modes of quantity — the Indefinite and the Semi-definite. 
 
 If this is the hottest day in the year, it is hotter than any other 
 day in the year ; it is hotter than yesterday or the day before; no 
 previous day in the year has been as hot as this ; nor has any day 
 been of the same temperature. If he is the greatest rascal in 
 Christendom, he has not an exemplary character ; there are others 
 more moral than he ; he is not a man to be trusted ; you must go 
 beyond Christendom to find a greater rascal. If, as Lord 
 Salisbury' said, the best man for the place is the man I like best, 
 then it is easy to make the selection, and if the appointment is in 
 my hands, the man I like best will get it. If this one is by far the 
 best for my purpose, this is the one I should like to have. If this 
 is the hottest day in the year, but yesterday was nearly as hot, 
 this is not by much the hottest day. If he is the least to be 
 trusted of any, and none are very worthy of trust, he must be 
 decidedly untrustworthy. If the best time to bathe is the morning, 
 and he bathed in the afternoon, he might have bathed at a better 
 time. These arguments are all valid and all useful, but are all 
 outside the scope of Traditional Logic.
 
 PURPOSIVE DEGREE 143 
 
 Purposive Degree. 
 
 This also exists in three modes, according as the degree is 
 suitable to the purpose in hand, unsuitable by excess, or 
 unsuitable by defect. The suitable degree is expressed by 
 * Enough,' which precedes the Abstract, and follows the Attribu- 
 tive quality, — Enough hardness ; hard enough. The unsuitable 
 degrees are indicated in the Abstract by * too much ' and ' too 
 little,' in the Attributive by ' too,' and ' not — enough.' Too much 
 or too little sweetness, too sweet or not sweet enough. The 
 Purposive Degree exists in all three forms — the minimal, maximal, 
 and exact, but after what has been said with respect to the 
 other quantities, it is not necessary to pursue the degree through 
 all its forms and all its degrees of definiteness, &c. It will be 
 enough to give a few examples of arguments that cannot be 
 conducted without this intensive quantity, and that, therefore, 
 cannot be conducted by Traditional Logic. 
 
 If his feet are too big for his boots, his boots are too small 
 for his feet. If it is only just large enough, it is not too large ; 
 but if it is more than large enough, there will be some over. If 
 the sapphire is not hard enough to scratch the diamond, the 
 diamond may be hard enough to scratch the sapphire. If the 
 speed is too great for the lubrication, the bearings will heat. 
 If there is not enough depth of water to float a barge, there is not 
 enough to float a battleship. If the air is too foul to support 
 the flame of a candle, and it requires a purer air to support 
 human life than to support the flame of a candle, the air is too 
 foul to support human life. If the meat is not sufficiently salted 
 to preserve it, it will go bad if it is kept long enough. If it has 
 been long enough in the oven, it will be cooked through, and if it 
 is left too long, it will be overdone ; but if you take it out too 
 soon it will be underdone. 
 
 Emphatic or Unexpected Degree. 
 
 This degree may be added to almost any of the foregoing. It 
 is signified in the Abstract by ' Such ' and in the Attributive by 
 * So,' Such brightness ; such very great tension. So hard ; so 
 long ; so sweet, so cool, so calm, so bright. It conveys that the 
 degree of quality experienced is unexpected, that we did not antici- 
 pate that it would be so much or so little, as the case may be.
 
 CHAPTER X 
 
 COMPREHENSIVE QUANTITY. CLASSIFICATION 
 
 Viewed in comprehension, qualities are contemplated with 
 respect to concretes, and have different modes of comprehen- 
 sion according as they are regarded with respect to those con- 
 cretes only in which they inhere or from which they have 
 been abstracted, or with respect also to concretes in which 
 they do not inhere, and from which, therefore, they cannot be 
 abstracted. When a quality is contemplated with respect solel}' 
 to the concretes to which it belongs, it is called a Common 
 Quality ; and when it is contemplated with respect both to those 
 concretes to which it belongs and to those to which it does 
 not belong, it is called a Proper Quality of those to which it does 
 belong. 
 
 From this description it appears that Comprehensive quantity 
 appears among quantities by courtesy only. It is, in truth, a 
 kind of quality that pertains to qualities only, and that every 
 quality must possess. 
 
 With respect to their comprehensiveness, qualities may be 
 regarded singly or in groups. A single quality may, as just shown, 
 be regarded as Common or Proper. If regarded as Common, 
 it may be regarded as common to several individuals, and in that 
 case it may or may not be selected to form the basis of a class. 
 
 If it is so selected, the quality is a Class-quality. 
 
 If it is not so selected, the quality is a Property of the class. 
 
 Or the single quality may be regarded as common to several 
 classes ; and in that case, it may or may not be selected to form 
 the basis of a larger class, including all the classes that exhibit 
 the common quality. 
 
 If it is so selected, the quality is a Generic quality, and is 
 sometimes called a Genus, though nowadays the term Genus is 
 usually employed to characterise a class composed of smaller 
 classes, and not to characterise the common quality that unites 
 these smaller classes in the larger.
 
 QUALITIES IN COMPREHENSION 145 
 
 If it is not so selected, it is a Property of the Genus, or Generic 
 Property. 
 
 If the single quality is regarded as proper, it may be regarded 
 as proper to an individual, or to a class of individuals. 
 
 If the quality is proper to an individual, it may be regarded in 
 any one of three aspects. 
 
 If it is regarded with respect to the individual primarily, the 
 consideration of the other individuals in the class, and of the class 
 itself, being secondary and subordinate, then the quality is a 
 Property of the Individual. 
 
 If it is regarded with respect equally to the individual in which 
 it is found, and to other individuals in the class to which the 
 individual belongs, then the quality is no longer a Property of the 
 Individual, but is an Individual Difference. 
 
 If it is regarded with respect equally to the individual to which 
 it belongs and to the class that includes that individual, then it is 
 an Accident of the Class. 
 
 Regarded as proper to a class, a quality may be contemplated 
 with respect not only to the members of the class to which it 
 belongs, but also with respect to other classes within the same 
 genus, that do not exhibit the quality. It is then a Specific 
 Differentia, or Specific Difference. 
 
 Regarded with respect, not only to the members of the class 
 to which it belongs, but also with respect to the genus which 
 includes that class, the proper quality of the class is an Accident 
 of the Genus. 
 
 But with respect to comprehension, qualities may be regarded 
 not only singly, but in groups ; and may be grouped together in 
 the following manner. 
 
 The group of qualities formed of the Class-quality and the 
 Class-Properties is a Description of the Class. 
 
 The Generic quality plus the Generic properties form the 
 Description of the Genus. 
 
 The Class-quality plus the Individual Difference form the 
 Identification of the Individual. 
 
 The Generic quality plus the Specific Difference form the 
 Definition of the Species. 
 
 In Tabular form, the scheme of Comprehensive Quantity is as 
 follows. 
 
 N.L.
 
 146 A NEW LOGIC 
 
 TABLE XIL 
 Comprehensive Quantities. 
 Reference of Term. Quality, 
 
 The Comprehensive Term refers to 
 A single quality regarded as 
 Common 
 
 to several individuals and 
 
 forming the basis of a class ... Class-quality, 
 not forming the basis of a class ... Property of the Class. 
 to several classes and 
 
 forming the basis of a larger class Generic Quality, 
 notformingthebasisofalargerclass Property of the 
 
 Genus. 
 Proper 
 
 to an individual, contemplated 
 
 alone ... ... ... ... Property of the 
 
 Individual. 
 
 with others in the class ... ... Individual Difference. 
 
 with the including class ... ... Accident of the Class. 
 
 A group of qualities, consisting of 
 
 The Class-quality and Class-properties Description of the 
 
 Class. 
 The Generic quality and properties ... Description of the 
 
 Genus. 
 The Class-quality and Individual Dif- 
 ference ... ... ... ... Identification of the 
 
 Individual. 
 The Generic quality and Specific Dif- 
 ference ... ... ... ... Definition of the 
 
 Species. 
 From this table it appears that a Genus is a class whose com- 
 ponent individuals are themselves classes ; and that the component 
 classes of a Genus are Species. 
 
 It will be immediately apparent that the comprehensive quanti- 
 ties include the Predicables of Traditional Logic, and it will be 
 evident also that these quantities are more numerous than the 
 Predicables. The difference is accounted for by the want of any 
 distinction in Traditional Logic between the Individual pro- 
 perty, the Generic, and the Class properties ; by the omission from 
 the Predicables of Descriptions, and of the Identification of the
 
 SUBSTANTIAL TERMS 147 
 
 Individual. Nevertheless, these are quantities that it is desirable 
 to distinguish, for, though definitions are of incalculable use and 
 value, descriptions have their place in statement and argument, 
 and nothing that pertains generally to statement or argument 
 ought to be excluded from Logic. In practice, we are as much 
 and as often concerned to describe and to identify as to define. 
 
 If we look back on the long array of quantities that have been 
 described, and turn back to the summary given in Table I., 
 p. 70, we shall find that there is yet one more division that may 
 be made of terms. We find that Attributive qualities cannot 
 stand alone in a proposition except as Object terms, unless the 
 proposition is merely Defining. If we define what we mean 
 by hard, or just, or savoury, or white, or take these words as 
 we find them in the dictionary and predicate of them their 
 dictionary meanings, then, and then only, can they stand alone 
 as Subjects in a proposition. On all other occasions of their use 
 they must either qualify a concrete thing, as a hard fate, a 
 just sentence, a savoury dish, a white horse, or they must be 
 attributed to a concrete thing; as His fate was hard, His sentence 
 was just. The dish is savoury, &c. This follows of necessity from 
 the fact that an attribute is contemplated as inherent in its concrete. 
 The moment it is separated from its concrete it is an abstract or it 
 is nothing. Abstract qualities may be regarded as qualitative or 
 quantitative, and in the latter aspect they may stand as Subjects 
 in propositions. Patience is a virtue. Beauty is skin deep. 
 Honesty is the best policy. Those terms, whether quantitative 
 or qualitative, that have the capacity of standing as Subject in a 
 proposition, are all grammatically noun substantives; and for this 
 reason may be called Substantial terms. Those which cannot 
 stand as Subjects are attributes, and the attributive term we are 
 already familiar with. We may therefore supplement the table of 
 primordial terms on p. 70 as follows. 
 
 TABLE XIII. 
 Table of Terms. 
 
 Q,., ,• (Individuals 
 uantitative \ 
 I Classes 
 
 Terms 
 
 • Substantial 
 
 L. ,.. .. (Abstracts ) 
 
 tQual.tatne [^^^^.^^^^^ Atlributive) 
 
 Terms. 
 
 L 2
 
 148 A NEW LOGIC 
 
 Classification. 
 
 Logic is so large a subject, and its ramifications are so numerous 
 and complicated, that it is not easy, when we arrive, as we have 
 now done, at the end of one ramification of the subject, to keep in 
 mind at what point the next branch starts away from the trunk, or 
 how far back towards the trunk we must go in order to reach the 
 next branch that we ought to follow. If the reader will turn back 
 to p. 67, and refer to the account of the three-fold or four-fold 
 process of Syncrisis that is there given, he will find that the 
 three aspects of the process are Generalisation, Classification, and 
 Abstraction. By Generalisation we form concepts of classes ; by 
 Classification we separate classes into sub-classes, and by Abstrac- 
 tion we reach the concept of Quality. 
 
 Classes and sub-classes may, as we have already found, be 
 regarded from various points of view ; but all the ways in which we 
 have hitherto contemplated them have this in common — that they 
 have all contemplated classes numerically. Nothing has been 
 considered but number. We have considered classes numerically 
 as complete or incomplete, as to their numerical proportion to 
 other classes, and as to the cardinal number or ordinal number of 
 the individuals they contain. The whole treatment of classes has 
 been numerical. Qualities have been considered as to their degree 
 or intensity, and as to their comprehensiveness ; and in the latter 
 respect we have, it is evident, reached the frontier of classification. 
 For classification results from contemplating classes with respect to 
 their qualities ; and in contemplating qualities comprehensively, 
 we have contemplated them with respect to the classes to which 
 they belong. Classification is the converse of this. It is the con- 
 templation of classes with respect to the qualities they manifest. 
 This is the branch of Logic that we are now to consider. 
 
 When, by abstraction, a quality of a thing is discriminated from 
 its remaining qualities, the remainder is at the same timic discri- 
 minated from the quality abstracted. Every process of abstraction 
 results, therefore, in the formation of two abstracts, or of abstract 
 and remainder, each of which is the complement of the other. If 
 two or more things are taken, and the same quality is abstracted 
 from each, so that they are combined in a general idea or concept, 
 two or more remainders are left, one belonging to each concrete 
 thing. These remainders may be as different as possible, but they
 
 CLASSIFICATION 149 
 
 are linked with the others into a class by the possession of the 
 common quality. When we take account of the likeness of the 
 concretes in respect of their possession of the common quality, we 
 are generalising. When we contemplate the unlikeness of the con- 
 cretes in respect of their other qualities, we are differentiating or 
 dividing. Foam, snow and chalk are, by virtue of their common 
 quality of whiteness, generalised into the class of white things. 
 Within this class they are divided or differentiated from each other 
 by virtue of their several proper qualities. Foam is a white liquid, 
 snow is a soft white solid, chalk is a hard white solid. All are 
 classed together as white ; each is separated from the others by 
 difference of consistence. Thus we arrive at the division from 
 one another of the individuals in a class ; but there is a further 
 step. 
 
 Chalk, I find, is not the only hard white solid. Sugar, porcelain, 
 marble, silver, and many other things, are alike in the two respects 
 of being both white and hard. These, then, constitute a class of 
 hard white things, within the class of white things, and different 
 from other things within the class of whites. Such a class included 
 within a class, and not constituting the whole of the including 
 class, is termed a Species ; to which the including class is the 
 Genus. The same class that, included in another class, is a species 
 of this other, may itself include yet other classes, and be of them a 
 genus. The process of dividing a genus into species, dividing one 
 or more of these species, now regarded as genera, into lower species, 
 and these again into lower still, may be continued until we are 
 arrested by the impossibility of finding any quality common to any 
 of the individuals of the last species and not common to all. That 
 species is an infima species, and its components are individuals only. 
 In the other direction, more than one species may be combined by 
 some common quality into a genus, and this genus may be found 
 to possess qualities in common with other genera, and so to form 
 with them species of some higher genus, and this process may be 
 continued until all classes of concretes, or of the concretes under 
 consideration, are included in one comprehensive class, the su})ii)iH)n 
 genus. The division of a class into sub-classes, or its constitution 
 as a genus and its division into species, is the process ordinarily 
 termed Classification. 
 
 Classification in this sense is a necessary condition of orderly 
 thinking. It is, indeed, implied and involved in all thought ;
 
 150 A NEW LOGIC 
 
 though thought is not Hmited, as the doctrine of the sj'llogism 
 implies, to the formation of classes and to nothing else. Prelimi- 
 nary to all thinking, there is a limitation, or classification, or defi- 
 nition, more or less definite, but always present, always presumed, 
 always understood, of the things thought about. It is impossible 
 to reason about men, or principles of law, or modes of action, or 
 shirts, or mental processes, or anything else, without first delimit- 
 ing the subject of thought from other things. Without classifica- 
 tion, the Universe is chaos. It is this preliminan,- delimitation 
 that logicians have denominated the suppositio, or Universe of 
 discourse. 
 
 Formal classification and formal definition are merely extensions 
 of this practice, and its execution with exactitude. They are the 
 accurate delimitation of classes, and of classes within classes. As 
 some vague and general delimitation of the subject of thought is a 
 necessary preliminary to thinking of any kind, so the accurate 
 delimitation of the subject of thought is a necessary preliminary 
 to accurate thinking. Hence the great importance of classifica- 
 tion. It requires accuracy, and is indispensable to accuracy. 
 No intellectual exercise is so conducive to a habit of accurate 
 thought, as the practice of defining and classifying. Let us 
 see, then, what are the essentials of a good classification. 
 
 The first essential is to know what it is that we intend to classify. 
 What are the things to which the classification is to apply ? What 
 are to be the limits of the classification ? Here we are introduced 
 to another aspect of the problem already treated of with reference 
 to propositions. In classifying, do we classify names, or thoughts, 
 or things ? It is not necessary to go over the whole ground 
 again, but it is necessary to give attention to certain of its 
 features. 
 
 In settling the subject-matter with which Logic is concerned, 
 every one admits that it includes words. The only questions have 
 been whether it includes thoughts and things as well. In settling 
 the subject-matter of classification, the opposite assumption is 
 usually made ; we speak of classifying things, and make little or no 
 reference to the part that thoughts and names take in the process. 
 Classification, as ordinarily understood, does not, however, apply 
 to things — certainly not to things alone. When, indeed, a cashier 
 takes a drawer full of money, and puts the bank notes in one heap, 
 the gold in another, the silver in a third, and the copper in a fourth,
 
 CLASSIFICATION 151 
 
 he does classify the things themselves ; but this is not the sense in 
 which classification is customarily understood. When we speak of 
 a classification of animals, we do not mean a segregation of the 
 animals themselves into groups — putting the deer into a pen, the 
 pigs into a sty, the birds into cages, and so on. We mean, 
 undoubtedly, a classification of the concepts of animals, not of the 
 animals themselves. 
 
 At the same time, our classifications are not of mere concepts, 
 as mental states only. When we classify animals, we classify 
 them, not as states of our minds, but as things having an existence 
 outside of our minds. In other words, the thoughts that we utilise 
 in the classification have an external reference. We classify our 
 concepts of the things in conformity with the resemblances and 
 differences that we believe to exist in the things. 
 
 This being settled, the first step in classification is to form a 
 generalisation of the things to be classified. Are we about to 
 classify animals ? Then we must form a general concept, includ- 
 ing all animals, and excluding all other things. We must fix the 
 denotation and connotation of animals as nearly as we can. We 
 must say what we intend to understand by animals — what are 
 the qualities this term is to connote, and what are the things to 
 which this connotation applies. We must make clear the distinc- 
 tion between animals and the things most like them ; we must 
 make clear the qualities by which things, such as zoophytes, 
 which appear to be different from animals, are included among 
 them. In short, the first step in classification is to form a class, 
 or to draw a definite boundary' around the things that are to be 
 divided into classes — to mark them off from other things — to 
 convert a vague concept into an accurate concept. This, of 
 course, presupposes that our classification is to be a scientific 
 or accurate classification ; for scientific, in this sense, means no 
 more than accurate. In short, we cannot speak or think of 
 anything without classifying it, in the sense of separating its 
 concept from the concept of other things. But to separate a 
 concept from other concepts is to define the thing conceived, 
 so that, while complete and accurate definition is a result of 
 classification, tentative definition is also a necessary preliminary 
 to classification. 
 
 The second requisite of a classification is that it should be 
 adapted to its purpose. Before any classification can be effected,
 
 152 A NEW LOGIC 
 
 its purpose must be decided on. Classification is often spoken of, 
 in books on Logic, as if there were but one ideally right mode of 
 it, — the Natural Classification — and all other modes were wrong. 
 This is a mistake. Classifications are made by us for our conveni- 
 ence ; and whether a classification is right or wrong depends on 
 whether it is or is not suitable to the purpose for which it is made. 
 Classifications are to economise thought ; to enable us to think of 
 things separately and orderly. We classify things in order that 
 we may the better and more clearly think about them, subdue them 
 to our purposes, and attain the ends in which the things classified 
 are concerned. The nature of the classification that we make ; 
 the mode of classifying ; the basis or principle of classification ; 
 ihe. fundiWientum divisionis ; must have direct regard to the purpose 
 for which the classification is required. In as far as it serves 
 this purpose, the classification is a good classification, however 
 ' artificial ' it may be. In as far as it does not serve this purpose, 
 it is a bad classification, however * natural ' it may be. ' Natural ' 
 classification is classification into natural kinds, and must fall with 
 the doctrine of Natural Kinds, now abandoned. A good classifica- 
 tion is a classification in which those things are grouped together 
 that are most alike for the purpose in view ; and those things are 
 separated which, for the purpose in view, are unlike. When the 
 purpose in view is to group together those things that have the 
 closest genealogical affinities, and therefore are usually alike in 
 most respects, the classification is called ' Natural ' or Scientific ; 
 since this is the purpose of that classification that we call 
 * Natural ' and Scientific. But when we have some other purpose 
 in view, the 'Natural' and 'Scientific' Classification may be a 
 ver}- unnatural and unscientific one. The Natural classification of 
 plants is a good classification for the purpose of revealing the 
 genealogical affinities of plants, but for the purpose of the cultiva- 
 tion of a garden it is a very unnatural classification. The gardener 
 does not apply the rose and the apple, the lily and the onion, the 
 potato and the winter cherry, to the same purpose ; and therefore 
 he does not classify these pairs together, and such a classification, 
 good for the purpose of the botanist, is bad for the purpose of the 
 gardener. The best and most natural classification of books for 
 the purpose of the librarian, is according to subject or author; for 
 the purpose of the bookbinder, it is according to size, price, and 
 style of binding. The classification by the gardener, of plants into
 
 TREE OF PORPHYRY 153 
 
 useful and ornamental, is a good classification when he is making 
 out his seed list, or arranging his plants in the garden ; but it is a 
 bad classification when he is sowing his seeds. He now wants 
 quite a different classification, into hardy, half-hardy, tender, and 
 stove plants ; and his classification into useful and ornamental is 
 useless. 
 
 When the things to be classified have been delimited, and the 
 purpose of the classification has been settled, the next step is to 
 find a fundamenhim divisionis, or principle of classification, by 
 which the things may be divided ; and the nature of this principle 
 must evidently depend on the purpose in view. Traditional Logic 
 asserts that the division must proceed upon the presence or 
 absence of a single quality, and that venerable tree of Porphyry, 
 which vies in antiquity with the great baobab, is put forward as 
 the model of the perfect system of Division — the process of 
 Dichotomy. But dichotomy is by no means the only proper mode 
 of division. Instead of dividing Corpus, in the Porphyrian method, 
 xnio A niniatum and Inanimatum, we may divide it into Perfectly 
 elastic. Imperfectly elastic, and Inelastic. Instead of dividing 
 Animal into Rationale and Irrationale — a very faulty division, since 
 most animals are to some extent rational, and the limits of 
 rationality cannot be accurately fixed — we may divide it into two- 
 footed, four-footed, six-footed, eight-footed, and many-footed; 
 and this division will be far sharper and better than that into 
 Rationale and Irrationale. So we may divide Corpus Viveus, not 
 into Sensibile and Insensibile, but into that which is locomotor 
 throughout life, that which is non-locomotor throughout life, and 
 that which is locomotor at one time of life, and non-locomotor at 
 another. 
 
 While I must deny that the method of Porphyry is the only 
 true or reliable method of classification, I must, on the other 
 hand, defend it from certain criticisms that have been passed upon 
 it. It is said that division according to the possession or absence 
 of a quality has no value at all, for, if we know the positive 
 qualities of the things included in the negative group, it ought 
 to be indicated by them, and not by a nomcn indcfinitiim ; and, if 
 we do not know them, the negative class is not a class at all, and 
 we have not made even a formal division, for the absence of a 
 quality cannot indicate anything. This criticism seems to me 
 ill founded. The positive qualities are already enumerated in
 
 154 A NEW LOGIC 
 
 those of the snppositio, or universe of discourse, or snmmiim genus, 
 that we are dividing ; and the presence or absence of an additional 
 quaHty within this genus, is a good, vahd, and useful distinction. 
 The instances in the tree of Porphyry are, indeed, not very happy, 
 but it is easy to find instances that are ; and the defect in the 
 Porphyrian tree is the selection of qualities that are indefinite, not 
 in the method itself. To divide insects into those which, in the 
 imago state, have jaws, and those which have not, would be a 
 valid and useful classification. It would, indeed, be absurd to 
 divide the contents of the Universe into things which have jaws 
 and things which have not. In such a division, things which have 
 not jaws would be indeed a nomen indcfinitum ; and it would be 
 impossible, as Lotze says, to hold together in the mind such a 
 chaos of disparate things. The things without jaws would include 
 triangles, beauty, sulphuric acid, and so forth. But no rational 
 system of classification is guilty of such absurdity. The criticism 
 applies to a division of things, into things with jaws and things 
 without jaws, but it does not apply to a division of insects on that 
 basis. A division of elements into those that tarnish in damp air 
 and those that do not, would be open to criticism ; but a division 
 of metals on the same basis would, for some purposes, be perfectly 
 sound. A division of substances into phanerogamic and aphane- 
 rogamic would be open to criticism, but a division of plants on 
 the same basis has been found to be not without value. 
 
 What is required in a. fundamentum divisionis is that it shall be a 
 single attribute. Whether the division is made according to the 
 presence or absence of this attribute, or according to its modes or 
 degrees, does not matter in the least, as long as the attribute 
 remains single, and the following conditions are observed. 
 
 1. The classes must be mutually exclusive. 
 
 2. They must together include all the things to be classified. 
 
 3. They must include nothing that is not in the group of things 
 to be classified. 
 
 If these conditions are observed, and the classification is adapted 
 to its purpose, it is a good classification. If the classification is 
 not adapted to its purpose, or if any of these conditions is broken, 
 it is a bad classification. The worst defect in a classification is 
 neglect of its purpose, the next grave is the inclusion of the same 
 thing in more than one group of the same rank ; the next is 
 faihjre to include something that ought to be included ; and the
 
 CLASSIFICATION 155 
 
 fourth is a defect, not so much in the classification itself, as in the 
 definition of the group of things to be classified. 
 
 These are the principles on which Classification should proceed ; 
 but, in practice, it is often difficult to give effect to them, and they 
 are often neglected. Non-compliance because of the difficulty of 
 compliance is to be condoned ; but non-compliance from neglect 
 of rules is not excusable. 
 
 The preliminary process, of delimiting the genus, or group of 
 things to be divided, is often difficult from the nature of the things. 
 There may be no sharp differences between them and other things. 
 In classifying Insanity, for instance, what are we to include, and 
 what to exclude ? Are we to include Hypochondriasis, Delirium, 
 Coma, Drunkenness, Hysteria, Hallucination ? Some persons 
 would include some of these and exclude others ; some would 
 exclude all; and some would, perhaps, include all. For the 
 purpose of classification, the classifier must first of all make up 
 his mind whether he will include any of them, and which. 
 
 The next step is to choose a fundajnentuni divisionis, that is 
 adapted to the purpose in view. The purpose must be clearly 
 conceived, and the principle of division chosen accordingly. 
 Suppose the things to be classified are the goods to be stowed in 
 a ship's hold. The purpose of the stevedore is to stow the goods 
 so that they may trim the ship, and be accessible when wanted. 
 He classifies them, therefore, according to their weights and the 
 ports for which they are destined. But the underwriter has 
 another purpose. His purpose is to charge his premium according 
 to value and risk. He, therefore, classifies the goods according 
 to their value and perishability. The purpose of the captor is yet 
 different. His purpose is to confiscate what is contraband of 
 war. He, therefore, classifies the goods according to what is 
 contraband, and what is not. 
 
 The worst and most frequent vice in classifying, is to proceed 
 on more than one principle, for classes of the same rank, in the same 
 classification. There is no objection to proceeding on more than 
 one principle if the principles are applied successively ; those 
 groups created by the application of the first principle being sub- 
 divided by the application of a second ; as when a bookseller 
 divides his books into bound and unbound, and each of these 
 again into folio, quarto, and octavo. There is no objection to 
 applying different principles in different classifications, so that the
 
 156 A NEW LOGIC 
 
 bookseller may divide his books into bound and unbound for one 
 purpose, and into folio, quarto, octavo, cSrc., for another. But he 
 may not divide them on both principles simultaneously in the 
 same classification. 
 
 The process here described is sometimes called Division, and is 
 distinguished from Classification, which is then said to be the reverse 
 process of collecting things, first into small groups, these into 
 larger, and these into larger still. Such a process may be called 
 Classification, but it is indistinguishable from Generalisation ; 
 it is Generalisation in successive steps ; and, although it is the 
 practice in Mental Science, of which Logic is an outlying member, 
 to call the same thing by different names, and different things by 
 the same name ; the practice is one that should not be encouraged. 
 I have treated Classification and Division under one heading 
 because, in my opinion, they are two names for one thing. It is 
 desirable that the one name Classification should alone be used, for 
 Division has already other meanings, which Classification has not. 
 
 The Categories. 
 
 Now that we have examined the several constituents of pro- 
 positions in all their numbers and varieties, we are at length in a 
 position to estimate the nature and meaning of the Aristotelian 
 Categories, the discussion of which, in books on Logic, is so 
 lengthy and so barren. Every logician has his own notion of 
 what Aristotle intended to enumerate in making out his list of 
 Categories, and I am not going to add another barren speculation to 
 the tale ; but if, instead of speculating as to what Aristotle's 
 intention was, a speculation that has the demerit or merit that 
 it can never be verified or disproved, we examine the Categories 
 themselves, and estimate what they are, it appears plain enough 
 that they constitute a list of the things that propositions may 
 express or refer to — an imperfect list, and a crude list, it is true — 
 but still they do enumerate some of the most important, as well as 
 some of the most trivial matters that are expressed or referred to 
 in propositions. 
 
 The first of the Aristotelian Categories is Substance, and the 
 meaning, as I take it, of placing Substance among the Categories, 
 is that the proposition refers to Substance, or says something 
 about Substance — that Substance is, or may be, expressed or 
 referred to in every proposition. This we have found to be the
 
 THE CATEGORIES 157 
 
 case. Every Subject-term, as has just been shown, must be sub- 
 stantival or substantial, and the Object-term also may be substantial. 
 This may not be the meaning that is usually read into the statement 
 that substance is a Category, but it is a meaning that may very 
 fairly be read into it, and that invests the statement with a 
 significance that it does not otherwise possess. Whether this was 
 what Aristotle meant by saying that Substance is a Category 
 cannot now be known, but it is at any rate an intelligible and 
 reasonable meaning, which is more than can be said for some of 
 the conjectures that have been made about it. 
 
 Quantity, the second Category, is another of the things that may 
 be, and usually is, expressed in a proposition. As we have seen, 
 either term in a proposition may express quantity, either extensive 
 or intensive, and thus, if we mean by a Category that which may 
 be expressed in a proposition, Quantity is properly a Category. 
 
 Quality is understood in Logic in two senses. It is one of those 
 equivocal words that Logic delights in. As applied to the 
 proposition as a whole, it means the character of the proposition 
 as affirming or denying the relation it expresses, or as containing 
 or not containing a negative term. But terms may, as we have 
 found, be qualitative, and may express many qualities besides 
 those of affirmation and negation. Whether we restrict the meaning 
 of Quality to affirmation and negation, or whether we let in all 
 the other qualities that terms may express, Quality is, in either 
 case, one of the things that can be expressed in a proposition, and 
 therefore is legitimately a Category in the sense here ascribed to 
 Category. 
 
 Relation, the fourth Category, is expressed in the Ratio of every 
 proposition. It is the function, and the sole function of the pro- 
 position to express a relation ; and the Ratio of every proposition 
 expresses a relation, and expresses nothing else. If, therefore, we 
 take the Categories to mean the things expressed or referred to in 
 a proposition, then Relation is very properly a Category. 
 
 Action and Passion are, as we have seen, kinds of relation, and 
 if Relation is a Category, Action and Passion are Categories of 
 course. There is no need to enumerate them separately from 
 Relation, but as they are separately enumerated in the Aristotelian 
 Categories, logicians have the less excuse for excluding them from 
 the logical scheme of propositions, and for declaring that the Ratio 
 of every proposition cannot be other than the verb ' to be.'
 
 15S A NEW LOGIC 
 
 When and Where have been shown to be quahfications of the 
 Ratio, and their inchision in a proposition converts the proposition 
 into a modal, and thereby excludes it from the ambit of Traditional 
 Logic. By including When and Where among his Categories, 
 Aristotle signified, if I understand him aright — and if I don't it 
 doesn't matter — that these modals at least may be legitimately 
 included among logical propositions. 
 
 Posture and Habit may qualify a term if the term happens to be 
 singular and personal also. Their triviality and unimportance are 
 blemishes in the scheme of Categories, and are scarcely consistent 
 with the enlarged and philosophical calibre of Aristotle's mind. 
 I should hazard the conjecture that they are interpolations by 
 some later and very inferior hand. If we include Posture and 
 Habit among Categories, I see no warrant for excluding Complexion 
 and Acuteness of \'ision. Dc minimis non curat lex.
 
 CHAPTER XI 
 
 NEGATIVE TERMS 
 
 Hitherto we have treated of affirmative propositions only ; but 
 in the course of thought, it is almost as frequent to deny as to 
 affirm the existence of a relation ; and until denial and its modes 
 have been examined, the treatment of the proposition is deficient 
 by a full moiety. 
 
 Denial is a denial of a relation, just as affirmation is affirmation 
 of a relation ; and therefore, strictly speaking, a negative proposition 
 is a proposition with a negative Ratio. It is usually possible, 
 however, though it is not always possible, to introduce a negative 
 into a term ; and there are many terms, such as immortal, ignorant, 
 unwise, disorganised, in which a negative is incorporated. Pro- 
 positions in which there is a negative term have, when the negative 
 is a Privative negative, a negative force, even though the Ratio is 
 affirmative ; but terms that are negative in form very often have 
 a positive signification ; and when such a term enters into a 
 proposition, that proposition is in sense affirmative, if it has an 
 affirmative Ratio, even though a term is negative. In many cases, 
 though not in all, as logicians assert, a negative may be transferred 
 from the Ratio to a term without altering the meaning of the 
 proposition. Thus, for 'Angels are not mortal,' we may substitute 
 * No angels are mortal,' and * Angels are immortal.' 
 
 Since negation may be effected by the use of a negative term, it 
 is necessary to give some attention to the nature and varieties of 
 these terms. 
 
 Negative terms may be contemplated in two ways. They may 
 be regarded with respect to the effect of the negative on the term 
 alone to which it is attached ; or they may be contemplated with 
 respect to other terms. We will consider first the effect produced 
 upon a term by attaching to it a negative. 
 
 The attachment of a negative to a term may have any one of 
 five different effects. Three of these we are already familiar 
 with. The attachment of a negative may limit a term, either 
 minimally, as when we add * not less than ' ; or maximally, as
 
 i6o A NEW LOGIC 
 
 when we add * not more than ' ; or exactly, as when we add 
 neither more nor less than ; or it may merely empty the term of 
 all contents, putting nothing in their place, and is then a Privative 
 Negative ; or it may take out all the contents of the term and 
 substitute other contents. In every case except the last but 
 one, it leaves the term still positive, and the proposition into 
 which the term enters is still affirmative, unless and until a negative 
 is introduced into the Ratio. 
 
 The Privative Negative. — When the attachment of a negative to 
 a term results in the emptying of the term of all its contents, 
 without replacing them by other contents, the term so produced 
 may be called the Privative Negative. The negative so attached 
 may be a negative prefix, such as un-, in-, dis-, or non- ; or 
 it may be the negative word * no ' or ' not.' To say that a thing is 
 imperfect, merely deprives that thing of perfection, without 
 replacing the perfection by any other quality. To say that it is 
 incomplete or unsuitable, or unintelligible, usually does no 
 more. To affirm that a man is untravelled, or inexperienced, or 
 uninterested, merely deprives him of having travelled, or gained 
 experience, or exhibited interest, and ascribes to him no positive 
 quality in place of those that are removed. If it is asserted that 
 no man has three legs, the assertion gives us no inkling of the 
 number of legs he possesses, nor even of whether he has any at all. 
 All the negative term gives us is that, if he has any legs, they must 
 be more or fewer in number than three. If I am told that there is 
 no balm in Gilead, I am not entitled to assume that Gilead con- 
 tains anything at all. I now know that it contains no balm, but 
 whether it contains anything else or not, the proposition gives me 
 no information and no hint whatever. 
 
 It needs a good deal of care to construct a negative qualitative 
 term that shall be purely Privative, and shall contain no hint of a 
 positive content. When a negative is attached to an adjective, the 
 resulting term is generally not privative, but more or less explicitly 
 positive. To say that Angels are immortal, affirms not only that 
 they do not die, but that they go on living for ever. To say that 
 a thing is immobile, asserts not only that it does not move, but 
 that it stays where it is ; and less explicitly, such terms as 
 unjustifiable, inexpedient, dishonest, unhappy, have all a positive 
 flavour, more or less pronounced. The qualitative term that 
 is most easily kept free from positive signification is the past
 
 NEGATIVE TERMS i6i 
 
 participle. Unmarried, unfinished, undefended, undefeated, are 
 pretty free from positive implication ; and though unnerved, 
 unhung, unlicked, are not wholly free, they are far from having the 
 depth of positive significance that attaches to improper, imprudent 
 and dishonest. Even the past participle, however, may convey 
 very positive signification, as in the case of disorganised. 
 
 Quantitative terms are much more easily kept free of positive 
 meaning. No man, no brilliancy, no litigation, no class of things, 
 not a penny, not a friend, not a bit, are purely privative negatives ; 
 but ' no gentleman ' carries a good deal of positive meaning, and 
 so does ' not a genius.' 
 
 The limiting negatives we have already made acquaintance with 
 in our examination of quantities. There we found that every 
 quantity has three assignable forms, the minimal, than which 
 it can be no less ; the maximal, that it cannot exceed ; and 
 the exact, from which it cannot depart in either direction. The 
 negatives by which these three forms are severally conveyed 
 are ' No less than,' ' No more than ' and ' Neither more nor less 
 than.' 
 
 It is odd that though logicians reject the maximal positive 
 quantity — Some only — they mention and examine the Maximal 
 or Exclusive Negative, ' Not more than,' in its equivalent form 
 ' None but ' ; and that though they welcome the minimal form of 
 the Particular — Some at least, — they do not examine or mention 
 the negative by which it is expressed — ' Not less than ' ; and of 
 course they have no place for the sign of the Definitive or Exact 
 form — ' Neither more nor less than.' 
 
 These forms of quantity have already been referred to, examined, 
 and utilised ; and all that now remains to be said of them is that, 
 rightly regarded, they are negative limitations of the terms they 
 qualify. They do not, as the Privative Negative does, empty the 
 term of contents, but they limit its extension strictly in one or 
 other direction, or in both ; and, as has been already sufficiently 
 explained, they are applicable to all forms of quantity, both 
 Extensive and Intensive. ' None but the brave deserve the 
 fair' is a maximal limitation of class; as is 'Birds are clothed 
 in nothing but feathers.' * Fish breathe no air that is not 
 dissolved in water' is a maximal limitation of part of a uniform 
 individual. 'The diamond is at least as hard as glass' is a 
 minimal limitation of an attribute; and ' His manner amounted 
 
 N.L. M
 
 i62 A NEW LOGIC 
 
 to neither more nor less than piggishness ' is an exact limitation 
 of an Abstract. 
 
 The Exceptive Negative differs from the Limiting negatives just 
 considered, in that it does not limit the term to which it is 
 attached, but, like the Privative negative, empties it of all contents. 
 Here the Privative Negative ceases its operations, and leaves the 
 term empty, but here the Exceptive Negative does not cease. 
 It goes on to fill up the vacancy with an alternative, and is 
 therefore always positive. The most general form of the Excep- 
 tive Negative is, in the Subject-term, 'What is not,' as in 'What 
 is not mortal is not a man * ; and in the Object-term, ' Except,' 
 as in ' He ploughed the whole field except the headlands.' 
 It is manifest at once that Exceptive Negatives are extremely 
 comprehensive quantities, — more so even than the 'Some' of 
 Traditional Logic ; for they include not only, as ' Some ' does, all 
 Particular quantities, but all Universal quantities also. Hence, 
 there are as many varieties of the Exceptive negative as there are 
 of Extensive quantities. What is not desirable may be everything, 
 each thing, or anything that is not desirable. It includes some 
 things, a great many, many, a few, and a very few things that are 
 not desirable. It includes every proportion of such things, from 
 nearly all to scarcely any ; and not only some, but the first, the 
 last, others, and the rest of them. It includes more if there be 
 more, and fewer if fewer are possible. It includes certain things 
 that are not desirable, as well as this and that ; and it includes, 
 moreover, only too many things that are not desirable, as well as 
 enough and too few. 
 
 Thus our three forms of quantity are increased to four. The 
 minimal form, signified by 'Not less than' and 'At least,' limits 
 the quantity downwards, and secures it against defect, while 
 leaving it quite undefined in the direction of greater number, 
 proportion, or magnitude. The maximal form, signified by 
 ' Not more than,' ' At most,' and ' Only,' limits the quantity 
 upwards, or maximally, and secures it against excess, while 
 leaving it open to defect. As 'not less than' and 'at least' 
 may include ' perhaps all,' so 'not more than ' and 'only' may 
 imply ' perhaps none.' It is usual, if it is intended to convey this 
 possibility, to add ' if any ' ; but I do not know that it is logically 
 necessary in all cases, though it seems to be necessary in some. 
 It is necessary with the singular quantity, as we shall find, and its
 
 NEGATIVE TERMS 163 
 
 use is desirable, though perhaps not imperative, in other quantities 
 when the meaning ' it may be none ' is intended. 
 
 The Exact form hmits the quantity in both directions ; and 
 lastly, the Exceptive form applies to all that is outside of or 
 beyond the quantity of the term. In order that the Exceptive 
 may be applicable to a term, it is necessary that the form of 
 that term should be exact or maximal, for a minimal term 
 may extend to all, and if it does, there are none left for the 
 Exceptive to apply to. 
 
 The Exact form is not often explicitly stated, but it may be 
 assumed, and usually is assumed, in spite of the teaching of 
 Traditional Logic, that when no indication of form is attached to a 
 term, the quantity of that term is to be taken as exact. Logic 
 tells us that the minimal form should always be understood, at 
 any rate in Particular quantities, but Logic gives no authority but 
 its own for the dictum, and we have learnt that the authority of 
 Traditional Logic is not decisive. In fact, the universal practice, 
 outside of books on Logic, is to take as exact every quantity 
 whose form is not explicitly stated. 
 
 If we adhere to this practice, and bear in mind that any form 
 of negative Subject-term may be combined in a proposition with 
 any form of negative Object-term ; and that in any such propo- 
 sition the Ratio also may be negative, we see that the choice of 
 propositions into which the negative enters is very large. If we 
 use No-A and No-B for the Privative negative, and not-A 
 and not-B for the Exceptive negative, we can frame six leading 
 types of propositions, and pursue the different shades of negation 
 through at least three and twenty degrees. 
 
 The six leading types of proposition are as follows : — 
 
 1. The Affirmative. A is B. Birds are clothed in feathers. 
 
 2. The Negative. A is not B. Birds are not clothed in 
 
 feathers. 
 
 3- 
 
 The Privative. 
 
 A is no-B. Birds are featherless. 
 
 4- 
 
 The Obverse. 
 
 A is not no-B. Birds are not featherless. 
 
 5- 
 
 The Exceptive. 
 
 A is not-B. Birds are clothed in what 
 are not feathers. 
 
 6. 
 
 The Exclusive. 
 
 A is not not-B. Birds are clothed in nothing 
 but feathers. 
 
 M 2
 
 i64 A NEW LOGIC 
 
 Each of these vahies of the Object may be combined with the 
 Privative Subject : 
 
 7. No A is B. No bird is clothed in feathers. 
 
 8. No A is not B. No bird is not feathered. 
 
 9. No A is no-B. No bird is featherless. 
 
 10. No A is not no-B. No bird is not featherless. 
 
 11. No A is not-B. No bird is clothed in anything 
 
 but feathers. 
 
 12. No A is not not-B. No bird is clothed in nothing 
 
 but feathers. 
 
 Or the different values of the Object may be combined with 
 the Exceptive Subject : 
 
 13. Not-A is B. Everything but a bird is feathered. 
 
 14. Not-A is not B. Everything but a bird is not 
 
 feathered. 
 
 15. Not-A is no-B. Everything but a bird is feather- 
 
 less. 
 
 16. Not-A is not no-B. Everything but a bird is not 
 
 featherless. 
 
 17. Not-A is not-B. Everything but a bird is clothed 
 
 in what are not feathers. 
 
 18. Not-A is not not-B. Everything but a bird is clothed 
 
 in nothing but feathers. 
 
 Or the negative Subject may be duplicated: 
 
 19. No not-A is B. Birds alone are feathered. 
 
 20. No not-A is not B. Birds alone are not feathered. 
 
 21. No not-A is no-B. Birds alone are featherless. 
 
 22. No not-A is not no-B. Birds alone are not featherless. 
 
 23. No not-A is not-B. Birds alone are clothed in what 
 
 are not feathers. 
 
 24. No not-A is not not-B. Birds alone are clothed in 
 
 nothing but feathers. 
 
 This list of negative propositions is long, but it is far from 
 exhaustive. The Exceptive term has been treated as if it were 
 one, whereas it is in fact many. Any of the quantities already 
 discovered to reside in terms, may qualify the Exceptive term, 
 and thus the Exceptive term may have a very large num'ber of 
 meanings as has already been shown.
 
 NEGATIVE TERMS 165 
 
 Of this great multitude of negative propositions, Traditional 
 Logic knows of five only, — the Simple negative, A is not B ; the 
 Privative negative, A is no-B ; the Obverse, A is not no-B ; what 
 it calls the Universal negative, No-A is B; and one kind of 
 Exceptive negative, A is everything but B. The remainder of those 
 that have been enumerated, and the additional multitude that can 
 be constructed, are utterly unknown to Traditional Logic. It 
 does not even know of their existence. Even of those that are 
 recognised, two only, E and O, the so-called Universal and 
 Particular negatives, are allowed to enter into the logical scheme 
 of Mediate Inference. The O proposition is one variety out of 
 eight of the Simple negative ; of the remainder Logic knows 
 nothing. The exclusion of the remaining vast multitude of 
 negative propositions, beyond the classical five, is owing to no 
 inherent defect or disqualification in them. They are all good and 
 valid forms of proposition. There is not one of them that is not 
 in frequent use. Even the highly elaborated form No. 24, with its 
 doubly negative Subject, its negative Ratio, and its negative Object 
 — four negatives in all — is in use, and expresses a meaning that 
 cannot be expressed otherwise. ' No one but Jones was appointed 
 solely on account of his merit,' ' Barbara Allen was the only • iP^^ 
 dancer dressed in nothing but a few beads.' Nor does our licence 
 to multiply negatives end here. In the Object-term as well as 
 in the Subject, the negative may be duplicated, and we can argue 
 quite well from propositions on the model ' No not-A is not no 
 not-B,' * No animals but those with wings are not confined 
 exclusively to the surface of the earth.' As this book is going to 
 press I find in the day's Times 'by not excepting him from the 
 list of Scottish members who had not mentioned,' &c. He was 
 therefore not no not-A. 
 
 If it is justifiable, and in accordance w^ith the true laws of 
 reasoning, to argue from ' Every bird has feathers,' to * No bird 
 is featherless,' it would be interesting to know why it is not 
 equally justifiable, and in accordance with those laws, to argue 
 from ' He will accept anything but money,' to ' He will accept 
 a pair of boots,' or from ' He has lost everything but honour,' 
 to ' He has lost his wits.' Traditional Logic does not admit the 
 validity of these inferences ; or, if it does, it knows not how to 
 attain them without making a long detour through a syllogism, 
 a course that no one but a logician would ever dream of taking.
 
 i66 A NEW LOGIC 
 
 They are quite beyond its competence ; but they are so clearly and 
 manifestly valid, that a Logic that does not provide for them 
 confesses its own futility. 
 
 It is often asserted, not, indeed, by logicians, but in common 
 discourse, that, in English, two negatives make an affirmative. 
 An inspection of the examples of the double negative given on a 
 previous page, will show that this is not always true. ' No bird is 
 featherless ' is indeed equivalent to ' Every bird has feathers ' ; 
 but ' Nothing that is not a bird has feathers ' does not positively 
 imply, though it strongly suggests, that birds have feathers. We 
 might say ' Nothing that is not a bird has five legs ' and still be 
 within the four corners of strict truth ; though we should certainly 
 be guilty of the suggcstio falsi that birds possess five legs. It is, 
 therefore, more accurate to say that the double negative is 
 always consistent witli the affirmative ; and we may go further 
 and generalise the statement thus : — Every proposition in which 
 the number of negatives is even, is consistent with the affirmative, 
 and therefore with every other proposition derived from the 
 affirmative, in which the negatives are even in number ; while 
 every proposition in which the number of negatives is odd, is 
 consistent with every other such proposition, derived from the 
 same affirmative, but is incongruous with the affirmative, and with 
 all its even negatives. 
 
 Even a single negative, introduced into an affirmative propo- 
 sition, does not necessarily make a proposition inconsistent with 
 that from which it is derived, but it always makes them incon- 
 gruous. Any single negative introduced into the proposition, 
 ' birds have feathers,' gives an inconsistent proposition. * No 
 birds have feathers,' ' Birds have not feathers,' ' Birds are 
 featherless,' are all inconsistent with 'Birds have feathers'; but 
 'Some birds have no feathers' is not inconsistent with 'Some 
 birds have feathers.' The two are not inconsistent, but they are 
 incongruous. If they refer to the same Subject, they are incon- 
 sistent ; if they refer to different Subjects, they are irrelevant. In 
 either case, they are incongruous. ' Everything but a bird is 
 not featherless,' contains three negatives, and is incongruous with 
 ' Birds are feathered,' from which it is derived. It is incon- 
 gruous, because it refers to a different Subject ; but it is not 
 inconsistent. If everything but a bird is not featherless, that is, 
 is feathered, it does not follow of necessity that birds are not
 
 SIGNIFICANT DENIAL 167 
 
 feathered, though it is strongly suggested that they are not. 
 ' Every vertebrate but a bird has a backbone ' is a materially true 
 proposition. Every such vertebrate has, in fact, a backbone; 
 but though I have strongly suggested that birds have no back- 
 bone, I have refrained from actually making the assertion. 
 The statements are incongruous, but they are not formally 
 inconsistent. 
 
 In books on Logic there are two muddles about the negative 
 term, and the two muddles are in some books muddled up 
 together, so as to make confusion worse confounded. Taking as a 
 text the Law of the Excluded Middle, which asserts that every- 
 thing must either be or not be, logicians apply this law to the 
 cases of the soul being square, and virtue being red, and ask 
 whether it is really necessary that the soul should be square or not 
 square, or, as they prefer to write it, not-square, and that virtue 
 should be red or not-red. Most logicians assert that these 
 alternatives are inescapable, and that we are compelled by the 
 Law of the Excluded Middle to accept one or the other. The 
 Law of the Excluded Middle will be discussed, together with the 
 other Laws of Thought, in a subsequent chapter, but this is the 
 place to discuss its application to terms. 
 
 With respect to such examples as virtue is not-square, the soul 
 is not-red. Professor Bosanquet argues that 'bare denial, whether 
 disguised as spurious affirmation, or taken as the mere exclusion 
 of mere suggested predicates, amounts in the strict sense to 
 nothing.' It is difficult to imagine a statement more contrary to 
 truth. Does it amount to notiiing to deny of a man that he is 
 honest, of a woman that she is virtuous, of a soldier that he is 
 brave, of a ship that she is seaworthy, or of a logician that he is 
 logical ? If bare denial amounts, as it may, to nothing, it is for 
 the very reason, and for no other than this, that the predicate has 
 not been suggested. Denial always refers, as will be explained 
 directly, to pre-negative affirmation. Denial is denial of some- 
 thing. Of what then ? Of some affirmation, made, suggested, 
 conjectured, or possible. It is this pre-negative affirmation that 
 gives to denial its whole content and meaning. The bare denial 
 of a suggested predicate may always be made, and always has 
 significance, for the very reason, on which all denial is founded, 
 that the suggestion has been made. To deny that the soul is red, 
 or that virtue is square, is nonsense, because the corresponding
 
 i6S A NEW LOGIC 
 
 affirmative suggestions have not been made ; but if it were 
 seriously suggested that the soul is red, or that virtue is square, I 
 see no reason why it should not be as seriously denied. The 
 significance of denial rests, not upon the congruity or incongruity 
 of the terms of the relation that is denied, but on the presence or 
 absence of pre-negative suggestion. Denial that the soul is red, 
 or that virtue is square, is without significance, not because the 
 terms are incongruous, but because and if the relation has not 
 been suggested. Denial that there is anyone in the next room is 
 equally devoid of significance if there has been no pre-negative 
 suggestion. If one should tell me, apropos of nothing, that 
 there is no one in the next room, the denial is as devoid of 
 significance to me as is the denial that the soul is red ; but if 
 I have heard a crash in the next room, and have said or thought 
 that there must be some one there, the denial is immediately 
 invested with significance. Much — fortune, life, honour — may 
 depend on it. 
 
 The other muddle about the negative term is again a compound 
 muddle. To clear it up it is necessary to answer not one question, 
 but two. It concerns first, the possibility of the Privative negative, 
 and second, the scope and range of the Exceptive negative. 
 When we speak of not-man and not-white, do we mean, by the 
 former, living beings only that are not men, and by the latter, 
 surfaces only that are not white, or do we mean everything 
 thinkable that is not man or not white, including, as Lotze puts 
 it, triangles,, melancholy, sulphuric acid, and so forth? The 
 controversy seems to me to be founded on the fallacy hereinafter 
 described as the fallacy of the previous question. The problem is 
 on a par with the problem, Why does the weight of a bowl of 
 water not increase when a fish is put into it ? In other words, 
 it assumes the previous solution of a problem that has not, 
 in fact, been solved. It is asking, before we have determined 
 whether there is anything at all in the jug, whether it is half 
 full at least ; or quite full. Not-man and not-white may be excep- 
 tive negatives, it is true, but they need not be exceptive : they 
 may be privative ; and if they are, then to ask the range of their 
 denotation is to ask how much beer there is in an empty jug : and 
 to ask whether they are infinite negatives or indefinite negatives 
 is to ask whether the empty jug is quite full or only partly full; 
 or more accurately, perhaps, whether the empty jug contains
 
 THE INFINITE NEGATIVE 169 
 
 all the beer in the universe, or only an indefinitely large quantity 
 of beer. 
 
 A negative term may, as we have seen, have a positive significa- 
 tion. But it need not have a positive signification, and in many 
 cases it has none. When I am told that there is no one in the 
 next room, do I take it to mean that the room is empty of men, 
 women, and children, or do I take it to mean that it contains 
 triangles, melancholy, sulphuric acid, fixed stars. All Fools' day, 
 and all other thinkable things except men, women, and children ? 
 No one can foretell what strange notions may not be entertained 
 by logicians, and when some of them say that this last is the 
 meaning that they understand by the negative term ' no one,' I 
 must suppose that they believe that this is what they ought to 
 understand by it ; but I have a shrewd suspicion that they are 
 mistaken as to their own meaning, and I am quite certain that I 
 do not myself read any such meaning into the term. 
 
 If silver is not gold, then, according to Traditional Logic, 
 silver is not-gold. Silver is, therefore, according to pre-Lotzian 
 logicians, triangles, melancholy, and the rest. A logician to whom 
 I put this consequence demurred. Silver is not-gold means, said 
 he, Silver is so7)ie not-gold. If this be so, then Logic is compelled 
 to accept the Hamiltonian quantification of the predicate, which 
 all logicians reject ; and it is compelled, moreover, to accept 
 
 * some ' in the sense of some only, which is opposed to the 
 unanimous teaching of logicians. 
 
 ' Silver is not gold,' or not-gold, may assert of silver either a 
 privative negative or an exceptive negative. If not-gold is 
 privative, the proposition asserts merely that silver is not gold, 
 without in the least implying what silver is, or even whether 
 silver exists. But if not-gold is an exceptive negative, then to 
 assert that silver is not-gold denies, indeed, that silver is gold, but 
 asserts that it is something. The full expression of this exceptive 
 negative is, of course, Silver is something that is not gold. But this 
 is not the only exceptive negative included in not-gold. I can, if I 
 please, limit the exceptive to one of the elements that is not gold ; 
 and, further, to one of the metals ; and, further still, to one of the 
 noble metals, that is not gold. An exceptive negative, therefore, 
 need not be a universal negative, but it may be a universal nega- 
 tive ; and if universal, it may be a limited or an unlimited universal. 
 
 * Every term that is not quantitative is qualitative ' has for its
 
 i;o A NEW LOGIC 
 
 subject a universal limited to the universe of terms. * Everything 
 that is not mental is material ' has for its subject an unlimited 
 universal. Lotze is therefore no more completely correct than 
 his antagonists. The Universal Exceptive may be a limited or 
 an unlimited universal, and if unlimited, it is an Infinite Negative. 
 The Infinite negative is a very unusual negative, but it is not an 
 impossible negative, and there is at least one occasion on which 
 it is requisite and necessary.
 
 CHAPTER XII 
 
 MODES OF DENIAL 
 
 The foregoing discussion on the character of the negative term 
 is a suitable introduction to the discussion of modes of denial or 
 negation. Affirmation and denial are complementary opposites. 
 When we deny, we deny something that has been, or might have 
 been, affirmed. The negative always has reference to an affirma- 
 tive. It implies or suggests at least a conceivable affirmative. If 
 I say * Birds do not possess hoofs,' I must have in my mind an 
 antecedent assertion, or suggestion, that birds do possess hoofs ; 
 and this assertion or suggestion is the basis and occasion of the 
 denial. Unless the affirmative suggestion had been there, there 
 would have been no reason or meaning in the denial. 
 
 Similarly, every affirmation suggests, or is suggested by, a 
 corresponding denial. If I say ' Birds are migrants,' I deny that 
 birds have fixed abodes ; and to elicit this denial, I must have 
 had the denied relation to some extent explicitly before my mind. 
 As the negative denies the affirmative, so the affirmative denies 
 the negative. ' Steel is hard ' denies that steel is not hard. 
 ' Brutus killed Csesar ' denies that Brutus did not kill Caesar. 
 But the affirmative does not need the antecedent suggestion of the 
 negative as urgently as the negative needs the antecedent suggestion 
 of the affirmative ; and, in many cases, does not need any negative 
 suggestion at all. There would be no need, occasion, utility, or 
 even sense, in denying that Brutus killed Cassius, unless there 
 had been some antecedent assertion or suggestion that Brutus did 
 kill Cassius; but the assertion that Brutus killed Caesar can stand 
 by itself, as a piece of news, without any antecedent suggestion 
 that Brutus did not kill Caesar. This relative urgency of antecedent 
 suggestion, in the two cases, corresponds with the psychological 
 law, that discernment of likeness always explicitly precedes dis- 
 crimination of difference, but discrimination of difference does 
 not, or does not so explicitly, precede discernment of likeness. 
 Affirmation and denial are complementary and inseparable. 
 Each supposes and implies the other; but affirmation usually
 
 172 A NEW LOGIC 
 
 suggests consequent denial only, while denial suggests a previous 
 affirmation. 
 
 The opposition of affirmation to the corresponding direct 
 denial, is but one instance of a law of opposition of much wider 
 and more general application, viz : — that Every proposition denies 
 every proposition inconsistent with it ; and from this law (which 
 is a U proposition in Hamiltonian, or rather, Thomsonian, 
 nomenclature) we may deduce, that Denial is the assertion of a 
 proposition inconsistent with that which is denied ; that the only 
 mode of denial is by assertion of the inconsistent ; and that the 
 assertion of every proposition denies every proposition inconsistent 
 with it. Thus, ' He has just had a good dinner,' denies and is 
 denied by not only ' He has not just had a good dinner,' but also 
 ' He has not dined ' ; ' He has just had a bad dinner ' ; ' He is 
 hungry ' ; ' He has been long without food ' ; ' His stomach is 
 empty ' ; ' He is starving ' ; and many other propositions incon- 
 sistent with the original. 
 
 Hence, in order to determine the modes in which denial may be 
 made, we must discover in what ways a proposition may be 
 inconsistent with another ; and this, in general terms, is easily done. 
 A proposition may be inconsistent with another proposition in its 
 Subject, in its Object, or in its Ratio ; and in either case will deny 
 this other proposition. So far, the matter is simple : but when 
 we enquire what terms are inconsistent, and what Ratios are 
 inconsistent, our difficulties begin. Evidently, Terms and Ratios 
 must be e.xamined separately with respect to their inconsistency 
 with other Terms and other Ratios ; and we shall find it necessary 
 to examine the inconsistency of Quantitative Terms separately 
 from the inconsistency of Qualitative Terms. 
 
 Inconsistency of Terms. 
 Quantitative Terms. 
 
 The consistency or inconsistency of quantitative terms with each 
 other is determined entirely by their form, as minimal, maximal, 
 or exact. The minimal form of a quantity may flatly deny the 
 maximal form of another, and yet may be wholly consistent with 
 the minimal and exact form of that other, and vice versa ; so that no 
 quantity can be denied by affirming another quantity, unless the 
 forms of both are stated. All and None are both consistent with
 
 DENIAL OF QUANTITIES 173 
 
 certain of the forms of Some ; and unless the form of this quantity 
 is explicitly stated, 'there need be no inconsistency, and can be 
 no denial. 'All ' is quite consistent with ' not less than some,' or 
 ' some at least,' and does not deny this quantity ; though it does 
 deny * not more than some ' or ' some only.' ' None ' is consistent 
 with ' not more than some,' or ' some if any,' and does not deny 
 this quantity ; but it docs deny ' some at least,' and ' not less than 
 some.' Even All and None are not necessarily inconsistent. * All 
 if any ' is quite consistent with None, and does not deny None. 
 
 Denial of the Singular Quantity. 
 
 This quantity is peculiar, in that the signs of form, when applied 
 to individuals, alter their significance, and do not mean quite the 
 same as they mean when applied to classes. ' A few only ' and 
 ' Not more than a few ' are maximal forms, and as such are 
 consistent with None. But * Gladstone alone,' and ' No one but 
 Gladstone ' are not consistent with ' No one.' The}^ are exact in 
 form, and mean ' Gladstone certainly, but no one else.' So, also, 
 'few if any ' is a maximal form, and is consistent with none, but 
 emphatically denies more than a few ; but ' Gladstone if any man ' 
 is more preferential than maximal. It is consistent, indeed with 
 no one, but it is consistent also with others besides Gladstone, and 
 though it declares that Gladstone has a preferential position with 
 respect to others, it does not exclude others. 
 
 Although, however, the signs of quantitative form are different 
 for the singular quantity from the signs applicable to other 
 quantities, the rules respecting the forms are the same, mutatis 
 mutandis, however the forms are expressed. 
 
 The exact form of the Singular quantity denies None and denies 
 Others. ' A boy alone rang the bell ' denies that no one rang the 
 bell, and denies also that more than one boy or any one but a boy 
 rang the bell. 
 
 The minimal form of the Singular denies No one, but does not 
 deny Others, or All. ' Gladstone addressed the meeting ' denies 
 that no one addressed the meeting, but does not deny that others, 
 or every one present, addressed it. 
 
 The maximal form of the Singular quantity denies Others, and 
 All, but does not deny No one. ' An infant alone, if any one, is 
 irresponsible.' 
 
 The preferential form is antithetic to the exceptive, and the two
 
 174 A NEW LOGIC 
 
 deny each other. 'A logician, if any one, should be consistent' 
 does not deny ' No one should be consistent,' nor does it deny 
 ' Others besides logicians should be consistent.' All that it denies 
 is that ' Others besides logicians should alone be consistent.' 
 
 Denial of Collective Quantity. 
 
 The antithesis of the Distributive Universal is None, but this is 
 not the antithesis of the Collective Universal. None is no one, 
 and no one, though it effectually denies Every one. Any one, and 
 Each one, does not effectually deny All taken together. All taken 
 together does not assert or posit one, and therefore to confront 
 ' all taken together ' with ' none ' is irrelevant. The true antithesis 
 of 'all taken together' is ' not all.' 'All the ships sailing out of 
 Liverpool are together enough to bridge the Irish Channel ' is 
 not denied by ' None of the ships sailing out of Liverpool is 
 enough to bridge the Irish Channel.' The negative is irrelevant, 
 and does not bear upon the affirmative assertion, either in the way 
 of denial or of corroboration. The only way to deny the assertion 
 by means of a negative term, is to assert * Not all the ships sailing 
 out of Liverpool are enough to bridge the Irish Channel.' This 
 is a denial, and a relevant and effective denial, and in no other way 
 can an effective denial of the Collective Universal be made, except 
 by a negative Ratio. 
 
 The Collective Universal cannot be maximal in form. If all 
 are taken together, they may not be more than all, but they 
 cannot be fewer, and the true maximal is ' not more, and it 
 may be fewer than.' An All that is minimal appears tautological, 
 for all must be all at least, and there seems no room for a possible 
 more, if all are accounted for. But a little consideration will 
 show that there are plenty of occasions for more than all. If the 
 engine can draw all the coaches and a guard's van in addition, it 
 can draw more than all the coaches. If the auctioneer conducted 
 in the morning one sale of 150 lots, and in the afternoon another 
 sale of 50, then in the day he sold more than all the 150 lots of 
 the first sale. ' All taken together ' denies, therefore, ' not all ' and 
 less than all,' and is denied by them ; but it does not deny 'None' 
 or ' More than all,' nor is it denied by these quantities. 
 
 The rules for denying the Collective Particular quantities are 
 the same as those for denying the Distributive Particular, and are 
 given below.
 
 DENIAL OF QUANTITIES 175 
 
 Denial of Distributive Quantities. 
 
 The Distributive Universal exists, as we have found, in three 
 varieties, Every, Each and Any. 
 
 ' Every one ' may be exact or inexact, and if inexact may be 
 minimal or maximal. ' Every one at least ' implies possibly more, 
 and in the distributive as in the collective quantity, there may 
 be more than all. ' There was transport for every one of the 
 wounded at least ' suggests that there may have been transport 
 for some of the unwounded. ' Every officer at least was armed 
 with a revolver ' suggests that some of the men also may have 
 been so armed. The minimal ' Every one ' denies and is denied 
 by ' None ' and by every maximal particular quantity. It does 
 not deny its own exact and maximal forms. 
 
 'Every one only' is exact. 'A medal was given to every 
 combatant only ' asserts that every combatant received a medal ; 
 denies that any non-combatant received a medal ; and denies, 
 though not very emphatically, that no one received a medal. 
 ' Every one ' applies distributively to each one, and the only 
 distributive quantity less than one is none. Consequently, to 
 make ' Every one ' explicitly maximal, that is to say, so to 
 express it that it may mean that quantity or less, we must express 
 it ' Every one if any one,' or use some equivalent. ' A medal was 
 given, if at all, to every combatant only,' fixes the form of Every 
 one as maximal. Such a maximal is not denied by None, or No 
 one, nor is it denied by any of the minimal particular quantities 
 included under Some at least ; nor is it denied by All or Every; but 
 it is denied by every maximal particular included under Some only. 
 
 ' Each one ' is almost always exact in form. ' Each if any ' is 
 a possible form, but is not often employed, and 'Each at least' 
 scarcely ever. Each denies and is denied by None, and by all 
 maximal particular quantities. 
 
 ' Any one ' cannot be maximal. * Any one if any ' is an 
 impossible quantity. It may, however, be minimal. Any decked 
 boat at least (and perhaps some without a deck) can cross the 
 North Sea. Any denies and is denied by None, No one, and all 
 maximal particular quantities. 
 
 Denial of Particular Quantities. — What is said here with respect 
 to the denial of Particular quantities applies to both the Collective 
 and the Distributive. For the sake of brevity, I will confine my
 
 176 A NEW LOGIC 
 
 examination of the modes of denial of Particular quantities to 
 denials by other members of the same series. Those who desire 
 to know how an Enumerative quantity can den}-, or be denied by, 
 a Proportional or an Ordinal, or any other kind of particular, can 
 easily work the problem out for themselves in the light of what 
 follows. 
 
 In the Particular, as in the Universal quantities, the mode of 
 denial depends on the form of the quantity, as minimal, maximal 
 or exact. 
 
 A minimal particular quantity denies, of the same series, 
 None. 
 
 All maximal quantities less than itself. 
 It does not deny. 
 
 Any maximal quantity greater than itself, even the Universal. 
 
 Any other minimal quantity, whether greater or less than itself. 
 
 Its own exact form. 
 
 For instance, ' A great many at least ' denies and is denied by 
 
 * Many only,' ' A good many only,' ' A few only,' ' A very few 
 
 only,' and ' None.' 
 
 It does not deny ' A very great many only,' or * Every one.' 
 Nor does it deny ' A very few at least,' * A few at least,' * A 
 
 good many at least.' 
 Nor does it deny * Not more than a very great many.' 
 Nor does it deny * A great many, neither more or fewer.' 
 A maximal particular quantity denies, of the same series. 
 
 All minimal quantities greater than itself, including the 
 Universal. 
 It does not deny 
 
 Any minimal quantity less than itself, even None; 
 Any other maximal quantity, or 
 Its own exact form. 
 For instance, ' Not more than a half ' denies * Not less than 
 two thirds,' ' than three fourths,' and all minimal proportions in 
 excess of a half, up to * all.' 
 
 It does not deny ' A fourth at least,' ' A third at least,' ' Not less 
 than a fifth,' or any other minimal quantity less than itself, even 
 None. 
 
 It does not deny ' Not more than a third,' ' Not more than three 
 fourths,' nor any other maximal quantity more or less than a half. 
 Nor does it deny an exact half.
 
 SQUARES OF OPPOSITION 
 
 177 
 
 The exact form of any particular quantity denies, of the same 
 series, All and None, and all other quantities except its own 
 maximal and minimal forms. 
 
 A small number of these relations of consistency and incon- 
 sistency are expressed by logicians in the Square of Opposition. 
 The quantities that enter into the Square of Opposition are 
 Distributive quantities only, and of distributive quantities none 
 but the Universal and the Indefinite Particular ; and of the 
 Universal and the Indefinite Particular none but the exact form 
 of the Universal and the minimal form of the Particular. As a 
 general guide to the inconsistency of quantities, the Square of 
 Opposition is, therefore, almost worthless. Even to display the 
 inconsistency of the only quantities it includes — the Universal and 
 the Indefinite Particular — it must be supplemented by three 
 other squares, one for the maximal Distributive * Some ' and one 
 each for the maximal and minimal Collective ' Some ' ; and even 
 then it will not display the inconsistency of semi-definite and 
 definite quantities. The Traditional Square of Opposition is as 
 follows. I discard the symbols A, E, I and O, and substitute for 
 them their equivalents — All are, None is, Some are, Some are not. 
 
 All are — 
 
 \ 
 
 \ 
 
 10 
 
 s 
 
 The Traditional Square of Opposition. 
 
 - — — Contraries — — — — None is 
 
 \ 
 
 \ 
 
 \ 
 
 \ 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 / 
 
 a 
 
 "^5. 
 
 ^^ 
 
 
 ^* 
 
 \ 
 
 \ 
 
 \ 
 
 \ 
 
 \ 
 
 s 
 
 a 
 
 \ 
 
 Some at least are 
 N.L. 
 
 — Sub-contraries 
 
 Some at least are not 
 N
 
 lyS A NEW LOGIC 
 
 This is all ven- well as far as it goes, and as long as the All 
 is distributive and the Some is Some at least ; but if, the All 
 remaining distributive, the Some is made maximal, or not more 
 than Some, or Some only, the Square must be remodelled, and 
 must be expressed somewhat as follows. 
 
 Square of Opposition of Maximal Distributive Quantities. 
 
 All are — — — — Contraries — — — — None is 
 I \ / I 
 
 1 \ /I 
 
 I \ / \ 
 
 \ / 
 
 ' / \ ' 
 
 I / \ I 
 
 I ^ ^1 
 
 Some only are not — — Sub-contraries — — Some only are 
 
 In the nomenclature of Traditional Logic, this would mean 
 that A is compatible with O, its contradictory in the 
 Traditional Scheme ; and E is subalternans, not to O, but to 
 I. E and O, instead of E and I, become contradictories, and 
 A and I become contradictories instead of subalterns. 
 
 In the square on top of p. 179 it will be seen that every quantity 
 has two contradictories, and therefore there are four pair of con- 
 tradictories, no contrary, and no sub-contrary. The reason is 
 manifest. Between * All together are ' and ' All together are not,' 
 there is no third alternative, and these are therefore contradictory. 
 And Some at least, is Some, it may be all, and must therefore be 
 taken as contradictory to whatever is contradictory of all.
 
 SQUARES OF OPPOSITION 179 
 
 Square of Opposition of Minimal Collective Quantities. 
 
 Some at least are — — Contradictories — — All are not 
 \ 
 
 ' N / ' 
 
 I 
 
 \ 
 
 
 I \ 
 
 \ 
 
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 / 
 
 •^ Q)^ -^ ^ 
 
 / 
 
 CO /ir ry. TO 
 
 ^ 0° % 5 
 
 \ 
 
 I 
 
 \ / \ I 
 
 All are — — — Contradictories — — Some at least are not 
 
 The Square of Opposition of Maximal Collective Quantities. 
 
 Some only are — — Contradictories — — — All are not 
 
 I X /I 
 
 I \ /I 
 
 I ^ ' \ 
 
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 I \ / \ 
 
 
 & > ,. "3 
 
 •3 ^"^ %. -3 
 
 
 I 
 
 / 
 
 \ 
 
 \ 
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 I ' 
 All are — — — Contraries — — Some only are not 
 
 N 2
 
 i8o 
 
 A NEW LOGIC 
 
 The Square of Opposition of Indefinite Comparative Quantities. 
 More are — — — Contraries — — — — Fewer are 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 OB 
 
 a 
 
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 •♦* 
 
 •a 
 
 en 
 
 
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 SP 
 
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 3 
 C/3 
 
 / 
 
 \ 
 
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 Fewer are not — 
 
 \ 
 
 Sub-contraries — 
 
 — More are not 
 
 The complement of the Residual quantity is necessarily exact. 
 * Some at least, it may be all ' may leave no residue ; hence there 
 can be but one Square for the Residual quantity. 
 
 The Square of Opposition of the Universal Residual Quantity, 
 Some only are — — — Equivalents — — — Some only are not 
 
 / I 
 
 \ 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 \ 
 
 / 
 
 Q 
 
 ^^ 
 
 
 -a 
 
 
 C 
 
 
 
 '■'■s- 
 
 I 
 
 .a 
 
 .S3 
 (fi 
 
 / 
 
 \ 
 
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 \ 
 
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 / 
 
 \ 
 
 / 
 
 / 
 
 The rest are not — — Contradictories 
 
 \ 
 
 \ 
 
 — The rest are
 
 SQUARES OF OPPOSITION 
 
 i8i 
 
 Purposive quantities require two Squares of Opposition, the 
 one to provide for exactly enough, the other to provide for the 
 maximal and minimal suitable quantity. 
 
 The Squares of Opposition of Purposive Quantities. 
 
 Exactly enough — — Equivalents — — Exactly enough 
 
 \ / 
 
 \ / 
 
 \ / 
 
 \ / 
 
 \ / 
 
 \ / 
 
 \ 
 
 en 
 
 a 
 o 
 O 
 
 9) /* 
 
 <£" 
 
 / 
 
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 ri 
 
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 Too 
 
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 many 
 \ 
 
 — — — Contraries — 
 
 — — Too few 
 
 / 
 
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 13 
 
 3 
 
 / 
 
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 \ 
 
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 \ 
 
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 Not less than enough — Subalterns — Not more than enough
 
 iS2 A NEW LOGIC 
 
 Qualitative Terms. 
 
 With respect to possibilities and modes of denial, qualitative 
 terms are divisible into five classes. 
 
 1. There are q.ualities which, starting from zero, proceed in one 
 direction only, and in that direction increase in intensity without 
 assignable limit. Such qualities, of which red, loud, wonderful, 
 horrible, are instances, can have no Contrary or Opposite, and are 
 deniable by the privative negative only. If we wish to deny that 
 a thing is red, or loud, or wonderful, or horrible, there is no means 
 at our disposal except that of saying that it is not red, not loud, 
 not wonderful, or not horrible, as the case may be ; or of asserting 
 of the thing some quality inconsistent with that which we desire 
 to deny. Although, however, the quality in toto cannot be denied 
 except in these two ways : any given degree of intensity, whether 
 maximal, minimal, or exact, may be denied by the assertion of 
 some inconsistent degree ; and the degrees that are inconsistent 
 may be ascertained from the examination of inconsistent 
 quantities just concluded, degree being substituted for quantity. 
 Quantities of this class I call Singly Unlimited. 
 
 2. The next class of qualities consists of those which, starting 
 from a zero point, depart from this point in opposite directions, 
 and proceed in both directions without limit. Thus 'hard ' starts 
 from a zero point, and proceeds through degrees of increasing 
 hardness without limit, there being no limiting point at which we 
 can say of a thing that it is completely hard, or deny that a 
 greater degree of hardness is conceivable. From the same zero 
 point starts, in the opposite direction, a range of degrees of 
 softness, which is similarly without assignable limit. 
 
 Such qualities, which I call Doubly Unlimited, are deniable, 
 not only in the same ways as the Singly Unlimited, but also by 
 the assertion of any degree of the opposing series. Very hard is 
 denied, not only by not very hard, but also by soft, rather soft, 
 very soft, and so on; and similarly, any degree of softness is denied 
 by the assertion of any degree of hardness. Every degree of each 
 series is negative with respect to every degree of the other series, 
 and suchnegaUvesjgirQ called Contrary. Contrasted with each 
 other, the degrees at opposite ends of the two scales are called 
 Opposites. 
 
 3. A third class of qualities consists of those which, starting
 
 DENIAL OF QUALITIES 183 
 
 from a zero point, proceed by successive degrees along a scale, but 
 instead of proceeding without limit, as in the cases of the previous 
 classes, arrive at length at a limit of completeness beyond which 
 they cannot proceed. More correctly, we may contemplate the 
 series as beginning at completeness, and from this point departing 
 without limit. Such qualities are perfection, truth, purity, safety, 
 definiteness, and so forth. If a thing is perfect, pure, or true, it 
 admits of no degrees of perfection, purity or truth. It either has 
 the quality or has it not, and no degrees of the possessed quality 
 are conceivable. But though the quality admits of no degrees of 
 intensity, it admits of unlimited degrees of approximation to, or 
 departure from completeness. A thing cannot have degrees of 
 perfection, but it may have illimitable degrees of imperfection. 
 Purity and definiteness must be complete or incomplete. If com- 
 plete, they admit of no degrees of intensity ; but if incomplete, 
 they may be incomplete through all degrees without limit. A 
 thing cannot be completely unjust, or completely imperfect or 
 unsafe, but it may be very or extremely unjust, imperfect, or 
 unsafe. 
 
 Complete qualities, like other qualities, may be denied by the 
 privative negative. It is a sufficient denial of perfection, or 
 justice, or safety, to say that a thing is not perfect, or not just, or 
 unsafe ; but in addition to this mode of denial, completeness of 
 any quality that is susceptible of completeness may be denied 
 by asserting any degree of incompleteness. Complementarily, 
 assertion of completeness denies incompleteness in all its degrees ; 
 and any degree of incompleteness denies every other degree with 
 which it is inconsistent, according to the scheme of inconsistent 
 quantities. 
 
 4. The fourth class of qualities consists of those which are 
 limited abruptly at both ends of a scale, the scale being 
 a scale, not of intensity, but of degrees of approximation or 
 departure. In the previous class, an abrupt limit of completeness 
 closes the scale at one end, and from this end we may depart, 
 without limit to our excursion. In the class now under considera- 
 tion, the scale is closed by completion at both ends, and the 
 extent of our departure from completeness at one end is limited 
 by the attainment of a complementary and opposite completeness 
 at the other. Fulness is a complete quality. There can be 
 degrees of approximation to fulness, and degrees of departure 
 
 .J^ 
 
 
 O-^ 
 
 7
 
 iS4 A NEW LOGIC 
 
 from it ; but there can be no degrees of intensity of fulness. 
 When we depart from fulness, however, we cannot depart from it 
 to an indefinite extent, as we can depart from justice and 
 perfection. A point is reached at length at which we are brought 
 up with a round turn, and find that we can proceed no further, 
 for we are confronted with emptiness, which is itself a complete 
 quality. We have now reached a blank wall, and must turn 
 back ; and the farther we recede from emptiness, the nearer do 
 we approach to fulness, until we are again brought up with a 
 round turn at a complete quality. 
 
 Qualities thus limited by completion at both ends of the scale 
 of departure or approximation, are deniable in more ways than 
 are those which are but singly limited. Fulness is deniable, not 
 only by the privative negative, not full, and by all degrees of 
 departure from fulness — nearly full only, not more than half full, 
 and so on — but also by all degrees of approximation to emptiness, 
 — partly empt}-, half empty, nearly empty — and also by complete 
 emptiness, a mode of denial that cannot be used in the case of 
 just, or perfect, or any other singly limited quality. Other pairs 
 of complete opposites are transparent and opaque, legible and 
 illegible, awake and asleep, wide open and shut. 
 
 5. Lastly, there are qualities that admit of no degrees at all, 
 either of intensity or of approximation, but that are simply 
 present or absent, such as metallic, moving, fallen, favourite, 
 previous. Such cases may be viewed as doubly complete 
 qualities, like those of the last class, in which the scale of inter- 
 mediate degrees of approximation has been removed, and the ends 
 brought together and coalesced into one. Such qualities can be 
 denied only by the privative negative, or by the assertion of a 
 quality which is equivalent to the privative negative. Metallic 
 cannot be denied except by non-metallic; but moving may be 
 denied both by not-moving and by at rest ; but at rest means no 
 more and no less than not moving. Such terms can have no 
 Contraries, but Contradictories only. 
 
 Traditional Logic admits into its scheme quantitative terms 
 only, two quantities only of quantitative terms, and two ways 
 only of denying the quantitative terms that it admits. Though 
 it recognises that there are contrary and opposite qualitative 
 terms, it does not mention denial of quality in its scheme of
 
 CONTRADICTION 185 
 
 negation. According to Traditional Logic, there are but two 
 ways of denying the proposition ' All soldiers wear red coats.' 
 It may be denied by the Contradictory, Some soldiers do not 
 wear red coats, and by the Contrary, No soldiers wear red coats. 
 To these denials Traditional Logic is limited, and when they are 
 made, its resources are exhausted. But in the actual practice of 
 daily life, the assertion that all soldiers wear red coats may be 
 denied in a score of different ways. It can be denied by All 
 soldiers wear coats that are not red, and by Some soldiers do 
 the like. It may be denied also by any assertion that is incon- 
 sistent with it. It can be denied by Some, or all soldiers wear 
 black, blue, green, or yellow coats. It can be denied by 
 Soldiers do not wear coats. It can be denied by Soldiers wear 
 no coats at all. It can be denied by Soldiers wear smocks or 
 blouses instead of coats. It can be denied by Soldiers are 
 always in their shirt-sleeves. 
 
 The merits claimed by Traditional Logic for the modes of 
 denial by the Contrary and the Contradictory, are that Con- 
 tradictories exhaust between them the universe of discourse, and 
 therefore of Contradictories one must be true and the other false ; 
 while Contraries do not exhaust the universe of discourse, and 
 therefore both may be false. Either All soldiers wear red coats, 
 or Some do not ; and there is no third alternative. It is the absence 
 of any third alternative that is said to exhaust the universe of 
 discourse. It means that between the two alternatives every case 
 is provided for. But between the Contraries, All soldiers wear 
 red coats, and No soldiers wear red coats, there is a third 
 alternative — that some do and some do not. Hence Contraries 
 are said not to exhaust the universe of discourse ; and it is plain 
 that both may be false. There is, no doubt, a certain utility in 
 making this distinction, though whether it is worth all the fuss 
 that logicians make about it, is another matter. 
 
 Contradiction, the opposition between All are — some are not, 
 and between None are — some are, is called by logicians the most 
 perfect form and the most important form of logical opposition. 
 Why it should be considered perfect, whether there can be degrees 
 of perfection, and what the meaning is of perfect, as applied to 
 logical opposition, are matters on which logicians do not enlighten 
 us ; but from the logical * square of opposition ' we may gather this — 
 that denial may have more than one degree of comprehensiveness.
 
 i86 A NEW LOGIC 
 
 ' No A is B ' is a more comprehensive denial of ' All A's are B,' 
 than is ' Some A's are not B.' ' Some A's are B ' does not so 
 comprehensively deny * No A's are B,' as * All A's are B ' denies it. 
 So far, Traditional Logic is justified; but from the square of 
 opposition we cannot gather the much wider generalisation that 
 denial may have many degrees of comprehensiveness, and that in 
 some cases the number of degrees may become infinite. 
 
 According to the Logic of Tradition, there are two ways and 
 two ways only of denying a proposition. We may deny by 
 affirming the Contradictory, or by affirming the Contrary. But 
 of pure denial of quantity there are many degrees, which may, 
 indeed, all be grouped as either Contraries or Contradictories, but 
 which are more conveniently regarded as of three kinds ; according 
 as they deny exactly what is asserted, or a portion only of what 
 is asserted, or more than what is asserted. 
 
 If the assertion is ' Every man in the regiment has all his teeth 
 sound,' the proposition is invalidated if I can show that one man has 
 one tooth slightly decayed. This is a denial of the least possible 
 comprehensiveness, and is a disproof or contradictory of the 
 assertion. If, however, I affirm that Every man in the regiment 
 has not all his teeth sound, or that Not every man in the regiment 
 has all his teeth sound, I deny exactly, in form, what is asserted, 
 neither more nor less ; but my denial is, in fact, vague, and may 
 cover every degree of comprehensiveness. But I may go much 
 further than this. I can assert that not a man in the whole army 
 has a sound tooth in his head. This is knock-down denial. It 
 denies all that was asserted, and a great deal more. It strips the 
 assertor stark naked of every rag of affirmation, and leaves him 
 nothing wherewith to cover his shame. The first denial is a 
 Contradictor}'; but so far from being 'the most perfect,' or the 
 most important mode of denial, it is manifest that it is little more 
 than a quibble ; and if this were all the evidence that could be 
 adduced in contradiction, the dentist who made the original 
 assertion would escape without even a reprimand. The second 
 mode of denial also must be regarded as a Contradictory ; but 
 though a perfectly valid denial, it is in a form that Traditional 
 Logic knows not as a Contradictory. The third denial might be 
 called a Contrary, but it is much more comprehensive than the 
 Contrary known to Logic. I dare say logicians, if they admitted 
 it into their schem^, would call it a super-Contrary; but at any
 
 DENIAL OF RATIOS 187 
 
 rate it is a far more effective and conclusive denial than either of 
 the Contradictories. Prove it, and the dentist who certified to the 
 soundness of the teeth of the regiment would not escape with a 
 reprimand: he would be cashiered. 
 
 Inconsistency of Ratios. 
 
 Inconsistency of Ratios is not susceptible of such systematic 
 treatment as is inconsistency of terms. A Ratio may always be 
 denied by the insertion of a negative, and usually it may be denied 
 in other ways also, and with various degrees of comprehensiveness. 
 Most Ratios have a complementary opposite, which is affirmative 
 in form, but denies and is denied by its opposite. ' He hit it ' is 
 deniable by * He did not hit it,' but it is also denied by, and 
 denies, ' He missed it.' In this case, the affirmative is denied by 
 other affirmative Ratios, such as * He went wide of the mark,' 
 * He very nearly hit it,' and by negative Ratios, other than the 
 direct denial, such as * He did not reach it,' ' He did not go near it.' 
 In other cases, the negative Ratio is the sole mode of denial, 
 though other Ratios may be incongruous, without being incon- 
 sistent. ' Brutus killed Caesar' is not deniable except by ' Brutus 
 did not kill Caesar.' ' Brutus saved Caesar's life ' is incongruous 
 with * Brutus killed Caesar,' but the two are not inconsistent, for 
 they may refer to different occasions. Of course, in denying by 
 means of an inconsistent Ratio, care must be taken that the Ratio 
 is actually inconsistent, and is not merely incongruous. ' He 
 said he would do it ' is not necessarily denied by ' He said he 
 would not do it ' ; nor by ' He declared he would not do it ' ; nor 
 even by ' He emphatically stated what he'd be before he would do 
 it '. All these he may have said, and yet he may have previously 
 undertaken to do it. Even Peter denied his Master. If the 
 assertion refers to one particular occasion of his utterance, then 
 these are effective denials; but if not, then the only effective denial 
 is ' He did not say he would do it '.
 
 BOOK II 
 
 EMPIRICAL REASONING
 
 CHAPTER XIII 
 
 EMPIRICAL REASONING 
 
 The Art of Reasoning has already been defined as that of 
 attaining, or constructing, or estabhshing, new propositions, from 
 propositions already in possession. It is the process by which the 
 mind, working on its own contents, rearranges them, and brings 
 them into new forms. It gives new lamps for old ones. The form 
 the new knowledge takes is the proposition. The material out 
 of which the new judgement is constructed consists of propositions, 
 or of those consolidated relations, that, as we shall presently see, 
 result from propositionising. But though propositions are con- 
 structed in this way, it is clear that this process does not take us 
 back to the ultimate origin of propositions. We are confronted 
 with the problem of the owl and the egg. If every owl comes 
 from an egg, and every owl's egg comes from an owl, which was 
 first, an owl or an egg ? If every proposition comes from a 
 previous proposition, and this from another, what was the origin 
 of the first proposition of all ? Every proposition, however, does » 
 not come from a previous proposition. Some propositions only are 
 thus derived. The remainder come directly, and all propositions 
 are derived directly or indirectly, from experience. Experience is 
 the ultimate source of all thoughts. y 
 
 Some little controversy has arisen as to the meaning of experience; 
 and by some, empiricism is taken to mean the mere succession of 
 impressions made on the senses, as if they were received passively. 
 This of course is not the case. The mind is active in receiving 
 impressions ; and by experience, I mean that active commerce 
 between the self and its circumstances, by which the mind not 
 merely is impressed, but perceives. The unit of knowledge is 
 not a Sensation, but a Percept. 
 
 The radical vice of the Logic of the Schools was its failure to 
 appeal to experience ; and its failure to appreciate that all know- 
 ledge is founded on experience, and drawn from experience. To 
 the Schoolmen, Logic meant, not the three modes of reasoning 
 specified in the Introduction to this volume, but solely the second
 
 192 A NEW LOGIC 
 
 of these modes — Deduction. Their efforts were concerned solely 
 with explicating the implications of propositions ; with deducing 
 results from postulated principles ; with speculating on the con- 
 sequences that followed from suppositions. In this there would 
 have been no harm if they had not mistaken postulates for facts, and 
 suppositions for truths. Instead of going to experience for their 
 principia or universals, they spun them out of their own bowels. 
 Some of their cobwebs have long been swept away, but as we 
 have already found, and shall find again in the next Book, many 
 still await the broom and dustpan of the reformer. 
 
 It was the recognition of this defect in Scholastic Logic that led 
 to the institution of Inductive Logic, as a separate branch of the 
 subject. The radical difference between Deductive Logic and 
 Inductive Logic, is that the one appeals to experience, and the 
 other does not. The mistake of the Schoolmen was that they 
 applied Deduction, which is the Logic of Consistency only, to the 
 discover}' of Truth. The mistake of the Inductive School, and of 
 present-day logicians, is that, though they recognise that the direct 
 appeal to experience cannot be made by any of the processes of 
 Deduction, they confuse the indirect appeal to experience with 
 the deductive process of syllogising ; and fancy that Mediate 
 Induction is the same as Mediate Inference ; whereas the two, 
 despite a superficial and deceptive similarity, are profoundly 
 different. Moreover, though the Inductive School broke in one 
 direction through the narrow and artificial limitations of Scholastic 
 Logic, yet it falls short in two ways of the revolution that was 
 necessary to bring this Logic into accordance with the practice of 
 reasoners. In the first place, it leaves the whole structure of 
 Deduction, limited, defective, and erroneous as it is, practically 
 unchanged. In the second place, it confines its appeal to 
 experience practically to the discovery of causation alone, and 
 ignores the multitudeof other relations that exist in the real world, 
 and that it is interesting and important for us to discover. 
 
 The function of Induction is to solve problems ; and the problems 
 that confront us, and demand solution by appeal to experience, 
 are by no means limited to causation. Causation is a very 
 important relation, no doubt ; but it is far from being the only 
 relation that we desire to discover, and that we must discover if 
 we are to adjust ourselves favourably to our circumstances. As a 
 guide to conduct, it is necessary that we should solve innumerable
 
 REFERENCE TO REALITY 193 
 
 other problems — discover innumerable other relations. Is it 
 raining ? Will it be fine to-morrow ? Who was it that called 
 when I was out ? Where did I put my hat ? Did Babylon ever 
 exist ? Do any ruins of it remain ? Do birds of a feather flock 
 together ; and if so, at what times, in what circumstances, in 
 what numbers, in what places ? Is the fleet efficient ? Is it in 
 home or foreign waters ? How is it distributed ? Have all the 
 ships their full complements of men, of guns, of stores ? Is ponos 
 kala-azar ? If not, what are the differences between them ? Which 
 is the best way to get to Bath, to Jericho, to Coventry ? Is he 
 rich or poor, stupid or clever, honest or dishonest ? All these and 
 many more are problems that it may be interesting and impor- 
 tant to discover ; none of them is a problem in causation. 
 
 Modern Logic, recognising the narrowness of Traditional Logic, 
 and its severance from experience, seeks to bring Logic into touch 
 with experience by declaring that all judgement refers to Reality. 
 The effort seems to me as naive and crude as the efforts of the 
 Inductive School are partial and restricted. Reasoning cannot 
 be based on experience by merely saying that it refers to reality. 
 The statement is flatly opposed to fact. Modern Logic, in 
 making the assertion, neglects that very appeal to experience on 
 which every material statement ought to rest. If space were of 
 four dimensions, I could tie a knot in a string without letting go 
 the ends. Supposing I were you, and supposing you were me, 
 and supposing we both were somebody else, our identities would 
 be confused. If all the earth were apple pie, and all the seas 
 were ink, and all the trees were bread and cheese, why then, 
 many inferences could be drawn from these propositions ; but to 
 say that in stating the propositions, in forming the judgements, in 
 drawing the conclusions, I am making any reference to reality, in 
 any recognisable or admissible sense of the word reality, seems to 
 me the merest moonshine. 
 
 That there are * real ' propositions, in the sense of propositions 
 that refer to reality, and affirm the existence in the real world 
 of a relation between real things, as well as propositions whose 
 relations and whose terms are merely postulated for the purpose of 
 the argument, I not only admit, but also contend. Both have 
 their appropriate places in Logic, the one as the unit of the Logic 
 of Experience, the other as the unit of the Logic of Consistency. 
 Either being wanting, Logic is deficient by a moiety ; but no 
 
 N.L. Q
 
 194 A NEW LOGIC 
 
 good purpose can be served by confusing them with one another, 
 or by pretending that a postulated proposition necessarily refers 
 to reality, when its ver}' nature is to be indifferent to reality. 
 
 Far from agreeing that every proposition refers to reality, I 
 consider it of the greatest importance to recognise the distinction 
 between the postulated proposition and the real proposition ; and 
 the corresponding distinctions between the Logic of mere Con- 
 sistency, and the Logic of Experience ; between the arguinentum 
 ex postiilato and the argumentum in materia; between the explica- 
 tion of what is implied in a proposition, and the investigation of 
 fact. This distinction was drawn by Mill, but his distinction was 
 not as complete and thoroughgoing as I would make it. He 
 recognised that a new method was necessar}' to complement the 
 Logic of Consistency ; but the new method that he and his 
 successors have adopted, is widely different from the method of 
 solving problems that is here propounded. Mill's Logic of 
 Induction is practically a method of determining causation 
 experimentally. Supposing that the method can be applied, 
 mutatis mutandis, to the solution of other problems than those of 
 causation, still, it sets forth one only of the two methods by which 
 problems are, in practice, solved. It sets forth the modes of 
 appealing directly to experience. The indirect appeal to experience, 
 which I call Mediate Induction, was known to him, but has 
 never been described as it is described here. That there is an 
 indirect as well as a direct appeal to experience, is, indeed, 
 common knowledge ; but this indirect appeal is confused by Mill 
 and the Inductive School, as well as by Modern Logic, with the 
 syllogism, to which it has a superficial and misleading resemblance. 
 What I believe to be its true nature, together with the resemblances 
 and differences between it and the syllogism, will be set forth in 
 the next chapter. 
 
 In the Logic of Consistency, the proposition is the grist that is 
 put into the inferential mill ; and the sole function of inference is 
 to grind it up, and present it in a new form. Until it is furnished 
 with a proposition, and a complete proposition, inference cannot 
 begin. But in most of the reasonings of actual life, the material 
 presented to the reasoning process is not a complete, but an 
 incomplete proposition ; and the main task of reasoning, the sole 
 task of Empirical reasoning, is the completion of the incomplete 
 propositions that are continually confronting us. In short, the
 
 PROBLEMS 195 
 
 task of Inference is the extraction of the implications of proposi- 
 tions ; the task of Empirical Reasoning is the solving of problems. 
 The aim of Inference is the maintenance of Consistency; the aim 
 of Empirical Reasoning is the discovery of Truth. 
 
 Well, Doctor, have you discovered the cause of my child's 
 illness ? — Why, yes, I have found that it was caused by the foulness 
 of your drains ; and I should advise you to put them in order. 
 
 What would it cost, Mr. Builder, to relay my drains from the 
 house to the sewer ? — I reckon it would cost about £1^0, but I 
 will send you a detailed estimate. 
 
 What is the prospect, Mr. Solicitor, of recovering from my 
 landlord the cost of relaying the drains ? — There is no prospect at 
 all. Your landlord is not liable, and you must pay the cost 
 yourself. 
 
 For the moment, we will not enquire how these conclusions are 
 severally reached. All we are to notice now is that these three 
 questions are problems ; and the three answers are their respective 
 solutions. It is quite clear that in each case the solution is more 
 than the mere extraction of what is implied in a proposition, and 
 therefore is reached by a process radically different from any of 
 the processes of Inference described in the next Book. By no 
 process of explicating the implications of any proposition in my 
 possession can I discover the cause of my child's illness, the cost 
 of relaying my drains, or the liability of my landlord to pay this 
 cost. In order to solve these problems, I must go outside the 
 proposition, for in fact, I have no complete proposition at my 
 service ; I have a problem only, and first of all, I must ascertain 
 the nature of a problem. 
 
 A problem is an incomplete proposition. It is a proposition in 
 which one of the three elements is wanting ; and is temporarily 
 replaced by a dummy ; and the problem is solved by supplying the 
 missing element. What is the cause of the child's illness ? In this 
 case the problem is. The cause of the illness is x : find .y. 
 What will be the cost of relaying the drains ? The problem is. A' 
 will be the cost of relaying the drains : find X. Can the landlord 
 be made to pay the expense ? In this case the problem is, The 
 landlord x {can, or cannot be made to pay) the expense : find x. 
 
 In the first problem, the Object-term is missing ; in the second, 
 it is the Subject-term that is missing ; and in the third, the 
 
 o 2
 
 196 A NEW LOGIC 
 
 element that is missing is the Ratio. Thus, any element in a 
 proposition may be missing, and its absence converts the pro- 
 position into a problem. In any case, the solution of the problem 
 lies in the supply of the missing element. 
 
 It will be seen by the examples given, that the scope of a 
 problem varies much. The problems of the doctor and the 
 builder were set at large. No hint was given to them of w'hat the 
 solution might be. The nature of the missing element was not 
 suggested. The solicitor's problem was more restricted. He was 
 not to search the universe for the missing element ; it was 
 suggested to him. All he was to do was to decide between two 
 alternatives. And in practice we find that problems may present 
 themselves with any degree of definiteness. Who killed Cock 
 Robin ? is an indefinite problem. Was it or was it not Sparrow 
 that killed Cock Robin ? is an alternative problem of much more 
 restricted scope. Is there any relation between drunkenness and 
 insanity ? Is there a causal relation between drunkenness and 
 insanity ? The latter is a much more restricted problem than the 
 former; but if an affirmative solution is found for the latter, it 
 still leaves us in doubt whether the drunkenness causes the 
 insanity, or the insanity causes the drunkenness, or whether both 
 are not concurrent effects or causes of some third condition. 
 Does or does not drunkenness cause insanity ? narrows the issue 
 to these definite alternatives. 
 
 The indefiniteness of a problem may reside in the scantiness of 
 our experience ; and in such a case, the vagueness with which it is 
 expressed is proper and unavoidable. Or it may lie in the mode 
 of stating the problem, and then it is avoidable and improper. 
 Did Sparrow kill Cock Robin ? sets three distinct and separate 
 problems, and it is impossible to tell, from the form of the state- 
 ment, which of the three is intended. It may mean, was it 
 Sparrow that killed Cock Robin ? It may mean, was it Cock 
 Robin that was killed by Sparrow ? Or it may mean, was killing 
 what Sparrow did to Cock Robin ? It is impossible to tell, from 
 the way in which the problem is stated, whether it is the Subject, 
 the Ratio, or the Object that is to be supplied. Hence, the best 
 way to state a problem is to substitute x for the missing element. 
 
 From this statement of the nature of the problem, the distinction 
 between Inference and Empirical Reasoning comes clearly into 
 view. Inference needs, as its first and indispensable requisite, a
 
 IiMMEDIATE INDUCTION 197 
 
 complete proposition. Ex nihilo nihil jit. From an incomplete 
 proposition no implication can be extracted. 'Give me a premiss,' 
 says the Deductive logician, * and I will tell you what it implies. 
 Give me an argument, and I will put it into convincing form. If 
 there are certain flaws in it, I can point them out. But these are 
 the limits of my powers. Incomplete propositions are of no use 
 to me ; I can do nothing with them. As to problems, I know 
 nothing of them ; they are not in my province. I can do nothing 
 with them until they are solved. When you have solved your 
 problem, bring it to me, and I will tell you whether it stands 
 certain tests that I consider important ; but until you have solved 
 your problem, you must excuse me ; my functions cannot begin.' 
 Confronted with the innumerable problems of practical life, may 
 we not fairly apply to the exponent of Traditional Logic the 
 question put by Dr. Johnson to Lord Chesterfield : Is not a 
 logician one who looks with unconcern upon a man struggling for 
 life in the water, and, when he has reached ground, encumbers 
 him with help ? 
 
 There are two ways, and two ways only, in which a problem 
 can be solved. If I want to know whether this jug will break if it 
 is dropped on the stones, I can drop it on the stones, and see what 
 happens. If I want to know whether there is anyone in the next 
 room, I can go there and look. If I want to know whether my 
 ship is arrived, I can go down to the docks and see. If I want to 
 know whether the piano is in tune, I can strike the notes and 
 listen. If I want to know whether the meat is tainted, I can find 
 out by smelling it. In short, one mode of solving problems is by 
 direct appeal to experience. This is the mode inculcated by John 
 Hunter's maxim, * Don't think : try.' This is the mode that alone 
 is indicated in the discovery of causation by the Inductive School 
 of logicians. 
 
 But the direct appeal to experience is often expensive ; often 
 tedious ; often dangerous ; often altogether impracticable ; and 
 then the second mode must be used. If I test the fragility of my 
 jug by dropping it on the stones, and it turns out to be fragile, I 
 have lost my jug. If I want to know whether this foreshore will 
 ultimately form the summit of a mountain, or whether this moun- 
 tain will ultimately be eroded and carried down in debris to the sea, 
 it would be tedious to sit down and watch. If I want to know 
 whether the bite of this cobra is fatal, I prefer some other method
 
 igS A NEW LOGIC 
 
 than that of letting him bite me, and waiting to discover whether 
 I live or die. And if I want to know whether the moon is 
 inhabited, it is quite impracticable to go there and look. 
 
 Nevertheless, there are means at my command, there is a mode 
 of appealing to experience, by which all these problems can be solved 
 with as assured a certainty as by the direct appeal. Without 
 breaking mj- jug, I can ascertain with certainty that it is fragile ; 
 without having seen this mountain upheaved from the sea, I can 
 be quite sure that its summit once was a sea-bottom ; without 
 being bitten by the cobra, I can make quite certain that its bite 
 would be fatal ; without going to the moon, I can be as sure that 
 it has no human inhabitants as if I had explored every foot of its 
 surface. In these cases I make no direct appeal to experience, 
 but I can appeal to experience indirectly, and thus solve my 
 problems with complete certitude. 
 
 When the direct appeal to experience takes the materials of 
 experience as they are, and merely notes them, without making 
 any alteration in them, the appeal is called Observation. But it 
 often happens that the real world affords no experience that 
 applies precisely to the problem, and then we must create a quasi- 
 artificial experience ad hoc. Such quasi-artificial experience is 
 called Experiment. If I want to know whether there is anyone in 
 the next room, I can go and look ; and the experience furnishes 
 me with a solution of the problem, without any artificial manipu- 
 lation of the materials by me. But if I want to know whether 
 the jug will break if it falls on the stones, the only way of appeal- 
 ing direct to experience is to create an artificial experience, ad hoc, 
 by letting it fall on the stones — unless, indeed, I wait until it has 
 fallen on the stones by accident. In the case of the jug, we may 
 be sure that such an accident will happen sooner or later, and 
 therefore, if we are not in a hurry, we may be content to wait 
 until the accident happens, and then we shall know ; but in many 
 cases, the precise experience we need is not likely to happen 
 accidentally; and then we must have recourse to experiment. 
 
 The direct appeal to experience has been shown to be often 
 inconvenient, often dangerous, often impracticable. These defects 
 are great and important ; but it has yet another defect, perhaps 
 more important still. The knowledge that we obtain from direct 
 appeal to experience is limited to what now exists or what now 
 happens. From it we can obtain no knowledge of the past or
 
 OBSERVATION AND EXPERIMENT 199 
 
 the future. We cannot transport ourselves back into the past, or 
 forward into the future, and observe directly what existed or 
 happened, what will exist or will happen. Neither by observation 
 alone, nor by experiment alone, nor by any combination of 
 observation and experiment alone, can either the past or the 
 future be ascertained. Yet the majority of the problems that 
 confront us in life belong to the past or the future. What was 
 the cause of my child's illness ? What will be the cost of laying 
 new drains ? These are types of the common problems of life. 
 To conclude, from any observation or experiment now made, what 
 must have been in the past, or what will be in the future, is an 
 exercise, not of the direct, but of the indirect appeal to experience. 
 All that the direct appeal can give us is what now exists, or what 
 now happens ; in short, what is presented to perception. 
 
 The direct appeal to experience is valid in proportion to the 
 faithfulness with which the experience fulfils the conditions of the 
 problem. If the problem is whether this jug will break if it is 
 dropped on a stone floor, the problem cannot be solved by obser- 
 vation or experiment alone, except by dropping this very jug upon 
 a floor of stone. If I drop another jug upon a stone floor, and 
 argue from the result what the fate of this jug would be under 
 similar experience ; or if I drop this jug on a feather bed, or into 
 water, or on a wooden floor or an iron plate, and argue from the 
 result what would happen if I dropped it on a stone floor, I am 
 employing not the direct, but the indirect appeal. The direct 
 appeal requires an experience of the very relation between the 
 very terms that I am seeking to establish. Any departure from 
 these conditions imports an element of indirectness into the 
 appeal. 
 
 It is true that neither observation nor experiment is often 
 applied, in this sense, to the direct solution of the problem in 
 hand. Both, and especially experiment, are usually made to 
 afford a basis for the indirect appeal ; and this teaches us two 
 things — first, the intimate association, in practice, of the direct 
 and the indirect appeal ; and second, the immense importance of 
 the indirect appeal to experience, by which the great majority of 
 problems are solved. 
 
 The indirect appeal to experience, as I conceive its nature, has 
 not hitherto been described, or even recognised, by logicians, 
 either of the Traditional, the Inductive, or the Modern School.
 
 200 A NEW LOGIC 
 
 No doubt all of them, and especially the two last, do recognise 
 that there are such things as problems, though they do not define 
 a problem, or show in what it consists, or even explicitly allude 
 to problems ; and no doubt logicians of each school do propose 
 methods for the solution of certain problems ; but they do not 
 recognise what seems to me to be the true nature of the indirect 
 appeal to experience, or that it is the general mode of solving 
 problems — the only mode by which the great majority of problems 
 can be solved. 
 
 The direct appeal to experience — Immediate Induction, as we 
 may call it — is not a mode of reasoning, as reasoning is under- 
 stood in Logic. Observation and experiment are processes in 
 which reasoning is in rudiment ; and the validity of observation 
 and experiment depends on the minimisation of reasoning — on 
 the elimination of reasoning, as far as reasoning can be eliminated. 
 The more complete the elimination of reasoning, the more valid 
 and trustworthy is the observation or the experiment. In other 
 words, direct appeal to experience gives results that are trust- 
 worthy in proportion as the appeal is direct, and as the indirect 
 appeal is eliminated. The total exclusion of the indirect appeal 
 is impracticable : all that we can do is to reduce it to a mmimum. 
 This is what Mill had in his mind when he said that what we 
 observe is usually a compound result, of which one tenth may be 
 observation, and the remaining nine tenths inference. ' I affirm . . . 
 that I saw my brother ... I only saw a coloured surface . . . and 
 ... I concluded that I saw my brother.' In other words, per- 
 ception is the interpretation of sensory impressions ; and in 
 proportion as interpretation enters into perception, in the same 
 proportion enters the liability to error. Interpretation of sensa- 
 tions, and their combination and elaboration into percepts, pertain 
 to Psycholog}-, and are out of place in Logic ; but this is one of 
 the points at which the two sciences come into contact.
 
 CHAPTER XIV 
 
 the indirect appeal to experience 
 Mediate Induction. 
 
 The direct appeal to experience we have found to be limited in 
 practicability, and restricted in usefulness. By far the greater 
 number of the problems that confront us must be solved, if 
 they are to be solved at all, by the indirect appeal. What, 
 then, is the nature of this appeal ? It seeks to solve this 
 problem by appealing to our experience of similar problems. 
 It seeks in experience a similar problem that has been 
 solved ; and applies the solution of that problem to the solution 
 of this. The problem is a proposition in which there are two 
 given elements and a missing element, or qusesitum. In the 
 indirect appeal to experience, we search experience for a pro- 
 position similar in the given elements ; and we adopt into our 
 problem the third element of that proposition as our qusesitum. 
 
 The similar proposition that is discovered in experience, we 
 will call the premiss. Then the first step in Mediate Induction 
 is to find a premiss. At once we see the radical difference 
 between this process and Inference, or Deduction. Deduction 
 cannot stir a step unless a complete premiss is given. The 
 whole process of Inference is founded and based on a given 
 premiss — on a postulate. Mediate Induction knows nothing of 
 postulates. To Mediate Induction no premiss is given. Its 
 function is, first of all, to find a premiss; and it is in the finding 
 of an appropriate premiss that the skill and acumen of the 
 investigator are first and most displayed. He searches experience ; 
 and from experience he selects whatever relation it contains 
 that most resembles, in its homologous elements, the given 
 elements of the problem. 
 
 The doctor is asked what was the cause of Johnny Jones' 
 illness ? He puts it to himself — * The problem is, Johnny Jones' 
 illness is caused by x. I am to find x. I must search experience 
 for a similar case — for a case as like as possible. I must find a
 
 202 A NEW LOGIC 
 
 case in which a similar iUness was traced to a cause, and I 
 may be sure that, if the illnesses are really similar in material 
 respects, and if the true cause of the one illness was discovered, 
 the cause of the other will be the same, or will be similar in 
 material respects.' He searches experience, and he finds what he 
 wants. He remembers Jenny Brown's illness, which was, in 
 material respects, similar to Johnny's ; he remembers that 
 Jenny Brown's illness was traced without doubt to foul drains, 
 to suppurating gums, to faulty diet, or what not ; and he con- 
 cludes, with assured certainty, that Johnny's illness was due to 
 the same cause, or to one that is similar in material respects. 
 What his warrant is for so concluding, we shall consider presently. 
 For the moment, it is enough to show what the course of the 
 reasoning is. 
 
 This, then, is the nature of the indirect appeal to experience 
 that I call Induction, or Mediate Induction. When a problem 
 is presented to us that does not admit of solution by direct 
 appeal to experience, we appeal to experience indirectly, by com- 
 paring the problem with some previous experience that is similar 
 in material respects. We cannot reproduce Johnny's illness. If 
 we could, it would not be the same illness, but another one. We 
 cannot set the cause in motion to produce the illness, for ex 
 Jiypothesif the cause is unknown. Direct appeal to experience 
 cannot be made. We therefore appeal to experience indirectly, 
 through the medium of some similar problem, the solution of 
 which is known. W^e search experience for a premiss — for a pro- 
 position known to be true in fact, and as like as possible to the 
 problem. We compare the problem with this premiss ; and, if 
 they are like in the two given elements of the problem, we 
 conclude that they are like in the third element also. Thus we 
 supply the missing element in the problem, by adopting into it 
 the homologous element of the premiss. The reasoning may be 
 represented thus ; the mark || being the sign of assimilation. 
 
 Jenny Brown's illness was caused by foul drains 
 
 "-Y" 
 
 II 11 II 
 
 .^. . . A , , A^- 
 
 Johnny Jones' illness was caused by (x) foul drains. 
 
 That this is the actual process of reasoning in the case
 
 INDUCTION AND SYLLOGISM 203 
 
 supposed, no one who follows it, and traces the operations of 
 his own mind, can, I think, have any doubt. At least, it com- 
 pares in this respect on equal terms with the syllogism ; for I 
 have never heard any reason for the assertion, that the syllogism 
 is the common form of all reasoning, except that it is so. Modern 
 Logic, as represented by Mr. Bosanquet, enumerates more than 
 twenty modes of reasoning — ten of judgement, dealing with 
 Simple propositions; and thirteen of Inference, dealing with Com- 
 pound propositions. I find it difficult to appreciate the niceties 
 of distinction that separate these forms from one another ; nor do 
 I find any one of them that is not either Inference as understood 
 in the next Book, or Mediate Induction as here explained. 
 
 Comparing Induction, as here described, with syllogising, we 
 find the following differences between them : — 
 
 1. The syllogism has three terms, and no more than three. The 
 fallacy of four terms is the cardinal fallacy of the syllogism, and 
 ipso facto falsifies any syllogism in which it occurs. The Induction 
 contains four terms, and cannot be constructed with less than four. 
 
 2. The syllogism consists of three, and no more than three 
 propositions, all of which must be complete. The Induction con- 
 sists of two propositions, one of which is incomplete when it 
 enters into the Induction, and is completed by the process of 
 reasoning. Since, however, the assimilation marks can be 
 expressed in words, it is possible to express the Induction in three 
 propositions ; but it may be expressed in two, which the syllogism 
 can not. 
 
 3. The syllogism contains two premisses; and no syllogism can 
 be constructed with more or less than two. The Induction need 
 contain but one premiss ; but Inductions can be constructed with 
 two or with three premisses, as will hereafter be shown. 
 
 4. The foundation of the syllogism is the Universal proposition. 
 Without a Universal, there must be an undistributed middle, with 
 all its dire consequences. The Induction is founded on an appeal 
 to experience. It needs a Universal, it is true ; but its Universal 
 is very different from that of Traditional Logic. The Universal 
 of Traditional Logic is a postulated universal, and need not be 
 true in fact. It may be wildly impossible. The Universal of 
 Mediate Induction is founded on experience. It must, therefore, 
 be consistent with experience ; and every Induction must contain 
 an appeal to experience.
 
 204 A NEW LOGIC 
 
 5. The syllogism must have a middle term, common to both 
 premisses. The Induction has no middle term. Those induc- 
 tions that have but one premiss, cannot have a middle term. 
 
 6. According to Traditional Logic, one premiss at least of the 
 syllogism must be affirmative. The single premiss of an induction 
 may be affirmative or negative. 
 
 The differences between Mediate Inference and Mediate 
 Induction are, therefore, profound and far-reaching. In all the 
 respects enumerated above, they differ ; but the main difference, 
 the important difference, the difference from which it results that 
 Induction is in daily and hourly use, while Inference is employed 
 on occasion only, is that Inference applies to postulates, and takes 
 no account of Truth or of experience ; while Induction rests on 
 experience alone. Whether the postulates of Inference are 
 materially true or not, has nothing to do with the course of the 
 argument, and is of no concern to it. For the purpose of Inference, 
 nothing is too impossible, too absurd, too preposterous, to serve 
 as a postulate. We can argue from the postulate that matter is 
 imponderable, that two straight lines can enclose a space, that 
 virtue is red and the soul is square; and our inferences will be 
 sound if the argument is properly conducted. But Induction 
 knows nothing of postulates. To Induction, the material truth 
 of its premiss is vital. Induction admits those premisses only 
 that are consistent with experience, — that are, or are believed to 
 be, true in fact. A premiss which is at variance with experience, 
 or which has no basis in experience, has no place in Induction. 
 In short. Inference is the maintenance of consistency only; 
 Induction is the discovery of truth — of fact. An Inference may 
 be perfectly valid, in the sense of consisting with its postulate, 
 and may stand every test of consistency that can be applied to 
 it, and yet may be of such a crazy character that we should 
 never dream of founding our conduct on it. If a canary bird 
 cannot live on any diet except one of wild elephants, then I 
 cannot expect to keep a canary bird alive in a cage unless I 
 provide a diet of wild elephants for it. The Inference is plain, 
 rigorous, unescapable. But in spite of the unexceptionable 
 validity of this inference, I should never dream of sending to 
 Africa for a consignment of wild elephants to feed my canary 
 upon. If I want to solve the problem, What the proper diet for a 
 canary is, I must cither appeal directly to experience, by trying
 
 INDUCTION AND SYLLOGISM 205 
 
 one diet after another till I find the one that suits ; or I must 
 appeal to my experience, or that of others, in similar cases. 
 There is no other alternative. In experience, and in experience 
 alone, is the solution of problems to be found. The conclusion of 
 an Inference is in the premiss that is supplied. The solution of 
 a problem is not in the problem. It must be sought from an 
 extraneous source ; and that source is experience. Inference is 
 formal proof: Induction is material proof. Inference finds what 
 is consistent with its postulate, and is indifferent to the truth of 
 the postulate: Induction sets out to discover what is true; and 
 the truth of its premiss is vital. 
 
 If every man is mortal, and Socrates is a man ; then Socrates is 
 mortal. The Inference is irrefragable ; and, if the premisses are 
 true in fact, the conclusion is true in fact. But Deduction does 
 not allow me to assume the truth of my premisses. It is this 
 incompetence on the part of Deduction to guarantee the truth of 
 its premisses, that led to the interminable discussions on the 
 nature of Universals, which dominated the Schools for centuries, 
 and which have been revived by Modern Logic. If I want to 
 discover whether Socrates is, in fact, mortal, Inference will not 
 assist me. I must have recourse to Induction. To discover a 
 fact, it is manifestly useless to postulate a premiss, which, ex vi 
 termini, may be true or not. To attain material truth, we must 
 start from material truth. To discover fact, we must have fact to 
 go upon. 
 
 ' Oh, but,' says the logician, ' I have fact to go upon. It is a 
 fact that all men are mortal, and you cannot gainsay it.' To this 
 there are four good and sufficient answers. In the first place, it 
 is not a fact. In the second place, if it were a fact, that has 
 nothing to do with the inference. In the third place, if you 
 assume it to be a fact, you have already begged your conclusion. 
 In the fourth place, if it be a fact, you know it to be so, not from 
 your postulate, which may not assert it except tentatively, and as 
 a postulate, but from experience ; and there is no appeal to 
 experience in your postulate. If you assume it to be a fact, you 
 assume what is not in the postulate, and you violate a Canon of 
 that very inferential process that you purport to employ. 
 
 It is not a fact, in the proper sense of fact, that all men are 
 mortal, A fact is a thing done ; and all men are not mortal in 
 the sense that their mortality is proved by their death having
 
 2o6 A NEW LOGIC 
 
 occurred. A fact is an event that has happened, and the event of 
 the death of all men has not yet happened, or there would be no 
 discussion about it. In literal truth, therefore, it is not a ' fact ' 
 that all men are mortal. 
 
 In the second place, whether all men are in fact mortal or not 
 has nothing to do with the process of inference. If all men are 
 mortal and Socrates is a man, he is mortal, no doubt. That is 
 true, and so is it true that if all men are immortal, and Socrates is 
 a man, he is immortal. Both inferences are perfectly valid, but 
 both cannot be founded on fact, and whether either of them is or 
 is not founded on fact, and if so which, makes not the slightest 
 difference to the validity of the inferences. 
 
 In the third place, if we believe that all men are mortal, in the 
 sense that all men now living will die, it is perfectly clear that 
 there must be some ground in experience for the belief. It is clear 
 that the knowledge that Socrates will die depends, not on the 
 postulated proposition that all men are mortal, but on empirical 
 grounds. 
 
 In the fourth place, if it is assumed that All men are mortal, this 
 postulate is assumed for the purpose of some argument, and any 
 conclusion derived from it will be as true as the assumption and 
 will have no other authorisation. It is a conventional assumption, 
 on a par with the assumptions about centaurs and jabberwocks, 
 and of neither more nor less validity, as an assumption, than these 
 are. If the assumption goes further, and is assumed to be true in 
 fact, the limits of Deduction are ipso facto exceeded, and we are 
 in another province of reasoning. Now it is necessary that we 
 should state the grounds of the assumption, and once the grounds 
 of an assumption are stated, it ceases to be an assumption. 
 
 ' Socrates is mortal ' is an answer to three main questions. * Is 
 it Socrates who is mortal ? Is it mortality that is an attribute of 
 Socrates ? Is or is not Socrates mortal ? ' Commonly, the last 
 question is taken to be that to which * Socrates is mortal ' is the 
 answer. But this is not explicit enough. It does not express the 
 doubt, if any doubt exists, in the mind of the questioner. What 
 he wants to know, if he wants to know anything on the subject, 
 is whether Socrates will die. If Socrates is already dead, the 
 solution is known. There is then no problem. It is only if 
 he is alive that we can possibly want to know whether he is 
 mortal.
 
 INDUCTION AND SYLLOGISM 207 
 
 Will Socrates die ? That is the problem. Formally stated, it 
 is Socrates a; {will or will not) die : find x. To solve this problem, 
 how do we proceed ? I say that we proceed to find a premiss in 
 experience. We search experience for the relation most resembling 
 the relation stated in the problem. We ask what our experience 
 is of the mortality of beings most like to Socrates. We compare 
 Socrates with other men in the material respect of mortality, and 
 we find, in experience, that, in this respect, men are divisible into 
 two classes— those whose mortality is proved, and those whose 
 mortality is not proved — those who are dead, and those who are 
 alive. Socrates belongs to the latter class. We have precisely as 
 much, and no more, warrant for concluding that Socrates will die, 
 as for concluding that every and any other man now living will 
 die. Our task is, not to bring Socrates into the class of those who 
 are dead, which would result in proceedings against us at the Old 
 Bailey ; but to find out how far Socrates, and other living men, 
 can be assimilated, in the material respect of mortality, to those 
 who have demonstrated their mortality by dying. How is this 
 to be done ? What have we to go upon ? What influences our 
 minds in concluding that Socrates will die ? Clearly it is not 
 that All men are mortal, for this is assuming what we have to 
 prove, an assumption quite legitimate, and even necessary', in the 
 Logic of Inference, but preposterous, in the literal sense, in mate- 
 rial reasoning. The question is What enables us to assimilate, in 
 respect of mortality, the great multitude of living men with the 
 greater multitude of men who have died ? Mill says it is our 
 knowledge of the Uniformity of Nature. Well, for one thing, 
 Nature is not uniform, as Mill admits ; but if it be, and if it is from 
 this that we get our assurance that Socrates and other living men 
 will die, whence do we get this knowledge of the Uniformity of 
 Nature ? On this, logicians are silent. I say that we get our 
 assurance that Socrates and the rest of us will die from no such 
 vague and inaccurate assumption. If we did, our assurance would 
 be as vague and as inaccurate as the assumption itself, since nothing 
 can be had out of a premiss that is not in it. Our assurance that 
 Socrates and the rest of living mankind will die, is neither vague, 
 except as to time and manner, nor inaccurate. It is precise, and 
 it is true. Whence do we obtain it ? I say that we obtain it from 
 experience, — from the uniform experience of mankind for innu- 
 merable generations, and in innumerable millions of instances, that 
 
 \ fifl
 
 2o8 A NEW LOGIC 
 
 no man has permanently escaped death. Given time, no man has 
 failed to exhibit mortality. In other words, the relation between 
 man and mortality is constant in experience. That, and that alone, 
 is our warrant for the conclusion that Socrates will die. 
 
 But can the relation between man and mortality be said to be 
 constant in experience, if there are multitudes of men who have 
 not proved their mortality ? Yes, for every man who has died 
 has lived for a certain time before dying, and the men now 
 living resemble in all material respects the men who have died — 
 among other material respects, they resemble t-hose who have died, 
 in that a certain period of living precedes their death. The rela- 
 tion, in men, between living and eventually dying, is constant in 
 the experience of the whole of mankind, without a single permanent 
 exception. It is this constancy in experience that enables, and 
 more than enables, that compels us to conclude, that the relation 
 will continue to be constant in experience. The living men are 
 temporary exceptions to this constancy in experience, but we are 
 unable to regard them as permanent exceptions, because the 
 relation that we have found constant is the eventual sequence of 
 death upon life. There have always been multitudes of temporary 
 exceptions : there has never been a permanent exception ; and 
 this undeviating constancy in experience allows, and compels, us 
 to conclude that there never will be a permanent exception, and 
 that Socrates and the rest of us will ultimately die. 
 
 Is this conclusion warranted ? Are we justified in concluding 
 that since, in the experience of mankind, a thing always has been, 
 therefore it always will be? This problem does not belong to 
 Logic. It pertains to Epistemology, and need not be considered 
 here. Those who wish to pursue the subject on these lines will 
 , find it treated in my book on Psychology. As far as Logic is 
 concerned, it is enough that constancy in experience does in fact 
 form the ground — the sole ground — of Material, as distinguished 
 from Formal reasoning. Of course, this doctrine is open to the 
 objection that it lays down, as the criterion of certainty, that very 
 indnctio per eniimcrationem simplicem, ubi non repevitur instantia con- 
 tradictoria, which Bacon put as the weakest form of Induction. 
 In this I do not agree with Bacon. I hold that every one of the 
 truths that we hold as most certain, rests upon the accumulation of 
 instances without exception. Is anything more certain than that 
 all matter gravitates ? And on what does this certainty rest,
 
 INDUCTION AND SYLLOGISM 209 
 
 except the accumulation of instances without exception ? Is 
 anything more certain than that resistance is never found apart 
 from extension ? The certainty rests on the same ground. Why 
 are we certain that the sun will rise to-morrow ? Have we any 
 better ground for our belief than the accumulation of instances 
 without exception ? How do we know that mutilation and injury 
 of the healthy body will certainly be accompanied by pain ? Is it 
 not from the same unvarying experience ? So far from the inductio 
 per cnumerationem simplicem being untrustworthy, it is the ground 
 of every one of our most certain convictions. Of course, Bacon's 
 aim was to deprecate the reception of simple enumeration as 
 sufficient proof, without searching for contrary instances, and such 
 an aim is wholly laudable ; but his maxim has been widely held to 
 mean that simple enumeration cannot under any circumstances 
 give a valid induction, and this opinion, I hold, is wrong. 
 
 The Deduction by which we prove the consistency of the 
 conclusion, that Socrates is mortal, with the postulates that All 
 men are mortal and Socrates is a man, is stated in the form of a 
 syllogism, thus : — 
 
 If All men are mortal ; 
 
 And Socrates is a man ; 
 Then Socrates is mortal. 
 
 The Induction by which we prove that Socrates will, in fact, 
 die, is as different in form as it is in conclusion. It is this : — 
 
 Men have, constantly in experience, been found mortal 
 ^ _ _>x 
 
 il II II 
 
 .-— ^ . 
 
 Socrates ipc) will be found mortal. 
 
 Or, in formal propositions, we may state the argument thus : — 
 Since men have, constantly in experience, been found mortal ; 
 
 and 
 Since Socrates resembles, in respects material to the argument, 
 
 men W'ho have died ; 
 Therefore, Socrates will die. 
 
 In this argument will be found certain characters that are 
 common to all Mediate Inductions, and that form the conditions 
 of validity of all such Inductions. 
 
 N.L. P
 
 210 A NEW LOGIC 
 
 1. The Ratio of the premiss predicates a relation that is constant 
 
 in experience. 
 
 2. One of the given elements in the Problem (in this case the 
 
 Subject) is assimilated to its homologue in the Premiss. 
 
 3. The other given element in the Problem (in this case the 
 
 Object) is identical with its homologue in the Premiss. 
 
 4. The quaisitum is obtained by adopting into the Problem the 
 
 remaining element (in this case the Ratio) of the 
 Premiss, with which the qua^situm is homologous. 
 
 5. The difference, as well as the likeness, of the assimilated 
 
 elements of the Problem and Premiss, is reflected in the 
 
 conclusion. Socrates differs from the men who have 
 
 proved their mortality by dying, in the fact that he is 
 
 alive. Hence the quaesitum 'will he found' is not the 
 
 same as its homologue * have been found ' in the 
 
 Premiss ; but reflects the difference between Socrates and 
 
 dead men. 
 
 If these statements are severally changed from assertions to 
 
 mandates, they become Canons of Induction ; and may be stated 
 
 thus : — 
 
 I. The First Canon of Induction is that the premiss must 
 predicate a relation that is constant in experience, or is subsumable 
 tinder one that is constant in experience. 
 
 Constancy in experience, of the relation expressed in the premiss, 
 is the very sine qua non of assured Induction ; for note the effect 
 of its absence. If Cassius is found murdered, why cannot I 
 conclude that, since Brutus murdered Caesar, therefore it was 
 Brutus who murdered Cassius also ? In all respects but the one 
 in question, the argument is valid. 
 
 Brutus murdered Caesar 
 
 II II II 
 
 (X) Brutus murdered Cassius. 
 
 Here are all the conditions, save the one in question, of valid 
 Induction. One given element in the problem — the Ratio — is 
 identical with its homologue in the premiss. The other given 
 element in the problem — the Object — is similar in all material 
 respects to its homologue in the premiss. Cassius, like Csesar, is 
 dead. Like Csesar he died of violence on the Ides of March ;
 
 CANONS OF INDUCTION 211 
 
 like Caesar, he was stabbed at the foot of Pompey's statue. In 
 all respects material to the argument, he resembles Caesar. Why, 
 then, is it unjustifiable to conclude that Brutus killed him ? for 
 Brutus unquestionably killed Cgesar. Because, and only because, 
 the relation between Brutus and murdered men is not constant in 
 experience. There are, in experience, many exceptions. Many 
 men have been murdered by persons other than Brutus, and 
 hence it is that the conclusion cannot be drawn. If no one in the 
 history of the world had ever been murdered except by Brutus, 
 and if Brutus had been known to murder many people besides 
 Caesar, the suggestion would be very strong indeed that Cassius 
 was killed by Brutus, and the onus w^ould lie on Brutus of 
 proving that he did not kill Cassius ; but as matters stand — 
 experience being what it is — if the fact that Brutus killed Caesar 
 is the only evidence in support of his having murdered Cassius, 
 the magistrate would have no alternative but to dismiss the 
 charge. 
 
 But does not this prove too much ? How is the Canon, that 
 the relation expressed in the premiss must be constant in 
 experience, consistent with the argument about the cause of 
 Johnny's illness ? In this instance, a conclusion which we feel 
 to be valid, is drawn from a premiss stating a single instance 
 only ; and how can it be said that any single instance is constant 
 in experience, any more than the single instance of Brutus killing 
 Caesar ? 
 
 The difference is that the causation of the illness was not 
 inferred from that premiss alone. Lurking in the background of 
 the mind is another premiss, which is not explicitly mentioned in 
 the argument, but which is in the argument, and is essential to 
 the argument. It is there, ready to come forward and assert itself 
 if, and when, called upon. It would be impossible to argue from 
 one case of causation to another, unless it were assumed that, in 
 experience, causation is constant : that the same cause always 
 produces the same effect, and the same effect is always due to the 
 same cause. This relation between cause and effect is, in fact, 
 constant in experience, and hence material reasonings based on it 
 are valid, if valid in other respects. 
 
 Then Induction, like syllogising, docs, after all, require two 
 premisses? Not necessarily. If the individual relation, 
 expressed in the premiss, is not itself constant in experience, it 
 
 P 2
 
 212 A NEW LOGIC 
 
 must be subsumed under a more comprehensive relation that is 
 constant ; but if the constanc}' in experience inheres in the very 
 relation of the premiss itself, then this premiss alone is sufficient 
 to warrant the conclusion. Since the mortality of men is 
 constant in experience, I can safely conclude, from this premiss 
 alone, that Socrates, or any other man, or any number of men, are 
 mortal ; but, when the constancy in experience is not expressed in 
 the premiss, but is assumed, something further in the nature of a 
 premiss is evidently required. Let us take another case. 
 
 I see a snake, the like of which I have seen but once before in 
 my life, and that was yesterday, when a similar snake bit my dog, 
 which died in ten minutes. That snake I killed ; and on seeing 
 this one, which is precisely similar in appearance, I conclude at 
 once that it is venomous. What is the process of reasoning, and 
 what is its warrant ? 
 
 The problem is ' This snake x {is or is not) venomous ' ; and the 
 induction is That snake was venomous 
 
 II II II 
 
 This snake (x) is venomous. 
 
 The conclusion is irrefragable ; and if I were to disregard it, I 
 should pay with my life for my indiscretion. There is no Universal, 
 in the sense attached to that word by Traditional Logic, in the 
 reasoning. I cannot afford to wait until I have collected all the 
 individuals that exist of that species, including the one now 
 under observation ; procured each of them to bite an animal ; and 
 observed whether the bitten animals live or die. This is the only 
 way known to Traditional Logic of obtaining a Universal, and, 
 without a Universal, Traditional Logic is powerless. When I 
 had completed the laborious task, then, and not till then, should 
 I be in a position to argue 
 
 All snakes of this species are venomous ; 
 This is a snake of this species ; 
 .*. This snake is venomous. 
 
 And this conclusion could not be reached until I had actually 
 determined by experiment, in the case of this very snake, that it 
 is venomous. The Universal would, therefore, be not only 
 impracticable, but utterly superfluous, and redundant, and
 
 UNIFORMITY OF NATURE 213 
 
 unnecessary. In practice I do not employ any method so absurd. 
 I employ Induction, and I say, ' This snake resembles precisely 
 that which I found yesterday to be venomous ; therefore this 
 snake also is venomous.' 
 
 This argument is in almost the same form as the argument 
 that, since Brutus killed Caesar, therefore he killed Cassius also ; 
 the only difference being the unimportant difference that, in the 
 case of the snake, the quaisitum is the ratio ; while, in the other, 
 it is the subject. Yet the one is felt to be irrefragably valid, and 
 the other to be utterly unwarranted. What is it that makes this 
 difference ? 
 
 Mill tells us that it is the uniformity of Nature. We can argue 
 from the venomousncss of one snake to the venomousness of the 
 other, because in this case Nature is uniform. We cannot argue 
 from the killing of Caesar by Brutus to the killing of Cassius by 
 Brutus, because in this case Nature is not uniform. The shapes 
 of flowers of one species are uniform, but those of different species 
 are not uniform; and the shapes of clouds are never uniform. 
 The sequence of night upon day, and of summer on winter, is 
 uniform ; but the sequence of rain upon wind, or of wind upon 
 sunshine, is not uniform. Logicians admit, in the words of Mill, 
 that ' The course of Nature is not only uniform, it is infinitely 
 various.' But in certain respects, surely. Nature is uniform. One 
 of the favourite instances given in the text books of Logic, of the 
 Uniformity of Nature, is the permanence and intransmutability of 
 the elements. Alas ! it is now discovered that certain of the 
 elements are transmutable ! 
 
 To rest the validity of reasoning on the Uniformit}' of Nature, 
 and in the same breath to admit that Nature is not uniform, is a 
 proceeding the like of which is scarcely to be found outside a book 
 on Logic. It is true, how^ever, that Nature is uniform in certain 
 respects, and that in those respects it is safe to rest our arguments 
 on the uniformity ; but until we have some criterion that enables 
 us to determine in what respect Nature is uniform and in what it 
 is not, the uniformity, where it exists, is of no value. Is there such 
 a criterion ? If there be, logicians are not agreed about it. Some, 
 indeed, offer as a criterion the Laws of Thought. Others regard 
 the Uniformity of Nature as based on induction from uninterrupted 
 experience ; and these I believe are right ; though why they should 
 rest the validity of argument on an imaginary and non-existent
 
 214 A NEW LOGIC 
 
 Uniformity of Nature, which they infer from uninterrupted 
 experience, rather than on the uninterrupted experience itself, I 
 do not understand. 
 
 The true reason that we can argue from ' That snake was 
 venomous,' to ' This snake, which is exactly like that, is 
 venomous ' ; while we cannot argue from ' Brutus killed Caesar ' 
 to ' Brutus killed Cassius,' seems to me to be this : Behind the 
 first argument lurks the supplementary premiss, not that ' Nature 
 is uniform,' but that * In experience, the relation between the 
 appearance of snakes, and their venomousness, is constant ' ; or 
 * The experience that snakes that are alike in appearance are alike 
 in structure and qualities, is constant.' The inference that, since 
 that snake was venomous, this snake, which exactly resembles 
 that, is venomous, does not rest solely on the likeness between 
 the snakes. It rests upon a constancy in experience. Constancy 
 of what ? A single instance is not constancy, in any proper sense; 
 and a single instance is all we have, so far, to go upon. The 
 second, the underlying, the silent premiss, which validates the 
 reasoning, is that the relation between the first snake and its 
 venomousness belongs to a class, or is subsumable under a relation, 
 that is constant in experience. It is not merely that the relation 
 between the appearance of snakes and their venomousness is 
 constant in experience. I could, and should, draw the same 
 inference if I had never seen or heard of any snake except the one 
 that bit my dog yesterday, and this one. The underlying premiss 
 is far wider and more comprehensive than this. It is that the 
 appearance of all animals is an index to their other properties — 
 nay, it is wider, much wider, still. The appearance, not only of 
 all animals, but of all organic beings ; not only of all organic 
 beings, but of all bodies whatever, is an index to their properties. 
 The experience, not only of ourselves, but of the whole human 
 race, is constant, that the more closely things resemble one 
 another in some properties, the more closely, on the whole, do 
 they resemble one another in other properties. The conclusion, 
 that the second snake was venomous, was felt at once to be 
 irrefragable. It was not merely arrived at without difficulty, but 
 was thrust and forced upon me. We now see why it was so 
 readily accepted — why it was inescapable. It rested on a 
 generalisation — on a constancy in experience — of boundless 
 extent.
 
 CONSTANCY IN EXPERIENCE 215 
 
 In every Induction, the relation expressed in the premiss must 
 be itself constant in experience, as in the case of the mortality of 
 man ; or it must be subsumable under a relation that is constant 
 in experience, as in the case of the venomousness of the snake. It 
 may, indeed, be plausibly argued that every premised relation 
 must, or may, be subsumable under one more comprehensive. 
 Even the argument from the mortality of man does not rest upon 
 the constancy of that relation alone. The relation may be sub- 
 sumed under a wider relation— that, not only of man, but of all 
 animals, of which man is but one, to mortality. Nor does the 
 subsumption end here. We have at the back of our minds, 
 unavowed, latent, tacit, but ready in reserve to be called into 
 action if necessary, the still wider relations, still constant in 
 experience, that all organic beings, animal and vegetable, are 
 mortal ; and that all material things are subject to decay and 
 dissolution. 
 
 In this sense, the contention of Traditional Logic is true, that 
 all reasoning — all Empirical reasoning — rests upon a Universal. 
 Constancy in experience is the Unknown God that the logicians of 
 the Schools ignorantly worshipped. I cannot but think that it 
 was some dim, undefined, vague, approximate appreciation of this 
 necessity that led to the interminable discussions on the nature of 
 Universals. As long as the Logic of Postulation was not dis- 
 tinguished from the Logic of Material Argument, it was impossible 
 to arrive at the true nature of Universals, for the Universal of the 
 one is profoundly different from the Universal of the other. The 
 postulated Universal can never validate an argument in materia, 
 any more than the true nature of centaurs or jabberwocks can be 
 ascertained by appeal to experience. It was the non-recognition 
 of the distinction between the discrete departments of Logic that 
 made all discussion on Universals barren, and led to endless 
 arguments in circles. The Universal of the Logic of Postulation 
 is a term having'a certain quantity, in a relation postulated for the 
 purpose of argument ; and all that is vital to the argument is that 
 the quantity of the corresponding term in the conclusion is not 
 greater than is warranted by the premisses. The Universal of 
 the Logic of Induction is not a term at all. It is a relation — a 
 relation that is constant in experience — and it is vital to the 
 argument that this relation should be constant. Discussion rages 
 round the meaning of the 'All men' in ' All men are mortal,' 
 
 ^1
 
 2i6 A NEW LOGIC 
 
 when the question actually at issue is the meaning, not of the 
 term, but of the copula. It is not what is meant by ' All men,' 
 but what is meant by All men arc mortal. In the Logic of 
 Postulation this means ' For the purpose of this argument, all 
 men are credited with the attribute of mortality, whether they 
 possess it or not.' In Material Logic it means * In experience, 
 the relation between men and mortality has been found constant.' 
 The difference in meaning is as profound as the difference in the 
 purposes of the arguments, and it is the attempt to make the one 
 meaning serve the purpose of the other that has sterilised the 
 secular discussions on the nature of Universals. 
 
 What logicians mean, or should mean, by Uniformity of Nature, 
 is constancy in experience, that is to say, the accumulation of 
 instances without exception. How many instances are required 
 before we can regard an experience as constant, what the effect is 
 on the mind of meeting with exceptions, and of the ratio between 
 instances and exceptions — these are problems in Epistemology, 
 and are out of place in Logic. An examination of them will 
 be found in my book on Psychology. All that need be said here 
 is that what is called by logicians the Uniformity of Nature, means 
 constancy in experience ; that, in every material argum.ent, the 
 relation in the premiss must be constant in experience, or must 
 be subsumable under one that is constant in experience. 
 
 The second Canon of Induction is that One element in the problem 
 must be assimilated to its homologous element in the premiss. 
 
 This canon is of the utmost importance in material reasoning. 
 The finding of a premiss has been said to be the first step in 
 Induction ; and the assimilation of an element in the problem, to 
 an element in some relation that is constant in experience, is the 
 first step in finding a premiss. The proposition in which this 
 similar element exists, then becomes the premiss. 
 
 In the Induction by which the cause of Johnny's illness was 
 ascertained, his illness was assimilated to Jenny's illness. That 
 was the first step in the argument. A premiss was to be found, 
 containing an element similar to an element in the problem. The 
 problem contains but two elements, the third being wanting, and 
 its supply being the solution of the problem. A premiss must be 
 found, such that one of its elements is assimilable to one of the 
 given elements of the problem. It is not necessary, for the solution
 
 THE DATUM 217 
 
 of the problem, that the assimilated elements should be precisely 
 or exactly similar. Precisely or exactly similar things are not to 
 be found in Nature. It is enough if they are similar in material 
 respects — in respects material to the argument. The two illnesses, 
 for instance, need not have presented symptoms precisely similar 
 in kind and degree at every stage, and on every corresponding 
 day of the illness. It is enough if they are so similar in 
 material respects as to give us confidence that they are due to 
 similar causes. In the Induction by which it is discovered that 
 Socrates will die, Socrates is assimilated in all material respects 
 to men who have died. It is not necessary that he should have 
 the same colour of eyes and hair, that he should have the same 
 stature, or speak the same language. These are not respects 
 material to the argument. It is enough that he is similar in those 
 respects which are material to mortality; in origin, in organisation, 
 in mode of maintenance, — in what is vaguely termed Nature. 
 When I assimilated the snake to the one which bit my dog the 
 day before, I did not stop to measure it, or to find out if it were 
 exactly the same size, or had the same number of rattles as the 
 snake I had found venomous. It was enough that it was similar 
 in shape, colours, and markings. These were all that were 
 material to the argument. If it is asked how we are to know 
 what is material to the argument and what is not, the only answer 
 is by a scrutiny of the problem. What is the nature of the 
 problem ? The problems run Is this snake venomous or not ? 
 Will Socrates die ? What is the cause of the child's illness ? 
 In deciding that the length of the snake, and the number of 
 rattles on its tail, are not material to the argument, I am influenced 
 by my knowledge of the nature of snakes. Logicians would say 
 that I reject these factors because I recognise that they are not 
 essential to venomousness. I prefer to discard the phraseology 
 and implications of Traditional Logic, which has never made 
 clear, which has never come to any permanent agreement as to 
 what is meant by * essential.' The phraseology' and implications 
 that belong to Traditional Logic, which is practically coincident 
 with the Logic of Postulation, are out of place in Material Logic. 
 Whether the qualities that I discard from consideration are or 
 are not essential, is beside the mark. The reason I discard 
 them from consideration is that, in experience, they are not 
 material to the argument. In this as in all else. Material
 
 2iS A NEW LOGIC 
 
 reasoning rests on experience. It is empirical from beginning 
 to end. For the same reason, in assimilating Socrates to other 
 men, in respects material to the argument about his mortality, 
 I do not take into consideration the colour of his eyes, and hair, 
 his stature, or the language he speaks : and I discard these 
 matters from consideration, not because they are not essential 
 to the nature of Socrates — for aught I know they may be as 
 essential as the possession of a stomach or a mind. The reason I 
 discard them from consideration is that, in experience, I have not 
 found men of one colour of hair or eyes, or of one stature or 
 language, more or less subject to mortality than other men ; and 
 therefore, for the purpose of the argument about mortality, they 
 are not material. 
 
 Let us take a new argument. I have a glass flower, and I wish 
 to know if it is fragile. According to this second Canon, I must 
 assimilate it to some thing or things that it resembles in respects 
 material to the argument. The only respect material to the 
 argument is the substance of which it is made, and I assimilate it, 
 therefore, to other glass things, and thus obtain the induction 
 
 Glass things arc, constantly in experience, fragile 
 This glass flower (x) is fragile. 
 
 This assimilation, of one of the given elements of the problem 
 with the homologous element in the discovered premiss, I call the 
 Datum. It is at once apparent that the Datum of the induction 
 corresponds with the minor premiss in the syllogism, and has by 
 logicians been mistaken for it. If, instead of searching in 
 experience for a knowledge of the fragility or toughness of things 
 similar to the flower, I assume as a postulate, ' Glass things are 
 brittle,' then upon this principium I can found a syllogism : — 
 
 All glass things are fragile; 
 This flower is a glass thing ; 
 . • . This flower is fragile. 
 
 In this syllogism the minor premiss — 'This flower is glass' — 
 has a deceptive similarity to the Datum — ' This flower is like other 
 glass things in respects material to the argument of fragility.' In 
 fact, however, the two are, or may be, widely different. The 
 minor premiss says * This flower is glass,' and we know that in
 
 THIRD CANON OF INDUCTION 219 
 
 Traditional Loji^ic, the Copula means ' is included in ' or has ' the 
 attribute of.' This is very different from ' is like for the purpose 
 of the argument.' In this particular argument it does not matter, 
 though we are freely at liberty to take as our postulate ' glass 
 things are unbreakable ' ; but in many arguments it is vital. If 
 dogs are paralysed by curare, I can argue, with complete validity, 
 that, since men are like dogs for the purpose of the argument, 
 therefore men can be paralysed by curare ; but this is not the 
 same as saying that since men are dogs, they can be paralysed by 
 curare. This is the form in which the argument must be put if it 
 is to be stated syllogistically. Of course, for the purpose of Infer- 
 ence, we can postulate what we please, and there is no barrier in 
 the conditions of Inference to prevent us from postulating that 
 men are dogs. But the present argument is an argument in 
 materia. What we want to know is not whether, in the world of 
 postulation, if dogs can be paralysed by curare, and if men are 
 dogs, certain conclusions can be drawn, but whether in the real 
 world, real curare will really paralyse real men ; and this we 
 cannot do by founding our argument on a premiss so inconsistent 
 with experience as that men are dogs. To attain a real conclusion, 
 the argument must be founded, not on a postulate, but on 
 experience ; and in place of a minor premiss, postulating that A 
 is B, we must have the datum, drawn from experience, that A is 
 like B in respects material to the argument. 
 
 The Datum requires its terms to be assimilated in respects 
 material to the argument. It knows nothing and cares nothing 
 about classes or attribution. All that is required in the Datum, 
 is that the homologous elements in the problem and premiss, that 
 form its terms, should be alike in material respects. However much 
 they differ in other respects, the argument will still hold good ; 
 but with the qualification stated in the fifth Canon of Induction. 
 
 The third Canon of Induction, or argument about Realities, is 
 that The second given element in the problem must be identical with its 
 homologous clement in the premiss. In other words, the problem 
 and the premiss must have an element in common. 
 
 We have seen that a problem is a proposition in which one 
 clement is missing. Two elements, therefore, remain, as given. 
 Of these, one is assimilated to an homologous element in the 
 premiss ; and the premiss is founded on this assimilation. The
 
 220 A NEW LOGIC 
 
 third Canon states that the other given element in the problem 
 must be identical with its homologuc in the premiss. 
 
 This Canon has some resemblance to the condition that the 
 syllogism must have a middle term ; but the common element of 
 the problem and the premiss in Induction is not comparable with 
 the middle term of a syllogism. For one thing, the common 
 element of the Induction need not be a term at all. It may be 
 the Ratio, as in the argument about the child's illness : — 
 
 That illness was caused by foul drains 
 This illness was caused by (x) foul drams. 
 
 In this case, since the Object-term of the problem is the quaesitum, 
 either the Subject or the Ratio, which alone are given, must be 
 identical with its homologue in the premiss. The Subjects are 
 not identical, they are assimilated ; consequently the remaining 
 elements, the Ratios, must be identical ; and we see that they are 
 so. If we substitute, for the Ratio of the premiss, one which is 
 not identical with the ratio of the problem, no conclusion can be 
 drawn. If, for 'That illness was caused by foul drains,' we sub- 
 stitute * That illness was preceded, or followed, or accompanied, 
 or not caused by foul drains,' we can no longer argue that this 
 illness was caused by foul drains. If men are, constantly in 
 experience, mortal, and Socrates resembles other men in respects 
 material to the argument, then we can safely conclude that 
 Socrates is in fact mortal ; but we cannot on this ground conclude 
 that he is reasonable, or polite, or wealthy. If it is a constant 
 experience that heat causes metals to expand, we may safely 
 conclude that heat will cause the mercury in a thermometer 
 to expand, since mercury resembles other metals in respects material 
 to the argument ; but we may not, on the ground of this premiss, 
 argue that cold will cause the mercury in a thermometer to con- 
 tract. For aught the premiss tells us, a thing once expanded by 
 heat may remain permanently expanded, and fail to contract on 
 the application of cold, just as the temper of steel, once drawn 
 by heat, remains permanently absent. 
 
 4 and 5. The quasitum is obtained by adopting into the problem 
 I the remaining clement of the premiss ; and The difference, as well as 
 
 \ the likeness, of the assimilated elements of the datum, is reflected in 
 
 \ the conclusion.
 
 THE QU/ESITUM 221 
 
 That illness was caused by foul drains 
 
 This illness was caused by {x) foul drains. 
 
 In this argument, the problem is This illness is caused by 
 X : find X. We find ourqujesitum by first searching experience for 
 a premiss. We look for a similar illness of which the cause is 
 known ; and we adopt into our problem the term of the premiss 
 homologous with the qusesitum of the problem. This operation 
 has already been sufficiently illustrated. What is important now 
 to notice is that the homologous term of the premiss is not 
 necessarily adopted into the problem holus-bolus, just as it stands 
 in the premiss. This cannot be done unless the likeness expressed 
 in the datum is complete. If the likeness of that element in the 
 datum which is furnished by the "problem, to the other element 
 which is furnished by the premiss, is incomplete, then whatever 
 difference exists between them, must be reflected by a modification 
 of the element of the premiss, which is adopted into the problem 
 to furnish the quaesitum. 
 
 If the illness of which I wish to know the cause, is plague, I 
 search experience for the disease, most like plague, whose cause is 
 known. My search discovers cholera, which resembles plague in 
 the material respects of being an acute specific disease, of occurring 
 in widespread epidemics, and of originating in the East ; but is 
 unlike plague in the majority of its symptoms. Since cholera has 
 considerable likeness to plague in some material respects, I may 
 safely conclude that it resembles plague generally in its cause ; but 
 since cholera and plague differ widely in other material respects, 
 I must conclude that it differs in some respects in its cause. 
 Cholera is, I know, due to a micro-organism ; and I may therefore 
 conclude that plague is due to a micro-organism ; but the 
 symptoms of plague are so different from the symptoms of cholera, 
 that I must conclude that the micro-organism of plague is 
 different from the micro-organism of cholera. The two conclusions 
 are drawn at the same time, in the same act of reasoning, and the 
 one is as valid as the other. 
 
 In the case just supposed, the difference between the terms of 
 the datum are qualitative, and the likeness and difference in the 
 conclusion also are qualitative ; but should the terms of the datum 
 be compared quantitatively, as well as qualitatively, then the 
 likeness and difference in the conclusion will not only be
 
 222 A NEW LOGIC 
 
 quantitative, but will have exactly the same quantitative ratio as the 
 terms of the datum. In this case, the ratio of the qusesitum, to 
 its homologous term in the premiss, is the ratio of the datum. 
 
 When the builder is asked for a rough estimate of the cost of 
 laving the drains, he searches experience for a similar job ; and 
 he finds one which is similar in all material respects, except that 
 the drain was twice as long. He concludes, therefore, that 
 it cost twice as much. The Induction may be expressed thus : — 
 
 That drain cost £^oo 
 
 This drain (half as long) costs (x) half as much. 
 
 As far as the terms of the datum — this drain and that drain — 
 are alike, the qusesitum can be assimilated to its homologous term 
 — ;^ioo — in the premiss; and we may conclude that since that 
 drain cost a considerable sum, this drain will cost a considerable 
 sum. As far as the terms of the datum are different, this 
 difference must be reflected in a difference of the quaesitum from 
 its homologous term in the premiss. As the difference in the 
 datum is a quantitative difference, the difference in the conclusion 
 must be a quantitative difference, and must have the same ratio 
 as the datum. Since one drain is half as long as the other, the 
 difference in the cost will reflect this difference, and the new drain 
 will cost half as much as the old. Since the ratio of the datum 
 is I : 2, the ratio of the conclusion will be i : 2. 
 
 But it happens that the length is not the only difference 
 between the terms of the datum. When that drain was laid, 
 materials were a fourth dearer, labour was 10 per cent, cheaper, 
 than it is now. These differences also will be reflected in the 
 conclusion ; and reflected in the same ratios. On account of the 
 first difference, the new drain will be cheaper in the ratio of 3:4; 
 on account of the second difference, it will be dearer in the ratio 
 of 10 : 9 ; and, generally, whatever ratio exists between the terms 
 of the datum, will be reflected in the ratio between the qusesitum, 
 and its homologue in the premiss. 
 
 It is clear, from this example, that Induction is applicable, not 
 only to qualitative reasonings, which alone are within the compass 
 of the syllogism, but also to quantitative reasonings. It has 
 already been shown that some of the reasonings of mathematics — 
 those which have equality, and the ratios of greater and less, for
 
 SIXTH CANON OF INDUCTION 223 
 
 their subject — which are altogether outside the range of 
 Traditional Logic, arc included in the scheme of reasoning here 
 propounded, and are accounted for and explained. We now see 
 the basis of proportional reasoning. It is clear that mathematical 
 reasoning is outside the scope of the syllogism, for mathematical 
 reasoning is not concerned with attribution of qualities, nor with 
 inclusion in classes and exclusion from them. But, undoubtedly, 
 mathematical reasoning is reasoning ; and no scheme of Logic, 
 from which mathematical reasoning is excluded, is complete. 
 Logic purports to give an account of reasoning in general, and to 
 omit any form of reasoning from its purview is to confess its own 
 inadequacy and imperfection. 
 
 6. Another Canon must be added to those already enumerated 
 before the conditions of Induction are complete. The sixth Canon 
 is this : — A problem must not be stated more definitely than the 
 facts allow ; or Nothing must be assumed in the problem that is not 
 warranted by experience. 
 
 Who killed Cock Robin ? This problem assumes the solution 
 of a number of preliminary problems ; and unless and until these 
 problems are solved — unless experience of their solution is 
 obtained, it is improper and ^iltra vires to set the consequent 
 problem. Who killed Cock Robin ? is an illegitimate problem, 
 unless Cock Robin was killed. It assumes that he was killed. It 
 assumes the solution of other problems also. Did he die of 
 violence or of disease ? Is he dead ? Was there ever any such 
 person ? All these problems must be solved, and the solutions 
 must be consistent with experience, before we can legitimately 
 frame the problem Who killed him ? The problem that Charles II. 
 is said to have set to the Royal Society, is illegitimate in this 
 respect. Why does a bowl of water weigh no more after a fish is 
 put into it, than it did before ? This problem assumes that the 
 bowl does weigh no more under these circumstances, an 
 assumption which is inconsistent with experience, and renders 
 the problem illegitimate. Are the rectilinear markings on the 
 surface of the planet Mars the product of the intelligent activity 
 of its inhabitants ? This problem assumes that there are such 
 markings on the planet, and, if they do not exist, is illegitimate. 
 Why has he not returned ? assumes that he has not returned, and 
 if he has returned, is illegitimate. What is the cause of the
 
 224 A NEW LOGIC 
 
 child's illness ? assumes that the child has, in fact, been ill. 
 What will be the cost of laying new drains ? assumes that new 
 drains can be laid. Can my landlord be made to pay the cost ? 
 assumes that I have a landlord, as well as that the drain can be 
 laid, and that it will cost something. Is Socrates mortal ? is an 
 illegitimate problem if Socrates does not exist. 
 
 We are now in a position to state in full the nature and 
 conditions of Assured Induction. 
 
 1. Induction is the solving of problems by indirect appeal to 
 
 experience. 
 
 2. A problem is a proposition of which one element — the 
 
 quaesitum — is unknown. 
 
 3. The solution of a problem is the discovery of the quaesitum. 
 
 4. A problem is solved by comparing it with a premiss. 
 
 5. The premiss is a proposition expressing a relation that is 
 
 constant in experience, or that can be subsumed under one 
 that is constant in experience. 
 
 6. The premiss must be such that, of the two given elements in 
 
 the problem, one is similar in material respects to its 
 homologous element in the premiss, and the other is 
 identical with its homologous element in the premiss. 
 
 7. The likeness of the assimilated elements of problem and 
 
 premiss is called the Datum. 
 
 8. The third element in the premiss is adopted into the 
 
 problem as the quaesitum, subject to such difference as is 
 required by the difference between the terms of the datum.
 
 CHAPTER XV 
 
 IMPERFECT INDUCTION 
 
 Induction may be imperfect in two ways. It may be so 
 conducted as to violate one or more of its canons, and so be falla- 
 cious ; or it maybe conducted in accordance with its canons as far 
 as we are able to observe them, but may be imperfect from lack of 
 matter. Induction is reasoning in materia. It is the solving of 
 problems by appeal to experience ; and it may be that experience 
 does not afford us the knowledge necessary- to furnish a full 
 solution. In this case, the reasoning will be imperfect, but not on 
 that account is it without value. Conclusions of great importance 
 can still be drawn, but they will not be assured conclusions. They 
 will be tentative, hypothetical, or conjectural conclusions. More- 
 over, reasonings of this kind have a great importance in showing us 
 in what respects our knowledge is defective, and in indicating 
 the directions in which extensions of knowledge are needed ; 
 whether such extensions are practicable or no ; under what condi- 
 tions they are practicable ; and how to set about them. Fallacious 
 inductions will be considered in the chapter on Fallacies ; Imperfect 
 Induction, in the second sense, falls to be considered here. 
 
 The first step in induction is to discover a premiss ; and the 
 premiss is found by means of a datum ; that is, by assimilating 
 one of the elements of the problem to the homologous element in 
 some relation that has been found constant in experience. This 
 process, without being fallacious, may be imperfect in four 
 ways. 
 
 1. No datum may be obtainable. 
 
 2. The datum, if obtained, may yield no premiss. 
 
 In either of these cases, we are at a standstill, and argument 
 cannot proceed. 
 
 3. What datum can be obtained may not be sufficiently alike 
 
 in its terms to justify an assured conclusion. 
 
 4. The premiss, if obtained, may not be constant in experience. 
 In either of these cases, a conclusion may be reached, but will 
 
 be hypothetical or conjectural. 
 
 N.L. Q
 
 226 A NEW LOGIC 
 
 I. No datum may be obtainable. We may not be able to find 
 any experience sufficiently like the problem to enable us to 
 construct a datum. Let the problem be What is the connection 
 between mind and matter ? or formally stated, Mind x (h connected, 
 in such a u'ay with) matter : find x. In order to solve the problem, 
 we must find a datum ; that is, we must assimilate one of the 
 given elements in the problem to something of which we have 
 experience, and which is like the given element in respects 
 material to the argument. But there is nothing in experience to 
 which we can assimilate either of the elements of the problem. 
 We know of nothing that is not mind, to which mind can be 
 assimilated ; of nothing that is not matter, which matter is like in 
 respects material to the argument. Experience furnishes no 
 material for a datum ; and the argument cannot proceed. Accord- 
 ing to one theory, indeed, the atoms of matter are assimilable to 
 vortices in the ether ; but then we have noexperienceof the ether, 
 so that does not help us. According to another theory, matter is 
 composed of ions of electricity; but when ions of electricity are 
 imaged in this connection, as components of matter, they are 
 imaged as very small particles of matter ; and the assimilation 
 does not help us, because it is not so much an assimilation, as an 
 identification. But one given element of the problem must, as 
 we have seen, be identified with its homologue in the premiss. 
 May we not then use this value of matter for the identified term ? 
 If we do, we are no better off, for we are still without a datum. 
 There is nothing in experience to which the other given element 
 — mind — in the problem, can be assimilated, and until a datum is 
 found, reasoning cannot begin. The problem is insoluble for lack 
 of a datum — for lack of the experience in which a datum can be 
 sought. 
 
 What is the nature of the absolute ? Formally stated, the 
 problem is, the nature of the absolute is x : find x. In order to 
 solve this problem, we must construct a datum, in which the 
 nature of the absolute is assimilated to something of which we 
 have had experience. But there is in experience no such thing. 
 Experience contains nothing, except the relative, to which we can 
 compare the absolute ; and the relative is not assimilable to the 
 absolute, since they are contradictories. But, it may be said, this 
 proves too much, for it prohibits us equally from ascertaining the 
 nature of the relative ; since there is nothing in experience to
 
 IMPERFECT INDUCTION 227 
 
 which the relative can be compared except the absolute. This is 
 not so, however. Relativity is a generalisation from innumerable 
 experiences of relatives. The absolute is an abstract obtained from 
 innumerable operations of abstraction, none of which has ever been 
 complete. We cannot abstract qualities in experience ; we 
 can conduct the operation mentally only ; and experience affords 
 us no instance of it. \Vc have experience of relatives — of one 
 thing being above or below another ; before or after another ; and 
 in other kinds of relations to others ; but we have no experience of 
 colour without surface, or of hardness without substance. Conse- 
 quently, we can find the nature of the relative, but we cannot find 
 the nature of the absolute. In such cases as these, a datum cannot 
 be found ; and when no datum can be found in experience, reason- 
 ing cannot proceed. Reasoning in materia is arrested by want of 
 a datum, just as reasoning ex postulato is arrested by want of a 
 postulate. 
 
 2. The second way in which Induction may be imperfect, with- 
 out being fallacious, is when it fails at the second stage. A datum 
 may be obtainable in experience ; but when obtained, it yields 
 no premiss. In this case also, argument is arrested. 
 
 Doctors, in the last generation, desired to know the cause of 
 traumatic fever. A datum was easily obtainable. Traumatic 
 fever is closely similar, in material respects, to specific fevers, 
 and its resemblance to specific fevers furnished an unimpeach- 
 able datum ; but, as the cause of specific fevers was unknown, 
 the datum afforded no premiss, and the reasoning could not 
 proceed. 
 
 What elements preponderate in the composition of the satellites 
 of Jupiter? The satellites of Jupiter are composed mainly of x : 
 find X. A datum is readily obtainable. The satellites of Jupiter 
 are assimilable — perhaps not in all material respects, but they are 
 assimilable — to our own moon ; but, as we do not know the com- 
 position of the moon, the datum fails to yield a premiss, and the 
 argument cannot be pursued. 
 
 Why do the Andes run North and South, while the Himalayas 
 run East and West ? There are plenty of data available. The 
 Rockies, the Apennines, the Aral mountains, run North and South. 
 The Pyrenees, the Alps, the Caucasus, run East and West. But 
 since, in none of these cases do we know what determined the 
 
 g 2
 
 228 A NEW LOGIC 
 
 direction of the mountain chain, these data fail to afford us any 
 premiss, and argument is arrested. 
 
 3. The datum, even if it yields a premiss, may not be sufficiently 
 ahke in its terms to yield a satisfactory or definite conclusion. In 
 this case, argument is not arrested. It still proceeds, and a con- 
 clusion is attained ; but we have already seen that when a 
 conclusion is attained by induction, it reflects, not only the 
 likeness, but the difference between the terms of the datum. If 
 these likenesses and differences are definite, clear, and sharp cut, 
 the conclusion is correspondingly definite ; but if the likeness 
 between the terms of the datum is but approximate and vague, 
 the conclusion also is but approximate and vague. Such a 
 conclusion, so obtained, is termed an hypothesis. 
 
 What is the cause of specific fever ? We have already seen 
 that a valid datum — valid in the sense of its terms being closely 
 similar in material respects — can be obtained from the likeness 
 of specific fevers to traumatic fever ; but this datum was useless, 
 because the cause of traumatic fever was equally unknown. 
 There was, however, another datum available and employed, a 
 datum far less satisfactory, in that its terms could be but vaguely 
 assimilated, but more useful in that it did yield a premiss, and 
 therefore some sort of a conclusion could be obtained from it. 
 
 Among the features common to most cases of specific fever, it is 
 ob5er\-ed that they do not, as a rule, originate de novo. Small pox, 
 scarlet fever, measles, typhus, whooping cough, croup, plague, 
 chicken pox, and so forth, are well known to be 'catching.' Those 
 who come into contact or association with persons affected by 
 these diseases, are apt to be themselves attacked soon after ; and 
 the more closely the cases are observed, the more seldom is it 
 found that such previous contact or association can be excluded. 
 Thus, by a process of generalisation, we reach the conclusion that 
 these diseases are communicable — that something conveying the 
 disease passes from one person to another. • At once the mind 
 searches for a datum — searches experience for a similar case, — 
 but no datum is yet obtainable, and we remain baffled. 
 
 Next it is to be noticed that when a person has been in con- 
 tact with an affected person, and so has caught one of these 
 fevers, the disease does not declare itself immediately upon the 
 infection ; but only after an interval, usually an interval of
 
 HYPOTHESIS 229 
 
 several days, docs the disease become apparent. Aj^ain the 
 mind seeks in experience for a similar case, and tries to establish 
 a datum; and this time, it is more successful. There are, in 
 experience, other cases in which a period of quiescence follows 
 a contact ; and then the period of quiescence is followed by 
 widespread activity. When seed is sown in the ground, nothing 
 appears to happen for a time ; but after an interval, the surface 
 is covered with sprouting vegetation. When carrion lies exposed 
 in summer, nothing appears to happen for a time ; but after an 
 interval, the carrion is found to be swarming with maggots. 
 These cases are widely unlike the case of fever, it is true ; but 
 still, they have a certain similarity. They are not sufficiently like 
 to fever to warrant a positive conclusion ; but they are sufficiently 
 like to warrant a tentative conclusion, or as it is usually called, to 
 suggest an hypothesis. The hypothesis, or tentative conclusion, 
 they suggest is that specific fevers may be due to something of 
 the nature of seeds or eggs, passed from the body of the person 
 suffering from the disease, to the bodies of those who come in 
 contact with him. The cases are sufficiently alike to suggest 
 this, and so to suggest, for the period of quiescence before the 
 fever shows itself, the title of 'the stage of incubation.' It is as if 
 something were being hatched. 
 
 For many generations, this hypothesis was itself incubated ; but 
 nothing hatched out, and it seemed as if the egg were addled ; but 
 it contained a germ of life, and in due time broke the shell. 
 
 The discovery of a datum whose terms are but vaguely and 
 loosely assimilable gives us a premiss of some sort — a premiss 
 from which we can reach no assured conclusion, but from which 
 we can reach the tentative conclusion that we call an hypothesis; 
 and this is the nature of hypothesis. Let us pursue the illustra- 
 tion of the specific fevers a little further. 
 
 When instruments and methods of research had reached a 
 sufficient degree of advancement, search was made for the eggs or 
 seeds which were conjectured, on other grounds than that it is a 
 specific fever, to be the cause of tuberculosis ; and, after long and 
 patient search, they were found, in the shape of a micro-organism. 
 The steps, by which it was shown that the organisms found are 
 indeed the cause of tuberculosis, need not concern us. It is 
 enough that they were found and proved to be the cause ; and 
 now this discovery furnished a new datum for the old problem.
 
 230 A NEW LOGIC 
 
 Specific fevers and tuberculosis are widely unlike, it is true. 
 Specific fevers are, for the most part, acute illnesses of short 
 duration : tuberculosis is a chronic disease of long duration. 
 Specific fevers are mostly evidenced by a rash on the skin : in 
 tuberculosis there is none. Specific fevers are, for the most 
 part, communicable : tuberculosis was not recognised to be com- 
 municable. Specific fevers have an incubation stage : tuber- 
 culosis was not known to have an incubation stage. Yet, in spite 
 of these differences, there are important similarities. Specific 
 fevers are fevers — they are accompanied by a raised temperature ; 
 so is tuberculosis. Specific fevers are wasting diseases ; so is 
 tuberculosis. The fact, however, that most influenced observers 
 in adopting, as a datum, what likeness there is between specific 
 fevers and tuberculosis, was that specific fevers had, as we have 
 seen, long been suspected to be due to infection by some minute 
 organism, and tuberculosis was now found to be due to such an 
 organism. The suspicion was an hypothesis, based on the vague 
 assimilation already stated. That hypothesis was now verified, in 
 a case sufficiently similar to warrant a conclusion that is more 
 than an hypothesis. Tuberculosis had not struck many observers 
 as being closely like specific fevers ; but at any rate it is a disease ; 
 it is a febrile disease, and a wasting disease ; and these important 
 similarities were enough to furnish a reliable datum. It was, 
 therefore, argued that, since a micro-organism had been found in 
 tuberculosis, which is in some material respects like specific 
 fevers, micro-organisms would be found in these diseases also. 
 Micro-organisms were, therefore, searched for in specific fevers, 
 and they were found. Now the datum that had so long before 
 been dropped, because it led to no premiss, was revived. 
 Traumatic fever is, in material respects, similar to specific fever ; 
 hence we may argue that, since specific fevers are due to micro- 
 organisms, traumatic fevers are due to micro-organisms. Search 
 was made for the micro-organisms of traumatic fevers, and they 
 were found ; but if they had not been found, we should still have 
 been justified in concluding their existence. The similarity, in 
 material respects, of the terms of the datum, warrants us in 
 attaching certainty to the conclusion or conclusions; for, in 
 every case of Induction, the conclusion is double. Since scarlet 
 fever is like, in material respects, to other fevers which are known 
 to be due to micro-organisms, wc are justified in concluding, nay,
 
 HYPOTHESIS 231 
 
 we are compelled to conclude, that scarlet fever also is due to a 
 micro-organism. And, since scarlet fever exhibits symptoms 
 different from the symptoms of those other fevers, we are justified 
 in concluding, and compelled to conclude, that it is due to a micro- 
 organism different from theirs. 
 
 Some diseases, which are like specific fevers in the material 
 respect of being due to micro-organisms, arise apparently spon- 
 taneously, without the affected person having been in contact or 
 in association with anyone who has the disease ; and affected 
 persons may live for long among those who are not affected, with- 
 out communicating the disease to them. The problem presents 
 itself: How is such a disease communicated ? We search 
 experience for a datum. Taking ague as the type of such a 
 disease, we look for another disease having the same incidence, and 
 we find in yellow fever a disease of much the same incidence. 
 This gives us a datum ; but as the way in which yellow fever is 
 communicated is unknown, the datum yields us no premiss, and 
 argument cannot proceed. However, cattle bitten by the tsetse 
 fly suffer thereafter from a disease which has the characters of a 
 specific fever. Cattle are not closely like men, it is true, but for 
 the purpose of the argument, they are fairly assimilable to men in 
 the material respect of suffering from disease. The disease in 
 cattle is not like ague, but, for the purpose of the argument, it is 
 similar in the material respect of being communicable. Here, 
 then, we get a datum and a premiss, affording, not indeed a 
 positive conclusion, but a tentative conclusion — an hypothesis. 
 From this datum and this premiss we may not conclude that ague 
 is communicated to men by the tsetse fly, but we may fairly get 
 the hypothesis : May not ague be communicated to man by the 
 bite of some fly ? Investigation being made, it is found that ague 
 is communicated by the bites of mosquitoes. At once this 
 gives us a datum for the disease of similar incidence, yellow 
 fever ; and we conclude that this too may be communi- 
 cated by the bites of mosquitoes. This, also, is found 
 correct, and now we get a group of hypotheses. In the material 
 respects of biting human beings, and of fostering internal parasites 
 of their own, and of infesting the bodies of those who suffer from 
 certain specific fevers, fleas, bugs, lice, ticks, and certain other 
 insects resemble mosquitoes. May not these parasites be the 
 communicators, then, of other specific fevers ? This starts
 
 232 A NEW LOGIC 
 
 us on a whole series of investigations, and the hypotheses prove 
 fruitful. 
 
 An hvpothesis, then, is a tentative conclusion derived from an 
 induction that is imperfect, in that the terms of its datum are not 
 closelv assimilable in material respects. As soon as the terms of 
 the datum become closely assimilable, the conclusion ceases to be 
 tentative and becomes assured ; the hypothesis ceases to be an 
 hypothesis, and becomes an assured belief. So long as the con- 
 tagium of fevers entered into a datum, whose other term was seeds 
 of plants or eggs of insects, no conclusion could be formed, for no 
 premiss was obtainable. But even if a premiss had been obtain- 
 able, the likeness, in respects material to the argument, of diseases 
 to plants and insects is so remote, that the conclusion would have 
 been not an assured conclusion, but an hypothesis only. 
 
 The researches of Pasteur into the nature of fermentation 
 furnished doctors with an hypothesis as to the nature of fever. 
 Fever is like fermentation in several respects. When a relatively 
 minute quantity of yeast is introduced into a vat of wort, a wide- 
 spread change ensues ; the whole of the wort after a time ferments, 
 but the walls of the vat take no part in the change. When 
 a relatively minute quantity of the contagium of fever is intro- 
 duced into the human body (it must be relatively minute, for no 
 one sees it pass), a widespread change ensues ; and it was argued 
 to be like fermentation in that this change was confined to the 
 fluid part of the body — the blood — and the solid tissues took no 
 part in it. Moreover, the nature of this change in the blood was 
 likened to fermentation. These conclusions were, however, 
 mere hypotheses, since the terms of the data — the human blood 
 and the wort in the one case, and the contagium of fever and the 
 yeast in the other — were not sufficiently alike, in material respects 
 to warrant an assured conclusion. They have since been found 
 erroneous. 
 
 4. The fourth occasion on which Induction may be imperfect 
 without being fallacious, is when, a datum being found, and 
 furnishing a premiss, and the datum being satisfactory in the 
 close assimilation of its terms, the relation expressed by the premiss 
 is not constant in experience. 
 
 An example of this imperfection is found in most text books on 
 Logic, though they do not assign to it what I consider its proper
 
 CONJECTURE 233 
 
 place in the scheme of reasoning. This is the discovery by Fermat 
 that 2^ ' + I is, for a great many values of x, a prime number, 
 and his argument that since it is a prime number for a great many 
 values oi X, it is a prime number for all. In this case, the datum 
 is unimpeachable. Whatever value is given to x, that case of 
 2^"" + I is, in respects material to the argument, precisely like all 
 other cases. If, therefore, the relation of 2^"" -f- i to a prime 
 number is constant in experience, or can be subsumed under a 
 relation that is constant in experience, the conclusion, that for any 
 given value of x, 2^* + i is a prime number, is certain and 
 irrefragable. But the number of cases in which the relation has 
 been experienced — that is to say, in which the sum has been 
 worked out for different values of a;, and the result found to be a 
 prime number — falls far short of constituting that constancy in 
 experience which enables us to draw an assured conclusion. What 
 constitutes constancy in experience for the purpose of Induction is, 
 as has been said, scarcely a matter for Logic. It belongs more to 
 Epistemology, But the few dozen cases in which the sum has 
 been worked out for different values of x certainly do not compare 
 with the number of cases in which, for instance, constancy has 
 been experienced in the sequence between life and death, or in 
 the coexistence of resistance and extension. Nor can the relation 
 of the formula to a prime number be subsumed under a wider 
 relation that is constant in experience. In the language of every 
 day life, no reason can be given why it should be a prime number; 
 and, since the relation is neither constant in experience nor 
 subsumable under a wider relation that is constant in experience, 
 we have no warrant for concluding that it is true for any value of 
 -V that has not actually been worked out. In fact, as is well 
 known, there is a value of x for which the relation is not true. 
 
 In the experience of our ancestors, the relation that metals are 
 heavier than water, was constant so far as experience went ; but it 
 was a very limited experience. The metals known to them were 
 so few, that the constancy with which they were found to be 
 heavier than water was not constancy for the purpose of sound 
 Induction. Although, therefore, any new metal that might be 
 discovered would be, for the purpose of the argument, closely 
 assimilable to known metals, and thus a satisfactory datum would 
 be found ; and although this datum would furnish a premiss, since, 
 in experience, metals had been found heavier than water; yet,
 
 234 A NEW LOGIC 
 
 since the relation expressed by this premiss was not constant, in 
 the logical sense, in experience ; the conclusion, that all metals 
 thereafter discovered would sink in water, would not have been 
 justified; and experience has shown that it would have been false. 
 
 If a certain train has been for years running punctually to time 
 every day, the argument, that it will run punctually to time on 
 any given day, will have a high degree of assurance. The datum 
 is unimpeachable in the closeness of assimilation of its terms. 
 The running of the train on the given day is in material respects 
 like its running in the past. The relation of its running to 
 punctuality is constant in experience, as far as experience goes ; 
 but it is a limited experience. It docs not extend to anything 
 approaching the illimitable number of times on which, for instance, 
 similar causes have been found to produce similar effects. Although, 
 therefore, we may attach to the conclusion a considerable degree 
 of assurance, we do not attach to it the same assurance that we 
 attach to the conclusion that the sun will rise to-morrow morning. 
 
 The unassured conclusion that is reached from a datum whose 
 terms are imperfectly assimilated, is called an Hypothesis : the 
 unassured conclusion that is reached from a premiss that is not 
 constant in experience, is called a Conjecture. 
 
 Among the many meanings that have been attached by logicians 
 to the word Analogy, one includes Induction, especially the two 
 forms of imperfect Induction last considered, which lead 
 respectively to hypothesis and conjecture. As Mill puts it, 'Two 
 things resemble each other in one or more respects ; a certain 
 proposition is true of the one, therefore it is true of the other.' 
 ' Two propositions resemble each other in one or more respects.' 
 That is an imperfect expression of the Datum. *A certain pro- 
 position is true of the one.' That is an imperfect expression of 
 the Premiss. ' Therefore it is true of the other.' That is an 
 unwarranted conclusion. 
 
 Mill saw that this argument is not valid in all cases, and he 
 proceeded to discuss what resemblances between the * two things,' 
 which I call the terms of the datum, justifies a conclusive argument. 
 His first statement is very similar to mine. * The circumstance in 
 which the two cases resemble, may be capable of being shown to 
 be a material circumstance ; to be that on which all the con- 
 sequences, necessary to be taken into account in the particular 
 discussion, depend.' This is very much the same as saying that
 
 ESSENTIAL LIKENESS 235 
 
 the resemblance must be material to the argument. As to the 
 condition that warrants a conclusion from the premiss, providing 
 the terms of the datum have a satisfactory similarity, it is, he 
 says, that ' it has been previously shown, by due comparison of 
 instances, that there is an invariable conjunction between the 
 former property or properties and the latter property.' This is 
 what I mean by the condition, that the relation of the premiss 
 must be constant in experience. * But in Analogical reasoning,' 
 he says, 'no such conjunction has been made out.' Analogical 
 reasoning in Mill's sense is, therefore, that variety of what I call 
 Imperfect or Unassured Induction that terminates in a conjecture. 
 
 If Mill had been content to adhere to this expression, I should 
 have no material difference with him ; but he subsequently 
 wavered in his statement. ' The cases in which analogical 
 evidence affords in itself any very high degree of probability, 
 are only those in which the resemblance is very close and 
 extensive.' In this expression he deserts that materiality which 
 he has previously asserted to be necessary, and accepts, instead, 
 closeness and extensiveness of resemblance. Thus it has happened 
 that subsequent logicians have taken it that the validity of an 
 Induction depends on the number of the resemblances between 
 the ' two things,' or upon the ratio between the number of 
 resemblances and the number of differences. This is manifestly 
 unsound as a basis for argument, and other logicians have per- 
 ceived this, and have contended that the likenesses between the 
 * two things ' must be estimated, not as to their number, nor as to 
 their ratio to the differences, but as to their fundamental or 
 essential quality. The resemblances, they say, must be funda- 
 mental or essential ; the differences superficial and unessential ; 
 then the argument will be valid. I cannot but think it a pity 
 to import into Material Logic a word which is the peculiar pro- 
 perty of Traditional Logic, and a word whose meaning, in this 
 Logic, has been the subject of endless discussion, and is even now 
 not defined. It does not seem to me to advance the matter any 
 further, nor to afford any firmer ground for argument, to say that 
 the resemblances between the things must be fundamental or 
 essential, than to say they must be more numerous than the 
 differences. 
 
 Glass and silver are ' two things that resemble each other in one 
 or more respects' ; ' A certain proposition ' — that it can be drawn
 
 236 A NEW LOGIC 
 
 into threads — ' is true of the one, therefore it is true of the other.' 
 In this case, the conclusion is warranted. 
 
 Glass and silver are two things that resemble each other in one 
 or more respects ; a certain proposition — that it can be made 
 into table-utensils — is true of the one ; therefore it is true of the 
 other. In this case also, the conclusion is true. 
 
 Glass and silver are two things that resemble each other in one 
 or more respects ; a certain proposition — that it is a good con- 
 ductor of electricity — is true of the one ; therefore it is true of the 
 other. In this case the conclusion is false. 
 
 Glass and silver are two things that resemble each other in one 
 or more respects ; a certain proposition — that it is fragile — is true 
 of the one ; therefore it is true of the other. In this case, also, 
 the conclusion is false. 
 
 Now, whether the resemblances and differences of glass and 
 silver are numerous or few ; whether they are fundamental or 
 superficial ; whether they are essential or unessential ; they remain 
 the same whether these substances are drawn into threads, made 
 into table-utensils, used in electrical apparatus, or otherwise 
 treated. It is clear, therefore, that it is neither the absolute 
 number nor the relative number, neither the fundamental nor the 
 essential quality, of the characters in which they resemble and 
 differ from one another, that gives validity to the argument, or 
 deprives it of validity. What quality is it then, in these 
 resemblances, that affects the validity of the argument ? I think it 
 is clear that the resemblance must be in material respects — in 
 respects that are material to the argument. If they are alike, and 
 so far as they are alike, in respects material to the argument, the 
 argument, that what is true of the one is true of the other, is valid, 
 provided that what is true of the one is constantly true in 
 experience. Glass is verj' unlike silver in many respects ; in the 
 fundamental, and I suppose essential, respects of not being a metal; 
 of being transparent ; of being brittle ; of not being an element; 
 of being a compound manufactured product, and so forth ; but for 
 the purpose of being used for making mirrors, glass is like silver, 
 in the material respects of taking a high polish, and reflecting, 
 under proper circumstances, a large proportion of the incident 
 light ; and in these respects, the likeness is constant in experience. 
 Consequently, we may safely argue that, if silver makes a good 
 mirror, glass also will make a good mirror.
 
 INDUCTION AND SYLLOGISM 237 
 
 The last example is a sound Induction, leading to an assured 
 conclusion ; and Analogy is sometimes allowed by logicians to lead 
 to assured conclusions ; but this admission is rare, and, when 
 made, seems to be made inadvertently. ' Analogy,' says one book, 
 * may have all degrees of value ' ; but more often it is said 
 ' Analogy is a kind of probable proof, based upon imperfect 
 similarity.' 'Analogical argument is only probable,' or some 
 equivalent phrase. It seems, therefore, that, as far as logicians 
 admit this form of reasoning, which they call, erroneously, as it 
 seems to me, Analogy, they admit the imperfect form only, in 
 which the terms of the datum are imperfectly assimilated in 
 material respects. They do not appear to recognise the separate, 
 valid, reasoning in materia that I call Induction. Lotze, indeed, 
 distinctly repudiates it. * I do not believe,' he says, ' in the 
 existence of proof by Analogy.' If Analogy is used in the 
 Aristotelian sense, and is restricted, as I think it ought to be, to 
 this sense, then I agree with Lotze, that there is no proof by 
 Analogy ; but he evidently uses it in the current sense, and in this 
 sense he is wrong. 
 
 Mr. Bosanquet erects Analogy into an important variety of 
 reasoning, and devotes a long chapter to it ; but he also regards it 
 as leading to conclusions that are uncertain and tentative only. 
 He regards the Analogical argument as an instance of the second- 
 figure of the syllogism with an undistributed middle. The con- 
 clusion, therefore, can never be indisputably valid. As an instance 
 of Analogy he gives the following : — 
 
 Cutting tools have edges and places for handles ; 
 These flints have edges and places for handles ; 
 . • . These flints are cutting tools. 
 
 As a syllogism, which Mr. Bosanquet considers it, this argument 
 is invalid by reason of its undistributed middle. I do not regard 
 it as a syllogism. It seems to me an argument in materia. It 
 purports to solve the problem Are these flints cutting tools ? The 
 problem is These flints x {are or are not) cutting tools : find x ; and 
 the Induction by which the problem is solved is 
 
 Things which have edges, etc., are, constantly in experience, 
 cutting tools. 
 
 These flints, which have edges, etc., {x) are cutting tools.
 
 238 A NEW LOGIC 
 
 This argument is, on the face of it, conclusive. If the flints 
 really have edges and places for handles ; and if such things 
 are, constantly in experience, cutting tools ; these flints are, 
 without doubt, cutting tools. Mr. Bosanquet omits, as he is 
 quite entitled to do, the constancy in experience. He omits it, 
 however, not deliberately and of set purpose, but because, as 
 it seems to me, its importance has not occurred to him ; and 
 consequently he is obliged to admit that the argument ' is at 
 variance with its matter, and represents no inferential neces- 
 sity at all.' This is true with respect to his argument ; it is 
 not true with respect to mine. The importation of the con- 
 stancy in experience converts the argument from an argument 
 ex postulato into an argument in materiel. As an argument ex 
 Postulato, all that we are warranted in inferring, is that the 
 characters of the flints are consistent with their being cutting 
 tools ; and to infer more than this would infringe the fourth 
 Canon of Inference. But when we know, or if we know, that 
 edges and places for handles are, constantly in experience, related 
 to cutting tools, we are justified in inducing, and compelled to 
 induce, that the flints are certainly related in the same way to 
 cutting tools. 
 
 The want of constancy in experience of the premiss, is not the 
 only way in which the Analogical Argument of logicians is 
 imperfect as an induction. Its imperfection may be that noted 
 under our third heading — the want of likeness in material respects 
 of the terms of the datum — of the ' two things ' which ' resemble 
 each other in one or more respects.' Another instance of Mr. 
 Bosanquet's will illustrate this. 
 
 A peculiar herring-bone structure is conjoined in the Pelar- 
 gonia with the characters of the Geraniese ; 
 
 The flowers with such seed vessels as exist in our wild geraniums 
 have the characters of the Geraniese ; 
 
 . • . That these flowers, e.g., our wild geraniums, should have the 
 peculiar herring-bone structure is exceedingly probable. 
 
 As thus stated, the argument is not very easy to follow; and I 
 think it gains in clearness, as well as in force, by being stated as an 
 induction, thus : — 
 
 Premiss. Pelargonia have, constantly in experience, a peculiar 
 structure of petal ;
 
 ANSWERS TO CRITICISMS 239 
 
 Datum. Wild geraniums resemble Pelargonia in the common 
 characters of Geranieae ; 
 Wild geraniums (probably) have this peculiar structure 
 of petal. 
 
 The reason for the introduction of probability into this conclusion 
 is the failure of the terms of the datum to resemble each other 
 completely in material respects. We know that geraniums resemble 
 Pelargonia in all the qualities common to Geranieae ; but we do not 
 know how far this resemblance is material with respect to the 
 peculiar structure of the petals. This imperfect assimilation, in 
 material respects, of the terms of the datum, vitiates the certainty 
 of the conclusion, and lowers it from an assurance to the rank of 
 an hypothesis. 
 
 From this discussion it appears that an Hypothesis is the 
 tentative conclusion of an induction that is imperfect, in the 
 incomplete assimilation, in material respects, of the terms of the 
 datum ; while a Conjecture is the conclusion of an Induction in 
 which the relation predicated in the premiss is not known to be 
 constant in experience, and is not subsumablc under a relation 
 that is constant in experience ; and that the Analogical reasoning of 
 logicians is not, properly speaking, Analogy at all, but is Imperfect 
 or Unassured Induction. 
 
 Some criticisms must be anticipated at this point. It has been 
 contended by an acute critic of these doctrines, that if I admit 
 resemblance in material respects as necessary to Induction, 
 the material respects are a Universal, and I am in the trap of the 
 pditio principii, and all the incurable vices of the syllogism. 
 It is further contended that if subsumption is admissible in 
 Induction, then is the syllogism admissible, for the syllogism is 
 subsumption. 
 
 With respect to the first contention, that resemblance in material 
 respects is a Universal, I am not concerned either to admit or deny 
 the impeachment. ' Universal ' is used in so many senses by 
 logicians, that one is never safe in denying anything to be a 
 Universal. If the term 'Sir Christopher Wren,' in the propo- 
 sition ' Sir Christopher Wren designed St. Paul's,' or if that pro- 
 position is, as some logicians contend, a Universal, then it is clear 
 that it would be very unsafe to deny that material respects, or any- 
 thing else, constitute a Universal; but that the acknowledgement
 
 240 A NEW LOGIC 
 
 that I employ Universals in reasoning lands me in the trap of the 
 peiitio priucipii, and the other incurable vices of the syllogism, I 
 do most strenuously and utterly deny. The syllogism is a definite 
 apparatus. It is a machine of complicated construction, of which 
 its Universal is but one part — a necessary part, no doubt — but still 
 only the mainspring or fly wheel. If I utilise a mainspring or a 
 fly wheel in my machine, it does not follow that this machine is a 
 timepiece or a steam engine. It may be a bottle-jack or a gas 
 engine. My Universal is the respects that are material to the 
 argument, in which respects the terms of my datum must be alike. 
 The Universal of the syllogism is the general rule, under which the 
 minor premiss must come as an instance. The two are as different 
 as likeness and subsumption, and cannot be more nearly assimilated. 
 I say that for the purpose of certain arguments with respect to the 
 storage and liberation of motion, the brains of animals resemble 
 in material respects electric accumulators ; but this is not sub- 
 suming the animal brain under the electric accumulator, or saying 
 that the brain belongs to the class of electric accumulators. 
 
 The second argument, that if subsumption is admissible in 
 Induction, then the syllogism, which is subsumption, is admissible, 
 is clearly fallacious by the rules of the syllogism itself, if the argu- 
 ment is syllogistically stated. For the subsumption that alone is 
 admissible into Induction is subsumption of an experienced relation 
 under a relation that is constant in experience ; but the sub- 
 sumption of the syllogism is the subsumption of any relation under 
 any relation that contains it. As a syllogism the argument is 
 
 Some forms of subsumption arc admissible into Induction ; 
 
 The syllogism is a form of subsumption ; 
 .". The syllogism is admissible into Induction. 
 Fallacy of undistributed middle. 
 
 Another criticism questions the statement that Induction knows 
 nothing of postulates; for, says the critic, are not working 
 hypotheses postulates? Certainly, they are; but Induction cannot 
 utilise them as premisses. The only position that an hypothesis 
 can hold in Induction is that of a tentative conclusion from a 
 material premiss. This tentative conclusion may become a work- 
 ing hypothesis ; that is to say, it may be postulated to be true 
 for the purpose of argument, and conclusions may be deduced from 
 it. Yes; deduced. That is to say, the moment it is postulated,
 
 INDUCTION AND DEDUCTION 241 
 
 it is taken out of the realm of Induction and introduced into that of 
 Deduction. I do not deny, and in a subsequent chapter I assert 
 and proclaim, that the conclusions of one mode of reasoning may 
 form the premisses of another; but I maintain that hypothesis has 
 no place in Induction except as a result of the Inductive process. 
 So, the conclusions of Deduction may be true ; but they cannot be 
 known to be true merely because they are valid deductions. To 
 ascertain their truth we must apply them direct to experience, and 
 see if they agree. It is true that if the postulated premiss happens 
 to be true, and the deduction is properly carried out, the conclusion 
 will be true; but this is an accidental result. It is no necessary or 
 inseparable condition of Deduction that its conclusions should be 
 true, or that its premisses should be true. 
 
 N.L. R
 
 BOOK III 
 
 INFERENCE OR DEDUCTION 
 THE METHOD OF EXPLICATION 
 
 R 2
 
 CHAPTER XVI 
 
 IMPLICATION AND THE LAWS OF THOUGHT 
 
 Every proposition implies certain others, which are necessarily 
 granted when the postulate is granted. In other words, the relation 
 expressed by a proposition may be expressed in several ways : it 
 may be expressed by other propositions derived from the postulate. 
 If All men are mortal, then No men are immortal. The second pro- 
 position is implied in the first. It is another way of stating the 
 relation expressed by the postulate. This process, of extracting 
 or explicating the implications of simple propositions, is called, by 
 logicians. Immediate Inference, and the implications thus extracted 
 are called immediate inferences. 
 
 The Mediate Inference of logicians is the extraction of 
 implications from Compound propositions. Logicians consider 
 that Mediate Inference is more than this, and enables us to proceed, 
 as they call it, from the known to the unknown. In this I think 
 they are in error ; and this is one of the fundamental differences 
 between the system of Logic here expounded and the systems of 
 Traditional and Modern Logic. In supposing that the syllogism 
 enables us to proceed from the known to the unknown, or to 
 discover anything beyond what is implied in the postulate, logicians 
 are, in my opinion, profoundly mistaken. This confusion of two 
 fundamentally different modes of reasoning will be considered 
 presently ; for the moment it is enough to notice that the syllogism, 
 whatever else it may be, if it be anything else, is certainly a mode 
 of extraction of implications from Compound propositions. If 
 All men are mortal and Socrates is a man, then, implied in this 
 double postulate, or compound proposition, is the implication 
 * Socrates is mortal.' The conclusion is a mode of stating part 
 of the sense contained in the postulate. It is one of the 
 implications of the postulate. 
 
 There are, as we have seen, three main forms of Categorical 
 proposition — the Simple, the Conditional, and the Compound. 
 The process of extracting the implications of Simple propositions 
 is called Immediate Inference. The process of extracting the 
 implications of Compound propositions is called Mediate Inference. 
 
 \
 
 246 A NEW LOGIC 
 
 No special name has been given by logicians to the process of 
 extracting the implications of Conditional propositions ; which is 
 included under Mediate Inference. 
 
 Some of the implications of propositions are so manifest ; so 
 thinly disguised ; appear so plainly in the statement of the pro- 
 position itself; grin at us so impudently through the structure 
 of the proposition ; that to call them inferences seems to invest 
 them with fictitious importance ; and to call the process of ex- 
 tracting them a process of inference, seems to dignify unduly a 
 ven*- simple affair. Hence, in the text books, the question is 
 usually debated whether Immediate Inference is a process of 
 inference at all. Other implications are so hidden, in such remote 
 recesses of the postulate, that it is a real, if not a very difficult, 
 exercise of ingenuity to explicate them ; and to these the title of 
 Inference is allowed less grudgingly; but the nature of the process 
 is not affected by the ease or difficulty with which it is performed; 
 and whatever title is given to such a simple transfer as from ' Men 
 are mortal ' to ' Men are not immortal ' may consistently be given 
 to the less obvious transfer from * Men are both mortal and 
 responsible ' to * Mortality is consistent with responsibility,' or 
 from * I saw him do it' to ' I was there when he did it.' 
 
 In most text books on Logic, there is much debate whether 
 Immediate Inference effects more than a verbal change ; and 
 whether, if it effects no more than a verbal change, it is entitled 
 to the glory of being called Inference. It is clear that it is a 
 verbal change ; and it is clear that, in such an instance as the 
 inference from Man is mortal to Man is not immortal, it is little or 
 nothing more than a verbal change. It would puzzle a sophist 
 to detect a difference of meaning between these two propositions. 
 But it is clear that between All birds are clothed in feathers, and 
 Anything that is featherless is not a bird, there is a certain 
 difference that is appreciable, and may on occasion be useful. 
 The difference is not altogether a difference in meaning. The 
 one statement is implied in the other; and the meanings cannot, 
 therefore, be diverse. But the two propositions look at the same 
 fact from different points of view. The attention is directed to 
 different aspects of the same fact. 
 
 The propositions of Logic are considered by the text books in 
 isolation from their context — apart from the discourse in which 
 they appear — and, so considered, much of their significance is
 
 USES OF INFERENCE 247 
 
 lost. The full use and value of a proposition can be known only 
 by its context. In the queer and obscure phraseology of Modern 
 Logic — in its statement, repeated with such wearisome iteration 
 and in so many ways, that judgement is the synthesis of differences 
 in an Identity — there seems to lie a discernment that every judge- 
 ment is an organised part of an organic whole; and that no one 
 judgement can have its full value assigned to it, except by estimating 
 its relations to the general scheme of knowledge. It would need 
 greater temerity than I can lay claim to possess, to interpret the 
 true meaning of the doctrines of Modern Logic concerning the 
 judgement ; but if this is the meaning, or one of the meanings of 
 these doctrines, I respectfully signify my agreement with it. At 
 the same time, I think that Modern Logic, impressed by the bald- 
 ness and superficiality of Traditional Logic, errs in the opposite 
 direction, and courts confusion by its constant asseveration that 
 knowledge is a single Identity. Nevertheless, if its teaching may 
 be interpreted as insisting on the interconnection of the various 
 constitutents of knowledge, and thus implying that a proposition, 
 considered apart from its context, is divested of much of its 
 meaning, then I think Modern Logic has reason. 
 
 Whether it is best to state the judgement in the form ' All 
 
 birds are clothed in feathers,' or in the form * Anything that is 
 
 featherless is not a bird,' depends on the context ; that is to say, 
 
 on the matter under discussion, or the purpose of the argument. 
 
 If the question, or doubt, or conjecture, is whether All birds are 
 
 clothed in feathers, or is What birds are clothed withal, then the 
 
 proposition ' All birds are clothed in feathers ' gives the most 
 
 direct and appropriate answer. But if the question is whether 
 
 this featherless creature is or is not a bird, then the proposition 
 
 * All birds are clothed in feathers ' does not give a direct answer. 
 
 But the variant or implication ' Whatever is featherless is not a 
 
 bird,' does give a direct and an appropriate answer. The two 
 
 propositions have precisely the same meaning, and each is 
 
 implied in the other. Both express the same relation between 
 
 birds and their clothing in feathers ; but the same explication is 
 
 not equally appropriate for every context, or for the purpose of 
 
 every argument. Each explication brings into prominence some 
 
 special aspect or implication of the relation, which is more 
 
 appropriate than the rest for some special purpose ; and, as every 
 
 proposition is, in actual reasoning, stated for some purpose, regard
 
 248 A NEW LOGIC 
 
 should be had to this purpose in stating the proposition. One of 
 the radical defects of Traditional Logic is that it steadily ignores 
 the purpose of its arguments. One of the merits claimed for the 
 system of Logic here expounded, is that it keeps steadily in view 
 the purpose of the argument. For aught that appears in the 
 text books, Inference, as a mode of argument, might have no 
 purpose at all. Its purpose is never alluded to. But the purpose 
 of an inference is vital to its validity as an inference. In the 
 course of the consideration of Inference, we 'shall come upon 
 abundance of instances of inferences that are valid for one purpose 
 and invalid for another ; and to ignore the purpose of the 
 argument is a direct incitement to fallacy, and a certain road to 
 fallacy. 
 
 To put the matter crudely, a proposition may be regarded in 
 the light of the questions to which it is an answer ; and is 
 modifiable, so as to answer directly each of these questions ; each 
 such modification being an implication, and being derivable by 
 the rules of Inference. Such a simple proposition as ' Brutus 
 killed Caesar ' answers at least twenty questions; and I daresay 
 many more. It answers Who killed Caesar ? and the reciprocal, 
 By whom was Caesar killed ? It answers Whom did Brutus 
 kill ? and the reciprocal. Who was killed by Brutus ? It 
 answers the specific question, Did Brutus kill Caesar ? the general 
 question. What did Brutus do to Caesar ? the more general 
 question. Did Brutus do anything to Caesar ? the still more 
 general question, What took place between Brutus and Caesar ? 
 and the yet more general question, Did anything take place 
 between Brutus and Caesar ? These are far from all the questions 
 to which the proposition is an answer. It answers also Who was 
 killed ? Who killed ? Was any one killed ? Did Brutus protect 
 Caesar ? Did Brutus defend Caesar from his enemies ? Did any 
 one but Brutus kill Caesar? Was it Brutus who killed Caesar? 
 Was it Caesar who was killed ? Did Brutus and Caesar ever 
 meet ? Were they living at the same time ? and so forth, and 
 so on. 
 
 All these questions are answered by the proposition ' Brutus 
 killed Csesar,' but all arc not answered with equal efficacy, or 
 with equal directness, by this mode of expressing the relation. 
 To give each question a direct answer, the proposition must be 
 so modified that, while the information it contains, that is, the
 
 THE LAWS OF THOUGHT 249 
 
 relation it expresses, is the same, the information or relation is 
 expressed in such a manner as is suitable to the occasion, or 
 is fitted to the purpose of the argument. This is done by 
 explicating the appropriate implication. As far as the content 
 of the proposition is concerned, it matters not whether we say 
 ' It was Brutus who killed Caesar,' or ' It was Caesar who was 
 killed by Brutus.' Both express the same relation, neither more 
 nor less ; but they are appropriate to very different occasions. 
 They are germane to the purpose of very different arguments. 
 They indicate different attitudes of the proposer's mind towards 
 the fact expressed in the propositions. The first answers directly 
 the question 'Who was it that killed Caesar?' and for the 
 purpose of this argument, the second proposition is inappropriate. 
 It gives an answer, but it gives an indirect and inappropriate 
 answer. To every argument, its purpose is vital ; and the form 
 or implication of the proposition must be found, that is 
 appropriate for the purpose of the argument. This is the 
 function, and this is the use, of Immediate Inference. It enables 
 us to put our arguments in telling form. It shows us what is 
 implied in a proposition ; enables us to extract from a proposition 
 all its implications ; guards us against error in the process ; and 
 teaches us to keep in view, in every argument, the purpose for 
 which the argument is undertaken. 
 
 The process of Immediate Inference is not, therefore, as it 
 often appears in the text books, a mere useless exercise of 
 perverted ingenuity. On the contrary, it is, on occasion, of real 
 assistance, and even necessity. It is not a waste of time to 
 ascertain in what ways, by what rules, the implications of 
 propositions may be explicated ; or what are the immediate 
 inferences that can be extracted from them. Still, this is not to 
 say that the immediate inferences of the text books are useful, or 
 even valid. 
 
 The Laws of Thought. 
 
 Under this title, logicians state what are, in their view, the 
 underlying conditions of valid inference. The term ' law ' is very well 
 known to be used in two senses. In one sense, it means observed 
 uniformity, and expresses a relation that is constant and 
 invariable in experience, and that man cannot alter. Such are 
 the Laws of Motion, of Gravitation, of Combining Proportion, of
 
 250 A NEW LOGIC 
 
 Evolution, of Survival of the Fittest, and so forth. In the other 
 sense, ' law ' means a rule of conduct. It means a mandate, or 
 a prohibition, that we are told to observe, but that we are at 
 liberty to disregard, if we choose to take the consequences of 
 so doing. It means a course of conduct enjoined upon us, but 
 that we may follow or not as we please. 
 
 The discrepancy among logicians, which is wide enough to 
 prevent them from agreeing as to the nature and province of 
 Logic, is deep enough to prevent them from agreeing as to the 
 nature of the Laws of Thought. According to some logicians, the 
 Laws are laws in the first sense. They are statements of observed 
 uniformity ; they are descriptions of conditions to which thought 
 must conform ; they are inviolable laws of nature ; they are 
 necessary laws, from which no departure can be made ; * As really 
 obeyed by all minds, they arc laws in the sense of scientific 
 uniformities.' According to others, they are laws in the second 
 sense. They are rules that we ought to observe, and that we 
 must observe if our Inferences are to be valid; but that we may 
 break, either deliberately or by inadvertence, on peril of the 
 consequence, that the reasonings conducted in violation of them 
 will be invalid. According to this view, they are precepts. They 
 set up a standard that it is desirable to follow ; but that we may 
 or may not attain. ' They may be compared with the laws of 
 Grammar as regards correct speaking and writing.' 
 
 A third opinion is that the Laws are laws in both senses. They 
 are inviolable laws of Nature, that we are compelled by the 
 constitution of our minds to observe, but that we can disregard 
 and violate if we please. Some text books explicitly state that 
 the Laws are laws in both senses ; all, I think, without exception, 
 whether or no they speak of them as laws of Nature, interpret 
 them as behests. Whether these laws are laws of Nature that 
 we are compelled by the constitution of our minds to observe, or 
 whether they are behests that we ought to observe, but may 
 disregard if we choose, I will not now argue ; but I feel con- 
 siderable difficulty in accepting the doctrine, inculcated by some 
 logicians, that they are both. 
 
 The first Law of Thought— the Law of Identity— is ' Whatever 
 is, is.' As it is difficult for the non-logical mind to understand 
 this proposition, at any rate in the sense in which logicians 
 understand it, they have furnished us with several alternative
 
 THE LAWS OF THOUGHT 251 
 
 expressions, such as 'Everything is identical with itself; 
 * A is A ' ; * Everything is what it is ' ; * Every object of thought is 
 conceived as itself ' ; ' A thing is what it is ' ; * If B is A, it is A ' ; 
 and so forth. I do not find the law anywhere stated as ' Eggs is 
 Eggs ' ; but this may be only an example, not a statement, of the 
 law. It is perhaps a corruption of * X is X '. 
 
 The second Law of Thought — the Law of Contradiction — 
 states that Nothing can both be and not be ; and of this also there 
 are many variants, each logician stating it better than any other. 
 ' A is B and A is not B cannot both be true together ' ; 'A cannot 
 both be B and not be B ' ; ' A is not non-A ' ; 'A cannot be both 
 B and non-B '. I have collected a dozen other methods of 
 expressing this Law, but it is not worth while to give them ; for, 
 taken in the ordinary sense, one is as good as another; and no 
 one helps us more than another to arrive at the sense that 
 logicians read into them. 
 
 The third Law of Thought — the Excluded Middle — runs 
 'Everything must either be or not be ' ; ' A is either B or not B' ; 
 and a dozen more variants of the same theme. 
 
 When a person who has not been suckled and weaned on 
 Traditional Logic, comes upon these Laws, and finds them in the 
 same book, and it may be in the same chapter, in which the 
 uselessness and tautology of the ' verbal proposition ' are set forth 
 with emphatic insistence, his first impulse is to ' hold up his hands 
 in respectful amazement.' If these are indeed the ultimate and 
 underlying laws of all thought ; if this is the grand climax of 
 Traditional Logic ; if this is the sublimation and concentrated 
 quintessence of the result of two thousand years of investigation ; 
 then the novice is inclined to say, with the boy who learnt the 
 alphabet, that it is scarcely worth while to go through so much 
 in order to attain so little. 
 
 The first thing that strikes us, upon an examination of these 
 Laws, is that, in form, they are neither mandatory nor prohibitive. 
 They tell us nothing that we are to do, nor do they tell us 
 anything that we are not to do. Their form is purely assertory'. 
 They assert, not what ought to be done, or what must not 
 be done; but what is, and what is not. They are in the form, 
 not of legislation, but of statements of fact — of generalisa- 
 tions. Yet most logicians interpret them as rules ; and when the
 
 252 A NEW LOGIC 
 
 exegesis of these interpreters is examined, it is found to amount 
 to this : — 
 
 The first Law of Thought means that a term, or a proposition, 
 is always to be used in the same sense in the same argument. 
 
 The second Law means that we ought not to contradict 
 ourselves. 
 
 The third Law means that every proposition ought to mean 
 something. 
 
 These are not, indeed, the very words in which the Laws are 
 expounded ; but, when the chapter in which they are explained 
 is boiled down, this is the residue that is left. The question 
 naturally arises in the mind of the reader, Why, if this is what 
 the Laws are intended to mean, are they not expressed in these 
 words? It requires some ingenuity to read these meanings into 
 them, and a plain man would scarcely guess that they are to be so 
 understood, until they are thus expounded to him. Why not, 
 then, cast them in the form that expresses clearly the meaning 
 that is intended ? 
 
 Modern Logic, however, possesses a much deeper insight ; and 
 the ordinary man is amazed, and almost appalled, by the revela- 
 tion of the profundity of meaning that Modern logicians find 
 lurking unsuspectedly in the deceptively simple-looking formula 
 ' A is A.' Thus says Modern Logic, as interpreted by Mr. 
 Bosanquet. 
 
 ' I. The Law of Identity must be taken to signify at least that 
 'it is possible to make judgments that have a meaning and are 
 ' true. 
 
 ' a. In the bare form " A is A," however, a form which is not 
 
 * drawn directly from Aristotle or from Plato, the law does not 
 ^ prima facie possess this significance, and therefore indeed not any. 
 ' If it means that A is A and no more, or is mere A, then it is 
 ' aggressively untrue, for it denies the synthesis of differences 
 
 * which alone can make a judgement. If, again, the law is taken 
 'as a mere symbol of the pervading unity of the Logical 
 'subject, and not as intended to exclude all differences from enter- 
 ' ing into it, then it is an inadequate symbol, erring by omission 
 
 * though not by exclusion. In an absolute tautology which excludes 
 'or omits difference, identity itself disappears and the judgment 
 ' vanishes with it. 
 
 ' Therefore, ft. We can only assign a meaning to the law A is
 
 THE LAWS OF THOUGHT 253 
 
 ' A if we take the repeated A to be not a specification of the 
 ' identical content, but an abstract symbol of its identity. The 
 
 * law will then mean that, in spite of or in virtue of the differences 
 'expressed in a judgment, the content of judgment is a real 
 
 * identity, that is to say, has a pervading unity. It says that 
 ' there is such a thing as identity in difference, or in other words, 
 ' there is such a thing as general affirmation — synthesis of diffcr- 
 ' ences referred to reality — which yet is true, that is to say, does 
 
 * not interfere with (but in fact is indispensable to) identity. 
 
 ' And, y. We are only expanding what is implied in the 
 
 * allegation of real identity if we say that the law " A is A " ulti- 
 ' mately asserts the thoroughgoing unity of Reality. A significant 
 ' judgment, symbolised by " A is A " lays down for itself no reser- 
 ' vation beyond that which its own content may dictate, and 
 ' claims therefore to be true without any reserve. Its simple 
 
 * affirmation leaves no room for any discontinuity in the real 
 ' world, such that on one side of it the judgment may be true, and 
 ' on the other false. If there were such a discontinuitv, the 
 'judgment, such is the claim of the categorical affirmation — and 
 
 * all affirmation qua affirmation is at least categorical — would have 
 
 * taken note of it within its content, and would in that respect 
 
 * affirm under a reservation. But once true, always true. All 
 
 * reservations necessary to truth are included in the content. 
 
 * Reality, therefore, is one throughout. Relation to time, for 
 'example, is not involved in the fact of affirmation, but only, if 
 
 * at all, in conditions belonging to the content affirmed which 
 'depend on facts in time. Affirmation as such is unconditional, 
 
 * that is to say, is not limited by conditions outside its own content, 
 
 * and so if true, is true without reserve. There is not one Reality 
 
 * of which it is true and another of which it is false. Reality is 
 ' what it is, and if it turns out not to be what we thought, then 
 'we have judged amiss, i.e. judged falsely.' 
 
 I have omitted two footnotes which go to elucidate still further 
 the meaning of this extraordinarily significant law, and I must 
 express the gratitude of the ordinary man to the original formulator 
 of the law, that he has left us no law stated in the form A B is 
 X + Y, for humanity staggers, and imagination boggles, under 
 the contemplation of what such a law might really mean, without 
 showing a sign of such meaning on the surface. 
 
 The first criticism of the Laws that suggests itself, is that, though
 
 254 A NEW LOGIC 
 
 they are called the Laws of Thought, it is manifest and unmis- 
 takeable that they make no reference whatever to Thought. They 
 refer to Things, not to Thought. The first Law does not say 
 Whatever is thought, is thought ; it says Whatever is, is. It 
 seems beyond question, and it has certainly never been directly 
 questioned by any logician, that ' Whatever ' means ' Whatever 
 thing.' Some of the alternative expressions distinctly and 
 expressly declare that the Laws refer to things, and are Laws of 
 Things. 'A thing is identical with itself ; * Nothing can both be 
 and not be ' ; * Everything must either be or not be.' These are 
 not Laws of Thought. They make no reference to thought. They 
 are statements, not about thought, but about things. Logicians, 
 in discussing them, understand by them, sometimes statements 
 about the nature of things ; sometimes statements of the ways in 
 which we ought to think of things ; sometimes statements of the 
 way in which we must think of things ; but no meaning is long 
 adhered to. In the practical affairs of daily life, we do, no doubt, 
 especially those of us that are unaccustomed to accurate thought and 
 expression, say * This is so ' when we ought to say * This seems to 
 me to be so ' ; but I do not think the most inaccurate and slipshod 
 thinker or speaker ever uses ' This is so ' for ' This is what I ought 
 to think is so.' This extreme of inaccuracy is reserved by logicians 
 for their own use. 
 
 If the first Law of Thought means what it says — Whatever is, 
 is ; a thing is identical with itself, — then I submit, it is not a Law 
 of Thought at all, but a statement about things, the objects of 
 thought. If it means ' We ought to think ' or * We are compelled 
 to think,' that whatever is, is ; or that a thing is identical with 
 itself; then, I respectfully submit, it should be stated in which- 
 ever of these forms is intended by the jurist who states the law. 
 If ' Nothing can both be and not be,' it is difficult to see how a 
 thing which is not a Law of Thought can be a Law of Thought. 
 If ' Everything must either be or not be,' a law must either be a 
 Law of Things or not be a Law of Things. If the Laws of Thought 
 are Laws of Things, why are they not so called ? If they are 
 Laws of Thought, why do they not refer to thought ? If they are 
 Laws of both Thought and Things, why are they not so called, 
 and why do they not refer to both ? Why arc they called Laws 
 of Thought and stated as Laws of Things ? 
 
 Granting, however, any and all of the meanings that logicians
 
 THE LAWS OF THOUGHT 255 
 
 so ingeniously read into these simple statements ; and granting 
 that they arc Laws of Thought and not Laws of Things; accept- 
 ing in full every gloss that can be put upon them ; we are still, as 
 it seems to me, far from possessing any code of rules for drawing 
 inferences from postulates. The meanings that Traditional Logic 
 finds in these Laws are that we must not equivocate ; must not 
 contradict ourselves ; and must not talk nonsense ; and the import- 
 ance of observing these behests appears from the foregoing 
 discussion ; from which it appears, also, that as with other behests, 
 the mere inculcation of them does not secure their observance. 
 But though the observance of these rules will preserve us from 
 some glaring blunders; though the rules, thus interpreted, tell us 
 some things that we may not do ; they do not tell us what we 
 may do, nor how we are to do it. It is important, no doubt, to 
 know that* A is A,' if we consider it sufficiently, and in a proper 
 spirit, means all that Modern Logic discovers in it ; but even this 
 amplitude of interpretation does not help us in the task of drawing 
 inferences from postulates, unless, indeed, we read into the Law a 
 further meaning, including an entire code of Rules. It may be 
 that such a code of rules is really inherent in the deceptively 
 simple expression ' A is A,' and that the code could be extracted 
 by a sufficiently competent intelligence ; just as, according to 
 Holmes, an archangel could, by a mere gesture, convey to another 
 archangel a history of the Universe ; but it would be unfair to 
 demand such a feat from the average undergraduate, who, after all, 
 is not an archangel ; and, in order to assist him in the task of 
 drawing conclusions from postulates, and of distinguishing valid 
 from invalid inference, without the necessity of having 
 
 His cogitative faculties immersed 
 In cogibundity of cogitation, 
 
 I have ventured to formulate certain Canons of Inference, which 
 seem to me to be required, and to secure the end in view.
 
 CHAPTER XVII 
 
 THE CANONS OF INFERENCE 
 
 The unit of Logic is the proposition. The unit of Empirical 
 or Inductive Logic is the proposition derived from experience. 
 The unit of Inference or Deductive Logic is the postulated pro- 
 position, whose nature has been explained in the first Chapter. It 
 was explained in the Introduction, that there are three main forms 
 of Reasoning, in the first of which we hold fast to the facts of expe- 
 rience, and never go beyond them. We travel on the firm ground 
 of experience and never do, or never ought to, take a step, until 
 we are assured of the firm ground on which we stand. In the 
 second mode of reasoning, we put out to sea. We leave the dry 
 land of experience behind us, and sail upon the illimitable ocean 
 of postulation. All our postulates do, it is true, originate in some 
 experience or other, but in the combinations and analyses we make, 
 in the rearrangements we effect, in the transformations v/e bring 
 about, we are not influenced by experience in the least. We are 
 in the fair}* realm of imagination and fancy, with which the 
 work-a-day world of experience has no concern. 
 
 Experience teaches us the forms of men and of horses ; and as 
 long as we remain in the realm of Induction, we may make no 
 suppositions about the forms of men and horses that are not 
 warranted by experience. But when we sail on the sea of postu- 
 lation, we may, in imagination, cut off the man at the waist, cut off 
 the horse at the root of the neck, join the mutilated man to the 
 mutilated horse, and so create a centaur ; invest him with life, and 
 with any other qualities we please. We may make him — still in 
 imagination — an Archer, or a Butcher, or a Chemist, or a 
 Drunkard. We may give him a serpent for a tail, and a cuttle 
 fish for a head ; and having created these postulates, we can 
 argue from them as if they were real. If a centaur has the body 
 of a horse, then a man could ride on his back. If he has the 
 intelligence of a man, then he can reason logically, unless, 
 indeed, his mind has been vitiated by the study of Traditional 
 Logic.
 
 THE SCOPE OF INFERENCE 257 
 
 But it is not only, nor chiefly, of concrete imaginings like 
 centaurs, that the power of postulation enables us to reason. Its 
 supreme value is in the power it gives us to reason of abstractions. 
 For the purpose of argument, we may postulate lines that are 
 straight ; circles that are perfect ; rigid levers ; strings without 
 weight, and perfectly flexible ; machines without friction ; perfectly 
 elastic bodies; vacua; hypothetical vortices in an hypothetical 
 ether; asymptotes; infinitesimal quantities ; and a thousand things 
 besides. It places at our disposal the whole field of mathematical 
 physics. It allows us to speculate as to space of more or less 
 than three dimensions ; it allows us to postulate that two straight 
 lines may enclose a space ; that any two sides of a triangle are 
 equal to, or less than, the third ; that light is corpuscular or undu- 
 latory. It allows us, having granted or assumed these postulates, 
 to trace the consequences that would flow from them if they were 
 true. Whether they are in fact true or not. Deductive Reasoning 
 does not inquire. It is as easy to reason deductively from postu- 
 lates that are materially true, as from postulates that are materially 
 false ; and from those that are materially false, as from those that 
 are materially true. It is easy, and it is legitimate, to argue from 
 postulates whose truth or falsity is doubtful or unknown to us. We 
 may postulate not only what is improbable, but what is impossible ; 
 not only what is impossible, but what is inconceivable ; not only 
 what is inconceivable, but what is nonsensical ; and arguments 
 founded on any of these postulates will be sound, valid, and incon- 
 testable, if they are conducted according to rule. There is but one 
 limit to the power of postulation, and that will be indicated 
 presently. 
 
 It is improbable that an earthquake will devastate to-morrow 
 the City of London ; but it is quite legitimate to argue from 
 this postulate, and to show the widespread ruin, the dislocation 
 of finance, of commerce, of politics, that would ensue from such a 
 catastrophe, if it were to take place. In other words, we may 
 postulate, for the purpose of argument, that London will be 
 destroyed to-morrow by an earthquake ; and the validity of the 
 argument is not affected, one way or the other, by the improbability 
 of the postulate. 
 
 It is impossible for me to jump over the house ; but if I could 
 jump over it, I should come down with a tremendous thump on 
 the other side. The validity of the argument is not in the least 
 
 N.L. s
 
 25S A NEW LOGIC 
 
 affected by your denial that I could jump over the house. I dare 
 say I could not. I am not so active as I was, and I was never a 
 good jumper ; but for the purpose of argument, I can postulate 
 that I could jump over the moon ; and having assumed this 
 postulate, I can deduce the consequences that would ensue if it 
 were true. Whether it is true or not does not in the least affect 
 the validity of my argument. 
 
 Not yet have we exhausted the powers of postulation. For the 
 purpose of argument, we may postulate not only what is 
 improbable ; not only what is impossible ; but what is actually 
 inconceivable. Grant me my postulate, and I can argue of the 
 square root of minus one ; of a fourth dimension in space ; of 
 eternity, and iniinity. Grant me my postulate, and I can show 
 what would follow if two straight lines should enclose a space ; 
 if any two sides of a triangle were less than the third ; if the 
 whole were less than its part ; and it is on such postulates as 
 these that the familiar reductiones ad absuvdum of Euclid are 
 founded. 
 
 The power of postulation extends beyond the inconceivable. 
 It includes even the nonsenical. If chalk is harmonious, and what 
 is harmonious is black, then chalk is black ; and the validity of 
 the deduction is in no way diminished by the nonsensical 
 character of the postulates. Much play is made in books on 
 Logic by such nonsensical statements as that virtue is red and the 
 soul is square ; but if I choose to postulate that virtue is red or 
 that the soul is square, all the king's horses and all the king's men 
 cannot prevent me from assuming these postulates for the 
 purpose of argument. If virtue is red, and I photograph it in 
 the ordinary way, it will come out white in the photograph. If 
 the soul is square, then its sides are equal, and its angles right- 
 angles. No arguments could be more valid than these. 
 
 Not even yet are the powers of postulation exhausted. It 
 extends beyond the nonsensical to the unintelligible. I may, if 
 I please, postulate that Brillig is a slithy tove, and that any 
 slithy tove can gyre and gimble ; and from these postulates I can 
 draw the irrefragable deduction that Brillig can gyre and gimble. 
 It is no more necessary to read a specific meaning into the terms 
 used in a deductive argument, than it is necessary to read a 
 specific meaning into the terms in the equation a -\- b =^ x y. 
 We may deal with tlie terms as symbols only, and, as long as
 
 THE FIRST CANON OF INFERENCE 259 
 
 our operations are conducted seciindtim artem, their conclusion will 
 be unimpugnable. But it is evident that this unimpuj^nability 
 refers to consistency only. The assumption of a postulate can 
 never guarantee the truth of a conclusion from it ; but the correct 
 performance of deduction docs guarantee that the conclusion is 
 consistent with the postulate. This is the function, and the 
 only function, of Deduction. Its province is not to ascertain 
 truth, but to ensure consistency, and to explicate meanings that 
 are in the postulate, but that may not be immediately apparent. 
 
 I have said that there is one limitation to the power of postu- 
 lation ; and the limitation is important. We may postulate 
 what is improbable, what is impossible, what is inconceivable, 
 what is nonsenical, even what is unintelligible ; but we may 
 not postulate what is self-contradictory. We may postulate that 
 there is a whale two hundred yards long ; that wax becomes 
 harder the more it is heated ; that time is eternal and space 
 infinite ; that the soul is square and virtue red ; that Brillig is a 
 slithy tove ; but we may not postulate that an irresistible force 
 can impinge on an immoveable body ; that there is an 
 unconscious mode of consciousness ; that matter can be refined 
 into immateriality ; that a privative negative has a denotation ; 
 that an infinite series is terminable ; or that an infinitesimal 
 quantity is of appreciable magnitude. Self contradictories we 
 may not postulate; but short of what is self-contradictor}-, we 
 may postulate what we please. 
 
 The first Canon of Inference or Deduction, is, therefore, that 
 Every Inference is deduced from a postulate ; and the second is that 
 For the purpose of argument we may postulate what we please, saving 
 only self-contradictories. 
 
 It is curious that no logician but Sir William Hamilton seems 
 to have had any inkling of this doctrine ; and it is more curious 
 that though Hamilton stumbled on it, he thought it applied to 
 Induction. But then Hamilton, like all other logicians, 
 considered that Induction was arrived at by means of the 
 syllogism, and his statement of the doctrine occurs in his treat- 
 ment of what he calls the Inductive Syllogism ; a creature that 
 in my opinion has no existence except in the imaginations of 
 misguided logicians. ' The logician,' he says, ' has a right to 
 suppose any material impossibility, any material falsity ; he takes 
 no account of what is objectively impossible or false, and has a 
 
 s 2
 
 26o A NEW LOGIC 
 
 right to assume what premisses he pleases, provided they do not 
 involve a contradiction in terms.' This is precisely the doctrine 
 that I advocate with respect to Deduction ; and for Deduction 
 it seems to me indisputably true ; but how Hamilton could have 
 supposed that it is applicable to Induction, or that it is possible 
 to derive a materially true conclusion from a premiss that is 
 materially false, passes my comprehension, and corroborates my 
 opinion that no doctrine is too extraordinary for a logician to 
 entertain. If any doctrine could involve a contradiction in terms, 
 I should have thought that this did. If, however, we separate it 
 from Induction, and apply it to Deduction, it expresses what I 
 believe is the exact truth. 
 
 If Hamilton's doctrine, as applied to Induction, is strange, it 
 is not stranger than that of some of his commentators. One of 
 these says that Hamilton's doctrine, quoted above, 'does not leave 
 it at all clear that logic — thus regarded — has any value whatever.' 
 If this were said of Hamilton's doctrine as applied to Inductive 
 Logic only, I should agree with it ; but it manifestly refers to the 
 whole of logic. Is there, then, no use in the Infinitesimal Calculus, 
 in Mathematical Physics, in Higher Mathematics generally, in the 
 reduciio ad absiirdtim ? It is true that mathematical reasonings 
 are excluded by logicians from the realm of Logic, or, if not 
 formally excluded, are by common consent ignored ; but this is 
 only another instance of the inefficiency of Logic as hitherto 
 understood. Mathematical reasoning is reasoning, and a science 
 which purports to expound the nature of reasoning must include 
 mathematical reasoning, or stand convicted of inefficiency. 
 
 Some adumbration of this doctrine seems to have been in the 
 minds of those logicians of whom Hamilton, again, is the most 
 conspicuous, who have applied the term * Formal ' to Logic. If it 
 is possible, as I have just contended, to argue from postulates 
 that are not merely impossible and inconceivable, but nonsensical 
 and unintelligible, I do not see how it can be denied, that the 
 latter, at any rate, are purely formal ; and, since the mode of 
 argument is the same in all, if it is formal in one, it is formal in 
 all. That all Logic is formal, I should strenuously deny ; but 
 that Deductive Logic is formal, cannot, in my view, be contested. 
 Those logicians who, like Thomson, confess that they do not 
 understand the distinction between material and formal, are out 
 of this argument ; and most of those who deny that Logic is a
 
 THE FIRST CANON OF INFERENCE 261 
 
 formal science do so, rightly as far as they go, by adducing 
 material reasoning in contradiction. Bain alone, as far as I know, 
 denies that Deduction is purely formal ; and the controversy is 
 not important enough to warrant a long digression to examine 
 his arguments. In my view, Deductive Logic is purely formal on 
 this ground and in this sense — that it consists solely in casting the 
 matter of the posulate into different forms. The postulate gives 
 us the matter in one form, and the task — the sole task — of 
 Deduction, is to convert the postulate, or part of it, into another 
 form, and to ensure that the two forms are consistent with each 
 other. 
 
 The doctrine here advocated casts light upon the contention 
 of Modern Logic, that every proposition refers to Reality. * All 
 propositions necessarily imply the existence of their subjects in 
 the appropriate sphere.' To this I can assent, if among the appro- 
 priate spheres is included the sphere of postulation. But when it 
 is said that In every judgement I assert a meaning, and assert that 
 meaning of ' Reality,' I must differ on more than one ground. In 
 the first place, many of the 'judgements ' of Modern Logic, if they 
 do indeed assert a meaning, do not convey any meaning to their 
 readers ; and in the second, any reference to Reality in Deductive 
 Logic is out of place, irrelevant, and confusing. The subject is 
 postulated, if as real at all, as real for the purpose of the argument 
 only. Whether it is or is not real in a more absolute and more 
 correct sense, is a matter with which the Logic of Consistency is 
 not concerned. 
 
 According to the Law of the Excluded Middle ; chalk is either 
 harmonious, or is not harmonious, and no third alternative is 
 possible ; but if, and as far as, Logic deals with Real existence, 
 there is a third alternative — that neither is true, for both are 
 nonsense. The Logic of Deduction, however, does not admit 
 the third alternative. It declares that, for the purpose of 
 argument, we may postulate what we please ; and that if chalk 
 is harmonious, and what is harmonious is black, then chalk is 
 black. Refuse to admit the postulates, and still the argument is 
 not invalid. It merely does not exist. There is then no argu- 
 ment. All Inference proceeds upon assumption, and cannot 
 begin until its postulates are granted ; but grant it its postulates, 
 and it can argue of anything. 
 
 It seems manifest that we may, if we please, interpret the first
 
 262 A NEW LOGIC 
 
 of the so-called Laws of Thought — whatever is, is — to mean what- 
 ever is postulated for the purpose of argument may form the 
 ground of argument ; and thus we may read the second Canon of 
 Inference into the first ' Law of Thought.' 
 
 Since all Inference is based on postulation, the argument, once 
 begun, must proceed on the basis of the postulate, and on no 
 other assumption ; and this gives us two more Canons of 
 Deduction ; the first of which is that A postulate, once granted, 
 viiist not be zuithdrawn nor ignored in the course of the argument. 
 The argument must proceed throughout on the basis of the 
 postulate. 
 
 The argument that if centaurs existed, they would make 
 splendid cavalry, cannot be controverted by denying that centaurs 
 exist. The postulate may be denied, but not in the course of the 
 argument. If it is questioned, it must be questioned before the 
 argument begins ; but having once been allowed or assumed, it 
 must not be denied in the course of the argument. If Consols 
 fell to 84, the cause, I say, was this or that, and you may contro- 
 vert my argument by any reasoning you please, but you may not 
 controvert it by denying that Consols did so fall. That is outside 
 the argument. That must be settled, if it is settled at all, before 
 the argument begins. If you question the postulate, you must 
 do so at the outset ; you may not postpone your objection until 
 the argument has led to a conclusion distasteful to you. To deny 
 the postulate does not invalidate the argument ; it renders argu- 
 ment on that basis impossible. I may argue that if women have 
 votes, they will involve the country in war, and you may seek to 
 refute my argument by any means that commend themselves to 
 you, even by breaking my windows, or chaining yourself to my 
 chairs and tables ; but you do not refute the argument by denying 
 that women will have votes. 
 
 Not only may the postulate not be denied : it must not be 
 ignored. The argument must proceed on the basis of the 
 postulate, and on that alone. I say that if centaurs existed, they 
 would make splendid cavalry, and you do not refute my argument 
 by saying that the horses of the other cavalry would be frightened 
 by them, or that they would need very large tents. Such state- 
 ments do not proceed on the basis of the postulate. They ignore 
 it. If Consols fell to 84, I say the cause was this or that ; and
 
 THE SECOND CANON OF INFERENCE 263 
 
 you do not refute my argument by saying that it was a good 
 opportunity to pick them up cheap. That is beside the question. 
 It ignores the postulate. I say that if women had votes, they 
 would involve the country in war ; and it is no counter argument 
 to say that they would never vote for any war that was not just. 
 This deserts the basis of the postulate. It is outside the argument. 
 It ignores the postulate. 
 
 With a little ingenuity, this Canon can be read into the second 
 Law of Thought. ' Nothing can both be and not be ' may be held 
 to mean that we must not or cannot assent to two propositions 
 that are inconsistent with each other. If this is made as a state- 
 ment of reality, it is certainly not true ; for many pairs of beliefs, 
 held in common by multitudes, are inconsistent. Multitudes who 
 hold that the country has a surplus of population, which is bad 
 for the country, are appalled at the declining birth-rate, and hold 
 that this also is bad for the country. If, however, it is held to 
 mean that we cannot assent to two propositions when we believe 
 them to be inconsistent with each other, then this Law of Thought 
 has a meaning, and a true meaning. To argue on the basis of a 
 postulate, and to deny the postulate, or to ignore it, is to hold two 
 inconsistent positions at once. 
 
 The remaining Law of Thought — the Law of the Excluded 
 Middle — asserts that everything must cither be or not be. We 
 may, perhaps, interpret this to mean that a postulate must be 
 either granted or refused, and that we must argue deductively on 
 the basis of a postulate or not at all. If this seems a free render- 
 ing of the Law, I can only put forward in excuse that free 
 renderings of the Laws of Thought arc the rule in Logic, and, 
 moreover, if these interpretations of the Laws are not admitted, I 
 can do very well without them. 
 
 So far, the Traditional Laws of Thought, if interpreted in 
 these senses, do express real conditions that are necessary for 
 Inference ; but they do not by any means express all the con- 
 ditions that are necessary, nor can they, by any artifice, be made 
 to express them all. There are two other Canons that are 
 necessary if Deductions are to be valid, or if they are to be made 
 at all ; and these are of as much value and as great cogency, 
 they are as indispensable, as those already stated. If the first of 
 the new Canons is violated. Inference is invalid ; unless the 
 second is admitted, Inference is impossible. The first Canon is
 
 264 A NEW LOGIC 
 
 stated by Hamilton, but no subsequent writer, except Prof. Carveth 
 Read, has recognised its importance sufficiently to repeat it or 
 adopt it ; and the second, though it has been tacitly assumed, or 
 no inference could ever have been made, has not, as far as I know, 
 been formulated by any logician. The omission of both these 
 Canons from every text book is one of the most surprising things 
 in Logic, fertile as Logic is in surprises. 
 
 The Fourth Canon of Inference is: Nothing may he assumed that 
 is not in the postulate. This is, of course, a corollary from the rule 
 that the argument must proceed on the basis of the postulate, 
 but it is expedient to divide this rule into two, and the fourth 
 Canon is its second implication. According to this Canon, we 
 may not go outside our premisses ; we may not go beyond the 
 evidence ; we may advance nothing that is not in our brief. 
 Grant me the postulate that his evidence was false, and I may 
 rightly infer that it was calculated to mislead the jury ; but I may 
 not infer, from this postulate alone, that he committed perjury. 
 To draw that conclusion, I must have the further postulate that 
 he knew his evidence was false. Granted that he was found dead ; 
 but I may not conclude, from this postulate alone, that he was 
 murdered, or that he committed suicide. Postulate that logicians 
 have stated three Laws of Thought, but we may not conclude, 
 from this postulate alone, that they have stated all the conditions 
 necessary to valid inference. Postulate that drink can cause 
 insanity, yet we may not conclude, from this postulate alone, that 
 his insanity was due to drink. Granted that Inductive Logic 
 must take account of the matter of which it treats ; it does not 
 follow that Deductive Logic is not a Logic of pure form. 
 
 No Canon of Inference is more important than this, for it is in 
 the breach of this Canon that most of the recognised fallacies of 
 Inference consist. It is the violation of this Canon that consti- 
 tutes all the formal fallacies of Traditional Logic, and many 
 other fallacies that that Logic does not recognise. 
 
 If there are degrees of importance in the Canons of Inference, 
 then the Fifth Canon is the most important of all, for it and it 
 alone renders inference possible ; it alone allows inferences to be 
 deduced, and all deduction is based directly upon it. It is this: 
 When a postulate is granted, all its implications are granted. The 
 other Canons state the conditions of Inference. The fifth Canon 
 shows the mode or method of Inference. It tells us what inferences
 
 THE FIFTH CANON OF INFERENCE 265 
 
 are, and how they are effected. This Canon will presently be 
 expanded into a series of Lemmas, which constitute the practical 
 rules that regulate the process of Inference. What the implica- 
 tions of a postulate are, and how they may be deduced from it, 
 will form the subject of the following chapters ; at present we are 
 to notice that every postulated proposition contains implications, 
 and that, when it is assumed or postulated, all its implications are 
 assumed or postulated along with it. 
 
 What is meant by an implication of a proposition has already 
 been explained in the last chapter. An implication of a proposition 
 is another way of stating the matter of the proposition, or of 
 a part of it ; and from the discussion in the present chapter it 
 follows that every inference, like the proposition from which it is 
 extracted, must be hypothetical. The process of inference is the 
 extraction or explication of some implication or meaning latent 
 in the proposition that is postulated for the purpose of the argu- 
 ment. We cannot begin to draw an inference until its premisses 
 are postulated. If this doctrine is correct, and if the Canons of 
 Inference here stated are sound and valid, then any doubt remain- 
 ing of the existence of the pctitio principii, said to be inherent in 
 every syllogism, is laid at rest. If the conclusion contains any- 
 thing that is not postulated in the premisses, the fourth Canon is 
 violated and the argument is unsound. In another sense oi petitio 
 principii— iov this, like every other cardinal term of Traditional 
 Logic, is ambiguous — the whole basis of Inference is that very 
 begging of the principiuni, or major premiss, that is in question. 
 Unless the premisses are assumed or begged for the purpose of the 
 argument, argument cannot proceed. State your syllogism. 'All 
 men are mortal ' — Stop there ! I deny your major. There are 
 cases to the contrary — Enoch, Elijah, Struldbrugs. Until this 
 preliminary difficulty is settled, you cannot proceed with your 
 argument. You are arrested at the outset, and cannot go on. 
 But put your premiss in the form ' If all men are mortal,' and you 
 disarm me. I am powerless now, and cannot hinder you. If all 
 men are mortal, and Socrates is a man, then, indeed, Socrates is 
 mortal ; and however I may deplore the prospect before him, I 
 have neither hope nor comfort to offer. But now you have 
 begged your pri^icipium ; and it is on this very pctitio principii that 
 the whole validity of your inference rests. The conclusion rests en- 
 tirely on the validity of the premiss ; and this premiss is postulated
 
 266 A NEW LOGIC 
 
 or begged for the purpose of the argument. I can demand the 
 warrant for your postulate, but I cannot do so as a Deductive 
 logician. As a mere deducer you are safe. I am powerless to 
 question the validity of your inference as an inference. Before I 
 have any right to demand the grounds or justification of your 
 principium, I must leave the domain of Inference, and enter 
 another realm. The Logic of Inference can no more question its 
 own premisses than a man can wheel himself along in a wheel- 
 barrow, or lift himself up in a basket. As long as the Deductive 
 logician is content to argue on an admitted assumption or 
 postulated premiss, he sails on the calm waters of Inference ; but 
 the moment he attempts to show a conclusion that is not already 
 begged in his principium, he strikes on a rock. He is now trying 
 to sail on dry land. He may, indeed, be on firm ground, but 
 firm ground is the last thing a ship desires to meet with. This 
 discussion on the peiitio principii, inherent in every syllogism, will 
 be resumed in the chapter on the syllogism.
 
 CHAPTER XVIII 
 
 immediate inference 
 The Implications of Simple Propositions. 
 
 The implications of Simple Propositions arc known in 
 Traditional Logic as Immediate Inferences ; but in this field, as 
 in others already examined, the narrow and conventional 
 boundaries of Traditional Logic are broken down by the New 
 Logic here expounded, and the field is indefinitely enlarged. The 
 two Quantities of Traditional Logic have been found to be the 
 meagre representatives of very many that are in actual use. 
 The two Negatives of Traditional Logic are the attenuated 
 remnant of scores of negatives that can be constructed, and are in 
 daily use. The Immediate Inferences of Traditional Logic are 
 three or four — the Converse, the Obverse, the Contrapositive, and 
 to these some add the Inverse ; the implications of simple propo- 
 sitions, derivable by the method of Explication here expounded, 
 are indefinitely multitudinous. 
 
 The general Canons of Inference are laid down in the last 
 chapter ; and, in accordance with them all inferences ought to be 
 made, and all valid inferences are made ; moreover, when a fallacy 
 in Inference is perpetrated, its perpetration is due to the breach of 
 one of these Canons ; but in order to discover what inferences may 
 be drawn from propositions, and how they are to be extracted, we 
 need guidance more specific than these Canons afford. The whole 
 scope of Inference, or Deduction, is indicated by the fifth Canon, 
 which asserts that when a proposition is granted, all its implica- 
 tions are granted with it. Since the implications are merely other 
 ways of stating the proposition, or part of it, this is self-evident ; 
 but this Canon does not give us any indication of what the 
 implications are, or of the ways in which they may be extracted 
 from the postulate. For these purposes we require further rules, 
 or further licences ; and these rules or licences are not the same 
 for all classes of propositions ; or rather, the Canons of Explica- 
 tion, as we may call them, that suffice for the extraction of the
 
 268 A NEW LOGIC 
 
 implications of Simple propositions, need the addition of others to 
 enable us to extract all the implications that are contained in 
 Compound propositions. In this chapter, we are concerned with 
 Simple propositions only, and the Canons for their explication 
 may be stated, as Lemmas to the fifth Canon of Inference, as 
 follows : — 
 
 The Canons of Explication of Simple Propositions. 
 
 Every postulated proposition implies 
 
 1. Ever}- equivalent and included proposition. 
 
 2. Ever}' condition necessary to the postulate. 
 
 3. The denial of every proposition inconsistent with the 
 
 postulate. 
 
 I. Every postulated proposition implies every equivalent and included 
 proposition. 
 
 Of these equivalent or included propositions there are three 
 varieties ; and to enable us to extract them all, we require three 
 Minor Canons of Explication, as follows: — 
 
 A. Every postulated proposition implies its reciprocal. 
 
 The proposition expresses, as we have already found, a relation 
 between two terms. The first Minor Canon of Explication declares 
 that ever}' relation implies a reciprocal relation ; — that whatever 
 relation the Object holds towards the Subject, is reciprocated by 
 the Subject towards the Object. If A is the father of B, then B 
 is reciprocally the child of A. If A is above B, then B is recipro- 
 cally below A. If A strikes and kills B, then B reciprocally is 
 struck and killed by A. If A includes, or is included in, B, then 
 B reciprocally is included in, or includes A. If A is an attribute 
 of B, then B reciprocally possesses the attribute A. 
 
 Traditional Logic knows nothing of the reciprocal proposition, 
 or of the reciprocity of terms. I know of no exponent of Logic 
 except Prof. Carveth Read, who makes any allusion to reciprocity, 
 or even mentions the reciprocal proposition ; and Prof. Carveth 
 Read attaches no great importance to it, and merely mentions it. 
 In place of the reciprocal. Traditional Logic offers us the converse, 
 which is a conventional and unnatural implication, which no 
 one but a logician would think of extracting from a proposition ; 
 which is never, in fact, used in argument outside of books on 
 Logic ; which cannot be extracted from any proposition but those
 
 THE RECIPROCAL 269 
 
 expressed by the copula ; and which cannot be extracted from 
 many of them without wresting and distorting their true meaning. 
 Even within this hmited class of propositions, conversion can be 
 applied to but one of the two pairs of relations that are, according 
 to Traditional Logic, expressed by the copula. It is applicable to 
 the relation of class inclusion and class exclusion only, and cannot 
 be applied to attribution. 
 
 Of the four meanings which alone are admitted by Traditional 
 Logic to be expressed by a logical proposition, it is agreed that one 
 is usually intended. It is generally agreed, by the exponents of 
 Traditional Logic, that the Subject is to be understood in exten- 
 sion, the Object in intention, — the Subject in denotation, the 
 Object in connotation — the Subject is a thing or class of things, 
 the Object a quality or attribute which is predicated of that thing 
 or of the things in that class. This is the meaning that the 
 exponents of Traditional Logic unanimously agree is to be under- 
 stood by the logical proposition. Yet when, in the next chapter, 
 they treat of the conversion of propositions, logicians ignore this 
 signification altogether, and substitute another. The proposition 
 which predicates a quality of a thing or of things in a class, is 
 never converted as if it had that meaning, but always as if it pre- 
 dicated inclusion or exclusion of things in a class. ' All trees are 
 tall ' expresses, according to the accepted convention of Logic, 
 * All things in the class of trees have the quality of tallness.' 
 It is possible, indeed, that it may have one of the other three 
 meanings ; but this is the meaning that is usually to be read 
 into it. But when they convert the proposition, do logicians 
 make the converse ' Tallness is an attribute of all trees ? ' 
 Never. The converse they construct is invariably ' Some tall 
 things are trees.' Why the meaning, which is said to be expressed 
 by a proposition, is always dropped, and replaced by a different 
 meaning when the proposition is to be converted, is not stated by 
 the text books, whose writers do not appear to be alive to their 
 own inconsistency ; but the reason is, no doubt, that the sense of 
 class inclusion is necessary to the propositions of the syllogism. 
 
 The converse of Traditional Logic is no easier — it is not so 
 easy — to construct as the reciprocal. The relation the converse 
 expresses is felt to be artificial and unnatural. It is, moreover, 
 inaccurate. If all trees are tall, that is, if all trees have the attri- 
 bute of tallness ; then that tallness is an attribute of all trees, is a
 
 270 A NEW LOGIC 
 
 natural, a complete, and an accurate converse, or reciprocal. The 
 terms arc identical ; the relation is reciprocal. Everything 
 expressed in the convertend is in the converse. There is nothing 
 in the converse that is not in the convertend. But if we convert 
 ' All trees are tall ' into ' Some tall things are trees,' the first 
 impression made on the unaccustomed mind is that this is a very 
 unnatural and artificial inference. It isonethat no one unacquainted 
 with the peculiar conventions of Traditional Logic would ever 
 think of. The convertend says nothing, and suggests nothing, 
 about ' Some tall things.' The term is an importation. It is a 
 violent wrenching of the meaning. It threatens, if it does not 
 actually invade, the integrity of the fourth Canon of Inference, 
 which forbids us to assume anything that is not in the postulate. 
 The term is dragged in neck and heels, and is stuffed into 
 a position for which it is palpably unfit. Moreover, the conver- 
 tend says * All trees are tall,' but the converse says nothing of all 
 trees. Nothing in Traditional Logic is more settled, about 
 nothing are the warnings of Traditional Logic more emphatic, 
 than that the predicate of an affirmative proposition is undistri- 
 buted. If we reconvert our converse, what do we get ? * Some 
 tall things are trees ' yields the converse * Some trees are tall 
 things,' so conveying the suggestion that some trees are not tall 
 things, which is contradictory of the original postulate ; and 
 transmogrifies the original attributive predicate into a class 
 predicate, which is contradictory of the logical doctrine that the 
 predicate is to be understood in intention. Traditional Logic 
 would, no doubt, deny that * some ' suggests * not all,' and would 
 refer to the conventional meaning ' some at least,' to which it 
 attempts to limit the 'some' of ordinary discourse ; but if Logic 
 is to be generally applicable to the reasonings of daily life, and 
 is not to be restricted to a few conventional forms, it must not 
 thus arbitrarily restrict the meanings of words in common use ; and 
 if it is to be a purely technical science and art, restricted to a few 
 artificial conventions, its claim to general usefulness must be 
 abandoned. If we adhere, as I submit we ought in this case 
 to adhere, to the connotative or attributive value of the predicate, 
 which is indicated as plainly as possible by the adjective ' tall,' 
 we get the reciprocal, ' Tallness is an attribute of all trees.' This 
 is, in the first place, natural. It commends itself to us at once, 
 as a manifest implication of the postulate. In the second place,
 
 THE CONVERSE 271 
 
 it is accurate. If the convertend expresses, as logicians tell us it 
 does, the relation of attribute to substance, then the converse 
 should express, as this does, the relation of substance to attribute. 
 In the third place, it is complete and ample. Whatever the con- 
 vertend says of all trees and of tallness, the reciprocal says of 
 tallness and of all trees. If the proposition is reconverted, it 
 reappears in the exact form of the original. 
 
 In a comprehensive and authoritative text book on Logic, the 
 converse of ' Every old man has been a boy ' is said to be ' Some 
 who have been boys are old men.' It will be noted that, in the 
 first place, the quantity of both terms has been altered ; a pro- 
 ceeding that I regard as doubly inadmissible, and one that strikes 
 us as strange from an exponent of Traditional Logic, which 
 requires such punctilious accuracy with respect to quantity. In 
 the second place, the converse conveys, not the same meaning as 
 the convertend, but a very different meaning. ' Every old man 
 has been a boy ' excludes entirely the possibility that any old man 
 could have been a girl. But ' Some who have been boys are old 
 men ' does not exclude, nay, it distinctly suggests, the possibility 
 that others who have been girls are old men. From the conver- 
 tend we can get the obverse, ' No old man has been a girl,' but 
 from the converse we cannot obtain this negative. If the implica- 
 tions of the converse are not the same as those of the convertend, 
 the meanings of converse and convertend cannot be the same ; and 
 in this case, they are plainly not the same. The true converse, or 
 reciprocal, should express exactly what is in the convertend, 
 neither more nor less ; and the terms should remain precisely the 
 same. It is not allowable to alter them in quantity, as Traditional 
 Logic does, neither is it permissible to alter an abstract term into 
 a concrete, as this Logic constantly does. The true reciprocal 
 of ' Every old man has been a boy,' is * A boy is what every old 
 man has been.' In this reciprocal, the terms are identical with 
 the terms of the postulate : the Subject is become Object, and the 
 Object, Subject, without alteration of either ; and the Ratio alone 
 is changed into its reciprocal. These are the only alterations. 
 The meaning of the proposition remains precisely the same. It 
 is not extended : it is not contracted : it is not modified. 
 
 The text books do not all give the same rules for the conversion 
 of propositions, and some of them give two rules only, which, by 
 themselves, are manifestly insufficient, for they are both negative,
 
 272 A NEW LOGIC 
 
 and telling us only what we must avoid, they say nothing of the 
 way the thing is to be done. The first rule is that the quality of 
 the proposition must not be changed ; the second is that no 
 term that is undistributed in the convertend, must be distributed 
 in the converse. Both rules are faulty. There are propositions 
 that cannot be converted without altering the quality ; and it is 
 not enough to prohibit an extension of distribution of a term. The 
 term must not only remain unincreased in quantity : it must remain 
 unaltered in any respect whatever except in case, and in one other 
 respect. And these rules omit altogether to state that the terms 
 are to be transposed. 
 
 Adding this condition, however, the whole scheme is radically 
 wrong. It gives us, at best, the very imperfect form of converse 
 that has already been examined. To many propositions it gives 
 us no converse at all, or no reasonable or correct converse. It 
 may give us a converse that is nonsensical. It is incapable of 
 giving a converse of the O proposition, which, by a correct method, 
 is as easily convertible as any other. The reciprocal relation is 
 open to none of these objections. It gives us in every case, with- 
 out difficulty, and without altering the sense, a true, accurate, 
 intelligible reciprocal, that cannot be mistaken for anything else. 
 Moreover, this transformation is effected by a single very simple 
 rule : — Transpose the terms without any alteration except what 
 necessarily follows from the transposition, and change the Ratio 
 into its reciprocal. 
 
 There are two alterations of terms which necessarily follow from 
 their mere transposition ; and when either of these alterations is 
 consequential on the transposition, that alteration must, of course, 
 be made; but no other alteration of a term is permissible. If 
 either Subject or Object is inflected, its case must be altered 
 when it is transposed; and if the Object is an attribute, it must 
 of course be converted into an abstract before it can stand as 
 Subject. 
 
 There are many propositions that admit of no converse, or of no 
 correct converse, by the Traditional plan of conversion. In no text 
 book of Logic known to me is any attempt made to convert a pro- 
 position constituted by an intransitive verb. As far as conversion 
 is concerned, intransitive verbs do not exist for Traditional Logic. 
 How to convert He fell. He dances, It rains, and so forth, Tradi- 
 tional Logic does not tell us, and does not appear to know.
 
 CONVERSE AND RECIPROCAL 273 
 
 ' He fell.' How is this proposition to be converted by the rules of 
 Traditional Logic ? First we must, by hook or by crook, intro- 
 duce the copula. A proposition that has no copula is inconvertible. 
 That the relation that the proposition expresses cannot be expressed 
 by the copula, is a matter to which Traditional Logic is indifferent. 
 If it cannot be so expressed, so much the worse for the relation. 
 The mnndate of Traditional Logic is simple: — Alter it into one 
 that can. Never mind that in so doing you alter the sense of the 
 proposition. Traditional Logic is not concerned with sense. 
 Get the copula in somehow. Rent. Si possis, rede; sed rem. 
 
 ' He fell ' must therefore be altered into ' He was a person who 
 fell,* or ' He is a person who fell.' Convert this according to 
 logical rule, and we get * A person who fell was he.' This is not 
 the converse of * He fell.' ' He fell ' tells us what he experienced 
 — what he underwent. The converse should tell us what was 
 experienced or undergone by him. It does not. ' A person who 
 fell was he ' tells us, not what he experienced or underwent, but 
 who a person who fell was. This is not what we want. The 
 true converse or reciprocal of * He fell,* which is short for * He 
 experienced falling,' is * Falling was experienced by him.' 
 
 Similarly, ' He danced ' cannot be converted, on the plan of 
 Traditional Logic, until it is transformed into ' He was a person 
 who danced ' ; that is to say, until a statement of historical fact is 
 changed into a definition or description. Then it is converted into 
 
 * A person who danced was he.' But ' He danced ' is not the 
 abbreviation of ' He was a person who danced.' The abbreviation 
 of this proposition is * He was a dancer,' and it is of this proposi- 
 tion that * A person who danced was he ' is a converse. * He 
 danced ' and ' He was a dancer ' have very different meanings ; 
 and their respective converses must have very different meanings 
 also. ' He danced ' is short for ' He performed the act of 
 dancing'; and the converse, or rather, the reciprocal, of this is 
 ' The act of dancing was performed by him,' or colloquially, 
 
 * Dancing was what he did.' 
 
 In order to convert * You shall have jam for tea ' by the method 
 of Traditional Logic, we must first transform it into ' You are a 
 person who shall have jam for tea,' and the converse will then be 
 ' A person who shall have jam for tea is you,* a proposition which 
 logicians are welcome to keep for their own use and delectation. 
 But if we look at the relation the proposition expresses, and find 
 
 N.L. T
 
 274 A NEW LOGIC 
 
 the reciprocal of that relation, its conversion into a rational propo- 
 sition becomes easy enough. The words ' for tea ' are a qualitica- 
 tion of the Ratio, and in logical order, the proposition is, ' You — 
 shall have for tea — ^jam.' The literal reciprocal is 'Jam shall be 
 had for tea by you ' ; but in common discourse, we do not express 
 ourselves with this pedantic exactitude, and the colloquial 
 reciprocal is ' Jam is what you shall have for tea.' 
 
 ' Anything but water is wholesome to drink ' becomes, by 
 logical conversion, ' Something wholesome to drink is anything 
 but water,' which is not English, and is scarcely sense. The 
 reciprocal is ' Wholesomeness to drink is found in anything but 
 water ' ; which is both good English and good sense. 
 
 The logical rule, that the quality of the proposition must not be 
 changed in conversion, is unnecessary, and would prevent us from 
 effecting some conversions that otherwise are possible. ' Nothing 
 is as painful as humiliation ' becomes, by the conversion of Tra- 
 ditional Logic, * Somethmg as painful as humiliation is nothing,' 
 which is ver}' like a contradiction in terms. The true reciprocal 
 is, of course, ' Humiliation is more painful than anything (else).' 
 In order to get the true reciprocal, we must violate the practice 
 of Traditional Logic, and look behind the words, to the sense that 
 they express ; we must violate its rule, and change the quality of 
 the proposition. 
 
 It is unanimously asserted by the text books that the O 
 proposition — the Particular Negative — Some A is not B — is 
 inconvertible ; and so it is by their mechanical process, which 
 looks to the words only, and takes no account of the sense. But 
 if we go behind the words, and pay regard to the sense that the 
 words express, it is convertible easily enough. The impossibility 
 is like the chalk lines that hypnotisers draw upon the floor, and 
 persuade their victims are insurmountable barriers. If ' Some 
 men are not honest,' then it is true enough that we cannot convert 
 this, according to logical rule, into * Some honest beings are not 
 men,' or, if we do, we shall make a material mistake. But this 
 inability arises from nothing inherent in the Particular Negative, 
 but from the application to it of a vicious method. It arises from 
 pretending that the negative proposition must express a relation 
 of class exclusion ; which it may not, and, according to logicians 
 themselves, it usually does not. If we take it, as they tell us it 
 ought to be taken, as expressing non-attribution, it is convertible
 
 THE SECOND MINOR CANON 275 
 
 easily enough. The reciprocal then if? ' Honesty is a quahty 
 which some men do not possess,' or ' Honesty is not a quahty 
 of some men.' 
 
 The reciprocal is but one of those implications of Simple 
 propositions that are called, in Traditional Logic, Immediate 
 Inferences. We have seen that every postulated proposition 
 implies every proposition that is equivalent to it, or is included 
 in it. Of those that are equivalent, the reciprocal is one. There 
 are others, however, and these are now to be considered. 
 
 B. The second Minor Canon of Explication states that Every 
 postulated proposition implies every proposition in which the Ratio of 
 the postulate is replaced by a Ratio that is, for the purpose of the 
 argument, equivalent to, included in, or implied in, the postulated 
 Ratio. 
 
 In other words, if a proposition can be expressed differently, by 
 the use of a different Ratio, without enlarging the meaning of the 
 proposition, it may be so expressed ; and such expression is a 
 legitimate Immediate Inference from the proposition. Every 
 Inference is another way of expressing the postulate, or part of 
 the postulate ; and if the Ratio is susceptible of being expressed 
 otherwise than it is expressed in the postulate, it may be so 
 expressed, and the expression is a valid inference. 
 
 If Brutus murdered Caesar, then Brutus wilfully and feloniously 
 killed and slew Caesar ; Brutus killed Caesar of malice aforethought ; 
 Brutus, being prompted and instigated by the devil, and not 
 having the fear of God before his eyes, did wilfully, maliciously, 
 and feloniously, kill and slay Caesar, against the Peace of our 
 Lord the King, his crown, and his dignity. These substituted 
 Ratios are equivalent to the postulated Ratio * murdered,' and may 
 therefore replace this Ratio in the proposition, and the Immediate 
 Inferences are valid. 
 
 If there is no balm in Gilead, then we may legitimatel}' infer 
 that balm is absent from Gilead ; that balm does not exist in 
 Gilead. If men like flattery, they are pleased by flattery ; they 
 are gratified by flattery ; they welcome flattery ; they would rather 
 be flattered than not. 
 
 These Ratios are equivalent, severally, to the Ratios they 
 replace ; but an inference is legitimate when the substituted 
 Ratio is not equivalent, if only it is included in, or implied in 
 
 T 2
 
 276 A NEW LOGIC 
 
 the postulated Ratio. If Brutus murdered Csesar, then Brutus 
 killed Ca?5ar, for killing is included in murder ; but of course the 
 converse is not true. We cannot infer from Brutus killed Caesar 
 to Brutus murdered Caesar, for murder is not, for the purpose of 
 the argument, equivalent to, nor included, nor implied in killing. 
 
 If there is no balm in Gilead, then we may legitimately infer 
 that balm cannot be extracted out of Gilead ; and that there is 
 no use in going to Gilead to get balm ; for these are implied in the 
 postulate, though they are not equivalent to the postulate. 
 
 These inferences are manifestly legitimate and valid. They 
 commend themselves to the hearer, and carry their validity on 
 the face of them. They cannot be doubted nor questioned ; but 
 they cannot be reached by any of the processes of Inference, 
 Immediate or Mediate, of Traditional Logic. That they are not 
 Immediate Inferences is manifest. They are neither converses, 
 obverses, contrapositives, nor inverses, and these are the only 
 Immediate Inferences of Traditional Logic. Neither can they 
 be reached through the syllogism. We might, indeed, construct 
 a quasi-syllogism that would give us the conclusion. We might 
 say : 
 
 All the persons that a man murders, he kills ; 
 
 Brutus murdered Caesar ; 
 . • . Brutus killed Cassar. 
 
 Whether logicians would admit this to be a valid argument, I 
 do not know ; but it is certainly not a syllogism. The proposi- 
 tions are not logical propositions, and are incapable of entering 
 into a syllogism, for they contain no copula. There are four terms, 
 and a syllogism cannot be constructed with more than three ; 
 and there is no middle term. A nearer approach to a syllogism 
 on the subject must be constructed somewhat in this way : — 
 
 The person who murdered Caesar was the person who killed 
 
 Caesar, 
 Brutus was the person who murdered Cassar ; 
 .*. Brutus was the person who killed Caesar. 
 
 This is not a syllogism ; at any rate some logicians would refuse 
 to recognise it, for the middle term is singular. 
 
 This is the nearest we can get ; but even this does not give us 
 our conclusion in its proper form. It gives us that Brutus was
 
 THE THIRD MINOR CANON 277 
 
 the person who killed Caesar, but it does not give us that Brutus 
 killed Csesar. What we want to know is not what sort of a 
 person Brutus was, but what Brutus did to Caesar. Waiving 
 this objection, however, is this the course of thought that the 
 mind goes through, in inferring, from Brutus murdered Caesar, 
 that Brutus killed Caesar ? I say with confidence that it is not. 
 The transaction in the mind is the intuitive realisation that killing 
 is, for the purpose of the argument, included in murder ; and that 
 if murder was done, killing must have been done. The mental 
 transaction is not a syllogistic process, but the substitution of one 
 ratio for another which is seen to include it. 
 
 If it stinks, it smells bad; if it is pouring in torrents, it is 
 raining ; if he is driving recklessly, he is driving without proper 
 care; if he battered it to pieces, he broke it; if he jumped down 
 from the window, he took the shortest way to the ground ; if he 
 sent the ball tlying, he moved it ; if he went from England to 
 France, he crossed the sea. All these inferences are irrefragable 
 and inescapable. They commend themselves to the reason with 
 irresistible force. But they cannot be reached by the syllogism, 
 or if they can, the process by which they are so attained is not 
 the process by which they are actually attained in practice. No 
 doubt we can get from London to Paris by going through Bombay 
 and Yokohama, but that is not the route followed by business 
 men who are anxious to reach their destination with the least 
 expenditure of time and trouble. 
 
 C. The third Minor Canon of Explication applies, to the terms 
 of the postulate, the same axiom that the second applies to the 
 Ratio. It states that Every postulated proposition implies every 
 proposition formed by the substitution, for either or both terms of the 
 postulate, of a term which is, for the purpose of the argument, equivalent 
 to, included in, or implied in the displaced term. In other words. 
 We may replace any term in a postulate by a term which is, for the 
 purpose of the argument, equivalent to, included in, or implied in the 
 displaced term. 
 
 a. Either term in a postulate may be replaced by a term that is, for 
 the purpose of the argument, equivalent to the displaced term. ' The 
 Marquis of Salisbury was prime minister,' implies ' The owner of 
 Hatfield was prime minister ' ; ' the Marquis of Salisbury was 
 first Lord of the Treasury ' ; ' The owner of Hatfield was first
 
 278 A NEW LOGIC 
 
 Lord of the Treasury.' These are, it is true, so many ways of 
 saying the same thing ; but then every Inference is another 
 way of saying the same thing, or of saying a part of the 
 same thing. The whole aim of Immediate Inference is to 
 discover in how many ways a thing may be said. Some of the 
 new ways are so Httle different from the postulate itself, that 
 logicians grudge to them the title of inferences ; but this is because 
 logicians misapprehend the true nature of Inference. Other new 
 ways of saying a thing put the matter in a form so different, and 
 perhaps so unexpected, that to them the title of Inference is freely 
 allowed ; but in nature the process is the same, and the result is 
 the same. Every inference is a restatement in a new form of the 
 whole or part of the postulate. 
 
 It is scarcely necessary to give more instances of the substitution 
 of equivalent terms, which is included under Jevons' Substitution 
 of Similars ; but it is worth while to notice that Similars are not 
 always substitutable. Pinchbeck is very similar to gold ; but 
 there are many arguments in which pinchbeck cannot validly be 
 substituted for gold. When we speak, in Logic, of equivalents 
 and similars, it is important to remember that what we mean is 
 things that are equivalent or similar for the purpose of the 
 argument. This is a matter to which logicians have given no 
 attention ; but it is of the utmost importance, as will be shown 
 again and again in the following pages. For the purpose of many 
 arguments, two crown pieces are equivalent to half a sovereign ; 
 but if half a sovereign will go through a certain slot, it will not 
 do to infer that two crown pieces will go through the same. For 
 the purpose of this argument, two crown pieces are not equivalent 
 to half a sovereign ; nor are they equivalent for the purpose of 
 the argument that half a sovereign weighs so many grains. For 
 the purpose of carrying certain information through the post, a 
 postcard is equivalent to a letter ; but for the purpose of carrying 
 the information privately, and for the purpose of the revenue derived 
 from the carrying, the postcard is not equivalent to the letter. 
 
 The substitution of an equivalent term produces so slight a 
 modification of the postulate, that it seems scarcely worth while 
 to call it an inference. Nevertheless, it is an inference, and may 
 be an inference of great importance. In a subsequent chapter we 
 shall find that it enables us to solve, with ease and certainty, 
 problems that have puzzled logicians for generations ; and we
 
 SUBSTITUTION OF TERMS 279 
 
 may note at once that it is the sole warrant for proceeding from 
 one step in the solution of an equation to the next. When we 
 say, because 
 
 (a + 6)2 = {a + b){a + b), therefore 
 (rt + 6)2 = a^ _j_ 2 a 6 + b\ 
 
 what is our warrant for arguing that the second equation is 
 equivalent to the first ? On what Law of Thought, or logical 
 principle, is the inference founded ? Do we rest our assurance, 
 that the second of these equations is equivalent to the first, on 
 the maxim that whatever is, is ? or on the maxim that nothing 
 can both be and not be ? or on the maxim that everything must 
 either be or not be ? Do we rest it on the Dictum de omni et 
 nullo, and argue that the second equation must be equivalent to 
 the first because what is predicated of everything in a class is 
 predicated of anything in that class ? The suppositions are 
 ridiculous. Our warrant is, plainly, and manifestly, and without 
 doubt, that any term in a proposition may be replaced by any 
 term that is equivalent to it. Here, a^ -{• 2 a 6 + 6^ is equivalent 
 to {a + 6) (^ + 6), and therefore may replace it in the postulate. 
 As stated elsewhere, logicians fight shy of mathematical reasonings, 
 and in most cases assume, and in some boldly state, that the 
 reasonings of mathematics are conducted on a plan different from 
 'qualitative' reasoning. They say, for instance, that the logical 
 argument 
 
 A — is — equal to B, and 
 
 B — is — equal to C 
 
 is conducted on a plan different from that of the mathematical 
 argument 
 
 A = B 
 
 B = C. 
 
 It would be premature and superfluous to deny that the mode 
 of reasoning is different in these two cases. The burden of proving 
 that they are different lies on those who make the assertion ; and 
 we are justified in ignoring it until it is proved. 
 
 6. Either term of a proposition may be replaced by one that is, for the 
 purpose of the argument, included in it. 
 
 If every building in the town was destroyed by the earthquake, 
 the town hall was destroyed. If it was cheap at fifty guineas, it
 
 2So A NEW LOGIC 
 
 was cheap at fift}' pounds. If every dog has his day, many dogs 
 have their days. If all men are mortal, some men at least are 
 mortal ; and any particular man is mortal. If the whole of the 
 milk was contaminated or adulterated, each pint of it was con- 
 taminated or adulterated. If all fruit is wholesome food, grapes 
 and oranges are wholesome food. 
 
 It is not permissible to replace a term by one that is merely 
 included in it. The substituted term must not only be included 
 in the term it replaces ; it must be included for the purpose of the 
 argument, or the inference will not be valid. If the whole town 
 was destroyed by the earthquake, it follows that the town hall 
 was destroyed ; but it does not follow that the school children 
 were destroyed, for, for the purpose of this argument, the school 
 children are not included in the town. But if the whole town 
 was depopulated by cholera, the school children are, for the 
 purpose of this argument, included in the town, and the town-hall 
 is not. For the purpose of the argument, ' It was cheap at a 
 guinea,' a pound is included in a guinea; but for the purpose of 
 the argument, ' A guinea is so called from the source of the gold 
 from which the first guineas were made,' a pound is not included 
 in a guinea. For the purpose of the argument, ' Milk should be 
 sterilised before it is consumed,' contaminated milk is included in 
 milk ; but for the purpose of the argument, * Milk is wholesome for 
 children,' contaminated milk is not included in milk. For the 
 purpose of the argument, ' All animals require organic food,' beetles 
 are included in animals ; but for the purpose of the argument, ' All 
 hollow-horned animals are ruminants,' beetles are not included in 
 animals. Of course, the statement, All hollow-horned animals are 
 ruminants, if it is taken literally, is untrue, and ought not to be 
 made ; but in colloquial discourse, in inexact writing, and in books 
 on Logic, hollow-horned animal usually means hollow-horned 
 mammal ; and the statement is allowed to pass. For the purpose 
 of the argument, ' Man is mortal,' woman is included in man ; but 
 for the purpose of the argument, ' Man is the masculine sex of the 
 human race,' woman is not included in man. ' Fruit is wholesome 
 food,' does not include in fruit, castor oil beans or the berries of 
 the deadly nightshade ; but for the purpose of the argument, 
 ' Fruit follows the flower,' these are included in fruit. 
 
 c. Either term of a proposition may be replaced by another term that 
 is, for the purpose of the argument, implied in the replaced term. It
 
 SUBSTITUTION OF TERMS 2S1 
 
 is not always easy to say whether a substitutable term is included 
 or implied in the term it replaces, nor does it matter ; for both 
 are equally substitutable. * He lives in Cheapside ' implies ' He 
 lives in London'; but London is not included in Cheapside for the 
 purpose of this or of any other argument. * There are eels in the 
 river ' implies ' There are fish in the river,' and yet fish are not 
 included in eels for the purpose of the argument, or for any other 
 purpose. It is easy to see, however, why these arguments are 
 legitimate. Though fish are not included in eels, the connotation 
 of having the qualities offish is included in the connotation of 
 eels ; and though London is not included in Cheapside, the quality 
 of being in London is included in the connotation of Cheapside. 
 Hence, though in denotation, London is not included in 
 Cheapside, nor are fish included in eels, yet in connotation the 
 first of each of these pairs of terms is included in the second ; and 
 the inference is on that account valid. Similarly, if cancer is a 
 fatal disease, it is a disease ; if these counters are beans, they are 
 vegetable products ; if he called a taxi, he called a cab ; if he ate 
 tuberculous meat, he ate what is unwholesome. 
 
 The question arises. How are we to distinguish a term that 
 may, for the purpose of an argument, be substituted for another, 
 from one that may not ? This is a question that Logic cannot 
 always answer, for in many cases, it depends on the purpose of the 
 argument, and the purpose of the argument is extra-logical. If 
 the quantity of a term is Distributive, we may always replace the 
 whole of a term by its part, and thus we discover the place of the 
 Dictum de omni et nxdlo in a comprehensive scheme of reasoning. 
 We find that, so far from its being the universal rule upon which 
 all reasoning depends, it is a small part of a sub-rule of a Minor 
 Canon of one of the Canons of Explication, all three of which are 
 Lemmas to one of the five Canons of Inference. 
 
 But if the quantity of the term is Collective, the part can no 
 longer be substituted for the whole : on the contrary, we may now 
 substitute the whole for the part. If some of the soldiers were 
 clad in kharki, we may not infer that all the soldiers were clad in 
 kharki ; but if some of the soldiers were sufficient to man the 
 rampart or to defeat the enemy, then it is certain that all the 
 soldiers were sufficient to man the rampart, or to defeat the 
 enemy. 
 
 If 1 infer from 'The Marquis of Salisbury was prime minister'
 
 282 A KEW LOGIC 
 
 to ' The Marquis of Salisbun- was First Lord of the Treasury,' it is 
 clear that this inference is not based solely upon the postulate, that 
 the Marquis was prime minister. I must have the further postulate 
 that the prime minister is equivalent to the First Lord of the Treasury. 
 If ever}- building in the town was destroyed by the earthquake, I 
 may infer from this postulate that the town hall was destroyed ; but 
 I cannot do so until I have assumed the further postulate that the 
 town hall was a building in the town. If from the postulate that 
 it was cheap at fifty guineas I infer that it was cheap at fifty 
 pounds, I make the silent assumption that fifty pounds is less than 
 fifty guineas. It is true that in each case the silent premiss is so 
 universally known, is so intimate a part of our mental equipment, 
 that we do not recognise that we are making any assumption at 
 all ; but it is there, nevertheless ; and strictly speaking, all these 
 inferences are drawn, not from simple, but from compound 
 propositions. But so to consider them would be pedantic formalism. 
 For all practical purposes, they are inferences from a single 
 postulate ; or, to put it otherwise, and more accurately, we are 
 entitled, when a postulate is granted to us, to add to it what 
 knowledge of its terms is already in our possession. 
 
 Otherwise, the replaceability or non-replaceability of one term 
 by another depends on the purpose of the argument ; and the 
 purpose of the argument is extra- logical, and is determined by 
 other considerations. Is china clay a mineral ? That depends 
 on the purpose of the argument. For the purpose of Geology, it 
 is ; but for the purpose of a lease of minerals, the Courts of Law 
 must be invoked to determine the question. Is marriage with a 
 sister-in-law a valid marriage, or not ? For the purpose of civil 
 law it is. For the purpose of the forum conscieniice it may 
 or may not be, according to the conscience of the person con- 
 cerned. For the purpose of administration of the Sacrament, 
 it is a valid marriage in law ; it is not a valid marriage in the 
 opinion of some of the clergy. Is the bursting of an aneurism 
 equivalent to an accident ? For the purpose of medicine, it is 
 not. For the purpose of the Workmen's Compensation Act, 
 it is ; for the purpose of an accident insurance policy, it may or 
 may not be. 
 
 These are questions that Logic cannot answer on the basis of a 
 single postulate. They depend on the purpose of the argument, 
 and for every different purpose, different accessory postulates are
 
 THE SECOND CANON OF EXPLICATION 283 
 
 required ; and though the Logic of Inference may assume what pos- 
 tulates it pleases, yet this assumption is rigidly limited as soon as 
 the purpose of the argument is determined. The purpose of the 
 argument is material. It belongs to matter, and not to form ; 
 and is outside the scope of Deductive Logic. The purpose of the 
 argument prescribes its own postulates, and with them Deduction 
 cannot interfere. Deductive Logic, as we have seen, has no 
 power to question its postulates. That is the function of 
 Empirical or Material Logic. All that Deductive Logic can do 
 is to work upon the material it assumes, or that is presented to it. 
 Having its postulates, Deductive Logic shows us how to mould 
 them into different forms according to its rules ; it is a guide to us 
 on our way, and a lantern to our feet ; it puts up sign-posts at 
 dangerous crossings, saying * Beware ! here you are likely to go 
 astray ; mind your steps ' ; it points out, when we have reached an 
 erroneous conclusion, exactly at what point of the journey we 
 took the wrong turning. All this Deductive Logic can do for us ; 
 but it cannot determine the purpose of our argument. It is a 
 route book which shows us whether we can reach our destination 
 or not, and how we can get there ; but no route book can decide 
 what our destination is to be. 
 
 The Second Canon of Explication states that Every postulated 
 proposition implies everything necessary to the postulate. 
 
 Strictly speaking, and if we adhere rigidly to pure logical form, 
 we should require an additional postulate, setting forth the 
 conditions necessary to our main postulate, to be formally stated. 
 But there must be some limit to formalism, or arguments would 
 be too voluminous to be serviceable. What is common knowledge 
 must be assumed to be known. The postulate ' Brutus killed 
 Caesar' implies the necessary conditions that Brutus and Caesar 
 both lived ; that they lived at the same time ; that once at least 
 they met ; that Brutus was capable of killing, and Caesar of being 
 killed. All these conditions are necessary to the postulate, and all 
 are therefore implied in it. It is absurd to say that we cannot arrive 
 at the conclusion * Caesar once lived ' from the postulate ' Brutus 
 killed Caesar,' unless we assume also the postulate that he who is 
 killed once lived ; for though Deductive Logic is the Logic of 
 Form, it would deprive it of nearly all its usefulness to insist on 
 such formalism as this. Some knowledge must be taken for
 
 284 A NEW LOGIC 
 
 granted, or we should never get on. If he saw her as he ran 
 down the hill, it is implied that he was there ; that she was there ; 
 that he could see ; that he looked in her direction ; that he and she 
 were there at the same time ; that she could be seen from where 
 he was running ; that there was a hill ; that he was higher up at 
 first, and lower down afterwards ; that the hill was not too steep to 
 run down ; and so forth, and so on. 
 
 To state these implications formally, as deductions worth 
 making from the postulate, may seem to be trifling : they are so 
 manifest. But they are by no means of trifling importance. They 
 are inferences that are frequently drawn, and that are often of the 
 utmost importance to draw. They are inferences on which fortune 
 and life may depend ; and yet neither Traditional Logic nor Modern 
 Logic knows anything about them, or has a word to say of them. 
 Who has not heard in a Court of Law, or on some other important 
 occasion, some such argument as this ? ' The prisoner admits 
 that he saw the prosecutor within five minutes of the commission 
 of the crime, therefore, within five minutes of that time, the 
 prisoner was on the spot.' * I have shown that there was a high 
 wall between them, and therefore the prosecutor could not have 
 seen the prisoner commit the crime.' * If I prove that the man 
 who is alleged to have been murdered died two years before the 
 prisoner could have met him, you must acquit the prisoner of 
 the murder.' ' Some one has been in the garden, for there 
 are footmarks in the snow.' ' The ship must have touched 
 at Singapore, for some of her passengers landed there.' ' The 
 water will never run out of this gutter, for it slopes in the 
 wrong direction.' ' If you caught fish out of that pond, there 
 must have been fish in it.' ' It has been raining, for the ground 
 is wet.' 
 
 Apart from the implication of the conditions necessary to the 
 postulate, there is no cogency or validity in these arguments. 
 Yet they are irresistibly cogent, and manifestly valid. They are 
 unknow-n to Traditional Logic, to Inductive Logic, and to Modern 
 Logic. In order to arrive at them by recognised logical methods, 
 we must convert them into syllogisms. ' If he saw her do it, he 
 must have been there when she did it ' is an argument that 
 commends itself to the reason as unimpugnably valid. Traditional 
 Logic w'ould, I suppose, call it an enthymcme, and would supply 
 a missing major premiss somewhat in this way : —
 
 THE THIRD CANON OF EXPLICATION 285 
 
 Everyone who sees a thing done must have been there 
 
 when it was done, 
 He saw her do it ; 
 . • . He must have been there when she did it. 
 
 This statement of the course of the argument may pass, though 
 I do not agree that it is the mental process by which the con- 
 clusion is reached ; but the trouble is that it is not a syllogism. 
 To get it into syllogistic form, we must put it something like 
 this. 
 
 Every one who sees a thing done is a person who was there 
 
 when it was done, 
 He is a person who saw a thing done ; 
 . • . He is a person who was there when it was done. 
 
 This is a syllogism, but it does not give us the conclusion 
 we want. We want He must have been there when she did it ; 
 and we get He is a person who was there when it was done. The 
 difference is not great ; it is perhaps not very material ; but 
 Traditional Logic is very punctilious. It demands the strictest 
 adherence to form ; and if we desire to alter ' He is a person who 
 was there when it was done ' into * He must have been there 
 when she did it,' we must go outside of Traditional Logic for our 
 authority. Traditional Logic gives us no rule for the conversion 
 of one of these forms into the other. Be it said that no authority 
 is needed, for the two are so plainly equivalent that they 
 commend themselves to common sense as having the same 
 meaning, then the strict formalism of Traditional Logic is 
 abandoned ; and then the same consideration will allow us to 
 infer directly from ' He saw her do it ' to ' He was there when 
 she did it,' without any necessity for going round through the 
 syllogism or the enthymeme. We may, therefore, fairly posit, as 
 the second Canon of Explication, that Every postulate implies all 
 the conditions that are necessary to the postulate. 
 
 The third Canon of Explication is that Everything inconsistent 
 ivith the postulate may be denied. 
 
 Every postulated proposition implies the denial of every propo- 
 sition that is inconsistent with the postulate, or with any of its 
 implications. We have seen that the positive implications of a
 
 286 A NEW LOGIC 
 
 postulate are of several different classes, and the postulate denies 
 ever}- proposition that is inconsistent with any implication in any 
 of these classes. We must take the classes separately, and thus 
 get several additional Minor Canons of Explication. The first of 
 these is 
 
 D. Every postulated proposition implies the denial of every proposition 
 in which the Ratio of the postulate is replaced by a Ratio that is, for the 
 purpose of thi argument, inconsistent with it. The Ratio that is most 
 plainly inconsistent with the postulate is its negative. ' All men 
 are not mortal ' is plainly inconsistent with ' All men are mortal,' 
 and is denied by this postulate. We may, therefore, on the basis 
 of this postulate, deny, in any way open to us, that all men are 
 not mortal. Hence ' All men are mortal ' implies ' All men are not 
 immortal,' * No men are not mortal,' ' Not all men are immortal,' 
 ' It is not true that all men are not mortal ' and other double 
 negatives of the postulate. ' All ships sail on the sea ' implies 
 ' No ships do not sail on the sea,' * Not all ships do not sail on 
 the sea,' ' It is not true that ships do not sail on the sea,' and so 
 forth. * Brutus killed Caesar ' implies ' It is not true that Brutus 
 did not kill Csesar.' 
 
 The Ratio of the postulate may be replaced by a Ratio that is 
 not the direct negative of that Ratio, but yet is inconsistent with 
 it. This is a very important and a very frequent mode of denial ; 
 and as it is inconsistent with the postulate, the postulate denies 
 all such negatives. If stones sink in water, then this postulate 
 implies the denial, not only of * Stones do not sink in water,' but 
 of * Stones float in water.' If Birds of a feather flock together, 
 then we may infer the denial, not only of ' Birds of a feather do 
 not flock together,' but of ' Birds of a feather are of solitary habit ; 
 live dispersedly ; are lonely ; segregate themselves.' If curses 
 come home to roost, they do not go abroad to roost, neither do 
 they fail to come home to roost. 
 
 E. The fifth Minor Canon of Explication permits us to deny 
 Every proposition in which a term of the postulate is replaced by one 
 that is, for the purpose of the argument, inconsistoit with the term it 
 replaces. The term that is most manifestly inconsistent with any 
 term is its direct negative ; and we may always deny a pro- 
 position in which a term of the postulate is replaced by its direct
 
 THE FIFTH MINOR CANON 287 
 
 negative, provided the direct negative is inconsistent, for the 
 purpose of the argument, with the term it replaces. This seems, 
 on the face of it, an unnecessary proviso. It seems that the 
 direct negative of a term must ahvays and for all purposes be 
 inconsistent with that term ; but it is not so. * Men who are not 
 clever' is, in one sense, the direct negative of ' Clever men,' yet, 
 though clever men are mortal, it would be unsafe to deny that 
 men who are not clever are mortal. Clever men and men who 
 are not clever are not, for the purpose of this argument, incon- 
 sistent. The negative of * clever men ' that is, for the purpose of 
 this argument, inconsistent with ' clever men ' is ' no clever men ' ; 
 and if clever men are mortal, we are safe in denying that no 
 clever men are mortal, and that there are no clever men who are 
 mortal. 
 
 If men are mortal, then we may deny that men are immortal ; 
 for mortality and immortality are inconsistent for the purpose of 
 this argument. If just acts are expedient, we may deny that 
 they are inexpedient ; but we may not deny that unjust acts are 
 expedient ; for just and unjust, though generally inconsistent, are 
 not inconsistent for the purpose of this argument. But if 
 expedient acts are just, we may deny that they are unjust, for, for 
 the purpose of this argument, just and unjust are inconsistent 
 terms. 
 
 The direct negative of a term is no more the only term incon- 
 sistent with the affirmative, than the direct negative of a Ratio is 
 the only Ratio inconsistent with its affirmative. If it is the last 
 straw that breaks the camel's back, we are warranted in denying 
 that it is the first straw that breaks the camel's back. If it 
 is the first step only that costs, we may safely deny that the 
 second step costs. If a little pot is soon hot, we may deny that a 
 big pot is soon hot, for a big pot is inconsistent, for the purpose of 
 this argument, with a little pot ; but we may not deny, on the 
 authority of the same postulate, that a little pot is soon cold ; for, 
 for the purpose of this argument, hot and cold arc not inconsistent. 
 If one and one are two, then we may deny that one and one are 
 three, for two and three are inconsistent for the purpose of the 
 argument ; but if two heads are better than one, we may not, on 
 the authority of this postulate, deny that three heads are better 
 than one, for, for the purpose of this argument, two and three are 
 not inconsistent. Traditional Logic is oblivious to the purpose of
 
 288 A NEW LOGIC 
 
 its arguments ; such inferences as these are, therefore, altogether 
 beyond its purview. 
 
 When the denial of an affirmative proposition is made by a 
 direct negative, whether in Ratio or term, the denial of this 
 negative must be made by the insertion of a second negative. For 
 this reason, a portion of this Minor Canon may be combined with 
 a portion of the last, in the statement that Every postulated propo- 
 sition implies all its double negatives, in which the negatives are 
 inconsistent with the elements they replace. Thus, the postulate ' All 
 men are mortal ' implies 
 
 No men are immortal. 
 No men are not mortal. 
 Not all men are immortal. 
 Not all men are not mortal. 
 All men are not immortal. 
 There are no men who are not mortal. 
 There are no men who are immortal. 
 There are not any men who are not mortal, 
 &c., &c. 
 
 Of all these double negatives which are implied in the postulate. 
 Traditional Logic knows of one only, which it calls the Obverse : 
 of all the remainder it is ignorant. The rule given in the text 
 books for obtaining the Obverse is * Change the quality of the 
 proposition, and substitute for the predicate its contradictory.' 
 The rule is lamentably defective. It does give us, from the 
 postulate All men are mortal, the obverse, No men are immortal ; 
 but here its powers end. It cannot furnish any of the other 
 double negatives instanced above ; it is often impracticable, for 
 many terms have no contradictories ; it is often ambiguous, for 
 some terms have more than one contradictor}' ; and it sometimes 
 plays us false, and gives us an obverse that is not implied in the 
 postulate. 
 
 The rule of Traditional Logic is often impracticable, for many 
 terms have no contradictory, unless indeed, we understand by the 
 contradictory the Infinite Negative ; and even if we do, the contra- 
 dictory may fail to give us an obverse, or may give one that is 
 absurd or unwarrantable. If indeed, we admit no proposition but 
 that constructed with the copula, the rule may be practicable, but 
 such arbitrary limitation of the power of propositionising I have
 
 THE OBVERSE 289 
 
 already repudiated. What obverse can we construct, on this 
 plan, of the proposition Brutus killed Caesar ? We can change 
 the quality of the proposition readily enough. It then becomes 
 Brutus did not kill Caesar. But what is the contradictory of 
 Caesar ? Is it some one who was not Caesar ? or every one, or any 
 one who was not Caesar ? In either case, the obverse so obtained 
 is not warranted by the postulate, is ultra vires, and fallacious. 
 What is the contradictory of the predicate of All ships sail on the 
 sea ? Is it what is not the sea ? Then the obverse commits us 
 to the statement that No ships sail on what is not the sea, which 
 is not implied in the postulate. The postulate does not permit 
 us to deny that ships sail on rivers, lakes and canals, even if they 
 sail on the sea also. Are we to take as the contradictory, the 
 Infinite Negative, Everything that is not the sea? Then the 
 obverse commits us to the statement that no ships sail on 
 triangles, melancholy, sulphuric acid, and other things outside the 
 suppositio. Be it said that * Dry land ' is the contradictor}' of 
 the sea, I deny that it so necessarily. If it were, the postulate 
 * The sea is His, and He made it,' would compel us to deny ' The 
 dry land is His, and He made it.' But for the purpose of the 
 argument, the dry land is the contradictory of the sea ? Very 
 likely, but the rule of Traditional Logic makes no reference to 
 the purpose of the argument. It says substitute the contradictor^-, 
 as if there were one contradictory, always available, and always 
 the same. It won't do. By the rule of Traditional Logic, no 
 obverse can be obtained. But by the Method of Explication we 
 can get the double negative, No ships do not sail on the sea, 
 which is clearly implied in the postulate 'All ships sail on the sea.' 
 
 F. The sixth Minor Canon of Explication permits us to deny 
 Every proposition inconsistent with any implication of the postulate. 
 To go through all the implications of the postulate, and find all 
 the double negatives of them all, would be an endless task ; but 
 since Traditional Logic has essayed a single instance, we may 
 examine this instance, and test its validity. Traditional Logic 
 recognises, as one of its Immediate Inferences, the Contrapositive, 
 which is the Converse of the Obverse. As the converse has been 
 shown to be faulty, and the obverse has been shown to be faulty, 
 it is one of those arguments, a fortiori, which Traditional Logic 
 admits its inability to explain, that the Contrapositive is faulty. 
 
 N.L. U 
 
 ^
 
 290 A NEW LOGIC 
 
 Whatever objections apply to the converse and the obverse, 
 apply with force at least undiminished to the contrapositive. 
 
 According to Traditional Logic, the obverse of * All men are 
 mortal,' is * No men are immortal,' and the converse of this is 
 ' Some immortal beings are not men.' This is the contrapositive 
 of the postulate, and is the only Immediate Inference that can be 
 formed on this plan. In my view, not one only, but many double 
 negatives are obtainable from this postulate, and each yields its 
 reciprocal. In my view, the true reciprocal of ' No men are 
 immortal ' is ' Immortality is an attribute of no men.' In this 
 reciprocal, the Subject, now become Object, is not changed from 
 * no men ' to ' men ' ; the affirmative Ratio is not changed to 
 a negative Ratio ; and the Object, now become Subject, is not 
 changed from an indesignate abstract to a quantitative concrete ; 
 four changes that I regard as unnecessary and inadmissible. An 
 additional objection to the contrapositive is that, like the obverse 
 from which it is derived, it is not always implied in, or even con- 
 sistent with, its postulate. ' All things are thinkable ' becomes, 
 in the contrapositive of Traditional Logic, ' Some unthinkable 
 things are not things.' 
 
 In this place we may dispose of the fourth of the Immediate 
 Inferences of Traditional Logic, a recent discovery, which is called 
 the Inverse, and is arrived at by a method so complicated that I 
 will not trust myself to attempt it, but will take, from a standard 
 text book, the following example. ' Every truthful man is trusted ' 
 — Inverse, ' Some untruthful men are not trusted.' Some logicians 
 doubt the legitimacy of this form of Inference ; and I must confess 
 to misgivings about it ; for, if it is valid, I see no reason why it is 
 not equally valid to infer from ' Every truthful man is mortal,' to 
 ' Some untruthful men are not mortal.' This puts on' inveracity a 
 premium, which is scarcely to be expected from the justice of Provi- 
 dence; and, what is more to the purpose, does not seem to me to be 
 implied in the postulate. I cannot help suspecting, therefore, that 
 those logicians have reason, who find, in the complicated process 
 by which the Inverse is obtained, some term distributed which 
 ought not to be distributed. 
 
 G. The last implication of the postulate is The denial of every 
 proposition that is inconsistent with a necessary condition of the postulate. 
 This extremely important implication of the postulate is unknown
 
 CONTRADICTION 291 
 
 to Traditional Logic, though it is the one most frequently utilised 
 in practical life. Who has not heard, in a Court of Law, or on 
 some other important occasion, some such argument as this: 
 * How could you have seen him do it, when you have admitted that 
 you were not there when he did it ? ' 'It cannot be true that you 
 have just come in from a long walk in the rain, for your clothes are 
 quite dry.' * You say you stayed at an hotel in Herm ; I will 
 prove there is no hotel on the island.' ' You fell out of a train 
 going sixty miles an hour, yet you can show no bruise or scratch 
 on your body, and no rent or soil on your clothing ! ' Apart from 
 the conditions necessary to the postulate, there is no contradiction 
 in these pairs of statements. In Logic they are not contradictories, 
 nor even contraries. The only contradictories known to Traditional 
 Logic are All are — some are not, None are — some are. What 
 perverseness of ingenuity, what cataractous blindness, must have 
 been combined to discover implications so far-fetched and useless 
 as the Contrapositive and the Inverse, and to overlook so manifest 
 and important an implication as the denial of the inconsistent 
 condition ! No prisoner has ever been prosecuted in a Court of 
 Law without Counsel for the prosecution seeking to show that the 
 evidence was inconsistent with innocence, which could therefore 
 be denied. No Bill has ever been opposed in Parliament without 
 the opponent seeking to show that the Bill was inconsistent with 
 some condition of justice or expediency, and so inferring that the 
 justice or expediency of the Bill could be denied. Yet the impli- 
 cations of consistency, and denial of inconsistency, with its 
 necessary conditions, that are contained in every postulate, have 
 been ignored and neglected by every logician, from the time of 
 Aristotle to the present hour. Is it any wonder that Logic in 
 its turn has been ignored, neglected, and derided, by practical 
 reasoners ? 
 
 The view of contradiction taken by Modern Logic is expressed 
 by Lotze thus : — ' If however there are only two specific forms of 
 P, ^^and^^, and S must have a specific form of P for its predicate, 
 then not only does the affirmation of one of them as predicate of 
 S involve the negation of the other, but also the negation of the one 
 involves the definite affirmation of the other ; p^ and p'^ are then 
 opposed to one another contradictorily.'' It is \\\\.\\ diffidence that 
 I attempt to interpret this dictum, but I do not think it can be so 
 interpreted that the predicates * saw him ' and ' was not there ' can 
 
 u 2
 
 292 A NEW LOGIC 
 
 stand as the only specific forms of predicate that ' I ' is capable of. 
 Many other things can be predicated of the first person singular; 
 and even in the present connection, ' I was blind,' ' I was looking 
 the other way,' ' I had my eyes shut,' equally carry the negation of 
 ' I saw him.' These are, therefore, modes of contradiction that 
 are unknown to Modern Logic ; and in fact, it never contemplates 
 the implication of what is necessary to the postulate, nor the 
 denial of what is inconsistent with such an implication, as a further 
 implication of the postulate. 
 
 Yet between ' I saw him do it ' and ' I was not there when he 
 did it,' there is a manifest inconsistency, which strikes home to 
 the conviction of every one who realises the circumstances ; and 
 either being postulated, the other may be denied on the strength 
 of the postulate. If I was not there when he did it, I could not 
 have seen him do it ; and, if I swear to both assertions, I am liable 
 to indictment for perjury. Yet, in uttering this manifest and palp- 
 able contradiction, I am infringing no rule of Logic, Traditional, 
 Inductive, or Modern. But surely the clear and inescapable 
 inference, that if one is true the other is false, is one that Logic 
 ought to be able to reach. We see at once that they are incom- 
 patible. They are so manifestly incompatible that it might be 
 plausibly advanced that no reason for their incompatibility need 
 be shown. Nor need it be shown in practice ; but if Logic in 
 any case traces the processes of reasoning, and shows the grounds 
 of judgement, surely it should do so in such a case as this. 
 Logic provides rules showing the incompatibility of such pairs as 
 All men are mortal — some men are immortal ; No man is perfect — 
 some men are perfect. It is not, therefore, because of the plainness 
 of their incompatibility that such inconsistent propositions have 
 been neglected : it is because they have been overlooked ; or per- 
 haps because they pertain to the matter and not to the form of 
 the postulate, and Logic fetters itself to verbal forms. 
 
 Traditional Logic would perhaps say that the argument ' You 
 cannot have broken your leg on that day, for you ran a race the 
 day after,' is a syllogistic argument, and not an Immediate 
 Inference. That it requires, in strictness, an additional postulate, 
 I should be prepared to admit ; but that the syllogism represents 
 the mental process actually performed, I should deny. The 
 syllogism by which the conclusion is supposed to be reached would 
 be something like this : —
 
 CONTRADICTION 293 
 
 No person who runs a race has recently broken his leg, 
 You are a person who ran a race ; 
 . • . You are not a person who had then recently broken your leg. 
 
 Is this the process the mind performs, and is this the conclusion 
 reached ? As far as I can trace the operations of my own mind, 
 neither is so. When I hear you assert that on a certain day you 
 broke your leg, and have it proved that on the following day you 
 ran a race, the contradiction, or as Logic would say, the contra- 
 riety, is in my mind immediate, I do not reach it through any 
 such Universal as ' No person who runs a race has recently broken 
 his leg.' I do not go over in my mind, and collect together all 
 the instances I know of persons who have run races, and then 
 consider whether or not their legs had been recently broken. Nor 
 do I perform the 'generic' judgement of Modern Logic, and say 
 to myself, * It is the nature of all persons who run races not to 
 have had their legs recently broken.' What passes in my mind, 
 as well as I can trace it, is the formation of an idea of a man with 
 a broken leg trying to run, and of his leg giving way under him, 
 and rendering running impossible. There may be persons who 
 reach the conclusion through the generic Universal, though I 
 should think they are exceptional ; but I cannot believe there are 
 any minds so constituted as to reach it through the distributive 
 Universal. My own description of my own mental process must, 
 I think, be accepted as that which obtains in my own case ; and 
 then it is conclusive that there is a case in which the reasoning is 
 not syllogistic, but is the intuitive recognition of the inconsistency 
 of the two propositions ; and the intuitive recognition that the 
 postulation of one implies the denial of the other. 
 
 Set out in full, the Canons of Explication of Simple propositions, 
 wliich, it must be remembered, are Lemmas to the fifth Canon of 
 Inference, are as follows : — 
 
 TABLE XIV. 
 
 The Canons of Explication, expanded. 
 
 Every postulated proposition implies 
 
 I. Every equivalent and included proposition; that is to say, 
 
 Minor Canons : 
 It implies A. Its Reciprocal. 
 
 B. Every proposition in which the Ratio of the
 
 294 A NEW LOGIC 
 
 postulate is replaced by a Ratio that is, for the 
 purpose of the argument, equivalent to, included 
 in, or implied in the Ratio of the postulate. 
 C. Ever}' proposition in which a term of the postulate 
 is replaced by one that is, for the purpose of 
 the argument, equivalent to, included in, or 
 implied in the term it replaces. 
 
 2. Every condition necessary to the postulate. 
 
 3, The denial of every proposition inconsistent with the 
 
 postulate, or with any of its implications ; that is to say, 
 
 Minor Canons : 
 
 It implies D. The denial of every proposition in which the Ratio 
 
 of the postulate is replaced by a Ratio that is, 
 
 for the purpose of the argument, inconsistent 
 
 with the Ratio of the postulate. 
 
 E. The denial of ever\- proposition in which a term of 
 
 the postulate is replaced by a term which is, for 
 the purpose of the argument, inconsistent with 
 the displaced term. 
 
 F. The denial of every proposition inconsistent with 
 
 any implication of the postulate. 
 
 G. The denial of every proposition inconsistent with 
 
 any condition of the postulate. 
 
 Of all the implications contained in this long array of classes — 
 eight classes in all, and every class containing many implications 
 — Traditional Logic knows of four implications only : — the 
 Converse, the Obverse, the Contrapositive, and the Inverse. Of 
 these, the Converse is strictly applicable to a small class only of 
 propositions, those, namely, that express class inclusion, though it 
 is usually applied wrongly to attributive propositions ; the Obverse 
 is not always to be had ; the Contrapositive, being the Converse 
 of the Obverse, partakes of the defects of both; and the Inverse 
 is altogether invalid. If, therefore, these were the only implica- 
 tions that could be extracted from propositions, our reasonings 
 from them would be so restricted as to be of little or no value ; 
 and would in many cases be invalid. Fortunately, however, in 
 actual reasoning, the behests of Traditional Logic have always 
 been disregarded. Every child in the nursery knows better than to 
 argue from ' Treacle is sticky ' to ' Some sticky thing is treacle,'
 
 COMMON IMPLICATIONS 2^)5 
 
 and is quite capable of forming the reciprocal ' Stickiness belongs 
 to treacle.' Who on this earth, except a logician, ever argued 
 from ' Brutus was a Roman ' to ' Some Roman was Brutus,' or from 
 ' Logicians bind themselves by pedantic restrictions,' to ' Some 
 people who do not bind themselves by pedantic restrictions are 
 not logicians ' ? But who is there that has not upon occasion used 
 some such argument as these ? — ' If but one prehistoric man 
 crossed the Channel, it shows that the Channel was not an impene- 
 trable barrier to immigration from the Continent.' * If he accepted 
 it with enthusiasm, we may conclude that he was pleased with it.' 
 ' If half a loaf is better than no bread, then a whole cake is better 
 than nothing to eat.' * If hard words break no bones, soft words 
 will certainly break none.' * You admit that the price of labour 
 determines the cost of production, for you said just now that the 
 cost of production is determined by the price of labour.' * If you 
 find that he took the money with the intention of converting it to his 
 own use, you must find him guilty of stealing.' * Some one has 
 been meddling with my papers, for they are not as I left them.' 
 
 * He is there, for I hear his voice.' ' If there are many modes of 
 reasoning unknown to Traditional Logic, Traditional Logic is 
 defective.' * You cannot say that the goose is despised, for 
 
 Of all the Poultry in the Yard 
 
 The Goose is most prefer'd ; 
 There is so much of Nutriment, 
 
 In that weak-minded Bird.' 
 
 * If his wife was a burden on the rates, he could not have been a 
 single man.' * She says she has had no medical attendance for 
 three years, and the doctor swears he attended her last summer : 
 both cannot be speaking the truth.' ' If there was enough to go 
 round, there is no reason why everyone should not have some.' 
 
 * If he was better after taking the medicine, it did him no 
 harm.' 
 
 These are samples of modes of reasoning in every day use. They 
 are useful, and they are valid, and they are commonly emplo\-cd ; 
 but none of them is attainable by any method of Traditional Logic, 
 unless, indeed, some of them may be artificially concocted into 
 syllogisms, which would not display the true form or process 
 of thought. Neither can I find in Modern Logic any allu- 
 sion to arguments of any of these classes. The only logician
 
 296 A NEW LOGIC 
 
 who has given any formula under which they can be subsumed is 
 Hamihon; who states that what is true in any one form of words 
 is true in any other form of words; but this, although it covers 
 many of the instances given, does not tell us how to find another 
 form of words in which a proposition may be stated. I claim it 
 as a merit of the Method of Explication that it assigns to them a 
 due position in the scheme of reasoning.
 
 CHAPTER XIX 
 
 THE COMrOUND PROPOSITION AND ITS IMPLICATIONS 
 
 A Compound proposition consists of two or more propositions 
 having a common element. 
 
 The common element may be the Ratio, or it may be a term ; 
 and the common term may occupy the same position in both 
 propositions, or may be the Subject of one, and the Object of the 
 other. 
 
 1. The common element may be the Ratio. ' He was murdered, 
 robbed, and flung into a ditch.' ' She made the bread, baked it, 
 cut it up, buttered it, and gave it away.' I cannot find any 
 reference to the implications of this form of Compound proposition 
 inany text book ; but it is a sound valid proposition; not infrequent 
 in use ; containing various implications ; and capable, therefore, 
 of forming the basis of argument. 
 
 2. The common element may be a term ; and there are three or 
 four forms of proposition having a term in common. 
 
 a. The common term may be the Subject in both propositions. 
 A is B and C. * Washington was good and great.' ' Electricity 
 causes lightning and thunder.' * He was murdered by Burke and 
 Hare.' ' Many of the audience applauded both the actors and the 
 actresses.' In the foregoing examples, not only the Subject, but 
 the Ratio is common to the two constituent propositions ; but this 
 is by no means necessary. The proposition is still Compound 
 if the Subject alone is common, the Ratios being different. 
 ' Washington was a great man, and achieved the independence of 
 America.' ' Electricity causes lightning and propels street cars.' 
 * He was drugged by Burke and stifled by Hare.' * Many of the 
 audience hissed the actors and applauded the actresses.' 
 
 h. The common term may be the Object in both propositions. 
 A and C are B. ' Titanium and Uranium are metals.' ' Paul and 
 Julius were shipwrecked.' * Lightning and thunder are caused by 
 electricity.' * Cancer and phthisis are fatal diseases.' As in the 
 previous case, the Ratio need not be common to the two pro- 
 positions. ' Some of them served, others betrayed, their party.'
 
 298 A NEW LOGIC 
 
 ' Burkc drugged, and Hare stifled him.' * Cancer is, and catarrh 
 is not, a fatal disease.' ' Dryness preserves, and moisture 
 deteriorates, most things.' 
 
 c. The common element may be the Subject of one of the 
 constituent propositions and the Object of the other. A is B and 
 B is C, or A is B and C is A. * Rain brings out slugs, and slugs 
 bring out birds.' ' The cost of labour depends on its efficiency, 
 and the rate of profit depends on the cost of labour.' ' Democracy 
 tends to despotism, and despotism tends to revolution.' ' Faith 
 excludes scepticism and scepticism excludes confidence.' Again, 
 in this case, the Ratios may be the same or different. ' Rain 
 brings out slugs, and slugs are eaten by birds.' ' The earth is 
 attracted by the sun, and the moon revolves round the earth.' 
 * The current in the coil magnetises the core, and the core reacts 
 on the current.' ' The master scolds the butler, and the butler 
 boxes the page's ears.' 
 
 It is at once apparent that the forms of the Compound pro- 
 position with a common term correspond with the figures of the 
 syllogism. A is B and C may be written 
 
 A is B 
 
 A is C ; which are the premisses of 
 the third figure, in which the middle term is the Subject of both 
 premisses. 
 
 The Compound proposition with a common Object-term forms 
 the premisses of the second figure. A and B are C may be written 
 
 A is C 
 B is C. 
 
 The Compound proposition, in which the common term is the 
 Subject of one and the Object of the other constituent, includes 
 the premisses of the first and fourth figures. 
 
 A is B and B is C, and B is A and C is B may be written 
 
 A is B 
 
 B is C ; which arc the premisses of 
 the fourth, or 
 
 B is A 
 
 C is B, which are the premisses of 
 the first figure.
 
 CANONS OF EXPLICATION 299 
 
 The syllogism is, therefore, closely related to the Compound 
 proposition, or at least, to those forms of the Compound proposition 
 in which the common element is a term ; and, in fact, the syllogism 
 may be regarded as neither more nor less than a mode of extracting 
 one of the implications contained in these forms of Compound 
 proposition. The premisses of a syllogism are, in ever)' case, a 
 compound proposition, or may be stated in the form of a com- 
 pound proposition. The conclusion of a syllogism is one of the 
 implications of the compound proposition which forms the pre- 
 misses. This implication is extracted by dealing with the syllogism 
 according to its rules. To this mode of extracting from a com- 
 pound proposition one of its implications, I offer an alternative by 
 which they may all be extracted, which I call the Method of 
 Explication, whose rules are a series of Lemmas to the Canons 
 of Inference. 
 
 Three of these Lemmas, with their derivatives, have already 
 been stated as the Canons of Explication of Simple Propositions. 
 Since they are applicable to Compound Propositions also, they 
 may be re-stated here, together with two new Canons, with which 
 they must be supplemented in order to enable us to extract all the 
 implications from Compound Propositions. 
 
 The Canons of Explication of Compound Propositions. 
 
 Every postulated proposition implies 
 
 1. Every proposition equivalent to or included in the 
 
 postulate. 
 
 2. Every condition necessary to the postulate. 
 
 3. The denial of every proposition inconsistent with the 
 
 postulate. 
 These apply equally to Compound and to Simple propositions. 
 The Compound proposition needs for its complete explication the 
 following additional Canons : — 
 
 4. When two terms are postulated in the same relation to a 
 
 third, it is implied that they are equivalent to, resemble, 
 or are consistent with one another with respect to that 
 third. 
 
 5. When two terms are postulated in inconsistent relations to 
 
 a third, it is implied that they differ from one another 
 with respect to that third, and that the third marks a 
 difference between them.
 
 300 A NEW LOGIC 
 
 Compound propositions are, as we have seen, of four or five main 
 forms, according as we reckon them. The first, in which the 
 common element is the Ratio, is unknown to logicians ; yet this 
 form of proposition is in common use, and has implications of its 
 own that are not neglectable. Traditional Logic may claim that 
 it can take the two constituent propositions of any compound pro- 
 position that contains two constituents only, and combine them 
 into the premisses of a syllogism ; but when the common element 
 of the propositions is the Ratio, Traditional Logic cannot do this. 
 
 If he was murdered, robbed, and flung into a ditch, Traditional 
 Logic may take two of these propositions and posit them as the 
 premisses of a sj'llogism or quasi-syllogism, thus 
 
 He was murdered ; 
 He was robbed ; 
 . ■ . Some one who was robbed was murdered, 
 
 I should doubt whether this is properly a syllogism. Traditional 
 Logic makes no distinction between the true copula and the 
 auxiliary ; but I think the distinction is clear, and is important ; 
 and that, in this case, neither of the premisses is in true logical 
 form. Waiving this objection, however, and the objection that 
 the middle term is singular, it remains that this, and * Some one 
 who was murdered was robbed,' are the only conclusions that 
 can be drawn from these premisses; and that Traditional Logic 
 must take the premisses two by two, and cannot consider all at 
 once. The Canons of Explication allow us to draw many con- 
 clusions, and need not disjoin the argument. By them we can 
 infer that he was there ; that he was not alone ; that he was 
 assaulted ; that he is dead ; that he did not retain all his property ; 
 was not left lying in the road; did not die a natural death, or 
 commit suicide ; that some one murdered and robbed him and 
 disposed of his body; that he was the subject of a crime ; and so 
 forth, and so on, all proper and legitimate inferences. 
 
 If she made the bread, baked it, cut it up, buttered it, and gave 
 it away, then a number of inferences lie latent in the proposition, 
 and can be explicated by the Canons of Explication, but not by the 
 syllogism. No proposition that is not in logical form may enter 
 into a syllogism ; and these propositions are not in logical form. 
 They contain no copula. The syllogism, unless several are com- 
 bined in a sorites, can deal with two premisses only at a time.
 
 EXAMPLES OF EXPLICATION 301 
 
 and here are five. The syllogism knows of no relation but inclusion 
 in, and exclusion from classes, and these do not express either. If 
 we try the syllogism on the first two propositions, we get the 
 premisses 
 
 She made the bread ; 
 She baked the bread ; 
 
 and, as neither of these contain the copula, the syllogism, if 
 rigorously applied, is helpless, and can give us no conclusion. 
 If, however, we waive this condition, as logicians constantly do in 
 practice, in the examples they give, though they lay down with 
 strictness the principle that the copula is indispensable, we may 
 get two conclusions, — The person who made the bread, baked it ; 
 and The person who baked the bread, made it. It is very doubtful 
 whether logicians would admit that these are logical conclusions, 
 but let us give Traditional Logic the credit of finding them. Now 
 compare this poor result with the multitude of conclusions that 
 the Method of Explication gives. By this method we may infer 
 all the reciprocals. The bread was made, baked, cut, buttered and 
 given away by her. We may infer all propositions with equivalent, 
 contained or implied ratios and terms. We may infer, therefore, 
 that she mixed the dough, kneaded it, and let it rise ; that she put 
 it in the oven, and left it there till it was baked ; that she divided 
 it into slices, spread butter on them, and distributed them. We 
 may infer all conditions necessary to the postulate. We may infer, 
 therefore, that she had flour, water, yeast, fire, an oven, a knife, 
 butter, and some one to give the bread to. She must also have 
 known how to make bread, and how to bake it. We may deny 
 all propositions inconsistent with the postulate. We may deny, 
 therefore, that she was without flour, and the other necessaries. 
 We may deny that she had lost an arm, that she failed to make or 
 bake the bread, that she left it uncut or unbuttered, that she kept 
 it, did not give it away, gave it away dry, or in loaves, and so forth, 
 and so on. 
 
 It is true that these are most of them very obvious inferences. 
 They only state over again, in other words, what was stated 
 in the postulate. They do not ' advance from the known to the 
 unknown ' ; but, in the first place, they compare in this not 
 unfavourably with the two conclusions that alone were obtainable 
 from the quasi-syllogism ; and in the second, to state in other
 
 302 A NEW LOGIC 
 
 words what is given in the postulate is the nature of all inference 
 or deduction. It is a mistake to suppose, as Mill and other 
 logicians suppose, that deduction ' proceeds from the known to 
 the unknown.' The utmost it can do is to render manifest what was 
 obscure. It is a mistake to suppose that we can get out of a thing 
 more than there is in. it, or out of two things more than is in them. 
 It is not possible to get more than a pint out of a pint pot, or more 
 tiian two pints out of two pint pots ; and it is impossible to get out 
 of a premiss or postulate, or out of two premisses or postulates, 
 more than they contain. The object and purpose of Inference is 
 to extract and state plainly what is implied in a proposition, but 
 may not be plainly apparent ; and if more is inferred than the pro- 
 position contains, the fourth Canon of Inference is violated, and 
 the inference is invalid. The syllogism is a method, a clumsy 
 and roundabout method, of extracting from a Compound proposition 
 one of its implications. The Method of Explication is, I submit, a 
 more direct, and a more efficacious method of extracting them all. 
 
 In the foregoing examples, the common element in the two 
 propositions, that combines them into a Compound proposition, 
 is the Ratio. Traditional Logic does not profess to treat Com- 
 pound propositions of this class. It confines its ministrations to 
 those in which the common element is a term ; and it is with 
 respect to these alone that the Syllogism and the Method of 
 Explication come into competition. Before contrasting the two 
 methods, however, it is necessary to note the important difference, 
 from the point of view of Inference, between the Simple and the 
 Compound propositions. 
 
 The third Minor Canon of Explication permits us to replace 
 any term in a postulated proposition, by any other term which is, 
 for the purpose of the argument, equivalent to, included in, or 
 implied in the term replaced. Our field of search, for a substitute 
 to replace a term in a simple proposition, is limited to the known 
 equivalents, contents, or implications of that term, as drawn from 
 its connotation or denotation ; and, by the fourth Canon of 
 Inference, we are forbidden to go beyond them. The compound 
 proposition gives us this great advantage, that it supplies us with 
 an equivalent, content, or implication, that may not be obtainable 
 from the mere connotation or denotation of that term, and would 
 be utterly inaccessible and unattainable unless specially granted 
 by the second postulate given in the compound proposition.
 
 TIIF. SECOND POSTULATE 303 
 
 From the simple proposition, ' Democracy ends in despotism,' 
 we can get, by the third Minor Canon of ExpHcation, * Mob-rule 
 ends in despotism,' ' Democracy ends in autocracy,' ' Democracy 
 ends in tyranny,' and a few more equivalents ; but we cannot 
 infer any relation between democracy and anything that is not 
 clearly equivalent to, included in, or implied in, despotism. We 
 cannot from this postulate infer any relation, for instance, 
 between democracy and revolution, or between democracy and 
 the character of the governed, or the morality of the governing 
 classes. But the additional postulate, that converts the Simple 
 proposition into a Compound proposition, may give us a 
 substitute for democracy or for despotism, that we could not by 
 any other means obtain. It may tell us that democracy leads to 
 despotism, and despotism leads to revolution ; and then it is clear 
 that, for the purpose of the argument, revolution is implied in 
 despotism, and may replace it in the first part of the postulate. 
 By this means we get ' Democracy leads to revolution ' ; and so 
 obtain an implication that we could not have obtained from any 
 Simple proposition. By the same means, if democracy leads 
 to despotism, and despotism deteriorates the character of the 
 governed, democracy leads to the deterioration of the character of 
 the governed. If democracy leads to despotism, and despotism 
 to corrupt government, democracy leads to corrupt government. 
 
 Logicians may declare that these conclusions could be reached 
 equally well by the syllogism, thus : — 
 
 Despotism leads to revolution, 
 Democracy leads to despotism ; 
 . ■ . Democracy leads to revolution. 
 
 Not being bound in syllogistic fetters, I should regard this as a 
 perfectly valid argument ; but Traditional Logic is precluded by 
 its own rules from so regarding it. The constituent propositions 
 are not in logical form : they have no copula. The middle term, 
 despotism, is undistributed ; for it is indesignatc in quantity, and 
 the rule is that an indesignate term is to be taken as particular. 
 Logicians of the Traditional School are precluded by their own 
 principles from attaining this conclusion, as well as the others, 
 by this method. Granting them the liberty of regarding this 
 specimen as a syllogism, and of thus attaining the conclusion, 
 still the syllogistic process, as a mode of inference, is immeasurably
 
 304 A NEW LOGIC 
 
 inferior to the Method of Explication here propounded ; and is so 
 for the following reasons : — 
 
 1. There are many compound propositions to which the 
 syllogism cannot be applied. There are none that do not yield 
 to the Method of Explication. 
 
 2. There are many inferences that cannot be attained by the 
 syllogism. There are none that cannot be extracted by the 
 Canons of Explication. 
 
 3. Syllogisms are divided into four figures and nineteen moods, 
 all of which must be remembered by the student. Explication 
 knows nothing of figures or moods. 
 
 4. The reasoning of the syllogism is not alwa^'s self-evident. 
 To render it so, syllogisms, of figures other than the first, must be 
 reduced to the first figure, by a process that is often complicated, 
 and therefore liable to error. The reasoning of the Method of 
 Explication is self-evident. As there are no figures, there is no 
 reduction. 
 
 5. The Canons of the Syllogism are not self-evident. They 
 have an appearance of arbitrariness, which logicians seek to 
 overcome by explanation and argument. The Canons of Expli- 
 cation are, I think, self-evident, and have the appearance of 
 truisms. 
 
 6. Finally, I say it with bated breath, but in my opinion the 
 Canons of the syllogism are not true ; while the Canons of 
 Explication seem to me self-evidently true. 
 
 This indictment of the syllogism is sufficiently formidable; and 
 the claims of the alternative method that I propose must, I fear, 
 appear extravagant ; but I will now endeavour to show that I have 
 not spoken without reason. 
 
 I. In the first place, there are many Compound propositions to 
 which the syllogism cannot be applied ; many cases of Mediate 
 Inference which cannot be brought under syllogistic methods. 
 
 This needs no proof. It is sufficiently notorious. It is admitted 
 in nearly every modern text book on Logic, and in many of old 
 time. There is a whole range of Compound propositions, typified 
 by the argument h fortiori, and A = B = C, A > B > C, which 
 thrust implications upon us ; which shout aloud their implications; 
 whose implications jump at us and hit us in the face; and yet, 
 when we try to apply the syllogism to them, and to show how the
 
 REASONING A FORTIORI 305 
 
 implications may be formally obtained, wc are obliged to confess 
 our failure. If A precedes or follows B, and B precedes or 
 follows C ; if A is the cause of B and B the cause of C ; if A 
 controls or depends on B, and B controls or depends on C ; if 
 A is simultaneous with B, and B with C ; if A kills B, and the 
 death of B saves C from the gallows ; in every case a plain, 
 unmistakeable, unavoidable, inference, not merely presents itself, 
 but flings itself violently at the assertor and receiver of the 
 proposition. Yet in not one of these cases is the syllogism 
 applicable ; in not one can Traditional Logic give the grounds of 
 the inference, or even assert that it is valid. For twenty centuries 
 Traditional Logic has been explaining how, if man is mortal, and 
 Socrates is a man, we can arrive at the conclusion that Socrates 
 is mortal. For twenty centuries Traditional Logic has shirked 
 the problem How, if A is greater than B, and B is greater than C, 
 we infer that A is greater than C. With respect to this problem, 
 Traditional Logic appears to have employed a modification of 
 the syllogism which is not among any of the authorised figures or 
 moods of that venerable institution, and which it does not openly 
 avow. It must run somewhat as follows: — 
 
 All reasoning is syllogistic. 
 Reasoning a fortiori is not syllogistic ; 
 . • . The less said about reasoning a fortiori, the better. 
 
 The plain truth is that, as explained in the chapter on the 
 Ratio, the limitation of the Ratio of the logical proposition to the 
 copula, and the limited interpretation that logicians place on the 
 copula, preclude the syllogism from taking count of any relation 
 but those of class inclusion and exclusion. In spite of the 
 asseveration of logicians, that the Predicate is to be understood in 
 intention or connotation, their practice, as shown by the rule of 
 conversion, is to understand every proposition as expressing 
 inclusion or exclusion ; and consequently, no other relation can be 
 dealt with by the syllogism. This is the reason it is incapable of 
 following reasoning of the a fortiori class. 
 
 If A is equal to B, and B is equal to C, then, to the non-logical 
 mind, it is an inescapable inference that A is equal to C. But 
 Traditional Logic is incapable of drawing the inference. It has 
 been attempting for many generations to find the process by 
 which the conclusion is reached ; and it has failed. It has failed 
 
 N.L. X
 
 3o6 A NEW LOGIC 
 
 mainly because of its unreasonable adherence to the copula. As 
 explained in a previous chapter, Logic demands that the 
 Compound proposition shall be stated in the form of premisses, 
 thus : — 
 
 A — is — equal to B ; 
 B — is — equal to C. 
 
 Here there are four terms, and the fallacy qiiatcrnio tcnninorum 
 is fatal to a syllogism. If Logic were to adopt the method of 
 Mathematics, and state the premisses thus : — 
 
 A — is equal to — B ; 
 B — is equal to — C, 
 
 which, to the non-logical mind, seems the natural and proper 
 statement, and expresses the relations as they actually exist in the 
 mind, this particular fallacy would disappear ; but the doctrine of 
 the copula forbids the adoption of this form, and Logic accordingly 
 rejects it. To suppose that there is one mode of Reasoning in 
 Mathematics, and another mode of reasoning in Logic, seems to 
 me a gratuitous and unwarranted assumption. If it is asserted 
 that the conclusion A = C, from the premisses A = B = C, is 
 reached by a process different from that by which we reach the 
 conclusion A is equal to C from the premisses A is equal to B and 
 B is equal to C, then it seems to me that the onus of proving 
 so strange a thesis lies on those who assert it ; and though the 
 assertion is made, or the assumption begged, in every text book of 
 Logic, I know of no attempt to prove it. 
 
 The argument may be, and in many books of Logic is, stated 
 thus : — 
 
 Things that are equal to the same thing are equal to one 
 
 another, 
 A and C are equal to the same thing ; 
 . • . A and C are equal to one another ; 
 
 but there are fatal objections, both logical and other, to this 
 course. For one thing, there is no mention of B in this argument ; 
 and, though it is alluded to as ' the same thing,' there is 
 considerable doubt whether Traditional Logic would admit B 
 and B to be the same thing without a preliminary syllogism to 
 prove it. Indeed, I doubt whether Logic would, or, on its own
 
 EXAMPLES OF EXPLICATION 307 
 
 principles, ought, to admit, that 'A and C are equal to one 
 another ' is equivalent to A = C. 
 
 But whether Traditional Logic would or would not admit the 
 equivalence of this syllogism with the argument that since A and 
 C are both equal to B, they are equal to one another, I should 
 reject the syllogism on the ground that it is not the process of 
 reasoning that the mind goes through in order to reach the 
 conclusion from the postulate. In my view, the conclusion can 
 be reached, and is in fact reached, from the postulate alone, 
 without praying in aid a pyiiicipiuui oi such gigantic dimensions, for 
 which the postulate gives no warrant whatever. All that the 
 postulate grants is * A is equal to B and B is equal to C This 
 grants us the particular case, but it does not grant us the general 
 principle. It may be that we have the general principle in our 
 minds, but it does not follow that we are entitled to use it, or 
 that we actually do use it, in reaching the conclusion A is equal 
 to C. For my part I should deny both the one and the other. I 
 see in the postulate ' A is equal to B and B is equal to C,' no 
 more warrant for assuming the general case ' Things that are 
 equal to the same thing are equal to one another ' than I see in 
 the postulate 'The ship went to sea and foundered in a storm ' the 
 general case ' Ships that go to sea founder in storms ' ; and when 
 we receive the postulate * A is equal to B and B is equal to C,' 
 we can, and in my opinion we do, proceed at once to the conclu- 
 sion ' A is equal to C,' without begging any principiiun, and 
 without the intermediation of any major premiss. 
 
 Granting, however, for the sake of the argument, that the 
 conclusion is, in this case, reached through the intermediation 
 of this major premiss, how if the postulate is A is greater than 
 B, and B is greater than C ? We cannot now beg the major 
 ' Things which are greater than the same thing are greater than 
 one another,' or, if we do, it does not help us towards a valid 
 conclusion. We could, indeed, beg as a major, ' A thing which 
 is greater than another, which other is greater than a third, is 
 greater than that third ' ; but in this case the lack of warrant, as 
 well as the lack of necessity, for the imported principiwii, is even 
 more plainly apparent. Many logicians, quorum pars mininm fui, 
 have attempted to supplant the Dictum dc omni et nullo by a more 
 comprehensive formula, which should include the argument 
 a fortiori and its congeners ; but no one has succeeded to the 
 
 X2
 
 3o8 A NEW LOGIC 
 
 satisfaction of any one else ; and if such a formula could be 
 found, Nve should still need some warrant for introducing it as 
 a major into our arguments. We should still be going beyond the 
 postulate, and so violating the fourth Canon of Inference. 
 
 \\'hen, however, we apply to these arguments the Method of 
 Explication, all difficulties vanish ; and not only is the conclusion 
 reached directly, but we see at once that it is inevitable, and 
 why it is inevitable. If A is equal to B, and B is equal to C, it 
 is manifestly given that C, for the purpose of the argument, is 
 equivalent to B, and may, by the third Minor Canon of Explica- 
 tion, replace B in the first constituent of the postulate, which then 
 becomes A is equal to C. It is given also that, for the purpose 
 of the argument, A is equivalent to B, and may replace B in the 
 second moiety of the postulate ; and thus again we get A is equal 
 to C. 
 
 If A is greater than B, and B is greater than C, then, for the 
 purpose of the argument, C is implied in B, and may be sub- 
 stituted for B in the first constituent — A is greater than B — of the 
 postulate. Also, for the purpose of the argument, A is implied in 
 B, and may be substituted for B in the second moiety of the 
 postulate ; and thus again we get A is greater than C. 
 
 An obvious difficulty confronts us here. If any term in a 
 postulate may be replaced by one that is implied in it, and if C 
 is implied in B, then C may be substituted for B, not only in the 
 first constituent of the postulate— A is greater than B — but in 
 the second constituent also ; and we should then get C is greater 
 than C, which is absurd. The objection would be perfectly valid 
 if the rule were as just stated ; but it is not. The rule is that 
 any term may be replaced by any other term, not that is generally 
 implied in it, but that for the purpose of the argument is implied in 
 it ; and the words italicised make all the difference. For what 
 is the purpose of the argument ? It is not to establish a relation 
 between A and B, or between B and C, for those relations are 
 already given. It is to find what else than B is greater than C ; 
 what else than B, A exceeds in magnitude ; or what the relation is 
 between A and C. For the purpose of this argument, A is not 
 implied in B in the proposilion A is greater than B. A does not 
 become implied, until B is introduced into the second constituent 
 of the postulate. For the purpose of the argument, C is not 
 implied in B in the proposition B is greater than C. C is not
 
 EXAMPLES OF EXPLICATION 309 
 
 implied in B until B is introduced into the proposition ' A is 
 greater than B.' This meaning of the phrase ' for the purpose of 
 the argument ' being understood, the Canon will be seen to be 
 impeccable, to whatever proposition it is applied. 
 
 If A revolves round B, and C is fixed to A, then, for the purpose 
 of the argument, C is implied or included in A, and may be substi- 
 tuted for it, and we get C revolves round B. If A depends on B, 
 and B depends on C, then, for the purpose of the argument, A is 
 implied in B, and depends on C. But if A cheats B and B cheats 
 C, we are clearly not entitled to conclude that A cheats C ; nor, 
 if A is killed by B and B is killed by C, are we entitled to con- 
 clude that A is killed by C. It is the difficulty of providing for 
 the first two cases, without including the two latter, that has 
 frustrated every attempt to discover a satisfactory formula, on 
 the lines of the Dictum, to account for these arguments. But 
 the Method of Explication renders the distinction clear, and 
 satisfactorily includes what ought to be included, and excludes 
 what ought not. If A depends on B, and B on C, then it is 
 evident that, for the purpose of the argument, ' A depends on B,' 
 C is implied in B, and may replace it ; and we may safely and 
 properly infer that A depends on C. But if A cheats B and B 
 cheats C, it is equally clear that C is not, for the purpose of the 
 argument, implied in B ; nor, if A is killed by B, and B is killed 
 by C, is C implied in B. 
 
 Still, even in the last two cases, we are not precluded from 
 drawing any inference at all. By the method of the syllogism, 
 indeed, no inference can be obtained from the premisses A killed 
 B, and B killed C ; but by the Method of Explication we can get, 
 by the first Canon, C died before A, and several others; by the 
 first Minor Canon, C was killed by B and B by A ; the third 
 Canon shows us that C did not survive A; and several others. 
 Finally, the fourth Canon gives us that A and B were both 
 homicides, and that they resemble each other in this respect. 
 
 If A is equal to B, and B is unequal to C, the syllogism does not 
 enable us to draw any conclusion ; but, by the third Canon of 
 Explication, we are permitted to deny any proposition inconsistent 
 with the postulate ; amongst others, we may deny any proposition 
 in which a term of the postulate is replaced by a term inconsistent 
 with it. For the purpose of this argument, C, if substituted for 
 B in the postulate A is equal to B, is inconsistent with B ; and
 
 310 A NEW LOGIC 
 
 we may therefore deny the proposition A is equal to C. By the 
 second Minor Canon, this implies A is unequal to C. The same 
 method will give corresponding results in all propositions of the 
 class. 
 
 2. Apart from the argument a fortiori and its congeners, there 
 is an immense range of propositions to which the syllogism is 
 inapplicable, and in which it gives no assistance : all of these 
 yield readily to the Method of Explication. 
 
 It is m}- knife : I know it by a nick in the blade, and a chip 
 out of the handle. It is not my knife, for mine is smaller than 
 that. He had been there, for his name was in the visitors' book. 
 He was not there, for I searched every room in the house without 
 finding him. Europeans differ from Asiatics, for the former are 
 capable of self-government, and the latter are not. Europeans 
 resemble Asiatics, for they both have the same physical structure. 
 These arguments are either not attainable at all by the syllogism, 
 or, if a syllogism can be constructed by which the conclusion can 
 be reached, it clearly does not represent the mental transaction 
 employed in attaining the conclusion. 
 
 It is my knife : I know it by a nick in the blade and a chip 
 out of the handle. If I reach this conclusion by the syllogism. 
 What is the missing major ? Is it * All knives with a nick in the 
 blade and a chip out of the handle belong to me ' ? Even a 
 logician would scarcely venture on such an assumption. More- 
 over, I know my knife by the particular size, shape, and position 
 of the nick in the blade and of the chip out of the handle. In 
 other words, I identify it as a particular individual thing, without 
 going through the medium of a universal. If an individual is a 
 Universal, then, I suppose, the missing major is universalised by 
 expressing the whole of the knife, but I do not see how this helps 
 us ; and if a singular proposition may be a Universal, and some 
 logicians contend that it can and ought to be so considered ; then 
 a fortiori, a proposition whose Subject is two, or three, or several 
 individuals of the same class, must be more than a universal, and the 
 distinction between the universal and the particular is submerged. 
 
 Is this the argument ? 
 
 My knife is one with a nick, &c. ; 
 This knife is one with a nick, &c. ; 
 .•. This knife is my knife.
 
 EXAMPLES OF EXPLICATION 311 
 
 This is no syllogism. The middle term, being in both 
 premisses the predicate of an affirmative proposition, is undis- 
 tributed. I do not see how the conclusion can be reached 
 through syllogistic reasoning ; but by the Method of Explication, 
 the course of the reasoning is clear enough, and the conclusion 
 may be reached secundum artem. By the third Minor Canon, we 
 are allowed to replace any term in a proposition by one that is, 
 for the purpose of the argument, equivalent to it. Very well. 
 In the first of these propositions, ' My knife ' is given equivalent 
 to * one with a nick, &c.' ' My knife ' may, therefore, replace the 
 term ' one with a nick, &c.,' in the second premiss ; and this gives 
 us at once the conclusion we seek — ' This knife is my knife.' No 
 major premiss — no Universal — is employed, for none is needed. 
 
 * That knife is not mine, for mine is smaller than that.' If this 
 is an enthymeme, what is the missing major ? I suppose the 
 complete syllogism would be something like this : — 
 
 No knife, than which mine is smaller, is mine ; 
 My knife is smaller than that knife ; 
 .'. That knife is not mine. Fesapo. 
 
 If there are people so constituted that they prefer to invent a 
 principium of this gruesome character, and to obtain, or fancy 
 that they obtain, their conclusion by means of it, I have no 
 objection, so long as they do not insist upon my doing the same. 
 For my own part, I prefer a more direct route to my destination. 
 If my knife is smaller than that, then that knife is inconsistent, 
 for the purpose of the argument, with my knife ; and what is 
 inconsistent with the postulate may, by the third Canon of 
 Explication, be denied. In other words, that knife is not mine. 
 
 ' He had been there, for his signature is in the visitors' book ' can 
 be reached by a syllogism if we invent the major ' All whose 
 signatures are in the visitors' book had been there ' ; but we are 
 not warranted in assuming this major. His signature may, for aught 
 the postulate grants, be the only one in the book. We may, 
 however, get the same conclusion, without the intermediation 
 of any major, by the first Canon of Explication. A postulate 
 implies ever}- condition necessary to it. A necessary condition 
 of writing his name in the visitors' book is that he must have 
 been there. On the other hand, * He was not there ' cannot be 
 reached syllogistically from ' I searched every room in the house
 
 312 A NEW LOGIC 
 
 without finding him,' unless we invent such a major as ' In all cases 
 in which every' room in a house is searched without finding a person, 
 that person is not there.' This is manifestly not the process of 
 thought by which the conclusion is reached. No such major would, 
 in fact, be constructed by the most enthusiastic syllogiser, unless he 
 wished to bring the syllogism into ridicule. The actual process of 
 thought is very different, and is that indicated by the fourth Canon of 
 Explication. Ever}- thing inconsistent with the postulate may be 
 denied. If I have searched every room in the house without 
 finding him, it is inconsistent with this postulate to say he was there ; 
 and that he was there may properly be denied. 
 
 ' Europeans differ from Asiatics, for the former arc capable of 
 self-government, and the latter are not.' No syllogism can be con- 
 structed to represent the course of thought by which this conclusion 
 is reached from the premiss. If the argument is considered, it 
 will be seen that the conclusion is attained directly from the single 
 premiss, and that no major is required ; unless, indeed, the fifth 
 Canon of Explication is taken as a major. When two terms are 
 postulated in inconsistent relations to a third, they differ from one 
 another with respect to that third. 
 
 There is an old example, first discovered by the Pert Royal 
 logicians, of a conclusion that is too manifest to be questioned, but 
 that baffles all the resources of Traditional Logic to attain. It 
 runs as follows : — 
 
 The Persians worship the sun ; 
 The sun is an insensible thing ; 
 . • . The Persians worship an insensible thing. 
 
 This is not a syllogism, for it contains no Universal, and the 
 middle term is undistributed. 
 
 It is clear, however, that, for the purpose of the argument — that 
 is, of what the Persians worship, — the sun is given equivalent to an 
 insensible thing, and may therefore replace it in the first premiss. 
 This replacement gives us the conclusion. Could any process be 
 more simple, or more manifestly indicate the actual process of 
 thought ? 
 
 These examples are sufficient to establish my first two theses — 
 that there are many Compound propositions to which the 
 syllogism cannot be applied : many inferences that it cannot attain ;
 
 LIMITATIONS OF THE SYLLOGISM 313 
 
 and that when the syllogism is insufficient and incapable, the 
 Method of Explication displays the course of the reasoning. 
 
 3. The next thesis is that the syllogism cannot extract, even 
 from those compound propositions to which it can be applied, any 
 but a very few of the implications they contain ; while the Method 
 of Explication can extract an indefinite number. If all birds fly 
 and no pigs f\y, no syllogistic inference can legitimately be drawn 
 from these premisses, for neither of them is in strict logical form. 
 But if we waive this objection, we can get, in Cesare, that No 
 birds are pigs ; and in Camestres, that No pigs are birds; but 
 beyond these inferences we cannot go. The resources of Traditional 
 Logic are exhausted. But by the Method of Explication we can 
 get much more than this. We can get * All birds can do what no 
 pigs can do ' ; and * No pigs can do what all birds can do.' We 
 can get ' Birds and pigs do not both iiy ' ; ' Birds and pigs differ 
 from one another in respect of flying ' ; and ' Flying marks a 
 difference between birds and pigs.' 
 
 The last three propositions are instances of a very important 
 advantage that the Method of Explication has over the sj-llogism. 
 In no syllogism does the middle term appear in the conclusion. 
 Yet it is often a very valuable result to get the middle term into 
 the conclusion ; and many arguments are undertaken with no other 
 purpose. If Hamlet lectured his mother on virtue, and if Hamlet 
 murdered Polonius, then the same man that lectured his mother 
 on virtue, committed murder. This is a significant implication of 
 the postulate. If most birds fly, and some fish fly, then some fish 
 are like most birds in respect of flying. If penguins and auks 
 can not fly, and other birds can, then penguins and auks are 
 unlike other birds in respect of flying, and the ability to fly marks 
 a difference between them.. If typhus fever has a confluent rash, 
 and typhoid fever a discrete rash, then typhus and typhoid have 
 different rashes, and the character of the rash marks a difference 
 between typhus and typhoid. Few inquiries are more important, 
 on occasion, than Are these things alike or different ? and In 
 what respects are they alike or different ? What is the resemblance 
 between this and that, what the difference between that and the 
 other ? These are problems which confront us daily and hourly, 
 but Traditional Logic knows nothing of them, and leaves us 
 without means of solving them. Modern Logic has detected the 
 omission of the middle term from the conclusion, and regards the
 
 314 A NEW LOGIC 
 
 omission as not inherent in the nature of syllogistic inference, but 
 as an accident. The middle term could be, and I gather that 
 Modern Logic considers that it ought to be, expressed in the 
 conclusion. If this the opinion of Modern Logic, it goes too far. 
 Whether the middle term ought or ought not to appear in the 
 conclusion depends on the purpose of the argument. It depends 
 on the aspect of the subject-matter in which we are interested. It 
 may be that an inference is useless to us unless the middle term 
 appears in the conclusion : it may be that the presence of the 
 middle term in the conclusion is surplusage and redundancy. It 
 depends on the purpose of the argument. 
 
 4. The fourth advantage of the Method of Explication over the 
 syllogism is that in the Method of Explication there are no figures 
 or moods to be remembered, and no need of reduction from one 
 figure to another to make the argument convincing. In some 
 syllogisms, the argument is not convincing. It is, at any rate, not 
 self-evidently valid. It does not at once carry conviction to an 
 ordinary mind, unaccustomed to the peculiarities of the syllogistic 
 figures. Take Fesapo, for instance : — 
 
 No applewoman sells flowers, 
 Selling flowers is a profitable occupation ; 
 . ■ . Some profitable occupation is not followed by applewomen. 
 
 There seems to be an hiatus here. Some step in the reasoning 
 appears to be left out. The sequence of the argument is not self- 
 evident. We have to go over it again to assure ourselves that 
 the conclusion is justified. Some assurance of its justification is 
 lacking. It is in order to supply this assurance that syllogisms 
 in the last three figures are reduced to the first; and this reduction 
 requires, in this case, two operations. First the major premiss is 
 converted, and becomes ' Selling flowers is not followed by apple- 
 women ' ; and next, the minor premiss is converted per accidens, 
 and becomes ' Some profitable occupation is selling flowers ' ; and 
 from these new premisses it is contended that the conclusion is more 
 self-evidently reached than from those of the original syllogism. 
 Whether this contention is justified, the reader must judge for 
 himself; but whether it is or no, it is, in my opinion, far more 
 satisfactory to follow a mode of reasoning which is transparently 
 and manifestly valid, and needs no reduction to another mode to 
 make it appear valid. By the Method of Explication, the con-
 
 REDUCTION 31S 
 
 elusion is thus reached ; — Since, by the first Minor Canon of 
 Explication, every postulate implies its reciprocal, ' No apple- 
 woman sells flowers ' implies ' Selling flowers is not followed by 
 applewomen.' For * selling flowers ' we may, by the third Minor 
 Canon, substitute the term ' a profitable occupation,' which is 
 postulated equivalent to it ; and thus we get ' A profitable 
 occupation is not followed by applewomen.' 
 
 By this method, whatever conversion of premisses is desirable 
 in order to make the argument self-evident, is effected in the course 
 of the argument, and is not left over to a subsequent process after 
 the argument is finished. By the syllogistic method, in short, 
 the proof of a conclusion requires further proof before it can be 
 fully accepted : by the Method of Explication but one process of 
 proof is necessary. At every step we are assured that we are on firm 
 ground before we go on to the next. By the institution of the 
 process of reduction, it is admitted and declared that no such 
 assurance is given by any figure of the syllogism except the first ; 
 for the purpose of reduction is, by bringing the other figures into 
 the first, to carry to the mind of the syllogiser that his argument 
 is valid. The purpose of reduction is to reassure the syllogiser ; 
 to convince him that his argument is not mere hocus-pocus ; and to 
 this end he is furnished with the mnemonic verses concerning 
 Barbara, Celarent, and the rest, to enable him to perform reduction 
 in every case. The process is by no means easy. In some cases 
 it is very elaborate ; and furnishes the novice with ample oppor- 
 tunities for error. Take, for instance, Bokardo, now known by 
 the more euphonious title of Doksamosk ; and let us try this 
 specimen : — 
 
 Some men are not vegetarians ; 
 All men are mortals ; 
 . • . Some mortals are not vegetarians. 
 
 In order to reduce this to Darii in the first figure, the following 
 series of processes must be conducted. First contrapose the major 
 premiss. Contraposition we have found to be not a very 
 simple process. To obtain the contrapositivc, we must first 
 obvert, and then convert the obverse. 
 
 Major premiss : Some men are not vegetarians ; 
 Obverse : Some men are non-vegetarians ; 
 
 Converse: Some non-vegetarians are men.
 
 3i6 A NEW LOGIC 
 
 Now take the proposition, thus obtained from the major premiss 
 of your syllogism, and make it the minor premiss of a new syllogism, 
 having the minor premiss of your old syllogism for a major. You 
 will then obtain the premisses : 
 
 All men are mortals ; 
 
 Some non-vegetarians are men ; 
 
 and from this you get the conclusion, ' Some non-vegetarians 
 are mortals.' This, by conversion, yields ' Some mortals are non- 
 vegetarians,' and finally, by one more obversion, you arrive at the 
 end of your long journey, and triumphantly attain the conclusion 
 ' Some mortals are not vegetarians.' 
 
 Whether the importance of the result is commensurate with the 
 time and trouble necessary to attain it, the reader must judge for 
 himself; but if, notwithstanding the reduction to Darii, he is still 
 unsatisfied with his syllogism, and cannot be convinced of its 
 validity without reducing it to Barbara, he will be pleased to know 
 that he is not at the end of his resources. All he has to do is to 
 substitute for his major premiss the contradictory of his conclusion. 
 By this means he gets a syllogism in Barbara, the conclusion of 
 which contradicts his original major. Thus he reduces his 
 syllogism to absurdity, a result not without further significance. 
 
 It does seem that if a simpler method of ensuring the validity 
 of a syllogism could be found, it would be preferable ; and such a 
 method is, I submit, found in the Method of Explication. By this 
 method, we are authorised to replace any proposition by its 
 reciprocal, and any term by its equivalent or its part. We may, 
 therefore, replace ' mortals ' by ' some mortals ' and ' All men are 
 mortals ' by ' Some mortals are all men.' ' Some men ' are 
 included, for the purpose of the argument, in ' all men ', and 
 may therefore be substituted for ' all men ' ; and thus we get 
 'Some mortals are some men.' But 'not vegetarians' is given, 
 in the major premiss, equivalent, for the purpose of the argu- 
 ment, to ' Some men,' and may therefore be substituted for 
 ' some men.' Hence we get, in three steps, * Some mortals 
 are not vegetarians.' Thus the two processes, of deriving the 
 conclusion, and assuring ourselves of its validity, are carried on 
 simultaneously, and attained in three ver}^' simple steps; and all the 
 many processes of reduction, together with their rules, the mne- 
 monic verses which enable us to remember them, and the quaint
 
 RULES OF THE SYLLOGISM 317 
 
 and curious names of the moods, in which the rules are summarised 
 and conveyed, may all be dispensed with, and relegated to the 
 limbo of antiquarian curiosities, where they may take their place 
 beside the pentacle and the philosopher's stone. Barbara will 
 then occupy the same glass case as Abracadabra and phlogiston, 
 as the crystal spheres of Ptolemy and the hypostatised ' forms ' of 
 Plato ; and the curious spectator will recognise the congruity of 
 them all. 
 
 5. The fifth advantage claimed for the Method of Explication is 
 that its Canons are sclf-evidcntly valid, while those of the syllogism 
 are not. We intuitively recognise that a proposition implies its 
 reciprocal ; that any term may be replaced by its equivalent ; that 
 when a postulate is granted, all the conditions necessary to it are 
 granted ; that every proposition denies what is inconsistent with 
 it ; and so forth. But we do not intuitively perceive the necessity 
 for every argument to contain three propositions and no more, 
 three terms and no more ; that the middle term must be distributed 
 at least once ; that the premisses must not be both particular, nor 
 both negative. We may be able to acquiesce in the validity of 
 these rules when they are explained to us, though for my own part 
 I am not able to do so ; but we certainly do not perceive it 
 intuitivelv. 
 
 6. Lastly, the rules of the syllogism are erroneous, and pro- 
 ductive of fallacy. That they arc in some respects erroneous has 
 been discovered by Modern Logic ; but the criticism of them by 
 Modern Logic is far less drastic and thoroughgoing than that to 
 which I should subject them. A distinction must be drawn here, 
 however. Some of its rules are untrue of the syllogism itself ; that 
 is to say, the syllogism does not, or need not, conform with them. 
 Others are valid as applied to the syllogism itself, but are not true 
 of reasoning generally. They are falsified, as Canons of Inference, 
 by our experience of inferences drawn by the Method of Explication. 
 If the syllogism poses as the Universal Principle of reasoning, 
 they are untrue ; if it is accepted as but one method, and that an 
 imperfect and clumsy method, of explicating some of the implica- 
 tions of the Compound proposition, they may pass as Canons of 
 that method.
 
 CHAPTER XX 
 
 THE FAULTS OF THE RULES OF THE SYLLOGISM 
 
 The first rule of the syllogism is that it must contain three, and 
 no more than three, terms. Otherwise put, this means that the 
 powers of the syllogism are limited to explicating those Compound 
 propositions that have no more than three terms. To propositions 
 more comprehensive than this, it is inapplicable, and in this rule 
 it confesses its incompetence to explicate them. But compound 
 propositions can be constructed with as many terms as we like, 
 and it is as easy to explicate these by the Method of Explication 
 as to explicate those with three terms only. The multiple 
 proposition is outside the purview of both Traditional and Modern 
 Logic. 
 
 'All wits arc envious and malicious.' From this postulate, 
 Traditional Logic can deduce but two conclusions : 
 
 All wits are envious ; 
 All wits arc malicious ; 
 . • . Some malicious people are envious. Darapti. 
 
 All wits are malicious ; 
 All wits are envious ; 
 . • . Some envious people are malicious. Darapti. 
 
 These are all the conclusions that Traditional Logic can give us ; 
 but it can give us these conclusions, and so far it may be patted 
 on the back, and commended. But if, instead of the Compound 
 proposition ' All wits are envious and malicious ', we give it the 
 postulate ' All wits are envious, malicious, untruthful and spiteful,' 
 neither Traditional Logic nor Modern Logic can extract any 
 inference at all. They can only contemplate it with helpless 
 stupefaction. Envy and malice are fair and proper subjects of 
 Inference ; but envy, malice, untruthfulness and spitcfulness are 
 outside the pale of reasoning, or, if admitted, must come in through 
 a turnstile, two by two, like schoolgirls under the eye of their 
 mistress.
 
 FAULTS OF THE SYLLOGISM 319 
 
 To the Method of Explication, four terms, or forty, present no 
 more difficulty than three. Grant the postulate ' All wits are 
 envious, malicious, untruthful and spiteful,' and this Method will 
 furnish you with the inferences that envy, malice, untruthfulness, 
 and spite are qualities of all wits ; that these four qualities are 
 consistent with one another ; that all wits are alike in possessing 
 them ; and many more. Nor arc the powers of the Method of 
 Explication limited to the Compound proposition with a multiple 
 Object-term. ' All anglers and some golfers are untruthful, and 
 addicted to exaggeration of their own success.' This contains 
 two Subjects, two Objects, and two Ratios; — eight propositions 
 altogether — and I do not know what Traditional Logic could do in 
 the presence of such a proposition, except sit down and cry ; but 
 to the Method of Explication it yields readily enough an innumer- 
 able multitude of implications. If Traditional Logic attempted 
 to deal with such a postulate at all, it must first break up the 
 postulate into its eight constituent propositions, and then take 
 them two by two ; but even then it would be helpless. For what 
 could it do with such a pair of propositions as * All anglers are 
 untruthful,' and ' All golfers are addicted to exaggeration of their 
 own success ' ? Traditional Logic might scratch its head into a 
 hole before it could make a syllogism out of such a pair. 
 
 Modern Logic would, I suppose, refuse to look at such a postu- 
 late, for, to Modern Logic, * Inference is the indirect reference to 
 reality of differences within a Universal by means of the exhibition 
 of this universal in differences directly referred to reality.' 
 Whether ' All anglers and some golfers ' constitute together a 
 Universal ; whether their unanimous and lamentable addiction 
 to untruthfulness and exaggeration are differences within this 
 universal ; whether, if so, all anglers and some golfers are exhibited 
 in these differences ; and whether or no the differences are directly 
 referred to reality ; are questions that I am not competent to 
 decide. At any rate, Modern Logic, through the mouth of 
 Mr. Bosanquet, is emphatic in asserting that ' Inference must have 
 three terms and no more.' 
 
 The second Canon of the syllogism states that the syllogism 
 must consist of three, and of no more than three propositions. 
 This rule seems, on the face of it, to deny the possibility of more 
 than one conclusion being deduced from any one pair of premisses. 
 There is no rule, as far as I know, explicitly stating that two
 
 320 A NEW LOGIC 
 
 premisses can lead to but one conclusion ; but such a rule seems 
 implicit in the second Canon of the syllogism ; and there is no 
 instance, in any text book, of a second conclusion being drawn 
 from any one pair of premisses, except the weakened conclusion, 
 in which we deduce a conclusion with respect to some, when we 
 are entitled to predicate it of all ; and the unique case of Camestres 
 and Cesare. I think, therefore, that it is not unfair to interpret 
 the Canon in this sense. Yet how many implications are there 
 not latent in every Compound proposition ! How many manifest ; 
 how many permissible ; how many possible ! Take as an instance 
 the teetotal argument, — 
 
 Every one who drinks poison commits suicide ; 
 Ever}' one who drinks wine, drinks poison. 
 
 From these premisses the syllogism permits of but one 
 conclusion : — 
 
 . • . Every one who drinks wine, commits suicide. 
 
 But from the same premisses, the Method of Explication will 
 extract twenty conclusions, all manifestly contained in the 
 premisses, and all valid ; for instance — 
 
 No one who drinks wine escapes death by suicide. 
 
 Drinking wine ensures death by suicide. 
 
 Drinking wine and suicide are compatible. 
 
 Every one who drinks wine, drinks poison and commits 
 
 suicide. 
 Some people drink poison in the shape of wine. 
 Some people commit suicide by drinking wine. 
 Every one who drinks wine poisons himself. 
 Some people poison themselves by drinking wine. 
 One way of committing suicide is to drink wine. 
 
 And so forth, and so on, indefinitely. It may be said, and it may 
 be freely admitted, that these are alternative conclusions, and that 
 in any one argument only one of them can appear, so that, after 
 all, there would be but three propositions in the argument. I do 
 not see why the conclusion from a compound proposition should 
 not itself be a compound proposition ; but waiving this, and
 
 VICES OF THE SYLLOGISM 32I 
 
 granting for the sake of argument that these examples do not 
 invalidate the syllogistic rule against the employment of more 
 than three propositions in an argument, it is very easy to construct 
 examples that do violate the rule. 
 
 If Many are called ; 
 Few are chosen ; 
 And Still fewer are found suitable ; 
 Then Very few of those who are called are found suitable. 
 
 If some are green, more are blue, a few are yellow, and the rest 
 are brown, then none of them is white. In these examples 
 advantage is taken of the quantities that Traditional Logic ignores ; 
 but without utilising these quantities, we may still construct 
 perfectly valid arguments with more than two premisses. Take, 
 for instance, the following : — 
 
 Ptomaine poisoning is due to eating toxic food ; 
 Several persons suffered at the same time from ptomaine 
 
 poisoning ; 
 They had all partaken of the same dish; 
 .•. The toxin may have been in that dish. 
 
 From the third Minor Canon of Explication we get out of the 
 first two premisses, the implication ' Several persons ate toxic 
 food.' The third premiss gives us that these persons had all eaten 
 of that dish, so that by the fourth Canon of Explication, toxic 
 food and that dish are consistent. In other words, that dish may 
 have contained toxic food. This is a conclusion that no syllogism 
 could extract. The syllogism knows nothing of what may have 
 been. The conclusion is a Modal proposition, and as such is 
 excluded from syllogistic Logic. But will anyone have the 
 temerity to maintain, either that this conclusion is not a valid 
 inference from the premisses, or that it is not a valuable conclu- 
 sion to obtain ? Surely it is as important to prove that that dish 
 may have contained the toxin, as it is to prove that Socrates is 
 mortal. It may be objected that here are two inferences, and not 
 one only ; and that the true form of the argument is a sorites, in 
 which the conclusion of one argument becomes the premiss of the 
 next. I do not see that the nature of the process is in any way 
 affected by the name we give it. Call it Sorites or Baralipton or 
 
 N.L. V
 
 322 A NEW LOGIC 
 
 anything you please, but you will not alter the fact that the 
 conclusion cannot be obtained by any process known to Tradi- 
 tional Logic, but is obtained with the greatest ease and certainty 
 by the Method of Explication. We have seen in our examination 
 of Bokardo, that the conclusion, even of a syllogism, cannot 
 always be attained by a single step ; but that, to assure ourselves 
 of its validity by the strictest syllogistic reasoning, may require as 
 many as seven successive operations. 
 
 The third rule of the syllogism is that the middle term must be 
 
 * distributed ' in at least one of the premisses. This is true if the 
 two quantities of Traditional Logic — the Particular and the 
 Universal — are the only quantities that exist. But if it is true, as 
 I maintain, that the quantities few, many, most, this, that, 
 scarcely any, nearly all, and the rest of them, were devised by 
 man to satisfy his needs, and to characterise quantities about 
 which he desired to reason ; then the rule, that the middle term 
 must be ' distributed,' in the sense in which Logic understands 
 'distributed,' is untrue, and falls to the ground. No logician 
 would admit that * Nearly all ' distributes the term it quantifies. 
 
 * Nearly all ' is a variety of * some,' and ' some ' is the mark of the 
 particular. But take the followmg argument : — 
 
 Nearly all in the pit were miners ; 
 Nearly all in the pit were killed ; 
 .'. Some of the killed were miners. 
 
 This inference is unimpugnably valid ; and so is the following : — 
 
 Very few people are strict vegetarians ; 
 Scarcely any strict vegetarians are vigorous ; 
 . ■ . Scarcely any people are vigorous vegetarians. 
 
 I don't know whether logicians would admit that this is a 
 syllogism. Probably they would not ; but then so much the 
 worse for Traditional Logic ; for it is indisputably a mode of 
 reasoning, and a valid mode. 
 
 The actual rule, which ought, in my opinion, to be substituted 
 for the rule of the distributed middle is this: — If the middle term 
 is quantitative (it need not be, but if it is) then it must not be of 
 less ample quantity than the term that replaces it. This follows 
 from the third Minor Canon of Explication ; which allows us to
 
 VICES OF THE SYLLOGISM 323 
 
 replace any term by one which is equivalent to it or is included in 
 it. A term which is of the same quantity as another is quantita- 
 tively equivalent to it. A term which is of less quantity than 
 another is quantitatively included in that other. It makes no 
 difference whatever to the validity of the argument how limited is 
 the quantity of the middle term, so long as the term substituted 
 for it in the conclusion is not of greater amplitude. In the last 
 example, the middle term — strict vegetarians — is undistributed in 
 the major as the predicate of an affirmative proposition ; it is 
 undistributed in the minor by the quantification ' Scarcely any.' 
 Yet, since vegetarians include vigorous vegetarians, the latter term 
 may be substituted for the former, and the middle, undistributed 
 as it is, is of sufficient amplitude for the purpose of the argument. 
 The fourth rule of the syllogism is that no term may be distri- 
 buted in the conclusion that is not distributed in a premiss. This 
 rule is good as far as it goes ; but it does not go far enough. It is 
 sufficient for the two quantities of Traditional Logic, but it is not 
 sufficient if the other quantities are allowed to enter into the 
 argument. If a semi-definite quantity is admitted, and it has 
 been shown that perfectly valid arguments may be constructed 
 with the semi-definite quantity, then the argument may be invalid 
 even though the rule is punctually observed. It will be invalid if 
 the quantity of a term in the conclusion, although not distributed, 
 is yet in excess of the term it replaces. 
 
 Most brave men are generous ; 
 Most sailors are brave men ; 
 .*. Most sailors are generous. 
 
 No term is distributed in this conclusion that is not distributed 
 in a premiss ; yet the argument is invalid. As a syllogism, it is 
 invalid because both the premisses are particular ; but the rule 
 against particular premisses will be shown presently to be itself 
 invalid. The fallacy in this argument must rest, therefore, on a 
 different ground ; and it is easy to see what the ground is. The 
 fourth Canon of Inference is violated. According to this Canon, 
 we may not assume more than is in the postulate. Among other 
 prohibitions, we may not replace a term by one of greater quantity. 
 A term may be substituted for any term that contains it ; but not 
 for any term by which it is contained ; and this is what is done in 
 
 Y 2
 
 324 A NEW LOGIC 
 
 this argument. ' Most sailors ' in the second premiss are substi- 
 tuted in the first premiss for ' Most brave men,' in order to get the 
 conclusion ' Most sailors arc generous.' But * Most sailors ' are 
 not given equivalent to, or less than, ' Most brave men.' They 
 are given, in the second premiss, equivalent to ' brave men ' ; and 
 ' most brave men ' is a term of less ample quantity than * brave 
 men.' Hence, in substituting ' most sailors ' for * most brave 
 men ' we are substituting a term of greater quantity for a term of 
 less— a containing term for a contained — and so are violating the 
 fourth Canon of Inference. The fallacy is a kind of illicit minor, 
 but a kind unknown to Traditional Logic. 
 
 The fifth rule of the syllogism is that one of the premisses at 
 least must be affirmative, and no conclusion can be drawn from 
 negative premisses. Modern Logic repudiates the rule, and I 
 respectfully signify my agreement with Modern Logic. Even 
 exponents of Traditional Logic so devoted as Jevons have long 
 recognised that a conclusion may be drawn from premisses, one 
 of which contains a negative ratio, and the other a negative term ; 
 and have offered an explanation that seems to me valid, — that an 
 affirmative ratio with a negative term makes, or may make, in 
 fact, an affirmative proposition. With this I should agree ; but 
 in this case, what becomes of the Universal Negative, the E 
 proposition, of Traditional Logic, with its negative subject ? 
 As far as I can see it becomes, or may become, a Universal 
 Affirmative. My objection to the prohibition of negative premisses 
 does not rest, however, on any quibble concerning the negative 
 proposition. When both premisses are negative, in the ample 
 sense of having negative Ratios, it is still possible to deduce from 
 them good, valid, and useful conclusions. 
 
 The coachman is not beautiful ; 
 Beauty is not necessary in a coachman ; 
 . • . The coachman is not incapacitated by his want of beauty. 
 
 I do not claim that this is a syllogism, and frankly, I don't care 
 whether it is or not ; but it is a good sound argument from two 
 negative premisses. So is the following : — 
 
 We have no paste ; 
 Paste is not a bait for pike ; 
 . • . Our want of paste docs not deprive us of a bait for pike.
 
 VICES OF THE SYLLOGISM 325 
 
 From the negative premisses 
 
 No pigs fly ; 
 No pigs hop ; 
 
 the syllogism can deduce no inference ; but the Method of 
 Exphcation allows us to infer that pigs neither fly nor hop ; that 
 some things that neither fly nor hop are pigs ; that all pigs are 
 alike in respect that they neither fly nor hop ; that any thing that 
 either flies or hops is not a pig ; and so on. 
 Mr. Bosanquet suggests the argument 
 
 No mere animal has language ; 
 A deaf mute is no mere animal ; 
 .'.A deaf mute has language, 
 
 and says ' Horrible as these arguments must appear to anyone 
 conversant with syllogistic rules, I do not see how they are to be 
 kept out if the argument from two negations in fig. 3 is admitted.' 
 This specimen seems to me plainly a fallacy quaternio terminorum, 
 perpetrable solely on account of a pecuhar English idiom. It has 
 been maintained above that an argument may have four terms 
 and still be valid ; but it is not maintained that a syllogism may 
 have four terms and still be valid. ' No mere animal,' in the 
 major premiss, is a negative term ; but ' no mere animal,' in the 
 minor, is an English idiom for ' not a mere animal.' The negative 
 belongs to the Ratio, not to the Object. Hence there are two 
 middle terms, — ' No mere animal ' and * a mere animal ' — and it is 
 plain that the second of these is neither equivalent to, included in, 
 nor implied in the first ; and may not, therefore, be substituted 
 for it. The pseudo-argument is a mere quibble. 
 
 The sixth and last of the primary rules of the syllogism is that 
 if one premiss is negative, the conclusion must be negative ; and 
 if the conclusion is to be negative, one premiss must be negative. 
 This is very far from the truth. It is as easy as possible to reach, 
 by the Method of Explication, an affirmative conclusion from 
 premisses, one of which is negative ; and a negative conclusion 
 from premisses, both of which are affirmative. It some of the I 
 jury were for the plaintiff, and some were not for the plaintiff", 
 then the jurors were divided in opinion. This argument violates 
 no fewer than five of the rules of the syllogism ; and yet it is
 
 326 A NEW LOGIC 
 
 perfectly valid. It has five terms; the middle term is not dis- 
 tributed ; both premisses are particular ; the affirmative conclusion 
 is drawn from premisses, one of which is negative ; the conclusion 
 is universal, though not only one, but both of the premisses are 
 particular. It is true that the argument is no syllogism, and does 
 not pretend to be a syllogism ; but it is a good, sound, valid argu- 
 ment for all that. The conclusion cannot be obtained by any 
 syllogistic process, but yet it is not only valid, but it is attained by 
 a single step — by a single process of inference. The Canon of 
 Explication that authorises us to draw the conclusion is the 
 second — a postulate implies all that is necessary to it. If some of 
 the jury were for the plaintiff and some were not, it is implied 
 that there was a jury; that the jurors had opinions ; that some 
 were of one opinion and some of another ; that their opinions were 
 divided. Again, 
 
 Many Irish go to America ; 
 Some do not leave it ; 
 .'. Some Irish remain in America, 
 
 and an irrefragable affirmative conclusion results from a negative 
 premiss, a valid conclusion from two particular premisses. 
 
 Nor is it true that if the conclusion is negative, one premiss 
 must be negative. 
 
 Most of tl'.e balls were black ; 
 The rest of them were white ; 
 . • . None of them was red. 
 
 This is not a syllogism, it is true ; but it is a perfectly valid 
 argument. It exhibits the power of the Residual quantity in 
 enabling us to draw a universal negative conclusion from 
 premisses, both of which are affirmative, and both particular. 
 
 Some of the men were Spaniards; 
 
 The rest were French ; 
 . • . All the men were Europeans, and 
 . • . None of them was Russian. 
 
 Here, again, Universal conclusions, both positive and negative, 
 are drawn from the same particular premisses. It is true that in 
 strictness we require further postulates about Europeans and 
 Russians, and cannot reach the conclusions unless these postulates 
 arc in our minds ; but in every inference something must be taken
 
 VICES OF THE SYLLOGISM 
 
 327 
 
 for granted. Some knowledge on the part of the reasoner must 
 be presupposed. We cannot even infer from ' Man is mortal ' to 
 
 * No man is immortal' unless we know that 'immortal' excludes 
 
 * mortal,' for the purpose of the argument ; and this knowledge is 
 not what biologists call an * innate quality.' A person who had 
 never heard the word immortal, and did not know what it meant, 
 would need a further postulate before he could draw the inference ; 
 but as most of us do not need the postulate, the logical necessity 
 for it, to those who do, escapes our notice ; and the logical 
 necessity for postulates about Europeans and Russians in the 
 one argument is not really greater than the necessity for a 
 postulate about ' immortal ' in the other. 
 
 Arguments in which universal conclusions are drawn from 
 particular premisses, negative conclusions from affirmative 
 premisses, and valid conclusions, either negative or affirmative, 
 from premisses, one or both of which is negative, present them- 
 selves in such profusion that it is difficult to make a selection ; 
 but perhaps the following will suffice : — 
 
 Particular negative conclusion from affirmative premisses ; 
 
 All men are mortal; 
 Some men are vegetarians ; 
 . • . Some mortals do not eat meat. 
 
 Universal negative conclusion from particular affirmative 
 premisses : 
 
 Some of the jurors were for the plaintiff; 
 Some of the jurors were for the defendant ; 
 . ' . The jurors w^erc not unanimous. 
 
 This is not the ' Universal Negative ' of Traditional Logic, 
 which needs a negative Subject, but it is not difficult to get such 
 a Universal Negative from particular affirmative premisses: 
 
 Some of them went East ; 
 The rest went North ; 
 . • . None of them went South. 
 
 Valid negative conclusion from two negative premisses : 
 
 No logician agrees with these doctrines; 
 No logician is infallible; 
 . • . Some fallible persons do not agree with these doctrines.
 
 328 A NEW LOGIC 
 
 Valid affirmative conclusion from two negative premisses : 
 
 Some were not killed ; 
 None were cowards ; 
 . • . Some brave men escaped. 
 
 Finally : 
 
 If This little pig went to market ; 
 and That little pig stayed at home ; 
 and The other little pigs scattered to different parts 
 
 of the country ; 
 then None of the little pigs remained together; 
 
 and thus every child in the nursery can reach a valid conclusion 
 from an argument which violates every rule but one of the 
 syllogism ; from an argument that has eight terms and four 
 propositions ; that has no middle term ; that has every term 
 undistributed and all its premisses particular ; that reaches a 
 universal conclusion from particular premisses ; a negative con- 
 clusion from affirmative premisses. Thus, out of the mouths 
 of babes and sucklings is the syllogism discredited, defeated, and 
 set at naught. 
 
 This view of Deduction, which regards it as the explication of 
 the implications that lie latent in every proposition, seems to me 
 to have many advantages. Neither Mediate nor Immediate 
 Inference is thus regarded in any book on Logic known to me, 
 though now and then Hamilton utters statements that are con- 
 sistent with this doctrine. Logicians do admit that Deduction is 
 the logic of Consistency, but in spite of this admission, they con- 
 stantly try to show how Deduction reaches the unknown from the 
 known. In my view it does nothing of the kind. It merely reveals 
 what is implied in the postulate. De Morgan draws a sharp dis- 
 tinction between knowing a thing from premisses and knowing it 
 with them. * Persons not spoiled by sophistry will smile when they 
 are told that knowing two straight lines cannot enclose a space, the 
 whole is greater than its part, &c. — they as good as know that 
 the three intersections of opposite sides of a hexagon inscribed 
 in a circle must be in the same straight line. Many of my 
 readers will learn this now for the first time ; it will comfort 
 them much to be assured, on many high authorities, that they 
 virtually knew it ever since their childhood.' In this passage,
 
 INDUCTION AND DEDUCTION 329 
 
 Dc Morgan is insisting on the doctrine that Deduction does 
 
 * enable us to proceed from the known to the unknown ' ; and if 
 the example he gives were, in fact, an instance of deductive 
 reasoning, his contention would be unassailable. But the reason- 
 ings of geometry and of mathematics generally are not deductive. 
 They are reasonings by quantitative analogy, as will be demon- 
 strated in a subsequent chapter ; and De Morgan's contention 
 falls to the ground. One of the capital grievances that I have 
 against Traditional Logic is its failure to discover the mode of 
 reasoning by quantitative analogy, and its confusion of this mode 
 of reasoning with the syllogism. 
 
 I do not think that any logician can contend that Immediate 
 Inference is anything but the extraction of implications from a 
 Simple proposition. The discussions, in books on Logic, as to 
 whether Immediate inferences are inferences or not, rest upon 
 the assumption that an inference is not an inference if it is plainly 
 and immediately apparent ; but if this is true of the inferences 
 from Simple propositions, it is equally true of inferences from pro- 
 positions that are Compound. I cannot see that the inference 
 that if all men are mortal and Socrates is a man, Socrates is 
 mortal, is any less apparent, or any more difficult to extract, than 
 the inference from ' All birds are feathered,' to ' Nothing that is 
 without feathers is a bird.' That the process of Inference is, in 
 fact, nothing more than the explication of meanings implied in a 
 postulate, seems to me to be proved beyond question by the results 
 of the Method of Explication, which enables us to arrive at all the 
 inferences that are attainable by the syllogism, and at a great 
 many more besides. 
 
 Part of the confusion as to the nature of Inference is due to the 
 practice of logicians of applying this term to Induction as well as 
 to Deduction. This seems to me to be regrettable. If I contem- 
 plate the postulate ' The sky to-night is red,' I can infer, according 
 to the Canons of Explication, ' Redness is in the sky to-night,' 
 
 * The sky is not blue to-night,' and so forth. But if I contem- 
 plate, not the postulate, but the fact, that the sky is red to-night, 
 and compare it with previous experience, I can argue, or infer, in 
 another sense of the word infer — I can induce — the conclusion 
 that it will be a fine day to-morrow. It is, of course, possible to 
 deduce this conclusion from a Compound proposition. For the 
 purpose of argument I may postulate ' A red sky at night will
 
 330 A NEW LOGIC 
 
 probably be followed by fine weather the next day ; and the sky 
 is red to-night.' From this postulate I can deduce the implication 
 * It will probably be fine to-morrow ' ; but this verbal explication 
 is totally distinct from material reasoning, and need have no 
 relation whatever to fact. The premisses are postulated ; and for 
 the purpose of argument I may postulate what I please. I can 
 postulate that if the sky is red at night, it will rain incessantly 
 for ten years, or it will never rain again ; and any implication I 
 may extract from that postulate, in conjunction with the further 
 postulate 'The sky is red to-night,' will be valid, for the purpose 
 of the argument, if it is conducted secundum artem. But when I 
 induce from ' The sky is red to-night ' that * It will probably be 
 fine to-morrow,' I do not go on postulation. I am now in the 
 region of material argument. I am appealing, not to a postulate, 
 but to experience ; and am proceeding from the known to the 
 unknown in a sense which is foreign to the proceedings of Expli- 
 cation. In Inference, or Deduction, or Explication, we proceed 
 from that which is explicitly given to that which is implicitly 
 given — from that which is manifest to that which is implied — from 
 that which is avowedly postulated to that which is unavowedly 
 postulated. With fact, with advance from the known to the 
 unknown, we have nothing to do, except in as far as ' the 
 unknown ' is a misnomer for * the unavowed.' 
 
 If the syllogism is, as I contend, merely one way of extracting 
 from the Compound proposition one of its implications, then the 
 question of the petitio principii said to be inherent in every 
 syllogism, takes on a new aspect ; and solvitur ambiilando. If the 
 whole syllogistic process is the extraction of an implication from 
 the postulate, then it is clear that we can get nothing out of the 
 postulate that was not in it. We are forbidden by the Fourth 
 Canon of Inference to do so. If the conclusion were not contained 
 in the premisses, it could not be got out of them. 
 
 The problem of the petitio principii inherent in the syllogism 
 has been stated by no one so neatly as by Prof. Carveth Read, 
 who puts it in the form of a dilemma. ' If «// the facts of the 
 major premiss have been examined, the syllogism is needless ; and 
 if some of them have not been examined, it is a petitio principii. 
 But either all have been examined or some have not. Therefore, 
 it is either useless or fallacious.' The dilemma is notoriously a 
 dangerous form of argument, epigrammatic as it is, and inde-
 
 THE PETITIO PRINCIPII 331 
 
 feasible as it appears; and this example is no exception to the 
 rule. Examination of the facts is irrelevant to the construction 
 of the syllogism. Whether they have all been examined, or 
 whether some of them have not, or whether none of them have 
 been examined, makes no difference to the validity of the con- 
 clusion as an inference from the premisses. It makes no differ- 
 ence to the consistency of the conclusion with the premisses, 
 which may not be regarded as true or false, except for the pur- 
 pose of the argument. If none of the facts have been examined, 
 the conclusion is yet valid as an inference— as a deduction — 
 if it is consistent with the premisses, whether they are true 
 or false. And it is not useless to have an implication, that 
 may not have been apparent, dragged into light and set plainly 
 before us. 
 
 If the syllogism were a means of ascertaining material truth, 
 Prof. Carveth Read's dilemma would be insurmountable and 
 inescapable ; but Prof. Carveth Read himself seems to recognise 
 what I think is the true function of Deduction when he says 
 * Logic discusses the proof or disproof, or (briefly) the testing of 
 propositions.' If by Logic is meant Deductive Logic ; if by proof 
 and disproof is meant demonstration of consistency and incon- 
 sistency with postulates ; and if by testing of propositions is 
 meant testing their consistency with the postulates from which 
 they are derived ; then this statement seems to me punctually 
 correct. 'Logic,' says Prof. Read, ' does not investigate the truth, 
 trustworthiness, or validity of its own principles.' If by Logic is 
 meant Deductive Logic ; and if by principles is meant postulated 
 premisses, then I am entirely at one with Prof. Read. Other 
 logicians state that Logic is the test of truth. I think that these 
 logicians also are right ; but that when they say Logic, they mean 
 Inductive Logic. I differ from all schools in denying that the 
 same Logic that tests the validity or consistency of Inference from 
 postulates can also discover material truth. It is true that, 
 formally, all writers on Logic now make some distinction between 
 these two provinces of Logic, and treat of the one under 
 Deduction, and the other under Induction ; but throughout their 
 treatment of Deduction, they assume, as Prof. Carveth Read 
 assumes in the passage above quoted, that the Universal of 
 Deduction is formed by the accumulation or examination of 
 material instances; and throughout their treatment of Induction
 
 332 A NEW LOGIC 
 
 they constantly endeavour to show that material fact is discovered 
 by the use of the syllogism — the Inductive syllogism as some 
 of them call it. In no book of Logic known to me is the 
 distinction between Inferential reasoning and Material reasoning 
 maintained throughout, or fully appreciated. 
 
 It is true that Modern Logic shifts the ground a little, and 
 interprets the Universal of Deduction, not as an enumerative, but 
 as a generic proposition. By this interpretation, ' All men are 
 mortal ' means not ' Every man has been examined with respect 
 to his mortality, and found to be mortal,' but ' Mortality is 
 a quality inseparable from our notion of man.' This is merely 
 taking * mortal ' in connotation instead of in denotation, or rather, 
 it is merely inserting mortal into the connotation of man : and 
 does not in the least extricate us from the dilemma. If ' mortal ' 
 is part of the connotation of ' man,' then when it is said that 
 Socrates is man it has already been said that Socrates is mortal ; 
 and to bring this out formally is merely explicating an implication 
 that is already there, not proceeding from the known to the 
 unknown. 
 
 If the Universal of Deductive Logic is obtained by enumera- 
 tion of all the instances contained under it, it is obtained from 
 experience of these instances. If it is obtained, as a generic 
 Universal, by the discovery that the predicate is an inseparable 
 quality of the subject, this also must have been gained from 
 experience. In either case we are importing experience into a 
 region of argument in which it has no place, is irrelevant and 
 misleading. The function of the syllogism is not to bring us into 
 contact with experience, but to explicate one of the implications 
 contained in a Compound Proposition. If an implication stares 
 us in the face, a formal syllogism is not needed, though many 
 syllogistic inferences are of this character ; but a few of the less 
 obvious implications contained in postulates can be extracted by 
 means of the later figures of the syllogism. This is the sole 
 function of syllogistic reasoning ; and this function it performs, 
 clumsily, it is true; with much creaking, jolting and rattling; 
 with an expenditure of labour out of all proportion to the result ; 
 but still the syllogism does perform a certain small function that 
 is occasionally useful. I am not among those, therefore, who 
 reject the syllogism as utterly worthless ; but I acknowledge that 
 it has the following defects : —
 
 THE VICES OF THE SYLLOGISM 333 
 
 1. It is not applicable to all Compound propositions, but to 
 those only in which the common element is a term. 
 
 2. Of those Compound propositions in which the common 
 element is a term, the syllogism is applicable to those only which 
 express relations of inclusion and exclusion. 
 
 3. Of those Compound propositions whose common element is a 
 term, and which express relations of inclusion and exclusion, the 
 syllogism is applicable to those propositions only in which the 
 Subject is definitely quantified. 
 
 4. Of those Compound propositions whose common element is 
 a term, and which express relations of inclusion and exclusion of 
 definitely quantified Subjects, the syllogism is applicable to those 
 expressing two quantities only of the Subject. 
 
 5. From propositions of the very limited class to which alone 
 it is applicable, the syllogism can extract but one, or at most 
 two, implications, out of the multitude they contain. 
 
 6. The syllogism cannot be applied without a knowledge of its 
 figures and moods. 
 
 7. The rules of the syllogism are faulty, and some of them are 
 untrue. 
 
 8. The syllogism is not self-evidently valid, but in all figures 
 except the first, needs reduction to the first figure to give 
 assurance of its validity. 
 
 g. This reduction is in some cases lengthy, difficult and 
 complicated, and therefore liable to error.
 
 CHAPTER XXI 
 
 THE CONDITIONAL PROPOSITION AND ITS IMPLICATIONS 
 
 The second Canon of Inference allows us to assume, for the 
 purpose of argument, any postulate we please. It follows, by the 
 first Canon of Explication, that we may assume or grant a postu- 
 late under any condition we please. The conditions under which 
 a postulate may be granted or assumed are virtually infinite, 
 and cannot be enumerated; but certain main classes may be 
 indicated. 
 
 1. The condition under which a postulate is granted may be 
 general or specific, and may have any degree of specificity. We 
 may take it that A is generally B, or that A is under some circum- 
 stances B, or we may state the circumstances with any degree of 
 minuteness of particularity. Pneumonia is generally dangerous : 
 Pneumonia is in some cases dangerous : Pneumonia when it is 
 septic is dangerous. 
 
 2. The condition may be single or multiple. If I am not 
 detained, I will come : if I am not detained, and it is fine, and I 
 am well enough to travel, and nothing intervenes, I will come. 
 
 3. The condition may attach to the Subject, or to the Object, 
 or to both, or to neither. A man, if he is young, is prone to fall 
 in love with a woman : A man is prone to fall in love with a 
 woman if she is attractive : Men, when they are young, are prone 
 to fall in love with women, if they are attractive : Birds, if it is 
 spring time, build nests. 
 
 4. The conditions under which a postulate is granted may be 
 positive or negative. Ships, if well classed, are insurable : Ships, 
 if not well classed, are dangerous risks. 
 
 5. The condition may qualify either an affirmative or a negative 
 postulate. Milk, if it is pure, is wholesome: Milk, if it is 
 contaminated, is not wholesome. 
 
 6. The condition may be sole or alternative. Much space is 
 given in text books of Logic to the alternative condition ; but I 
 do not find any mention of the sole condition, though it is by no
 
 THE DISJUNCTIVE PROPOSITION 335 
 
 means unknown or unimportant in argument. Like the alterna- 
 tive condition, it cannot be fully stated in a single proposition, 
 but it is less complicated in form than the alternative condi- 
 tion, to which it is allied, and to which it is an appropriate 
 introduction. 
 
 The sole condition is in fact, paradoxically, a double condition. 
 It states that under a certain condition, and under no other 
 condition, is the postulate granted. The only way to make him 
 pay is to get judgement against him, includes two conditions — If 
 you do not get judgement against him, he will not pay: if you 
 do, he will. The only way to be successful is to work hard — If 
 you do not work hard you will not be successful : if you do, 
 you will. 
 
 This example of a condition that is apparently single, though 
 really double, is a useful introduction to the alternative condition, 
 or, as it is called, the Disjunctive proposition, which purports to 
 be a single postulate, but in fact contains necessarily three, and 
 may ambiguously contain six propositions : that is to say, two 
 undistinguishable alternatives, of three propositions each. 
 
 The alternative condition is expressed by what is called the 
 Disjunctive proposition, and is characterised by the words 'Either 
 — or.' The proposition so constituted is, however, an abbreviated 
 and approximate construction, and does not express the full sense 
 in the mind of the utterer. For this reason, the Disjunctive 
 proposition, * A is either B or C,' has been the subject of secular 
 controversy, as to whether it implies 'and may be both,' or should 
 be accepted to mean * and cannot be both.' On one side are the 
 great names of Whately, Mansel, Mill, Jevons, Venn, and 
 Keynes ; and on the other are the equally great names of Kant, 
 Hamilton, Thomson, Bode, Ueberweg, Bain, Bradley, and 
 Fowler. I feel it presumptuous of me to interfere in a battle of 
 such giants; but it appears to me that one set of antagonists has 
 been looking at one side of the shield, and the other at the other : 
 so that both are right and both are wrong. 
 
 The Disjunctive proposition is of very peculiar character, and 
 really embodies half-a-dozen propositions in what is ostensibly one, 
 though really two, propositions, each of which is compounded of 
 three others. ' A is either B or C ' may mean 
 
 .... ^ ^ rand if it is B, is not C 
 
 A IS either B or C^ i r ■. • r- • i. o 
 
 land II it IS C, is not B.
 
 336 A NEW LOGIC 
 
 In this case, A cannot be both B and C. But the meaning 
 may be 
 
 » . . , „ „ rand if it is not B, is C 
 A IS either B or C-^ j -r -^ • .. ^ • t-. 
 
 land II it IS not C, is B. 
 
 In this case, A ma\' be both B and C. 
 
 It is clear that the two sets of propositions are inconsistent with 
 each other. It is clear that ' A is either B or C ' cannot have both 
 meanings simultaneously. But it seems to me equally clear that 
 it may have either of the two meanings that we choose to ascribe 
 to it. In this case, as in the case of 'some,' logicians have 
 attempted to fix arbitrarily a single meaning to an expression 
 which is in its nature ambiguous. The meaning is not to be fixed 
 by any declaration of logicians that it is this or that. Logicians 
 have no power to enforce their decrees ; and still less are their 
 decrees enforceable when they are, as in this case, contradictory. 
 The only way to fix the meaning of the phrase in use is to indi- 
 cate, when it is used, which meaning is to be attached to it ; and 
 this can easily be done by affixing the necessary qualification 
 
 * A is either B or C (and may be both) ' : ' A is either B or C (and 
 cannot be both).' 
 
 Although authority, however high, could not, even if it were 
 unanimous, fix which of the meanings is to be read into the Disjunc- 
 tive proposition, the subject-matter may determine the meaning 
 for us. It depends upon whether the B and C of the proposition 
 are compatible or incompatible. If they are incompatible, A 
 cannot be both B and C. If they are compatible, A may be both 
 B and C. If it is said that a man is either honest or dishonest, 
 we know he cannot be both, for honesty and dishonesty are 
 incompatible : if it is said that he is either knave or fool, we know 
 he may be both, for knavery and folly are compatible. Such 
 extensions or fixations of the meaning of Disjunctive propositions 
 may or may not be legitimate in logic, according as we are or are 
 not entitled to take into consideration the connotation and denota- 
 tion of the words we use. If we are not entitled to infer, from 
 ' He saw her do it,' to * He was there when she did it,' then we are 
 not entitled to infer from ' He is either honest or dishonest ' that 
 
 * He cannot be both.' If we are permitted to make the assumption 
 in the second case, because of our knowledge of the subject-matter 
 of the postulate, equally we are permitted to make it in the first
 
 DISJUNCTIVE PROPOSITIONS 337 
 
 case. If the Formal nature of Deduction is insisted upon, and 
 applied with rigcnir, then we are not entitled to infer that he 
 cannot be both honest and dishonest, until we have assumed the 
 further postulate that honesty and dishonesty are incompatible. 
 Unless the compatibility or incompatibility of the alternatives is 
 postulated or known, the Disjunctive proposition remains ambigu- 
 ous, and we are left in the dark, with all our authorities, from Kant 
 and Whately to Keynes and Fowler. 
 
 There is a cognate problem that may be examined before we 
 leave this part of the subject. ' A, if it is not B, is not C ' ; Aye, 
 but may it not be both ? Of course it may, but it would be ultra 
 vires to speculate whether it is or not. The postulate gives us 
 nothing of what happens if A is B ; and to guess what might 
 happen if the postulate were other than it is, is ultra vires and 
 extra-logical. So, too, is it extra-logical to speculate what would 
 not be the case if the postulate were other than it is. 
 
 7. Logicians give a good deal of attention to conditionality, but 
 I do not find any reference by them to the restriction or denial, in 
 the postulate, of conditionality. Such restriction or denial is, 
 however, not infrequent in practice. Since, for the purpose of 
 argument, we may postulate what we please, we may postulate 
 that our postulate is without any specific condition, or without 
 any condition at all. * Whether I am ill or well, I will go ' 
 excludes conditionality on the state of my health. * Whatever 
 happens, I will go ' excludes conditionality on events. ' In any 
 case, I will go ' excludes all conditionality. 
 
 It is evident that we are here brought into contact with the 
 * apodeictic ' proposition. ' It is unconditionally true ' has much 
 the same meaning as ' It is certainly true ' — ' It must be true.' 
 
 A good many distinctions have been made by logicians among 
 Disjunctive propositions. They have been divided into the 
 Conditional, the Hypothetical, the Inferential Disjunctive, the 
 Contingent Disjunctive, the Divisional Disjunctive, and so on. 
 Those who are interested in them will find these matters discussed 
 in the larger text books, where they will find also that different 
 logicians allocate these names differently among the different kinds 
 of Disjunctives. The divisions are not important enough to 
 discuss here. 
 
 The Consequent, as well as the Condition, of a Conditional 
 proposition may vary without limit. It may be general or 
 
 N.L. z
 
 338 A NEW LOGIC 
 
 specific, sole or multiple, positive or negative, and of any quantity 
 in its terms. In fact, any form of postulate whatever may be 
 granted under any condition whatever. It is clear that the more 
 numerous and the more comprehensive the conditions, the more 
 limited is the postulate ; and vice versa. ' It will do if it is strong 
 enough ' restricts the postulate less than ' It will do if it is strong 
 enough, and light, and elegant, and cheap.' * I will come if it is 
 fine' gives us a less restricted postulate than ' I will come if it is 
 fine, and if I get my work done in time, and if I am not prevented.' 
 
 The Implications of Conditional Propositions. 
 
 A Conditional proposition contains two or more complete 
 propositions ; and each of these contains all the implications 
 that we have already found to reside in Simple propositions, and 
 that are explicable by the Canons of Explication. Any of these 
 implications may be substituted, in either or both the constituent 
 propositions of the Conditional, without altering the meaning ot 
 the whole. ' If trees are skilfully pruned, their crop is increased ' 
 is not altered in meaning by substituting the reciprocal, in either 
 or both constituents. It is still true in the form ' If skilful pruning 
 is applied to trees, increase is produced in their crop,' nor is the 
 Conditional * If men are honest, they pay their debts ' altered in 
 meaning by substituting the double negatives * If men are not 
 dishonest, they do not fail to pay their debts.' ' If logicians are 
 right, I am wrong ' is not altered in sense by substituting the 
 equivalent terms ' If the writers of text books on Logic are 
 correct, the author of this book is mistaken.' Such implications 
 follow, of course, from what has already been said of the 
 implications of Simple propositions, and from the Canons of 
 Explication. But in addition to these, the Conditional proposition 
 has, by virtue of its constitution, an additional implication, not to 
 be found in Simple propositions. 
 
 In books on Logic, it is laid down that, in order to deduce a 
 conclusion from a Conditional proposition, the Antecedent must 
 be affirmed, or the Consequent denied : and that no conclusion 
 can be reached, either by denying the Antecedent or by affirming 
 the Consequent. These rules are laid down ; but, as far as I 
 have been able to ascertain, no reason is given for either of them, 
 except that it is understood that the nature of the Conditional
 
 IMPLICATIONS OF THE HYPOTHETICAL 339 
 
 proposition renders them applicable. It is not, I think, pretended 
 that they rest upon the Laws of Thought, which are advanced as 
 the Canons of all Inference; and the only approximation to a 
 reason that is given for them is that it is recognised, somehow, 
 that a conclusion is not justifiable when the antecedent is denied, 
 or the consequent affirmed simply; while, in the opposite case, a 
 conclusion is legitimate. Good and sufficient reasons may, however, 
 be found in the Canons of Inference here inculcated. 
 
 The Antecedent, or, as I think it ought to be called, the 
 Condition, may not be denied, because it is part of the postulate ; 
 and the third Canon of Inference forbids us to withdraw the 
 postulate in the course of the argument. The Consequent may 
 not be affirmed unconditionally, because the postulate grants it 
 under a condition ; and to assume it without this condition is a 
 violation of the fourth Canon, which forbids us to assume 
 anything that is not in the postulate. So far, the negative rule 
 is amply justified by the Canons of Inference, and cannot be 
 obtained from the Laws of Thought — at any rate, I know of no 
 attempt to obtain it from them. 
 
 It is said, further, in the text books, that we are at liberty to 
 afiirm the Antecedent and to deny the Consequent. These, 
 however, are beyond our powers. They are altogether ultra vires 
 of Inference, for they go beyond the postulate, and violate the 
 fourth Canon. What the postulate grants is that If A is B, it is C. 
 There is nothing in this postulate to warrant the denial of the 
 Consequent. The postulate does not deny that A is C. On the 
 contrary, it affirms that under a certain condition A is C. Yet it 
 is sufficiently clear that if A is not C it is not B. By what 
 process of explication, in conformity with what Canon of Inference, 
 is this conclusion reached ? It is reached, validly and justifiably, 
 under the fifth Canon, which states that when a postulate is 
 granted, all its implications are granted. The inference that, if A 
 is not C it is not B, is an implication of the postulate, and is 
 allowed by the third Canon of Explication, which says that 
 everything inconsistent with the postulate may be denied. We 
 have found one meaning of this to be that a postulate implies all 
 its double negatives. Hence ' If A is B it is C ' implies that if A 
 is not C it is not B. But it is most particularly and especially 
 to be noted that this implication does not deny the Consequent. 
 There is not, in the postulate, any warrant for the denial of the 
 
 z 2
 
 340 A NEW LOGIC 
 
 Consequent. The Consequent is part of an affirmative postulate, 
 and to deny it would be a violation of the fourth Canon of 
 Inference, which forbids us to go beyond the postulate. What is 
 stated in the implication * If A is not C it is not B,' and all that we 
 are warranted by the Canons of Inference in inferring, is not that 
 A is not C, but that 7/ A is not C, the condition does not hold 
 good, and A is not B. The postulate being a conditional postulate, 
 every implication it contains must also be conditional. To deny 
 that A is C, on the ground that if it is B it is C, is manifestly and 
 grossly fallacious. To make such a denial, we must drag in a new 
 postulate in the course of the argument, and so violate the fourth 
 Canon of Inference. If, in the course of the argument, we may 
 assume the postulate that A is not C, by the same authority we 
 may assume that A is not B, and so reduce the postulate to nullity, 
 and the argument to absurdity. 
 
 The text books give us licence to affirm the Antecedent, and 
 the stock argument from the Conditional proposition is thus 
 given : — 
 
 If A is B, it is C. 
 But A is B. 
 . • . A is C. 
 
 Why, of course it is, but the conclusion is extra-logical ; or at 
 least, it is outside the logic of Inference from a single postulate, 
 with which we are now concerned. The postulate gives that if A 
 is B, certain consequences follow. But, you say, A really is B, 
 and therefore the consequences really do follow. No doubt they 
 do, but in order to get them you must assume another postulate, 
 beyond and in addition to your original postulate, which is all that 
 you have to go upon in the Conditional proposition. I give you 
 that if A is B, it is C ; and you tell me that A really is B, and 
 therefore really is C. I thank you for nothing. Your assertion 
 is impertinent. It gives me no assistance in explicating the 
 implications of the postulate. When I have the postulate. If A 
 is B, it is C, the assurance that A really is B carries me no 
 forwarder in extracting the implications of what I have. It 
 introduces a new element. It destroys that very conditional 
 character of the proposition on which all my inferences from it 
 must depend. For the purpose of deducing the implications of 
 the postulate, it is mere surplusage, and is irrelevant. For the
 
 THE HYPOTHETICAL SYLLOGISM 341 
 
 purpose of argument, I may postulate what I please ; and my 
 postulate is then assumed to be true for the purpose of the 
 argument. To tell me that it is true in fact, implies that my 
 argument has some purpose other than its legitimate purpose — 
 implies that it is concerned with fact, and is a material argu- 
 ment. To grant that the postulate is true for any purpose other 
 than the purpose of the argument, grants that for which the 
 Logic of Inference does not thank you, for which it has no use, 
 and with which it is incompetent to deal. Give to the Logic of 
 Inference a postulate, and that Logic will show you all the 
 implications of the postulate ; but whether or no the postulate 
 is true in fact, is not, to the Logic of Inference, a matter of the 
 least concern. To assume that the postulate is true in fact, and 
 to suppose that any inference, properly so called, can be drawn 
 from this assumption, is to commit the fallacy that will presently 
 be explained, the Fallacy of Confusion of the Modes of Argument.
 
 BOOK IV 
 
 ANALOGY, &c.
 
 CHAPTER XXII 
 
 ANALOGY 
 
 Analogy was defined by Aristotle as to-oVrj? \6yoiv — com- 
 parison of Ratios : Euclid uses Analogy and Proportion as 
 convertible terms ; and to this sense I propose to restore the term 
 Analogy, which has been sadly perverted and extended in meaning 
 by logicians. Mill says ' There is no word, however, which is used 
 more loosely, or in a greater variety of senses, than Analogy,' but 
 instead of restoring it to its original and proper use, he unfortunately 
 lent the great weight of his authority to the employment of 
 Analogy to denominate Induction, especially those modes of 
 unassured Induction that have been described in the chapter on 
 that subject in this book. I regard this misapplication of a useful 
 term, which already had a definite and restricted meaning, 
 sanctioned by the usage of two thousand years, as regrettable. 
 Analogy is a reasoning process quite distinct from both Induction 
 and Deduction; and has a range of application, and a domain of 
 usefulness, peculiar to itself. At the present time. Analogy is 
 used, in the writings of logicians, sometimes, though rarely, in its 
 original and proper meaning; sometimes to mean Inference; 
 sometimes to mean Induction, especially Imperfect Induction of 
 low validity ; and sometimes in a slipshod way, to mean any kind 
 of resemblance between any two things. 
 
 The use sanctioned by Mill has already been quoted. ' Two 
 things resemble each other in one or more respects ; a certain 
 proposition is true of the one, therefore it is true of the other.' 
 It is clear that this is not that comparison of ratios to which 
 Aristotle and Euclid applied the term, and to which it has been 
 applied ever since their time. Understood in the sense sanctioned 
 by Mill, Analogy is the comparison, not of two ratios, but of two 
 terms ; or rather, of two whole propositions, element by element, 
 beginning with one pair of homologous terms. In Analogy 
 proper, there is no assimilation or comparison of the terms of the 
 sub-relations. It does not matter to Analogy how dissimilar or 
 incomparable these terms are. The comparison is of ratios, and
 
 346 A NEW LOGIC 
 
 of ratios alone. ' A is like B ' is not an Analogy, for what are 
 compared are terms. ' The ratio of A to B is like the ratio ot 
 C to D ' is an Analogy, and is the only form of true Analogy. 
 ' Smith is like Brown ' is not an Analogy, for what are compared 
 are terms. ' The devotion of Smith to his business is like the 
 devotion of Brown to his wife ' is an Analogy ; for this comparison 
 is not of terms, but of relations between terms. The terms are 
 not compared. There is no comparison of Smith with Brown, or 
 of Smith's business with Brown's wife. The comparison is 
 between the relation of Smith to his business, and the relation of 
 Brown to his wife. Smith's business and Brown's wife are neither 
 compared nor comparable ; and whether Smith and Brown are 
 alike or not, has nothing to do with the analogy. All that are 
 compared are the ratios. 
 
 An Analogy is stated in a proposition ; and a proposition consists 
 of two terms united in a relation by a Ratio. The peculiarity of 
 the Analogical proposition is that its terms are themselves relations. 
 The abstract or generalised form representing all relations has 
 hitherto been expressed in the form 'A is B ' ; but it may be 
 expressed more correctly in the more generalised form A : B. In 
 the Analogical proposition, each of the terms of this relation is 
 itself a relation. The Subject-term, A, is a relation : let us call 
 it a : b ', and the Object-term, B, also is a relation : let us call it 
 c : d. Then the whole analogical proposition becomes (a : b): 
 (c : d); or a : b : : c : d. But this is the expression of a proportion. 
 We see, therefore, what Euclid means when he says that Analogy 
 is the same as Proportion. 
 
 Analogy is as indifferent to the nature of the terms of its 
 sub-relations as Inference is indifferent to the truth of its 
 postulates. (The statement is itself a good example of Analogy.) 
 The nature of Analogy is not altered, and its truth is not altered, 
 by altering the nature of its terms, so long as the proportion 
 between them is maintained. Analogy is still Analogy, whether 
 its terms are concrete or abstract, whether they, or either of them, 
 are persons, or things, or qualities, or numbers, or what not. 
 
 'The relation of a parson to his parishioners is like the relation 
 of a shepherd to his flock ' is an Analogy. ' The relation between 
 resistance and extension is like the relation between colour and 
 surface ' is an Analogy. ' The relation between the angles at the 
 base of an isosceles triangle is like the relation between the sides '
 
 NATURE OF ANALOGY 347 
 
 is an Analogy. ' The relation between two and four is like the 
 
 relation between six and twelve ' is an Analogy. Every comparison 
 
 of relations is an Analogy, and every Analogy is a comparison of 
 
 relations. 
 
 Wc have seen that Analogy and Proportion are the same thing. 
 
 A proportion maybe expressed a : b : : c : d,or \t may be expressed 
 
 ct c ... 
 
 Y =^ -,; and thus we discover that the equation of fractions is 
 
 Analogy, and the statement of such an equation is the assertion of 
 an analogy. 
 
 We have already seen that our warrant for arguing from 
 
 {a + bf = (a + 6) {a + 6) 
 to {a^bf = a'^ + 2ab-\- 6^ 
 
 is given by the third Minor Canon of Explication, which allows us to 
 replace any term in a proposition by its equivalent. But this Canon 
 will afford us no warrant for arguing that \i a = b, then a^ = 6^ ; 
 nor can any warrant for this conclusion be extracted from the Laws 
 of Thought or the Dictum de omni et millo. But if we realise the 
 nature of an Analogy, we see at once that the conclusion is 
 justified, and why it is justified. Analogy is a comparison of ratios, 
 and is indifferent to the nature of its terms. In quantitative 
 reasonings, therefore, it is indifferent to the quantities of the terms, 
 and regards nothing but the ratios between them. In this case, 
 the ratio of equality between a and b is compared with the ratio 
 between a^ and 6^ ; and though the terms have been altered, it is 
 at once recognised that the ratio between them has not been 
 altered. Hence, whatever ratio existed between a and b will exist 
 between a^ and b^. The ratio between a and b is one of equality ; 
 therefore the ratio between nP and b'^ is one of equality. In this 
 case, again, the New Logic here propounded offers an explanation 
 of mathematical reasoning, which Traditional Logic does not 
 attempt, and seems to regard as outside of its province. The 
 divorce of Mathematical reasoning from Logic appears to me 
 illogical. If Logic purports to discover, describe, and explain 
 modes of reasoning, it must include modes of reasoning about 
 quantity, or confess its inadequacy. Logic assumes that quantitative 
 reasonings are so different in nature from qualitative reasonings, 
 that the science and art which comprise the latter need take 
 no account of the former. In this, Logic appears to me to be
 
 348 A NEW LOGIC 
 
 profoundly mistaken. Logic does not include mathematics, in the 
 sense that Logic need teach the operations of addition and sub- 
 traction, and of the solution of equations ; but Logic does include 
 mathematical reasoning, in the sense that Logic is bound to show 
 by what modes of reasoning mathematics conducts its operations 
 and reaches its conclusions. Mathematical reasonings are reason- 
 ings, and the science and art of reasoning should include every 
 kind and variety of reasoning. The subject will be resumed later 
 on in this chapter. 
 
 It has already been explained that a proposition expresses the 
 formation or establishment of a relation. The formed or established 
 relation is differently expressed. The established relation becomes 
 a term, which may enter, as a term, into a new relation, and be 
 expressed in a new proposition. ' Chalk is white ' expresses the 
 establishment of a relation between chalk and whiteness. The 
 established relation is expressed by 'the whiteness of chalk.' 
 ' Brutus killed Caesar' expresses the formation of a relation : the 
 relation thus formed is expressed by 'The killing of Caesar by 
 Brutus.' * Some men are vegetarians ' expresses the formation 
 of the relation ' the vegetarianism of some men.' 
 
 Analogy is the comparison of relations. It is the comparison, 
 not of the formation of relations, but of fully formed relations. It 
 is the comparison of relations, not in the making, but after they 
 are made. It expresses the formation of a relation between the 
 results of previous processes of the same kind. But whereas 
 Induction and Deduction attain the establishment of relations of 
 all orders and of every kind, Analogy is capable of forming but 
 two relations — likeness, and its opposite, unlikeness ; of which 
 equality and inequality, identity and non-identity, are derivatives. 
 
 The formation of relations of likeness and unlikeness is at the 
 base of all reasoning. In Induction, the first step, upon which 
 the whole process depends, is the discovery of a Datum ; that is to 
 say, the discernment of likeness between an element in the Problem, 
 and an homologous element in some proposition derived from 
 previous experience. The next step is the establishment of identity ; 
 that is, of complete likeness, between the second element of the 
 Problem and its homologous element in the premiss. The third 
 step is the assimilation of the third element in the premiss to the 
 qusesitum. In Inference, if one proposition, or ratio, or term, is 
 equivalent to, or included in, or implied in another ; the equivalence,
 
 NATURE OF ANALOGY 349 
 
 or inclusion, or implication, rests upon likeness. If one term is 
 excluded from, or inconsistent with, another, the exclusion or 
 inconsistence rests upon unlikeness. In both Induction and 
 Deduction the gist of the process lies in the substitution of one 
 term or ratio for another. In both cases, the proposition which is 
 the subject of the reasoning process is altered. In Induction an 
 incomplete proposition is completed : in Deduction, the Ratio or a 
 term is replaced by a new Ratio or term. Analogy differs from both 
 of these modes of reasoning in that its proposition undergoes no 
 alteration. In Induction and in Deduction, the proposition, 
 having been stated, is then modified secwidwn artem, and appears 
 in the conclusion in a new form. In Analogy, the proposition is 
 stated merely. When it is stated, the reasoning process is complete. 
 The reasoning process is the discernment of likeness, or the dis- 
 crimination of difference, between two Ratios, and the proposition 
 expresses the likeness or difference ; and when the likeness or 
 difference is stated, the analogy is complete ; the reasoning process 
 is at an end. This dissimilarity between the process of Analogy 
 and the processes of Induction and Deduction may be the reason 
 why Analogy, as understood in the Aristotelian and Euclidian 
 sense, is excluded from all books on Logic. Presumably, it is not 
 regarded as a reasoning process at all. The term * Analogy ' 
 is, indeed, used freely enough by logicians ; but by analogy they 
 do not mean analogy as defined by Euclid and Aristotle, and 
 as it is understood by me. 
 
 * The relation of a parson to his parishioners is like the relation 
 of a shepherd to his flock.' ' The relation of the Government to 
 the country' is like the relation of the brain to the rest of the body.' 
 'The relation of the trunk of a tree to its limbs is unlike the 
 relation of the trunk of a man to his limbs.' These are analogies. 
 They are propositions expressing likeness and unlikeness of 
 relations ; they express the result of a reasoning process — an 
 elementary process of reasoning, but still a process of reasoning ; 
 and one that in many cases requires and evinces a very high degree 
 of intelligence. When Oken discovered that the relations of the 
 parts of the skull to one another resemble the relations of the parts 
 of the vertebra to one another, he discerned an analogy in the 
 Aristotelian sense. When Goethe discovered that the relations 
 of the parts of the flower to their stem resemble the relations of 
 the leaves to the branch, he discovered a true analogy. But it
 
 350 A NEW LOGIC 
 
 would require some hardihood to maintain that these discoveries 
 were not instances of reasoning. If they were not attained by 
 a process of reasoning, how were they attained ? If, indeed, 
 Induction and Deduction are the sole processes of reasoning, 
 then the insight of Oken and Goethe must receive some other 
 name ; but then it will be a matter of words, and of names ; 
 and I will be no judge of such matters. But unless we choose 
 to limit the meaning of reasoning arbitrarily, according to the 
 preconceptions and prejudices of logicians, I know not how such 
 exercises of high intelligence as these are to be excluded from 
 reasoning. If there are any who say that these are instances, not 
 of reasoning, but of imagination ; then I shall be glad to have a 
 definition of imagination that shall exclude reasoning. 
 
 When it is said that the relation of a parson to his parishioners 
 is like the relation of a shepherd to his flock, the analogy is full- 
 blown, and completely expressed ; as it is also in the following 
 examples : — 
 
 The horsemen dashed among the rout, 
 As deer break through the broom. 
 
 It is not growing like a tree, 
 
 In bulk doth make man better be. 
 
 From rainbow clouds there flow not 
 
 Drops so bright to see, 
 
 As from thy presence showers a rain of melody. 
 
 But more often a part, sometimes a very large part, of the 
 analogy is left to be understood, just as, in what is erroneously 
 called an enthymeme, one or both premisses of an Inference are 
 omitted, and left to be understood — just as the Object-term of an 
 intransitive verb is left to be understood. 
 
 The Assyrian came down like a wolf on the fold. 
 
 In this analogy, the Object-term of one relation, and the Ratio of 
 the other, are left to be understood. The full analogy is * The 
 Assyrian came down (on Israel) like a wolf (comes down) on the 
 fold.' ' He is as slow as a slug' (is slow) leaves both Ratio and 
 Object of one relation unexpressed. * Ghost-like, I paced round 
 the haunts of my childhood ' compresses the whole of one of the
 
 EXAMPLES OF ANALOGY 351 
 
 constituent relations, together with the mark of assimilation 
 characteristic of Analogy, into a single word. 
 
 On the other hand, the relations compared maybe so numerous, 
 and so complex, that a page, many pages, a whole book, may be 
 occupied in their expression ; and thus an analogy is expanded 
 into a parable or allegory, as in the Pilgrim's Progress, the Holy 
 War, the Tale of a Tub, the Hind and the Panther, &c. An 
 analogy that is completely expressed is sometimes called a Simile, 
 while an analogy from which several elements are dropped out is 
 called a Metaphor. The same analogy may of course be expressed 
 with any degree of fulness. * The Government stands to the 
 nation in the relation of the brain to the body ' is a fully 
 expressed analogy. * The Government is the brain of the nation ' 
 is a metaphor ; and ' The brain of the nation ' as a synonym for 
 * the Government ' is a metaphorical expression which is not 
 even a full metaphor. 
 
 As already stated, pure Analogy compares relations only, and 
 makes no comparison of the terms of the sub-relations. If I say 
 he is as slow as a slug, I compare nothing but his motion to the 
 motion of the slug ; and even the motions I compare only as to 
 their rapidity. I take no account of their direction, continuity, 
 or other qualities. In drawing the analogy, I make no comparison 
 between him and a slug. I do not liken him to a slug in shape, in 
 absence of limbs, in sliminess, or in the possession of horns. I 
 / compare nothing but a pair of simple relations. But in literature 
 Analogy is seldom as pure as this. There is nearly always, in 
 literary Analogy, a covert suggestion of hkeness, not only of the 
 relations, but of the homologous terms of the relations also. 
 
 When Byron says ' The Assyrian came down like a wolf on the 
 fold,' he does formally compare nothing but the two relations of 
 action ; but under cover of this assimilation of Ratios, he contrives 
 to sneak in an assimilation of the Assyrians to wolves, and so 
 invests them with some of the ravenousness and remorselessness 
 of the wolf. * Protestantism will end by destroying the nation, as 
 gangrene destroys the members of the human body.' Here the 
 intention is not only to compare the destructive action of 
 Protestantism to the destructive action of gangrene, but, under 
 cover of this comparison, to invest Protestantism with some of the 
 horror and loathesomeness with which gangrene is regarded. In 
 describing the stillness of a child, holding its breath in some 
 
 '1^'^ .■-•■"' .^^ J^"^ -f '" J^'
 
 352 A NEW LOGIC 
 
 hiding game, we should rather say it is 'as still as a mouse' than 
 'as still as death.' It is the stillness alone that is formally 
 compared, and for the purpose of emphasis, ' as still as death ' is 
 the stronger and more appropriate expression ; but we find it 
 difficult to avoid a comparison of the terms also ; and though, 
 strictly speaking, it has nothing to do with the analogy, we feel it 
 more appropriate, as some comparison of the terms will be made, 
 whether we like it or no, to let the harmless child be compared to 
 the harmless mouse. If we wanted to find a comparison for the 
 stillness of a snake about to strike, or a tiger about to spring, 
 we should rather select * as still as death,' because of this 
 well-nigh unavoidable comparison of the terms, as well as of the 
 ratios. 
 
 It is in the comparison of qualitative relations only that this 
 habit of comparing the terms also exists, and in this region the habit 
 is inveterate. If I say ' You are as slow as a slug,' ' You serve him 
 as faithfully as a dog,' * You are as illogical as a logician,' my 
 interlocutor would be apt to turn upon me with indignation, and 
 demand ' Do you say I am a slug ? ' 'Is thy servant a dog, that 
 he should do this great thing?' ' Do you take me for a logician?' 
 Patience, my friend ; those w^ere not my assertions. I compared, 
 not you to a snail, but 3'our motion to that of a snail ; not you to 
 a dog, but your faithfulness to that of a dog ; not you to a logician, 
 but your illogicality to that of a logician. I compared, in short, 
 not the terms but the relations. My explanation is not likely to 
 give satisfaction, however. My interlocutor will still have his 
 grievance ; for the habit of importing into the comparison of 
 relations, a comparison of their constituent terms also, is, with 
 qualitative ratios, inveterate. 
 
 This importation or inclusion of the terms into the com- 
 parison does not, however, merge Analogy into cither Induction 
 or Deduction, or approximate it to them. It remains a distinct 
 process even when it is not pure. When it is said that the 
 Assyrian came down like a wolf on the fold, there is a certain 
 assimilation of the Assyrian to the wolf. He is invested with 
 some of the ravening and ruthlessness of the wolf; but these 
 qualities are attributed to the Assyrian by no process of reasoning. 
 Their possession by the Assyrian is not necessarily implied in the 
 analogy; neither is it given as the solution of a problem. It is 
 merely hinted at. It is suggested. It is sneaked in. It partakes
 
 QUANTITATIVE ANALOGY 353 
 
 of the nature of an assertion, though it does not attain to the 
 positivencss of an actual assertion. As far as it goes, however, it 
 is merely assertory, and not argumentative. The reasoning 
 process is at an end when the relations have been compared ; and 
 any comparison of the terms is surplusage. 
 
 Applied to qualitative relations, Analogy belongs more to 
 Rhetoric than to Logic. It gives to a statement emphasis, 
 impressiveness, picturesqueness, and often intelligibility, that it 
 would not otherwise have, and that can be given in no other way. 
 Hence it is especially frequent and valuable in poetry, for it adds 
 to mere assertion a powerful reinforcement. ' Her feet appeared 
 and disappeared beneath her petticoat ' is a dry statement of fact. 
 ' Her feet beneath her petticoat, like little mice stole in and out ' 
 raises the dry statement of fact into poetry. ' He argued forcibly ' 
 is a statement of fact that we may accept without being impressed 
 by it. ' He argued with sledge-hammer force ' is immensely more 
 impressive. ' The bullets fell thickly ' is far less impressive than 
 ' The bullets fell like hail.' 
 
 But comparison of qualitative relations is of more use than 
 merely to add picturesqueness and emphasis to a statement. It 
 has a very high value in explanation. By assimilating them to 
 what is familiar, it enables us to appreciate and comprehend 
 relations that are unfamiliar, and that we should find it difficult to 
 appreciate without Analogy. Used in this way. Analogy has 
 received yet another name — that of Illustration. Few novices in 
 electrics are able to grasp the meaning of the passage of electricity 
 along a wire, of its storage in accumulators, of the difference 
 between amperage and voltage, without help from the illustration 
 of the flow of water in pipes, its accumulation in cisterns, and the 
 difference between volume and pressure. The apprehension of the 
 origin of all animals from a single form, by variation in innumerable 
 directions, determined by the competition for food, &c., is greatly 
 assisted by the analogy of the branches of a tree, ramifying in 
 innumerable directions, that are determined by the competition 
 for lit^ht. 
 
 The vast majority of words have been put to their present uses 
 by the agency of analogy or metaphor in a nearer or remoter 
 ense. 
 
 But the great value of Analogy in reasoning is in its application 
 to quantitative ratios ; and when applied to quantitative ratios, it 
 
 N.L. A A
 
 354 A NEW LOGIC 
 
 is always pure. It never includes any of that assimilation of the 
 terms of the compared ratios that we have seen to be the rule in 
 qualitative analogy. When we compare the ratio of two to six with 
 the ratio of seven to twenty-one, and declare the ratios to be alike 
 or equal, we never take it that this declaration carries any similarity 
 or equality of two to seven or of six to twenty-one. We compare 
 the ratios only, and there the comparison ends. So far from assimi- 
 lating the terms, the whole validity of mathematical analogy lies in 
 keeping the comparison of ratios pure, and eschewing altogether any 
 comparison of terms. If a = b, then I may conclude by x\nalogy 
 that a^ has the same ratio of equality to 6^; but it would vitiate the 
 argument altogether to predicate the same ratio between the terms, 
 and to say that a = a^ or b = b^. The whole validity of the argument 
 lies in assimilating the ratios and ignoring the terms. Similarly, if 
 a > b, then I intuitively perceive b}' Analogy that this ratio remains 
 unaltered by any equivalent alteration of the terms ; so that 3^^ is 
 still greater than 36. The several steps in the solution of every 
 equation or Euclidian theorem are analogies. They are recog- 
 nitions of the equality of ratios, in spite of the alteration of the 
 terms between which the ratios subsist. 
 
 Much ingenuity has been expended by logicians in explaining 
 how it is that we instantly apply to every triangle, parallelogram, 
 or circle, the conclusions proved by Euclid about any similar 
 triangle, parallelogram, or circle. The explanations given are 
 various ; but the favourite is that the transfer depends on the 
 essential qualities of these figures, or on the fact that the 
 conclusions that we thus transfer depend on essential qualities 
 and not on accidental qualities. The explanation seems to 
 me to explain nothing. When we ask what these essential 
 qualities are, and how they arc to be distinguished from non- 
 essential qualities, logicians are non-plussed. It is the story of 
 the Uniformity of Nature over again. It is a verbal explanation 
 that does not explain. 
 
 It is not as if the explanation were difficult. It is simple 
 enough. Once the nature of Analogy is appreciated, the explana- 
 tion jumps at you, and hits you in the face. What Euclid 
 demonstrates, when he shows that the angles at the base of an 
 isosceles triangle are equal, is a similarity of ratios. It is an 
 analogy. The ratio of the angles to one another is shown to be 
 the same as the ratio of the sides to one another ; and the reason
 
 QUANTITATIVE ANALOGY 355 
 
 we immediately and intuitively accept this as true of every isosceles 
 triangle, as well as of the one on which it has been demonstrated, 
 is that in quantitative analogies we take no account of the terms, 
 but look to the ratios alone. The reason that we accept the 
 equality of the angles as true, whatever the length of the sides, or 
 whatever the size of the contained angle, is that the length of the 
 sides and the size of the angle do not enter into the ratios that are 
 compared. They have nothing to do with the case. No alteration 
 in the length of the sides of an isosceles triangle alters the ratio 
 between them, so long as the triangle remains isosceles. No 
 alteration in the size of the contained angle alters the ratio of 
 the angles at the base to one another. Alteration of the length of 
 the sides, so long as it does not alter their ratio, or alteration of the 
 size of the contained angle, have no more to do with the compared 
 ratios than the birds and the blossoms of spring. The sides and 
 the angles are the terms of the ratios ; and it is the ratios, and 
 not the terms, that are compared. 
 
 ' Things that are equal to the same thing are equal to one 
 another.' This is an analogy. To say that two things are each 
 equal to a third, is to state two relations of equality. To say that 
 the two things are equal to one another, is to discern a ratio 
 between them similar to that already discerned between each 
 of them and the third. The whole process is an assimilation 
 of ratios — an Analogy. It is true that this axiom has already 
 been regarded as an Inference, and has been shown to be provable 
 by the Canons of Inference, and it may be alleged that this lays 
 me open to the charge of inconsistency that I have made against 
 my predecessors. But there is no inconsistency. The axiom may 
 also be regarded as an Induction, without laying me open to this 
 charge. That the axiom is in fact a comparison of ratios, and 
 that the ratios are intuitively perceived to be alike, is indisputable ; 
 and therefore it is indisputable that its validity rests on Analogy. 
 But this does not prevent us from postulating, if we choose to do 
 so, that two things are each of them equal to a third. For the 
 purpose of argument, we may postulate what we please; and when 
 this postulate is granted, we may deduce from it, secundum artem, 
 the inference that, in that case, the things are equal to one another. 
 And if any real A is equal to any real B, which, in its turn, is 
 equal to a real C, the problem ' Is or is not this A equal to this C ? ' 
 may be solved by the method of Induction. 
 
 A A 2
 
 356 A NEW LOGIC 
 
 Analogy has been defined as the comparison of Ratios, and the 
 
 discernment of their likeness or unlikeness ; and this definition is 
 
 true and is adequate with respect to qualitative analogies. But 
 
 the comparison of quantitative Ratios permits of more extended 
 
 reasoning than this. When quantitative ratios are unlike, we may 
 
 often go further than the mere discrimination of unlikeness, and 
 
 discern in what respect or degree they are unlike. We may see not 
 
 ci . . c 
 
 only that a : 6 or y- is unlike c; rf or -%' but we may discern that the 
 
 one Ratio is greater or less than the other, and this is a mode of 
 reasoning frequently employed in mathematics, and extremely 
 useful. I am offered odds of 5 to 4 by one, and odds of 11 to 8 by 
 another. Which ought I to choose ? This I cannot determine 
 except by Analogy. Comparison of the Ratios shows not only 
 that they are unequal, but that the Ratio of 11 to 8 is greater 
 than that of 5 to 4, and those are the odds, therefore, that I ought 
 to accept if I bet at all. Which motor car has the best chance 
 of surmounting the hill, that of 12 horse-power which weighs 
 15 cwt., or this of 20 h. p. which weighs 28 cwt. ? I cannot 
 tell except by Analogy, which shows me that the ratio of 20 to 28 
 is less than the ratio of 12 to 15, and enables me to fix my choice 
 on the car of lower power. 
 
 The greater part of geometrical and algebraical reasoning, and 
 a large part of purely arithmetical reasoning, proceed by Analogy, 
 as is manifest when it is avowed that a large part of mathematical 
 reasoning consists in the establishment and manipulation of 
 Ratios. The demonstrations of Euclid are successive analogies. 
 The rule-of-three sum is an analogy. The algebraic equation, 
 when it deals with fractions, is an analogy. Analogical reasoning 
 is of incalculable importance ; but it is a kind of reasoning that 
 logicians have not discovered, and to which no logician makes 
 any allusion whatever. They do indeed speak of ' reasoning by 
 analogy,' but in so speaking they are guilty of the fallacy of 
 equivocation ; they pervert the use of words, and mean, not 
 Analogy, but a totally different process.
 
 CHAPTER XXIII 
 
 COMPOSITE REASONING 
 
 We have now reviewed in turn all the processes of Reasoning, 
 and the subsidiary factors and processes that are ancillary to 
 reasoning. We have analysed them into their elements, described 
 their forms and varieties, formulated the Canons by which they 
 are regulated, and investigated the conditions of their validity. 
 It yet remains to show how they are combined together. 
 
 In their origin, all modes of Reasoning spring from one root — 
 from the discernment of likeness and the discrimination of 
 difference, which are two aspects of the one fundamental process 
 of comparison. All reasoning is, in the last resort, and when 
 analysed out, comparison, and the consequent discernment of 
 likeness and discrimination of difference. Hence the simplest of 
 all instances of reasoning — the instance of Axioms — may be referred 
 to either type of reasoning indifferently. They are explicable, we 
 find, as examples of Induction, of Deduction, or of Analogy ; and 
 there is nothing inconsistent or paradoxical in this triple 
 explanation. It merely means that, in these simple cases, the 
 three types of reasoning, which all spring from a single root, are 
 as yet undifferentiated. As we rise to more and more complex 
 instances, to more and more specific examples, the differentiation 
 becomes more and more complete, until the three modes of 
 reasoning are at length discrete and separate. This fundamental 
 identity of origin must not be confused with that superficial 
 similarity of composition which has led to the imperfect 
 discrimination of one form of reasoning from another, and 
 which we have found to be such a radical defect in existing 
 systems of Logic. Logicians hold, or, without explicitly teaching, 
 their whole system is founded on the notion, and penetrated with 
 the notion, that the three modes of reasoning here distinguished — 
 Induction, Deduction and Analogy — merge and blend into one 
 another; and the boundaries of the three are by them blurred and 
 confused. I hold, on the contrary, that while they are identical 
 in origin, and are branches of a single trunk, yet they are, except
 
 iD 
 
 S A NEW LOGIC 
 
 in their origin, distinct and separate ; and that we may always 
 identify the mode of reasoning we employ, if we take the trouble 
 to do so. But although the three forms of reasoning are 
 completely distinct and discriminable, it does not follow that 
 either need be employed alone to the exclusion of the others. On 
 the contrar}', it very seldom happens in argument, or even in 
 Mathematical computations, that we adhere exclusively to one 
 mode for long together. Seldom do we pursue an argument 
 through more than a very few steps without employing every 
 process of reasoning, and alternating them repeatedly. It is this 
 alternation of argument, and not the confusion of one mode of 
 argument with another, that constitutes Composite reasoning as I 
 understand it, and Method as understood in some Text books. 
 
 I want to know the nature of Light, and the mode of its 
 promulgation. This is a Material argum.ent. It seeks to 
 ascertain Truth — Fact — and consequentl}^ my first task is to find 
 a premiss — to find in experience a case as similar as possible. 
 Unfortunately, there is nothing in experience that is closely 
 similar. Light is promulgated in all directions from a centre : 
 What can I find in experience that is at all similar ? I can find 
 plenty of instances in experience of things being transferred from 
 place to place — an arrow from a bow, a stone from the hand, a 
 bullet from a gun, leaves and light objects by the wind, dust in a 
 storm, and so forth ; and from these not very similar data I can 
 form the hypothesis that light is particulate, and is projected in 
 streams of particles from the luminous body. So far Mediate 
 Induction : now Inference comes into play. If light consists of 
 particles thrown off from the luminous body, then, by the second 
 Canon of Explication, we may infer that the luminous body will 
 waste away in proportion to the amount of light it disperses. 
 Follows Immediate Induction — the direct appeal to experience. 
 Do luminous bodies waste away ? Yes, candles, lamps, fires, all 
 consume away in giving off light, and roughly and generally, 
 the consumption is in proportion to the amount of light given off. 
 Here, then, is some corroboration, by the direct appeal to 
 experience, of the hypothesis ; but this hypothesis is not the 
 only one possible. Light is the promulgation of something in all 
 directions from a centre. There arc other cases of such promul- 
 gation that will yield data. When a stone is thrown into a pond, 
 waves are propagated from the centre of disturbance in all
 
 COMPOSITE REASONING 359 
 
 directions in one plane. When a bell is struck, waves are 
 propagated froni the centre of disturbance in all directions 
 in all three dimensions. Moreover, there is a further simi- 
 larity in a material respect. The intensity of the waves of 
 water and of air is inversely proportional to the square of the 
 distance from their place of origin. So, too, is the intensity of 
 light. Here, then, arc data; and data that yield premisses; and 
 from these premisses we may draw conclusions, which, since the 
 terms of the data are not closely assimilable, are tentative 
 conclusions, or hypotheses only. So far Induction ; now comes 
 Inference into play. If Light consists of undulations, then, by 
 the second Canon of Explication, there must be a medium of 
 which it is undulations. Water, we know, is an undulatory 
 medium ; so is air. As light travels otherwise than through water, 
 by the third Canon of Explication, the undulations of light are 
 not aquatic. As it travels through a vacuum, and through 
 transparent solids, by the same Canon, they are not aerial. Direct 
 appeal to experience fails to find any medium, and therefore the 
 hypothesis is dropped, as, on the whole, less consistent with 
 experience than the corpuscular hypothesis. Presently, however, 
 Analogy is called in ; and by comparison of relations it is 
 discovered that a corpuscular light must travel faster in water 
 than in air : an undulatory light faster in air than in water. 
 Again direct appeal is made to experience, by means of an 
 experiment special!}- devised for the purpose ; and experiment 
 shows that the rate is faster in air. From this it is concluded 
 that the promulgation of light must be undulatory, even though 
 experience yields no medium of which it can be undulations. 
 
 The conclusion of the analogical argument may be put in the 
 form of a ' Conditional syllogism.' If light travels faster in air 
 than in water, it is propagated by undulation ; but it does travel 
 faster in air than in water ; .". it is propagated by undulation. 
 This is a perfectly sound and valid argument, that has led to a 
 valuable discovery : why then was it condemned in the chapter 
 on the Conditional proposition ? The condemnation was 
 launched, not against the combination of different modes of 
 reasoning in a composite argument, but against the confusion of 
 two modes of argument. The argument from If A is B, it is C 
 is an argument from a postulate, and in reasoning from a postulate, 
 we are not entitled to go beyond the postulate ; but no prohibition
 
 36o A NEW LOGIC 
 
 was uttered against combining the argument from postulation 
 with the argument from experience, as long as we recognise that 
 we are employing two modes of reasoning, and do not deceive 
 ourselves into the belief that we are using one only. The fault 
 that is charged against Traditional Logic is not that of using 
 the argument that it calls the hypothetical syllogism, but of 
 calling that argument an Inference, and supposing that in thus 
 reasoning, we are using but one mode of reasoning. The 
 reasoning is a composite argument, combining Inference with the 
 direct appeal to experience, or Immediate Induction. It is a 
 perfectly valid argument, and my objection to it was raised, 
 not against its validity, but against the supposition that in using 
 it, we are employing Inference or Deduction alone. Deduction 
 is formal Logic, and exceeds its function if it takes account of 
 material truth. In fact, by its very nature it is incapacitated from 
 taking account of material truth. The ' hypothetical syllogism ' 
 is not formal. It is a combination of the formal argument and 
 the material argument. Since it is valid, logicians have con- 
 cluded that no objection can be taken against it as an Inference. 
 But an Analogy may be valid, and yet not be an Inference. 
 It is not the use of the composite argument called the hypothetical 
 syllogism that is here condemned ; it is the failure to discern that 
 it is a composite argument. 
 
 What is the cause of specific fevers ? We have already seen 
 how, from the datum, that they are like hving organisms, in 
 coming into existence after the lapse of an interval succeeding a 
 contact, the hypothesis was formed that they might be due to 
 something of the nature of eggs or seeds ; how this hypothesis was 
 formed also, from another datum, to account for tuberculosis ; and 
 how the direct appeal to experience discovered micro-organisms 
 in tuberculosis ; but the crucial question remained. Are these 
 micro-organisms indeed the cause of the tuberculosis ? Do they 
 constitute the tuberculous infection ? Direct appeal was again 
 made to experience. The organisms were injected into guinea- 
 pigs ; and the guinea-pigs suffered from tuberculosis. But is the 
 tuberculosis due to the properties of these organisms as living 
 organisms, or do they act merely as mechanical irritants ? 
 Recourse is had to Inference, which tells us that if they act by 
 their vital properties as living organisms, they will so act when 
 they are alive, but not when they are dead ; while if they act as
 
 COMPOSITE REASONING 361 
 
 mechanical irritants or as chemical poisons, they will act equally 
 well whether alive or dead. Direct appeal to experience is made 
 again. The organisms arc killed by boiling, and again injected ; 
 and tuberculosis does not follow. The hypothesis that the 
 organisms produce tuberculosis by their vital activity is verified 
 by the direct appeal to experience. But in some respects 
 material to the argument, specific fevers are like tuberculosis. 
 From this datum we obtain, by Mediate Induction, the hypothesis 
 that specific fevers are due to micro-organisms. Similar direct 
 appeal to experience confirms this hypothesis. 
 
 The main topic of Inductive Logic, as expounded in the text 
 books, is the direct appeal to experience. Inductive Logic lays 
 down the conditions under which this appeal should be made, in 
 order to test hypothesis and conjecture. This is a very important 
 topic ; but it covers but one moiety of the field of Induction. The 
 indirect appeal to experience, w^hich is equally important, is 
 always regarded as a mode of syllogising, which it is not. 
 
 Is fermentation due to the presence of living yeast cells ? By 
 Deduction we can infer that if it is, then fermentation will not 
 occur if yeast cells are excluded ; if, though they are admitted, 
 they are first killed ; or if, though not killed, their vital activity 
 is arrested ; that the presence of matter other than yeast cells 
 will not produce fermentation ; and that the introduction of 
 living and active yeast cells will always produce fermentation 
 in fermentable matter. All these are Deductions. They are 
 all explications of the postulate that fermentation is due to 
 the activity of living yeast cells. They do not depend in the 
 least on the truth of the postulate, and are equally true 
 as deductions from the postulate, whether there are or are 
 not such things as yeast cells ; whether there is or is not such 
 a thing as fermentation. All of them, however, can be put to 
 the test by direct appeal to experience. Yeast cells, supposing 
 that they exist, can be excluded from fermentable matter by 
 allowing no air to reach it that has not been filtered through 
 cotton wool. Yeast cells can be killed by heat before they are 
 added to fermentable matter. If the fermentable matter is kept 
 at a low temperature, the vital activity of the yeast cells is 
 inhibited. Under none of these circumstances does fermentation 
 take place. Neither does it take place if, while yeast cells are 
 excluded, other living organisms are introduced into fermentable
 
 362 A NEW LOGIC 
 
 matter ; and finally, the introduction of living yeast cells into 
 fermentable matter that is kept at a proper temperature, and 
 contains nothing to prevent the vital activity of the cells, is 
 always followed by fermentation. Thus the direct appeal to 
 experience converts the conjecture into a proved Induction. 
 
 The original conjecture, that fermentation ma.y be due to the 
 action of living yeast, was arrived at by Empirical reasoning — by 
 Indirect or Mediate Inductions — something in this way: — Yeast 
 is very often, perhaps always, present in fermenting liquor : and 
 the quantity of yeast increases as the fermentation goes on. 
 Now it is fairly constant in experience that a condition that is 
 always present when a change takes place, and especially when 
 the quantity of the condition bears a relation to the quantity of 
 the change, is causally connected with that change. It is fair to 
 conclude, therefore, as a conjecture, that it is probable that 
 yeast is causally connected with fermentation. But if }'east is 
 not only causally connected with fermentation, but produces 
 fermentation by the vital activity of its cells, then Inference 
 allows us to deduce the consequences set forth above, and the 
 direct appeal to experience enables us to discover whether these 
 consequences tally with fact, and thus the chain of reasoning is 
 complete, and we are led to the discovery of truth.
 
 CHAPTER XXIV 
 
 FALLACIES 
 
 Of all the anomalies and antinomies of Traditional Logic, of 
 all its defects and futilities, none strikes a new-comer as so 
 anomalous or so extraordinary as the fact that the fallacies it 
 enumerates, specifies, and describes, are not breaches of its own 
 rules. If the syllogism were the universal principle of reasoning 
 that Traditional Logic claims that it is, it would clearly be 
 impossible to perpetrate any fallacy without infringing some rule 
 of the syllogism. Yet not one of the fallacies of the Sophistici 
 Elenchi is a breach of any syllogistic rule. The very fact that 
 there are fallacies that admittedly have nothing to do with the 
 syllogism, and can be perpetrated though every syllogistic rule 
 is punctually observed, is of itself proof that the syllogism is not the 
 only mode of reasoning, and ought to have aroused a suspicion, 
 at least, that there is some other mode of reasoning besides and 
 apart from the syllogism ; but this suspicion seems never to have 
 arisen in the minds of logicians. 
 
 Modern Logic provides many modes of reasoning, but these 
 are to be regarded, not as substitutes for the syllogism, but as 
 variants of it ; whichever they may be, however, Modern Logic 
 does not recognise, any more than Traditional Logic, that a fallacy 
 in reasoning, if it is indeed a fallacy, must be a breach of some 
 Canon of Reasoning. In any complete scheme of Logic, every 
 fallacy should be referable to the Canon that it violates, thus 
 revealing how and why it is a fallacy, and placing it in its proper 
 position in the scheme of fallacies. Nothing of the sort is 
 attempted in any book on Logic known to me. There are many 
 different classifications of fallacies, but there is no classification 
 founded on the Canons that are fallaciously broken ; and the 
 reason is that there is no system of Rules to which fallacies can 
 be referred. There is no recognition in any book on Logic that 
 such reference is necessary or desirable ; and to this necessity or 
 desirability, Modern Logic is as blind as Traditional Logic or 
 Inductive Logic.
 
 364 A NEW LOGIC 
 
 Not only are the Classical fallacies extra dictionem not breaches 
 of any of the rules of the Syllogism, or of those of Immediate 
 Inference, but by no means, by no skill, by no artifice, can these 
 fallacies be brought into conflict with the Laws of Thought, or 
 with the Dictum dc omni et nulla. Surprising and marvellous as 
 are the meanings read into the Laws of Thought by Modern 
 Logic, I do not find it suggested that any of them contains a 
 prohibition of the fallacy of many questions, of arguing post hoc, 
 ergo propter hoc, of the ignoratio clcnchi, or of any other of the 
 fallacies extra dictionem of Traditional Logic. 
 
 If, therefore, a scheme of Logic is propounded, in which every 
 
 one of these fallacies falls naturally into place as the breach of 
 
 a recognised Canon, constructed, not with a view to catching 
 
 the fallacies, but with an eye solely to the exigencies of the 
 
 scheme ; surely that in itself substantiates a claim on logicians 
 
 for the consideration of that scheme. The Canons of Inference, 
 
 and the Canons of Induction, as laid down in this book, were 
 
 formulated as guides to those two modes of reasoning respectively : 
 
 not until they were completed for this purpose, was it discovered 
 
 that every one of the classical fallacies of Traditional Logic is a 
 
 breach of one or other of these Canons. This being so, I submit 
 
 that the scheme is entitled to assume to itself some of the 
 
 prescription that attaches to the venerable antiquity of these 
 
 fallacies ; and that this result may fairly be claimed as a 
 
 corroboration of the accuracy and comprehensiveness of the 
 
 scheme. At any rate, I submit that this result may be advanced 
 
 as an indication that the New Logic here propounded is superior 
 
 in amplitude and adequacy to previous systems, none of which 
 
 can show a similar result. 
 
 The fallacies here enumerated and examined include all the 
 fallacies of the Sophistici Elenchi, together with others, that have 
 not hitherto been recognised by logicians. One or two of them 
 are sufficiently frequent, and sufficiently important, to have been 
 recognised by practical reasoners, though no book on Logic treats 
 of the fallacy of jumping to a conclusion, and no one but Prof. 
 Carveth Read mentions the fallacy of failing to recognise that 
 circumstances alter cases. 
 
 The Aristotelian division of fallacies, into fallacies in dictione and 
 fallacies extra dictionem is scarcely sound. Fallacies in dictione 
 are mistakes, rather in the art of expression, or of interpretation
 
 FALLACIES 365 
 
 than of reasoning. They are confusions of meaning;, and are 
 sources of fallacy rather than themselves fallacies. This 
 distinction, valid though it is, is perhaps a little too fine to be 
 practically workable ; and, for practical purposes, we may divide 
 fallacies on the Aristotelian plan into Fallacies in didione and 
 Fallacies extra dictionem. 
 
 Of Fallacies in didione, the Aristotelian class of Equivocations 
 is a natural and valid class, and may stand. The fallacies of 
 Composition and Division are particular cases of Equivocation, 
 and are not entitled to separate treatment. Next will come a fallacy 
 new to Logic, though familiar enough to practical reasoners — 
 the fallacy of Bivocation. The fallacies of the Accent and of 
 Figure of Speech are unknown in English, and there are two 
 common fallacies in didione that Aristotle does not mention. 
 One of these, the fallacy of Emphasis, is confused by Jevons, 
 and most other writers, with the fallacy of Accent ; the 
 other is unnoticed hitherto by any logician, though fallacies of 
 Punctuation are, in practice, common enough, and misleading 
 enough ; especially in English. It is of sufficient importance in 
 practice to require, in some cases, the judgement of Courts of 
 Law to determine the proper interpretation to be placed upon 
 the presence or absence, or the position, of a comma ; yet it is a 
 matter to which no logician has given any attention. 
 
 Fallacies extra dictionem are the only true fallacies, properly so 
 called. They are the only mistakes in the reasoning process 
 itself. Each of these fallacies is a breach of some one or more of 
 the Canons of Reasoning ; and they fall naturally into classes, 
 according to the kind of reasoning in which they occur, and 
 according to the Canon of that mode of reasoning that they 
 violate. Thus we get the three classes, of Fallacies of Empirical 
 Reasoning, or Induction ; Fallacies of Inference, or Deduction ; 
 and Fallacies of Analogy. These include all the fallacies extra 
 dictionem of Aristotle, and several others, that neither he, nor 
 any other logician, has recognised ; though some of them are 
 suflficiently patent, and sufficiently frequent, not only to have been 
 recognised, but actually to have been named by practical 
 reasoners. In addition, there is a fourth class of fallacies, that 
 has hitherto lain undiscovered and unappreciated. The perpetra- 
 tion of fallacies of this class is the besetting sin of logicians 
 themselves, and is one of the chief defects of Traditional Logic.
 
 366 A NEW LOGIC 
 
 They are Fallacies of Confusion of the Mode of Argument, and 
 will need careful attention. 
 
 The classification of fallacies here adopted is, therefore, as 
 follows : — 
 
 I. Fallacies ?nZ)/c^/o»^. 
 
 Fallacies of Equivocation. 
 Fallacies of Bivocation. 
 Fallacies of Amphiboly. 
 Fallacies of Punctuation. 
 Fallacies of Emphasis. 
 II. Fallacies extra Dictionem. 
 
 Fallacies of Confusion of the Mode of Argument. 
 Fallacies of Empirical Reasoning, or Induction. 
 Fallacies of Inferential Reasoning, or Deduction. 
 Fallacies of Analogy. 
 
 I. Fallacies in Dictioxe. 
 The Fallacy of Equivocation. 
 
 The fallacy of Equivocation is a pervading and ubiquitous 
 fallacy. It varies in subtlety from a manifest pun, that would 
 not deceive a child, to a confusion the most subtle, the most 
 difficult to detect, to recognise, and to avoid, of all fallacies ; 
 and of all fallacies it is the most frequently perpetrated. Nothing 
 is more frequent in reasoning, and especially in disputation, than 
 the use of a term in two or more senses, without any appreciation 
 on the part of either of the disputants, or of the single reasoner, 
 that it is used in more than one ; nor is there any source so 
 fertile of difference of opinion. In fact, difference, that appears 
 to be difference of opinion about facts, is very often, unknown 
 to the disputants, diff"erence about the meaning of words ; and 
 no controversy can be useful or fertile, that is not preceded by 
 a definition of the words to be used, and an agreement about 
 the meanings to be attached to them. It is not too much to 
 say, that in most controversies, each party uses some important 
 term, on which the controversy hangs, in a sense different from 
 that understood by the other party ; or uses the term, first in 
 one sense, and then in another, without any recognition or appre- 
 ciation of the equivocation. It requires an effort, and a consider-
 
 EQUIVOCATION 367 
 
 able effort, to adhere to the same meaning in using a word of 
 current and large signification, throughout a controversy that is 
 at all prolontjed. 
 
 It is idle to discuss the advantages and disadvantages of 
 Socialism, until we have settled and agreed upon the meaning 
 that is to be attached to ' Socialism.' When one disputant under- 
 stands by it the organisation and management of industries by 
 the State, and another takes it to mean the equalisation of 
 reward for labour, and a third intends by it the abolition 
 of private property, it is evident that the argument of each will 
 be to the others, beside the mark, irrelevant, and mistaken. It 
 is idle to discuss whether it is right for a clergyman to repel 
 from the communion table (which he erroneously calls the 
 altar) a man who has married his sister-in-law, until we have 
 settled what meaning is to be attached to ' right.' Does it mean 
 consistent with statute law ? or with canon law ? or with the 
 custom of the Church, or of some part of the Church ? or with 
 the scruples of the clergyman ? or with some code or rule of 
 morality ? While the dispute is in progress, any of these mean- 
 ings may be temporarily uppermost in the minds of either of 
 the disputants, and be shortly replaced by another, without any 
 appreciation, even by himself, that he has shifted his ground ; 
 and it is unlikely, unless care is taken both to define the term 
 and to keep to the definition, that both disputants w'\\\ use the 
 word in the same sense at the same time. A totally different set 
 of meanings clings about the word when the question is asked 
 whether women have a ' right ' to the suffrage. Is the ' right ' a 
 legal right, a constitutional right, or a moral right ? If a legal 
 right, what is the law that gives it to them ? If a constitutional 
 right, what is the meaning of * constitutional ' ? Does it mean 
 consistent with established custom, or consistent with the fiction 
 that taxation and representation go together, or with the 
 principle that they ought to go together ? Or does it mean that 
 the granting of the suffrage to women would be beneficial to 
 them, or to the nation ? If a moral right, it means consistent 
 with some scheme of morality, but with whose scheme ? Yours, 
 or mine, or his ? Any discussion that ignores these ambiguities 
 in the meaning of ' right,' is barren ab initio. 
 
 Does the syllogism contain a pditio priiicipii ? That depends 
 on the meaning we attach to pditio principii. If we take it in
 
 368 A NEW LOGIC 
 
 the literal sense, of begging or assuming a principium, or major 
 premiss, then the syllogism certainly contains a petitio principii, 
 for in every syllogism the premisses are assumed for the purpose 
 of argument. If we take it as assuming that the major premiss 
 is true, outside the purpose of the argument, then we beg, not 
 the principium, but the truth of the principium, a very different 
 thing, as will presently be shown. If we take it in the Aristotelian 
 sense, to mean the assumption in the premiss of the conclusion 
 that is to be proved, then the syllogism must contain a petitio 
 pri)icipii, or the conclusion could not be deduced from it. 
 
 The Aristotelian fallacies of Composition and Division are 
 merely instances of equivocation. They reside in the ambiguity 
 of the word 'All.' The ' all' of the Universal proposition is out 
 of place, and ought not to be used. What is meant by it is 
 ' every.' What is meant by ' All men are mortal ' is ' Every man 
 is mortal.' Strictly speaking, ' all ' is a collective, not a dis- 
 tributive quantit}' ; but Traditional Logic, with its usual per- 
 versity, chose the wrong word, though the right one was 
 available. If ' All men are mortal ' is understood in the proper 
 and strict sense of the word ' All,' then any individual man is 
 not necessarily mortal. This is clearly brought out if we add 
 the definite article. * All the men will receive five shillings ' does 
 not mean ' Every man will receive five shillings.' In the Aristo- 
 telian scheme of fallacies, those of Composition and Division are 
 regarded as separate forms, but it is manifest that they are merely 
 special cases of equivocation, and are not entitled to separate 
 treatment, any more than is the following : — 
 
 No fool can design a battleship ; 
 \> He is no fool ; 
 
 .•. He can design a battleship. 
 
 This argument is manifestly fallacious, and the fallacy consists 
 in the equivocation of the term ' no fool.' In Traditional Logic 
 it is invalid on the ground that both premisses are negative. It 
 is true that it is invalid, and that both premisses are negative ; 
 but we have seen, in the chapter on the syllogism, that the 
 negative quality of both premisses does not necessarily invali- 
 date an argument. The true ground of the invalidity is 
 equivocation. In the major premiss ' no fool ' means ' no one 
 who is a fool ' : in the minor, * no fool ' means ' one who is not
 
 BIVOCATION 369 
 
 a fool ' ; and in reaching the conclusion, the latter meaning has 
 been illegitimately substituted for the former. The equivocation 
 is brought out more clearly if we substitute for the major, one 
 of its implications. ' No fool can design a battleship ' may, by 
 transfer of the negative, be explicated, without change of 
 meaning, into ' A fool cannot design a battleship.' It is now 
 clear that from a premiss postulating who cannot design a battle- 
 ship, we are not entitled to infer who can. 
 
 The Fallacy of Bivocation. 
 
 There is a fallacy cognate with the fallacy of Equivocation, 
 and not very infrequently perpetrated, but unmentioned, as far 
 as I know, by any writer on fallacies, even De Morgan. Equivo- 
 cation is giving the same name to different things, and treating 
 them in statement or argument as if they w-ere the same. The 
 fallacy of Bivocation is giving two names to the same thing, 
 and treating it in statement or argument as if it were not 
 one, but two. Thus I have heard instances of deliberation and 
 choice, exercised by the lower animals, adduced as proof that 
 these animals were capable of reasoning ; and I have heard 
 that argument met by the objection that these instances of 
 deliberation and choice were evidence, not of reason, but of a 
 high degree of sagacity only. In this case, the two names, 
 sagacity and reason, were given to the same thing, which was 
 then treated not as one thing, but as two contrasted things. 
 Instances of the same fallacy are to be found in those books on 
 Logic which treat of Enumerative Induction and Generalisation 
 as different processes ; which give the name of Classification to 
 successive steps of Generalisation, and yet regard them as different 
 things. The term Classification is, in Logic, both equivocal and 
 bivocal. It is equivocal in that it is applied both to Division 
 and to Generalisation, which are different ; it is doubly bivocal 
 in that it as well as Generalisation are applied to the same thing, 
 and it as well as Division are applied to the same thing. 
 
 When Jenner discovered that, under the one name of typhus 
 fever, two distinct diseases were included, he exposed a fallacy of 
 equivocation. Though certain symptoms are common to both 
 diseases, and thus led, not merely to the inclusion of both in one 
 class, but to the confusion of the one with the other ; yet certain 
 
 N.L. B E
 
 370 A NEW LOGIC 
 
 other symptoms are proper to each disease respectively, and thus 
 distinguish the one from the other. But when Kraepehn gives to 
 some cases of insanity the title of dementia prsecox, and fails to 
 show that there is any s^-mptom proper to those cases and 
 unshared by other cases of insanit}', he perpetrates a fallacy of 
 bivocation. He calls the same thing by two names, and forth- 
 with treats it as two different things. 
 
 A term is, of course, not necessarily bivocal because it has a 
 synonym. Mariner and seafaring man are not bivocal, though 
 they both refer to the same thing. They are not bivocal, because 
 it is recognised and understood that they refer to the same thing, 
 and they are used in statement and argument not bivocally but 
 as equivalents. But if it were denied that A. B. is a seafaring 
 man on the ground that he is only a mariner, the term would be 
 bivocal. 
 
 The Fallacy of Amphiboly. 
 
 The fallacy of Amphiboly, or ambiguity in the construction of 
 sentences, is rarely illustrated in text books of Logic by any 
 other than the stale examples, copied from book to book, of 
 'Aio te, ^acida, Romanos vincere posse,' and ' The King yet 
 lives that Henry shall depose ' ; and we are consequently led to 
 suppose that it is a fallacy so rare, that it may be practically 
 neglected. Nothing could be much more erroneous. It is one 
 of the most frequent sources of confusion, especially in compo- 
 sitions in the English language, which, being destitute of inflection, 
 depends for the accuracy of its meaning on the proper order of 
 its words. 
 
 A familiar example, and one that deceives no one, is ' A small 
 labourer's cottage,' for 'a labourer's small cottage,' or *a small 
 cottage for a labourer.' It is not generally recognised, though it 
 is interesting as illustrating the use of inflections, and the necessity 
 of supplementing the absence of inflections by the ordering of 
 the words, that the first construction may be made grammatically 
 and syntactically accurate, though the sense is of course altered, 
 by changing the inflection. If, instead of writing ' a small 
 labourer's cottage,' we write *a small labourers' cottage,' the 
 expression is punctually correct, and is univocal. It cannot 
 now be understood ambiguously ; for the plural of the substantive, 
 ' labourers,' excludes the possibility that the singular adjective can
 
 AMPHIBOLY 371 
 
 apply to it, and leaves outstanding, as the only alternative, that 
 * a small ' qualiiics ' cottage.' 
 
 The fallacy is n(jt always as transparent as it is in the case just 
 cited. * A lady's sound, quiet hack ' is grammatically as correct 
 as *a lady's hack, sound and quiet,' but it does not mean the 
 same. The first means ' a sound quiet hack, belonging to a lady,' 
 the second means ' a sound quiet hack, suitable for a lady to 
 ride.' 
 
 Nowhere do we find the fallacy of Amphiboly so rampant as in 
 Acts of Parliament, despite the labours of Parliamentary draughts- 
 men in interpreting the intentions of legislators. 
 
 ' Habitual drunkard means a person who, not being amenable 
 to any jurisdiction in lunacy, is, notwithstanding, by reason of 
 habitual intemperate drinking of intoxicating liquor, at times 
 dangerous to himself or others or incapable of managing himself 
 and his affairs.' 
 
 What is the effect, on the meaning of the rest of the definition, 
 of the insertion of the words ' not being amenable to any j urisdiction 
 in lunacy ' ? Does it or does it not mean that the drunkard must 
 be partially insane, or must be bordering on lunacy, — not insane 
 enough to be certified as a lunatic, but yet to some extent disordered 
 in mind ? High authorities are divided on the question. 
 
 How does * by reason of the intemperate drinking of intoxi- 
 cating liquor' affect the meaning of 'at times dangerous, &:c.' ? 
 Does it mean that any person who becomes dangerous, &c., when 
 he is drunk, and is also in the habit of intemperate drinking of 
 intoxicating liquor, may be regarded as an habitual drunkard ; or 
 does it mean that, however dangerous, &c., a man ma}' be when 
 he is drunk, and however habitual may be his intemperate 
 drinking, he is not an habitual drunkard within the meaning of 
 the Act, if his dangerousness can be ascribed to the single state 
 of drunkenness in which he then was, and need not of necessity 
 have been due to his long-continued drinking ? The question 
 had to be taken to the Court of Appeal for decision. 
 
 * At times.' How much of the following clause does this affect ? 
 Does it qualify ' dangerous to himself and others ' only, or does 
 its effect extend to the subsequent clause, * incapable of managing 
 himself and his affairs ' ? Again, authorities are divided in 
 opinion. 
 
 ' Incapable of managing himself and his affairs.' Must he, in 
 
 B B 2
 
 372 A NEW LOGIC 
 
 order to be an habitual drunkard within the meaning of the Act, 
 suffer from both incapacities, or is one enough ? Again, different 
 authorities interpret the Act in different senses. 
 
 As with this Section of this Act of Parliament, so with other 
 Sections and other Acts. Nothing is more difficult, in many cases, 
 than to interpret the intention of the Legislature from the wording 
 of the Statutes ; and the greater part of the difficulty arises from 
 what Aristotle called Amphiboly — the ambiguous or indefinite 
 construction of sentences. 
 
 The commonest fault of construction is misplacement of the 
 relative. ' There was a swallow's nest in the shed, which was 
 pulled to pieces by sparrows.' The writer probably did not mean 
 what he said, that the shed was pulled to pieces by sparrows. 
 Even careful writers, e\-en distinguished writers, and reputed 
 masters of style in English writing, sometimes slip into this 
 mistake. ' Not because the bishops obtained any gifts or graces in 
 this consecration which she herself respected ' writes Froude, 
 evidently meaning ' not because the bishops obtained, in their 
 consecration, any gifts or graces that she herself respected.' And 
 again ' a feeling approaching to contempt . . . has prevented them 
 from carrying the weight in the councils of the nation which has 
 been commanded by men of no greater intrinsic eminence in other 
 professions.' Froude did not mean to convey that the nation has 
 been commanded by men of no greater intrinsic eminence &c. 
 What he meant was that the feeling has prevented them from 
 carr\'ing, in the councils of the nation, the weight which has been 
 commanded by &c. 
 
 The Fallacy of Punctuation. 
 
 Much confusion in the meaning of written sentences arises 
 from neglect of punctuation, and from erroneous punctuation. 
 Punctuation is becoming a lost art. Many writers, perhaps not 
 recognising its importance, and certainly shirking its difficulties, 
 leave it to the printer to insert what stops seem to him expedient. 
 Most printing offices have their own rules and conventions with 
 respect to punctuation, which are applied indifferently to all 
 writings, and from which some printers will not be moved by any 
 entreaty or objurgation on the part of an author, to depart. In 
 very many cases, however, the punctuation determines the meaning, 
 and, this being so, it is no more justifiable to tamper with the
 
 FALLACY OF PUNCTUATION 373 
 
 punctuation adopted by an author, than to garble the words of 
 his text. 
 
 * Do you know,' a lately deceased author was asked, ' a man 
 with one eye named Matthews ? ' ' No,' was the answer, ' what ^ 
 was the name of his other eye? ' If the question was put in the 1 
 form which is given to it above, the retort was completely justified, 
 and was logical. The question, in the form here stated, clearly 
 attributes the name to the eye, and not to its possessor. Strictly 
 speaking, the proper construction is, ' a man named Matthews, 
 with one eye ' ; but this construction is rather pedantic, and is a 
 little awkward. The original arrangement can be deprived of its 
 ambiguity, and the intended meaning conveyed with certainty, by 
 proper punctuation. If it had been written *a man, with one eye, 
 named Matthews,' the retort would have been inappropriate, for 
 the separating commas accurately indicate that the words they 
 enclose constitute a clause qualifying the word ' man,' and that 
 in true construction, the sentence runs, *a man — named Matthews.' 
 It is now a frequent practice to omit the first of the commas 
 limiting a qualifying clause, and the omission does not often lead 
 to ambiguity, since the first comma is understood. The sentence 
 would still pass, and would still be unambiguous, if it were 
 written * a man with one eye, named Matthews.' The vice of the 
 practice is that the omission of the first comma is apt to lead to 
 the omission of the second ; and there are cases in which the 
 omission of even the first comma alters the meaning of the 
 sentence. ' The object in my view was the construction of an 
 unambiguous sentence.' This means that the construction of an 
 unambiguous sentence was the object I desired to attain. ' The 
 object, in my view% was the construction &c.,' means ' My 
 opinion is that the object was the construction 6cc.' If we retain 
 the second comma and drop the first, as the custom is with 
 qualifying clauses, we lose this meaning, and restore the former. 
 * The object in my view, was the construction &c.,' means the 
 object I desired to attain. The single comma is, in fact, redundant 
 and awkward. It breaks the continuity of the words at a place at 
 which there is no break in the continuity of the sense. The 
 second meaning cannot be conveyed by punctuation without the 
 insertion of both commas. It can, of course, be conveyed by 
 altering the arrangement of the words. 
 
 ' She cooked the meat and the potatoes and the beans she kept
 
 374 A NEW LOGIC 
 
 raw till next day.' What was the fate of the potatoes ? That 
 cannot be determined except bj' punctuation. Insert a comma 
 after ' potatoes,' and the potatoes were cooked. Take out the 
 comma and insert it after ' meat ' and the potatoes are kept raw. 
 
 ' O fools, and slow of heart to believe all the prophets have 
 spoken ' characterises the persons addressed as unworthy because 
 they are slow to believe. ' O fools and slow of heart, to believe 
 all the prophets have spoken ' characterises them as unworthy for 
 precisely the opposite reason. 
 
 ' General Kharki, the Commander in Chief having secured his 
 communications, determined to advance.' General Kharki and 
 the Commander in Chief are, in this sentence, two different 
 persons. ' General Kharki, the Commander in Chief, having 
 secured his communications, determined to advance.' The effect 
 of inserting the comma is to identify General Kharki with the 
 Commander in Chief, who are now no longer two, but one. 
 
 It is the less excusable to ignore this source of confusion, since 
 most of us were made familiar with it in the nursery. The 
 following lines are familiar to most children : — 
 
 I saw a little ant swallow up a whale ; 
 
 I saw the sea full of good sparkling ale ; 
 
 I saw^ a glass full fifteen yards deep ; 
 
 I saw a well full of men's tears that weep ; 
 
 I saw two watery eyes all in flames of fire ; 
 
 I saw a house high as the moon and higher; 
 
 I saw the sun upon the darkest night ; 
 
 At least I saw the man who saw this wondrous sight. 
 
 The assertions are sufficiently outrageous and incredible as they 
 stand ; but if we take away the stops from the ends of the lines, 
 and insert them after the first substantive in each line, they are 
 changed into very commonplace assertions. They then become 
 a series of rhetorical inversions : — I saw a little ant ; Swallow up 
 a whale I saw the sea ; Full of good sparkling ale I saw a 
 glass ; &c. 
 
 The Fallacies of Accent and Emphasis. 
 
 These two fallacies may be treated together ; the rather, since 
 English logicians have gratified their insatiable appetite for
 
 FALLACY OF EMPHASIS 375 
 
 perpetrating fallacies, by confusing them together. In English, 
 we speak of the emphasised syllable of a word as the accentuated 
 syllable, and say we place the accent, when we mean the emphasis, 
 on this or that syllable. Then, since emphasis is employed to 
 render prominent, not only one syllable in a word, but also one 
 word in a sentence, this word is spoken of as accentuated ; and the 
 misplacement of emphasis on words is regarded as an example of 
 the fallacy of the accent. A more transparent equivocation has 
 never been perpetrated, even by logicians. The Aristotelian 
 fallacy of the accent was the omission or misplacement of the 
 accent-mark on a letter or syllable in a word, and the consequent 
 alteration of the meaning of the word. In English, we have no 
 accent marks, and the fallacy, strictly speaking, does not exist. It 
 is, however, represented by the wrongful omission or insertion of 
 the aspirate, which is conveyed in Greek by an accent mark. ' I 
 never said that nothing made 'er hill ; I said she lived at Maida 'ill.' 
 This is a fallacy of the accent in the Aristotelian sense, and it 
 would be a fallacy of the same kind to speak of the great 'art of 
 the English nation. These are evidently puns, and, as such, are 
 simple and crude examples of equivocation. 
 
 The fallacy of emphasis is much more frequent, and, though not 
 of much importance, and rarely the cause of serious misunder- 
 standing, deserves a brief notice. We have already seen that the 
 problem Did Brutus kill Caesar ? contains three distinct problems, 
 which may be explicated by appropriate construction. They may 
 also be brought out by the distribution of emphasis. Did Bruttis 
 kill Caesar ? Did Brutus kill Caesar ? Did Brutus kill Casar ? 
 The affirmative proposition ' Brutus killed Caesar,' though it cannot 
 be said to contain three propositions, is a proposition with three 
 aspects, either of which may be so prominent in the mind as to 
 relegate the other two to a position of insignificance. In speaking, 
 emphasis may stand in the place of formally correct composition 
 of the sentence, since emphasis can indicate what aspect of the 
 proposition it is that attention is to be concentrated on ; but in 
 written composition, italics, the equivalent of emphasis in spoken 
 discourse, are to be sparingly employed. The proper way to 
 convey the meaning with accuracy, is to compose the words of the 
 sentence in due order ; and in nothing is mastery of the English 
 language so displayed as in the due order and arrangement of words. 
 Italics are permissible to indicate foreign words, or technical terms
 
 376 A NEW LOGIC 
 
 of art, thus drawing attention to a change of medium, and saving 
 the reader from a momentary embarrassment ; but italics are very 
 rarely permissible for the purpose of mere emphasis. The free 
 employment of italics in written discourse is comparable with 
 swearing in speaking. It shows that the WTiter who uses them is 
 unable to convey the emphasis he desires by the choice of 
 appropriate words, or by arranging them in appropriate order, and 
 therefore must resort to adventitious and illegitimate means to 
 attain his end. They are comparable with the Elizabethan stage 
 directions. ' This is a forest ' ; * A room in the palace.' With 
 appropriate scenery, such directions are not required ; and with 
 appropriate choice and arrangement of words, italics are rarely 
 required for the purpose of emphasis. 
 
 Dr. Johnson's reading of the ninth commandment is well known, 
 and is, no doubt, correct for the occasion on which it is usually 
 read ; but there are as many alternative readings as there are words 
 in the sentence, and the emphasising of each word imports a 
 new suggestion into the sentence. Thou shalt not bear false 
 witness (but other people may). Thou shalt not bear false witness 
 (for I will prevent thee). Thou shalt not bear false witness (in 
 spite of the suggestion that thou wilt or mayst). Thou shalt not 
 bear false witness (but thou mayst hint it ?). Thou shalt not bear 
 false witness (but thou mayst bear true witness). Thou shalt not 
 bear false witness (but thou mayst treat him falsely in other ways). 
 Thou shalt not bear false witness against thy neighbour (but thou 
 mayst bear false witness in his favour). Thou shalt not bear false 
 witness against thy neighbour (only against other people's neigh- 
 bours). Thou shalt not bear false witness against thy neighbour 
 (but hast free licence to bear false witness against other people, 
 not thy neighbours).
 
 CHAPTER XXV 
 
 fallacies extra diction em 
 Fallacies of Confusion of the Modes of Reasoning. 
 
 Thi;se are the most fundamental and far-reachinj:^ of all fallacies. 
 They are fallacies, hitherto unrecognised and undescribcd, to 
 which logicians are especially prone, and which no logician up to 
 now has escaped ; but which are not confined to books on Logic. 
 The several modes of reasoning we have found to be three, 
 Inference, Empirical Reasoning, and Analogy ; and the realm of 
 Logic includes, also, the subsidiary or preliminary processes of 
 Abstraction, Generalisation, Classification and Definition. The 
 last four are different aspects of one process : the first three are 
 different processes, distinct, discrete, and neither interchangeable 
 nor miscible. These three modes of reasoning may, as we have 
 seen in the last Chapter, be employed alternately or in succession, 
 in trains of reasoning, to attain results ; and such successive or 
 alternate employment involves no fallacy, as long as their use 
 in combination does not degenerate into confusion of one with 
 another. But when they are confused with each other, or with 
 a subsidiary process ; when it is sought to deduce a conclusion 
 from an Analogy, or a material conclusion by means of Inference ; 
 or when Generalisation is called Induction ; then is perpetrated a 
 fallacy of confusion in the mode of reasoning. This is the fallacy 
 of the hypothetical syllogism : this is the fallacy of the petitio 
 principii said to be inherent in the syllogism : this is the fallacy of 
 supposing that we can 'reason from analogy' ; this is the fallacy 
 that vitiates every book on Logic that has ever been written. 
 
 It is postulated that A is C under the condition that A is B. 
 If, when A is B, it is C, then certain inferences may be drawn 
 from this postulate. To add that A is really B, when all that the 
 postulate gives, and all that Inference needs, is that if A is B it 
 is C, is ultra vires of Inference, irrelevant, and fallacious. But 
 surely, an objector may say, in the actual reasonings of life, to 
 which you so desire to make the processes of Logic apply, such
 
 378 A NEW LOGIC 
 
 arguments are often stated, and useful conclusions and sound 
 conclusions are drawn from them ? Certainly they are, — but 
 not in the Logic of Inference; not by means of Deduction. If 
 parsley is fatal to parrots, my parrot will die if I feed it on parsley. 
 But parsley really is fatal to parrots. Is it not useful to know that 
 my parrot will really die if I feed it on parsley ? Certainly it 
 is. It is useful in materia. It is useful in the regulation of conduct. 
 It is useful as an empirical proposition. But it is utterly useless 
 as an aid or an adjuvant to the argument from the postulate. If 
 parsley is fatal to parrots, then if I feed my parrot on parsley, it 
 will die. This conclusion from the premiss is valid as it stands, 
 and its validity is not enhanced by a hair's breadth by the 
 knowledge that parsley really is fatal to parrots. Parsley may 
 be the most wholesome diet in the world for parrots, and yet the 
 validity of the conclusion — I do not say its truth — the validity of 
 this conclusion, as an inference from the postulate, will not be 
 impaired by the breadth of an electric ion. I say that if parsley 
 is fatal to parrots, my parrot will die if I feed it on parsley ; and 
 you tell me that parsley really is fatal to parrots. Your assurance 
 is totally irrelevant to my argument. Don't you see what you 
 are doing ? You are giving me unconditionally that knowledge 
 that I already had conditionally. You are destroying that very 
 condition which is an integral part of the reasoning, and without 
 which reasoning of that kind cannot exist. In the same argument 
 and in the same breath, you assert and deny conditionality — you 
 deny that to be a condition which you have just asserted to be 
 a condition. If you tell me that parsley really is fatal to parrots, 
 — that its fatality to parrots is constant in experience — that is 
 useful information, for which, in another connection, I should be 
 obliged. It would enable me to solve the problem, if such a 
 problem were in my mind, Will or will not my parrot die if I 
 feed it on parsley ? But it does not assist me in the least in 
 drawing, from the postulate 'If parsley is fatal to parrots' the 
 inference, ' Parsley will be fatal to my parrot.' 
 
 If, as Sterne speculated, I should see a white bear, what then ? 
 Why, then a white bear would be seen by me ; I should be in 
 the presence of a white bear ; a white bear must have been 
 born ; it is not true that there is no such thing as a white bear; 
 and so forth. All these inferences are valid inferences from the 
 postulate, and are valid whether the subject of them is a white
 
 CONFUSION OF ARGUMENTS 379 
 
 bear, or a centaur, or a phoenix, or a jabberwock. Whether parsley 
 is or is not, in experience, fatal to parrots, is as irrelevant and out 
 of place in the one argument, as whether white bears, or centaurs, 
 or phoenixes, or jabberwocks, really exist, is irrelevant and out of 
 place in the other ; or as whether Socrates really is or is not mortal 
 is out of place and irrelevant in the syllogism. 
 
 Almost every logician points out that the conclusion of a 
 syllogism may be true, though its premisses are false. 
 
 All large glass bottles are covered with the craters of 
 
 volcanoes ; 
 The moon is a large glass bottle ; 
 .'. The moon is covered with the craters of volcanoes. 
 
 In this case, the conclusion happens to be true, though the truth 
 of the premisses leaves something to be desired ; and instances 
 to the same effect arc adduced by most logicians ; who, neverthe- 
 less, on another page, blandly assure us that the truth of the con- 
 clusion depends on the truth of the premisses. A just appreciation 
 of the nature of Deduction would have shown them that it is 
 not permissible even to discuss the truth of the conclusion of 
 an Inference. We might as well discuss whether it is white or 
 black, transparent or opaque. Inference is not concerned with 
 material truth. It is concerned solely with consistency, and to 
 discuss the truth of its conclusions is fallacious. It is a fallacy of 
 Confusion of the Modes of Reasoning. 
 
 It is this confusion of the argument in materia with the argument 
 from postulates that constitutes the fallacy of supposing that, if a 
 man's reasoning is consistent, his conclusions must be true 
 that since his conclusions are true, his reasoning must be valid ; 
 that if we can find a flaw in his reasoning, his conclusion must be 
 false ; and that if his conclusions are not true, his reasoning must 
 be invalid. All these are fallacies not infrequently perpetrated ; 
 none of them is enumerated among the fallacies of the Sophistici 
 Elenchi, or in any subsequent chapter on fallacies. They eluded 
 even the vigilant and penetrating eye of De Morgan ; but they 
 are brought to light by the system of Logic here expounded. 
 
 The problem of the petitio principii in the syllogism is put in 
 various ways in books of Logic. It is put variously: If all men are 
 mortal, and Socrates is a man, how do we know that Socrates is
 
 38o A NEW LOGIC 
 
 mortal ? Docs the conclusion tell us anything new ? Do we 
 gain any knowledge from the argument ? Have we not already 
 stated the conclusion in the premisses ? Every reader who has 
 come thus far with me will see that the answers to these questions 
 are — We do not know fnv>i tJiis arginncnt, that Socrates is really 
 mortal ; the conclusion tells us nothing that is not in the premisses. 
 We gain from the argument, no accession of knowledge ; all that 
 we gain is a new statement of part of the premisses, in which the 
 conclusion is implicit, and is explicated by the argument. 
 
 Prof. Carveth Read comes nearer than any other writer to the 
 doctrine here propounded. He distinguishes between the formal 
 character and the material character of the syllogism. As formally 
 stated, it is, he saj's, useless or fallacious ; but nevertheless, those 
 who perceive its material grounds retain and defend it. He 
 describes the material argument, and appreciates that it is distinct 
 from the formal argument, but, like all other logicians, he still 
 regards the material argument as a syllogism. This is the point 
 at which I part company with him, and with all my predecessors. 
 He and they look on the syllogism as having two aspects, or as 
 capable of being put to two uses — the formal use and the material 
 use. My contention is that the material argument never is a 
 syllogism. To the syllogism it has a superficial and deceptive 
 resemblance, which has blinded every logician to the profound 
 and fundamental difference between them. The Datum resembles 
 the minor premiss ; but it is radically different in that, while the 
 minor premiss predicates inclusion in a class or exclusion from a 
 class, the datum predicates likeness for the purpose of the argument. 
 The identical elements of problem and premiss simulate the middle 
 term of the syllogism, by appearing in identical form in both the 
 propositions that make up the argument ; but they are radically 
 different, for the identical elements of Empirical Reasoning need 
 not be terms at all. They may be Ratios. The premiss of 
 Empirical Reasoning bears a deceptive resemblance to the major 
 premiss of the syllogism, for both arc Universals ; but they are 
 profoundly different ; for the premiss of Empirical Reasoning 
 predicates a relation that has been found constant in experience, 
 and may be a relation of any kind whatever; while the premiss of 
 a syllogism is detached from experience, and expresses the 
 relation of class inclusion or class exclusion, and that relation 
 only.
 
 FALLACIES OF INDUCTION 381 
 
 Petitio principii is, literally, assumin;:^ a principiiim, or major 
 premiss ; and this is what every argument ex poslulato does, and 
 must do. In the syllo^^ism, and in Deductive reasoning generally, 
 it is no fallacy : it is a necessary preliminary to the reasoning 
 process. In material argument, to assume, as constant in 
 experience, a relation that is not in fact constant, is fallacious ; 
 but the fallacy is not petitio principii ; it is the fallacy of jumping 
 to a conclusion. What is ordinarily meant and understood by 
 petitio principii is the fallacy of assuming that a conclusion, validly 
 and properly deduced, secundum artcm, from postulates, is true in 
 fact ; and this is the fallacy now under consideration, of Confusion 
 of the Mode of Argument. 
 
 The confusion between Analogy and Empirical reasoning, 
 which appears in Mill's description of Analogical reasoning, and 
 is followed by all his successors, including the exponents of 
 Modern Logic, is not so much a confusion of modes of reasoning, 
 as an equivocation. It is the application of the term Analogy to 
 a process that is not Analogy. These logicians give to one thing 
 a name that had already been applied to another and very different 
 thing. How far they confuse the two things, is difficult to 
 discover. Many writers have detected the equivocation, and, 
 though they retain the names Analogy and Analogical reasoning, 
 have recognised that what they so denominated is not what 
 Aristotle meant by Analogy. Although, however, they describe 
 correctly, if very incompletely. Empirical reasoning under the 
 name Analogical reasoning, they still unanimously confuse the 
 reasoning so described with the syllogism, and thus perpetrate 
 the fallacy of Confusion of the Mode of Reasoning. 
 
 Fallacies of Empirical Reasoning. 
 
 Fallacies of Induction are violation of its Canons. 
 
 The first Canon of Induction is that the relation expressed b}' 
 the premiss must be constant in experience, or must be subsumable 
 under one that is constant in experience. We have already seen, 
 in the discussion on Imperfect Induction, that this mode of reason- 
 ing is not necessarily vitiated by want of constancy in experience 
 of the premiss. A conclusion, and a valid conclusion, can be 
 drawn from a premiss that is not constant in experience. A con- 
 clusion from such a premiss must, however, be recognised to be
 
 382 A NEW LOGIC 
 
 conjectural only, or it will be fallacious. Fallacy resides, not in 
 drawing a conclusion from a premiss that is not known to be 
 constant in experience, but from regarding such a conclusion as 
 assured. The fallacy is so frequent in the reasonings of daily life, 
 that it has received a colloquial title ; yet it does not appear to be 
 known to logicians, not one of whom has ever mentioned the 
 fallacy of jumping to a conclusion ; which is said, I know^ not 
 with what truth, to be perpetrated with special frequency by the 
 female sex. 
 
 ' The Robinsons have returned to town, for, as I passed their 
 house, I noticed that their blinds were up.' Displayed as a formal 
 induction, this would run : — 
 
 Proniss. The raising of blinds is, constantly in experience, 
 a sign that the householder's family is at home. 
 
 DaUim. The raising of Robinson's blinds is like, in respects 
 material to the argument, the raising of other people's blinds. 
 
 Conclusion. The raising of Robinson's blinds signifies that his 
 family is at home. 
 
 This conclusion would be unimpeachable, if the relation 
 expressed in the premiss were, in fact, constant in experience, or 
 were subsumable under one that is constant in experience ; but it 
 is neither, so that the conclusion is not warranted as an assured 
 conclusion. Nevertheless, though not constant in experience, the 
 relation is tolerably frequent in experience ; and does justify a 
 conclusion, but a conjectural conclusion only. The want of 
 constancy in experience of the premiss must be reflected in a want 
 of assurance in the conclusion ; and if the conclusion is stated 
 with this qualification, it is unimpeachable. The proper form of 
 the conclusion from this premiss is ' It is probable,' or ' There is 
 evidence,' or * I conjecture,' that the Robinsons have returned 
 to town. 
 
 ' His red nose proclaims him a toper ' is a fallacy of jumping to 
 a conclusion. It assumes that the relation between redness of the 
 nose and excessive drinking is constant in experience, which it is 
 not. The datum is satisfactor}'. The redness of his nose is like, 
 in all material respects, to the redness of the nose that is produced 
 by drinking ; but the want of constancy in experience of the 
 premised relation, that redness of the nose is produced solely by 
 drinking, is so great, that we are scarcely justified in concluding 
 even that there is evidence that he is a toper.
 
 THE ACCIDENT 383 
 
 As long as Fermat was content with surmising, from the result 
 of his calculations, that 2 '•^ "^ + 1 is probably always a prime 
 number, he kept within his warrant, and was justified in this 
 conclusion ; but as soon as he concluded that it certainly is so, he 
 jumped to a conclusion; for the relation had not been verified 
 sufficiently often to be constant in experience, in the sense in which 
 constancy is to be understood in this connection ; and it could not 
 be subsumed under any relation that is constant in experience. 
 
 The second Canon of Induction is that the terms of the datum 
 must be assimilated, in respects material to the argument ; and to 
 argue from a vague and approximate assimilation, or from an 
 assimilation, however close, that is not material to the argument, 
 is fallacious, and is a fallacy frequently perpetrated. 
 
 There is no fallacy in arguing from a vague and approximate 
 assimilation of the terms of the datum, if the conclusion from 
 such a datum is accepted as tentative, and is not regarded as 
 assured. The conclusion is then an hypothesis, and is perfectly 
 justifiable as such ; but fallacy lies in taking an hypothesis for an 
 assured conclusion. 
 
 The main source of the fallacy that resides in the breach of this 
 Canon is the assimilation of the terms of the datum in respects 
 that are not material to the argument. 
 
 Has this insect a sting ? Yes, for it is like a wasp, which, con- 
 stantly in experience, possesses a sting. But is it like a wasp in 
 material respects ? Is it hymenopterous ? Has it the features 
 which mark it as belonging to the great family of bees and wasps ? 
 No, but it is like a wasp in size, and colour, and marking, and 
 mode of flight. It won't do. Size and colour and marking and 
 mode of flight are not respects material to the argument. These 
 may all be imitated by moths ordiptera. To conclude that it has a 
 sting because it resembles a wasp in these respects is fallacious. 
 
 Will this mile of railway cost more to la}- than that ? No, 
 because it is no longer. But is length the only or the chief respect 
 in which resemblance is material to the argument ? No. That 
 mile runs on the flat ; this must run through a tunnel. That mile 
 runs through agricultural land ; this must run through a town. 
 That mile runs over uninterrupted land ; this must cross a bridge 
 of wide span. To extract an assured conclusion from such a 
 datum is fallacious.
 
 384 A NEW LOGIC 
 
 Will this war be successful ? Yes, because that war, waged 
 asi^ainst a nation no more numerous, was successful. But is the 
 numerousness of the antagonist nation the only, or the chief, 
 respect material to the argument of success in war ? It is not. 
 We are to consider whether it is warlike, wealthy, brave, prepared ; 
 whether its armies are well organised and well disciplined ; 
 whether it is well supplied with material of war. All these, and 
 other circumstances, are material to the argument. 
 
 The omission of some material resemblance from the datum 
 constitutes the fallacy of the Accident, in the Aristotelian sense. 
 The fallacy is usually confused, in the text books, with the fallacy 
 a dido secundum quid ad dictum simplicitcr. It is, in fact, very 
 different. The Aristotelian fallacy of the Accident was the taking 
 of an accidental quality for an essential quality. We have already 
 seen that the term * essential ' may be replaced, with great advan- 
 tage to clearness of expression and dcliniteness of meaning, by 
 * material to the argument ' ; and, if we make the substitution in 
 this case, the fallacy of the accident is the fallacy of taking, for 
 a similarity material to the argument, a similarity that is not 
 material ; and this is the fallacy under consideration. It is the 
 construction of a datum on the ground of a likeness that is not 
 material to the argument. It is a curious result of the demoralising 
 effect of the study of Traditional Logic, that whenever logicians 
 depart from the teaching of Aristotle, they are invariably wrong ; 
 while in matters in which he is wrong they follow him with servile 
 imitation. 
 
 The third Canon of Induction is that the second given element 
 in the problem must be identical with its homologue in the premiss. 
 It is not at all infrequent for an inaccurate thinker to take for 
 identical, things that are not identical. Breach of this rule 
 constitutes another of the recognised fallacies of Traditional 
 Logic. 
 
 If Johnny's illness is like, in material respects, to Jenny's, and if 
 Jenny's illness was caused by a faulty diet, then, since uniformity of 
 causation is constant in experience, Johnny's illness was caused by 
 a faulty diet, or by something that is like, in material respects, to 
 faulty diet. As already set forth, the Induction is 
 
 Jenny's illness was caused by faulty diet 
 
 Johnny's illness was caused by {x) faulty diet.
 
 INDISCRIMINATION 385 
 
 In this argument, the identical homologous elements are the 
 ratios ; and if these elements are indeed identical, and the illnesses 
 are in fact alike in material respects; and if causation is, in 
 experience, constant ; then the reasoning is unimpeachable ; and 
 the cause of Johnny's illness is discovered. But how if the 
 elements that are taken to be identical are not in fact identical ? 
 What effect will this have upon the validity of the argument ? 
 How if Jenny's illness was preceded merely, and was not caused, 
 by unsuitable diet ? How if it was neither caused nor preceded, 
 but accompanied, by faulty diet ? Then, clearly, there is no 
 reason for supposing that Johnny's illness was thus caused. The 
 reasoning is then fallacious ; and the fallacy, in this particular 
 instance, is the fallacy known to Traditional Logic as non causa 
 pro causa, or post hoc, ergo propter hoc. This fallacy is utterly out 
 of place in Traditional Logic, which knows nothing of causation, 
 or of the means whereby causation may be ascertained ; and its 
 presence in that Logic makes us wonder, first how it ever 
 obtained admission ; and second how, being in, it did not stimu- 
 late logicians to discover the rule whose breach constitutes the 
 fallacy. 
 
 The relation of causation is far, however, from being the only 
 relation that is the subject of investigation ; nor is the ratio the 
 only element in the problem that is, on occasion, identified with 
 its homologue in the premiss ; so that the fallacy non causa pro 
 causa is but a sample of the fallacies of this class. It may, how- 
 ever, be taken as a type of the class. In this, as in other matters, 
 Traditional Logic, in departing from the teaching of Aristotle, 
 has gone astray. To /x?) ultiov ws clltlov does not signify taking 
 that for a cause which is not a cause ; it signifies taking that 
 for a reason which is not a reason ; and is thus, on the one 
 hand, identified with the fallacy now under consideration ; and 
 on the other, is with difficulty distinguished from the current 
 meaning of the non sequitur, into \Yhich logicians have corrupted 
 the Aristotelian fallacy of the Consequent. Thus, by departing 
 from Aristotle they have got their whole scheme of fallacies, if that 
 can be said to be a scheme which has no organisation, arrange- 
 ment, or coherence, into an inextricable muddle. 
 
 Let the problem be With what percentage of sewage in the 
 water will tench thrive ? Tench will thrive with x per cent, of 
 sewage in the water : find .v. It is found in experience that carp 
 
 N.L. c c
 
 3S6 A NEW LOGIC 
 
 will live in water containing, say, three per cent, of sewage : hence 
 the Induction : — 
 
 Carp live in three per cent, of sewage. 
 
 Tench thrive in (.v) three per cent, of sewag^e. 
 
 In this induction, the datum is sound. Carp are, in respects 
 material to the argument, like tench. The identified homologues 
 are the Ratios ; and these we see, are wrongly identified. All that 
 experience proves is that carp will live in three per cent, of sewage, 
 and if we concluded that tench, which are like carp for the purpose 
 of the argument, also will live in three per cent, of sewage, we 
 should be abundantly justified. But we have concluded more than 
 this. \\'e have concluded that tench will not only live, but thrive, 
 in water of that degree of pollution, and in so concluding we have 
 committed the fallacy under consideration, of taking that for 
 identical which is not identical. The true title of the fallacy 
 should be, not non causa pro causa, but non idem pro eodem. 
 
 The identified elements, so far from being always causes, need 
 not even be Ratios. They may be terms. Take an example, the 
 like of which has served us before. Does this insect possess a 
 sting ? Yes, for it is like, in all material respects, to those other 
 insects which possess what I take to be stings. 
 
 Those insects possessed stings ; 
 
 This insect (x) possesses a sting. 
 
 The Induction is correct at all points, except in the identification 
 of the second term in the problem with its homologue in the 
 premiss. The datum is quite satisfactory. This insect is so like 
 those insects of which I have had experience, and have found to 
 possess what I take to be stings, that I am safe in arguing from 
 the one to the other. The relation expressed in the premiss is, 
 as previously shown, subsumable under one that is constant in 
 experience. But the argument is fallacious because the elements 
 taken as identical are not in fact identical. What I have taken 
 to be stings, in examining the insects, are not stings, but 
 ovipositors. Consequently, the argument, that this insect possesses 
 a sting, is unsound ; and is unsound because it contains the fallacy 
 non idem pro eodem. 
 
 The Fourth and Fifth Canons of Induction are that the 
 quaesitum is obtained by adopting into the problem the homo-
 
 THE PREVIOUS QUESTION 387 
 
 logous element of the premiss ; and that the difference, as well as 
 the likeness of the datum, must be reflected in the conclusion. 
 
 The adoption into the problem of the homologous term of the 
 premiss, is fallacious only when the fifth Canon is neglected, and 
 the non-assimilation in any respect, of the terms of the datum, is 
 not allowed for and reflected in the conclusion. If 1 argue that 
 since t)'phoid fever is due to a micro-organism, typhus, which is 
 like typhoid in so many respects, is due to the same micro- 
 organism, or fail to recognise that there must be some dissimilarity 
 in the bacilli, corresponding with the differences between the two 
 diseases, I commit a fallacy of this nature. The fact that a 
 burglary has been committed in my house, as well as in 
 Robinson's, justifies the conclusion that both were committed by 
 members of the same — of the criminal — class; but it does not 
 justify the conclusion that they were committed by the same 
 men. It does, however, justify an hypothesis that they were com- 
 mitted by the same men. The fact that this picture is like, in 
 the material respects of handling, technique, and general nature 
 of the subject, to pictures by Corot or Millet, warrants the con- 
 clusion that it was painted by some one of the school of Corot 
 or Millet ; but the inferiority in its design and execution forbid 
 the conclusion that it was painted by Corot or Millet himself. 
 
 This is not one of the recognised fallacies of Traditional Logic, 
 but it is well known by practical reasoners that ' circumstances 
 alter cases' ; and that there is fallacy in arguing from one case 
 to another that is not precisely alike in material respects. It 
 might appropriately be called the fallacy of indiscrimination, since 
 it depends on want of discrimination between the terms of the 
 datum. 
 
 The Sixth and last of the Canons of Induction is that Nothing 
 may be assumed in the problem that is not warranted by 
 experience. Breach of this Canon is the fallacy known to 
 Traditional Logic as the fallacy of many questions. It should 
 rather be called the fallacy of the previous question, for it is the 
 illegitimate assumption of an answer to some question that should 
 have been answered, and has not been, before the problem was 
 stated. It is, indeed, a true begging of the question ; for the 
 problem is a question, and it begs the problem. But it is not a 
 petitio principii, for it does not beg a principium or major premiss. 
 
 c c 2
 
 388 A NEW LOGIC 
 
 It does not beg a premiss at all. Nor does it, like the so-called 
 pctitio pn'ncipii of the syllogism, beg the conclusion in a premiss. 
 What it begs is the problem or question. 
 
 The fallacy of many questions, or, as it should rather be called, 
 of the previous question, is usually considered a rare form of 
 fallacy, and, like the fallacy of the accident, and of amphibology, 
 is usually illustrated by the same stale example copied from one 
 book to another iisque ad nauseam. It is in fact a very frequent 
 form of fallacy, and one that often escapes recognition. Seldom, 
 indeed, does it appear in the bald form usually cited, — 'Yes or 
 no, Sir, have you left off beating your mother ? ' 
 
 \\'hy does bread and butter always fall with the buttered side 
 down ? is a ' fallacy of many questions' until it is established that 
 it does so fall. What is the connection between changes of the 
 moon and changes of the weather ? is a fallacy of the previous 
 question until it is established that there is a connection. What 
 is it that makes food that is cooked in copper vessels poisonous ? 
 is a fallacy of the previous question until it is established that 
 food so cooked is poisonous. Are the rectilinear markings on 
 Mars canals ? is a fallacy of the previous question until it is proved 
 that such markings exist. Why are savage races always cruel ? 
 is such a fallacy until it is proved that they always are cruel. 
 
 This fallacy is not in the argument, nor in the conclusion of 
 the argument. It is in the statement of the problem ; and, as 
 the statement of the problem is the first step in Empirical 
 Reasoning, the fallacy is the most fundamental of the fallacies 
 of Empirical Reasoning, and should, perhaps, have been con- 
 sidered first. Whatever its place in Empirical Reasoning, it 
 has certainly no place in syllogistic reasoning; and, when we 
 find it among the classical fallacies of Traditional Logic, we 
 know not whether to admire most the acumen that discovered a 
 fallacy to the nature and origin of which Traditional Logic gives 
 no clue, or the want of acumen that stopped short at that stage, 
 and failed to discover the mode of reasoning which accounts for 
 the fallacy, finds a place for it, and supplies a Canon which 
 forbids it. 
 
 Fallacies of Inference. 
 
 The first Canon of Inference is that ever}' Inference is deduced 
 from a postulate. It follows that, in arguing of consistency.
 
 FALLACIES OF INFERENCE 389 
 
 and in explicating the implications of propositions, we may not 
 go outside the field of postulation. We may not assume nor 
 regard the material truth of the postulate. To do so would be 
 to commit one of those fallacies of confusion of the mode of 
 argument that have already been described. 
 
 The second Canon of Inference allows us, for the purpose of 
 argument, to postulate what we please, except self-contradic- 
 tions. This Canon forbids us, therefore, to limit our postulates 
 to what is materially true. It forbids us to object to any 
 argument on the ground that its postulates are improbable, 
 impossible, inconceivable, absurd, or nonsensical. But the Canon 
 does limit us strictly in one direction. It forbids us to postulate 
 what is self-contradictory. Any argument, therefore, is fallacious, 
 which is founded on such postulates as that an irresistible force can 
 be applied to an immoveable body; that there is an unconscious 
 mode of consciousness ; that matter may become immaterial ; 
 that a material argument need take no account of its matter; 
 that eternity had a beginning ; that infinite space has a limit ; or 
 any similar proposition. It may seem an unnecessary precaution 
 to forbid the postulation of self-contradictories, but experience 
 shows that it is by no means unnecessary. Instances given in a 
 previous chapter show that logicians themselves are by no means 
 insensible to the lure; and the postulation of an unconscious mode 
 of consciousnes is not rendered any the more justifiable by substi- 
 tuting for the term ' unconscious,' the term ' subliminal,' which 
 means the same thing, thus hiding the fallacy of Self-contradiction 
 behind the fallacy of Bivocation. Self-contradiction is a very 
 important fallacy, and not the less important that, although it 
 seems, on the face of it, so manifestly fallacious that no one is 
 likely to fall into it ; in practice, it is committed without any 
 recognition of its fallaciousness. 
 
 The Canon allows us to postulate what we please for the 
 purpose of the argument ; and it is important to observe the 
 limitation : fallacious to exceed the limitation. The argument 
 must be limited by its purpose ; and to go outside the purpose of 
 the argument is to commit a fallacy, which is unknown to 
 Traditional Logic, but is none the less important. The pen is 
 mightier than the sword ; but it would be a fallacious inference 
 from this postulate to argue that we ought therefore to arm our 
 cavalry with quill pens, or even stylographs, in place of the arme
 
 390 A NEW LOGIC 
 
 blanche. This is a fallacy, gross as a mountain, open, palpable ; yet 
 it does not come under any of the recognised fallacies of Traditional 
 Logic. It might, perhaps, be twisted into an equivocation ; but 
 it is not reall}- an equivocation. The fallacy consists in applying 
 the postulate outside the purpose of the argument. The pen is 
 mightier than the sword for the purpose of producing effects on 
 the course and destiny of nations, not for the purpose of action 
 on the field of battle. 
 
 What is not a mineral, must be either an animal or a vegetable; 
 and the Court of Appeal may hold that China clay is not a 
 mineral ; but it would be fallacious to argue, from these postulates, 
 that their lordships held China clay to bean animal or a vegetable. 
 I do not know how Traditional Logic would place this fallacy, 
 but to me it is clearly a neglect of the purpose of the argument. 
 The Court of Appeal holds that China clay is not a mineral for 
 the purpose of a certain lease of minerals; and to apply this 
 postulate outside the purpose of the argument is fallacious. 
 Traditional Logic knows nothing of the purpose of its arguments, 
 and this is one of the grave charges of ignorance and neglect that 
 I make against Traditional Logic. In Deduction, the purpose of 
 the argument is all important ; and no Deduction can be properly 
 conducted which leaves the purpose of the argument out of 
 account. For the purpose of some arguments, the whole includes 
 the part : for the purpose of other arguments, the part includes 
 the whole. For the purpose of the argument as to the position of 
 Eastcheap, Eastcheap is included in London ; but for the purpose 
 of the argument as to whither I must go from Birmingham to get 
 to Eastcheap, London is included in Eastcheap. 
 
 An instance of Fallacious reasoning may often be referred to 
 different fallacies, according to the way in which it is regarded. 
 The contention of Modern Logic, that every proposition refers to 
 Reality, may, as we have seen, be regarded as a fallacy of 
 confusion of the mode of argument. It may also be regarded as 
 a fallacy of neglecting the purpose of the argument. In the Logic 
 of Consistency, the purpose of the argument is to explicate the 
 implications of propositions; and for this purpose, it is not 
 material whether the proposition does or does not refer to reality. 
 
 Fallacies of neglect of the purpose of the argument will be 
 mentioned again, and other examples given, under breaches of 
 the fourth Canon of Inference.
 
 IGNORATIO ELENCHI 391 
 
 An argument, once begun, must proceed on the basis of the 
 postulate; and thus we obtain the third Canon, that a postulate, 
 once granted, must not be withdrawn nor ignored in the course of the 
 argument. I may, for the purpose of argument, postulate that 
 chalk is white, or that Brutus killed Caesar; and I may, for the 
 purpose of argument, postulate that chalk is not white, or is 
 black ; and that Brutus did not kill Csesar, or saved his life ; but 
 I may not, for the purpose of the same argument, assume con- 
 tradictory postulates ; nor may I, having once assumed a postulate, 
 permit it to be denied or ignored in the course of the argument. 
 The fallacy that lies in the breach of this Canon, consists in sup- 
 posing that by denying a postulate, we refute the argument 
 founded on it. If I argue that, if London were to be destroyed 
 by an earthquake to-morrow, the finance of the whole world would 
 be dislocated, you do not refute this argument by denying that 
 London will be destroyed by an earthquake. I say that if women 
 have votes, they will always vote for war rather than against it ; 
 and you do not refute this argument by denying that women will 
 have votes. I say that if my scheme of Logic is valid, Aristotle 
 and all his successors and followers, down to the present day, are 
 wrong ; and you do not refute this argument by denying that my 
 scheme is valid. 
 
 If a pint of petrol contains so many calories, and a pound of 
 coal so many; and if a pound of coal represents so many foot- 
 pounds of energy ; then, with a little calculation, I can tell you 
 how many foot-pounds of energy are represented by a pint of 
 petrol. You may deny that the number of calories that I have taken 
 to be in a pint of petrol is correct ; you may deny that the number 
 of foot-pounds of energy, or the number of calories, that I have 
 postulated to be in a pound of coal, is correct ; but these denials 
 do not in the least vitiate the calculation. The sum is correctly 
 done, and you do not convict me of a mistake in my arithmetic, 
 by proving that I began with the wrong figure. By so doing you 
 may invalidate my result, no doubt ; but you do not invalidate 
 the process by which I reached it. The addition and subtraction, 
 the multiplication and division, are correct to a decimal point ; 
 and this is all that the Logic of Inference requires, and all it can do. 
 The Logic of Inference cannot determine experimentally how 
 many calories there are in a pint of petrol. All it can do is to 
 take the postulates given to it, and draw inferences from them.
 
 392 A NEW LOGIC 
 
 Without being specifically denied, the postulate may be ignored ; 
 and this is a very frequent fallacy. I argue that if he is sufficiently 
 good-natured, he will do what I ask ; and to say that he is a fool 
 if he does, does not invalidate my argument, which is founded 
 solely on the postulate of his good nature, and does not take account 
 of his wisdom. To say that he would be a fool to do it, and he is 
 not in fact a fool, is to controvert the argiimentnm ex postulato by 
 the argumentuin i)i })iaterid, and is a fallacy of confusion of the 
 mode of argument. If I were arguing the matter of fact, whether 
 he will do it or not, the retort would be material to the issue ; but 
 I am not. I am arguing from my postulate alone ; and in 
 Inferential argument, the conclusion is but another way of stating 
 the postulate itself. The inference cannot, therefore, be contro- 
 verted, except by showing that it is not contained in the postulate. 
 To say that he is sufficiently good-natured to do it, is another way 
 of saying that he will do it if I appeal to his good nature ; and if 
 the one is true, the other is true also. Inference does not assert 
 that either is true. It asserts only the implication of the one 
 in the other. 
 
 I say that, if the Bill is passed into law, it will remove a 
 grievance. It is no answer to this argument to deny the postu- 
 late, and assert that the Bill will not pass ; nor is it any answer 
 to ignore the postulate, and say that I, who have imposed so many 
 grievances, am a fine person to talk about removing one. 
 
 Denial and ignoring of the postulate together make up the 
 fallacy known in Traditional Logic as the ignoratio elcnchi. In 
 that Logic, it is an illogical intruder. It violates no rule of the 
 syllogism ; it is a breach of no Law of Thought, of no recognised 
 rule of Immediate Inference. It floats in the air, unattached and 
 unaccounted for. Nor has Inductive nor Modern Logic any place 
 for it. Neither provides a Canon that is broken by the ignoratio 
 elenchi. In the scheme here propounded, it fits into its place, as 
 a breach of a recognised and formulated rule of Inference, a rule 
 not made for the purpose of providing an explanation of the fallacy, 
 but forming an integral and necessary part of the scheme. This 
 accidental consequence of the rule seems prima facie evidence both 
 of its validity and its necessity. 
 
 Violation of the fourth Canon of Inference provides a greater 
 variety of fallacies than violation of any other. It is the illegiti-
 
 SYLLOGISTIC FALLACIES 393 
 
 mate assumption of something that is not in the postulate that 
 constitutes the fallacy of four terms, when this is not an equivo- 
 cation, the undistributed middle, and the illicit major and minor 
 of syllogistic reasoning. It is to the same assumption that we owe 
 the fallacy of the Consequent, the fallacy a dido secundum quid ad 
 dictum simplicitey, the fallacy a dicto simpliciter ad dictum secundum 
 quid, De Morgan's fallacy a dicto secundum quid ad dictum alterum 
 quid ; as well as other fallacies not hitherto recognised. 
 
 If Some fish fly, 
 And All eels are fish ; why may we not conclude that 
 Some eels fly ? 
 
 Because, says Traditional Logic, the middle term is undis- 
 tributed. Because, says the Method of Explication, we have 
 assumed what is not in the postulate. We have replaced, in the 
 major premiss, the term 'Some fish' by the term 'some eels'; 
 but ' some eels ' is not given equivalent to, included in, or implied in 
 ' some fish.' ' Some eels ' is indeed, included in ' all eels,' and the 
 substitution of some eels for all eels is warranted. But all eels are 
 given, for the purpose of the argument, included in * fish.' They 
 are not given included in 'some fish ' ; and therefore they may not, 
 nor may * some eels,' be substituted for * some fish.' To make 
 this substitution is to assume what is not in the postulate. 
 
 We may, indeed, give to the argument a specious appearance of 
 correctness by stating it thus, in Hamiltonian terms : 
 
 Some fish fly ; 
 All eels are some fish ; 
 . • . All eels fly. 
 
 Again Traditional Logic would ascribe the fallacy to the undis- 
 tributed middle. The Method of Explication ascribes it to the 
 ambiguity of the middle. The ' some ' of the major premiss is 
 
 * this some.' The ' some ' of the minor may be ' that some ' or 
 
 * the other some ' ; and owing to this ambiguity, we are never 
 justified in replacing one ' some' by another. 
 
 The fallacy of the illicit major rests on the same ground, of 
 assuming something that is not in the postulate. 
 
 Prisoners who are found guilty are punished; 
 He was not found guilty ; 
 He was not punished.
 
 394 A NEW LOGIC 
 
 In Traditional Logic, this is an illicit major. The predicate of 
 the conclusion is distributed ; the predicate of the major premiss 
 is undistributed; and thus there is illicit process of the major. 
 By the Method of Explication, the defect is more easily identified. 
 It is said in the conclusion that he was not punished ; but there is 
 nothing in the postulate about those who are not punished. The 
 postulate applies to those only who are punished ; and to con- 
 clude from this postulate anything about those who are not, is to 
 assume what is not in the postulate. 
 
 Traditional Logic forbids us to draw any inference at all from 
 these premisses ; but the Method of Explication is not so 
 niggardly. There is a sound inference, and an inference that may 
 be useful, to be drawn from them. If prisoners who are found 
 guilty are punished, and he was not found guilty, then we may 
 safely and rightly infer that not on the ground of being found 
 guilty was he punished. 
 
 The illicit minor is even more plainly a breach of the fourth 
 Canon of Inference. 
 
 If The syllogism is a defective mode of argument ; 
 and Some logicians argue by the syllogism ; 
 
 why are we not justified in concluding that 
 
 All logicians employ a defective mode of argument ? 
 
 Because, says Traditional Logic, the Subject of the conclusion is 
 distributed, but in the minor premiss the same term is not dis- 
 tributed, and thus there is illicit process of the minor. The 
 Method of Explication gives an explanation, that is more direct, 
 ' All logicians ' have been substituted for ' some logicians ' ; but 
 'all logicians' are not postulated equivalent to, included in, or 
 implied in * some logicians,' and therefore, in making the sub- 
 stitution, we are assuming what is not in the postulate. 
 
 The fallacy of concluding a dicto simpliciter ad dictum secundum 
 quid is a breach of the same rule. It is the assumption of some- 
 thing that is not in the postulate. It is the replacement of a 
 term by another that is not, for the purpose of the argument, 
 equivalent to, included in, or implied in it. Arsenic is a poison, 
 it is true ; but drop doses of Fowler's solution are not poisonous. 
 For the purpose of the argument, arsenic means arsenic in appreci- 
 able quantity : for the purpose of the argument, arsenic in drop
 
 FALLACY OF THE CONSEQUENT 395 
 
 doses of Fowler's solution is ncglcctable. Conversely, though 
 arsenic in drop doses of Fowler's solution is not poisonous, it 
 does not follow that arsenic simpliciter is not poisonous. In 
 short, * arsenic ' and ' the quantity of arsenic contained m a drop 
 of Fowler's solution ' are not, for the purpose of the argument 
 about poisoning, convertible or substitutable terms. To substitute 
 the one for the other is to assume what is not in the postulate, and 
 thus to violate the fourth Canon of Inference. 
 
 The fallacy of the Consequent is usually called the nonsequitur, 
 and is defined by Jevons as ' any argument which is of so loose 
 and inconsequent a character that no one can discover any 
 cogency in it.' The fallacy of the Consequent is nothing of the 
 kind. As defined by Aristotle, it is the unconditional affirmation 
 of a postulate that has been granted subject to a condition. To 
 argue from If A is B, it is C, to A is C, is a fallacy of the Conse- 
 quent in the Aristotelian sense. In Traditional Logic, it is a 
 breach of no rule except the rule created ad hoc, that we may 
 not affirm the consequent of an hypothetical proposition. In the 
 scheme here propounded, it falls into an appropriate place, ready 
 and prepared for it, as a breach of the fourth Canon of Inference. 
 If wc affirm unconditionally that which is postulated under a 
 condition, we exceed the limits of the postulate, and assume what 
 is not postulated. 
 
 All these fallacies are violations of the fourth Canon of Infer- 
 ence, but these are far from being all the fallacies that arise from 
 breach of this Canon. They are all the fallacies of this kind that 
 Traditional Logic recognises; but they are 'far from being all that 
 are committed. To discover the remainder, we must go through 
 the Canons of Explication, and show how the licence granted by 
 each of them may be exceeded, and thus give rise to a fallacy of 
 this description. 
 
 The first Minor Canon of Explication allows us to infer, from 
 every proposition, its reciprocal. It does not allow us to infer 
 what purports to be the reciprocal, but is not. If a peach tree 
 sometimes bears nectarines, it does not follow that a nectarine 
 tree sometimes boars peaches. If Brutus killed Casar, it will 
 nut do to infer that Caesar killed Brutus. If Democracy ends in 
 despotism, it does not follow that despotism ends in democracy. 
 Ponos is kala-azar implies kala-azar is ponos, but Ponos is a form 
 of kala-azar does not imply Kala-azar is a form of ponos. The
 
 396 A NEW LOGIC 
 
 converse of Traditional Logic, without being positively untrue, 
 contains a suggestio falsi. ' Some human beings are writers of 
 books on Logic,' becomes, when converted according to rule, 
 ' Some writers of books on Logic are human beings' ; thus convey- 
 ing the distinct suggestion that some other writers of books on 
 Logic are not human beings. I have been under the painful 
 necessity, in the course of this book, of criticising with some 
 severity the writers of books on Logic ; but I have never 
 ventured, and should not venture, to suggest that they are 
 outside the pale of humanity. This suggestion comes from them- 
 selves, and I trust they are pleased with it. This fallacy may be 
 called the False or Illicit Reciprocal. 
 
 The second Minor Canon of Explication allows us to infer 
 every proposition with a Ratio that is, for the purpose of the 
 argument, equivalent to, included in, or implied in the Ratio of 
 the Postulate. It is not difficult to slip into the substitution of a 
 Ratio that is ostensibly equivalent, &c., to the postulated Ratio, 
 but is not equivalent, &c., for the purpose of the argument. ' He 
 killed her,' may be fallaciously taken to mean ' He murdered her.' 
 ' He stole it,' may be fallaciously substituted for ' He took it' 
 ' He paid willingly ' may be fallaciously inferred from ' He paid 
 promptly.' Hard words break no bones, it is true ; but it would 
 be fallacious to infer from this postulate that hard words are 
 innocuous. Soft words butter no parsnips ; but not from this 
 postulate may we infer that a soft answer does not turn away 
 wrath. In this instance, all three elements in the proposition 
 have been replaced by others ; and the replacement is perfectly 
 legitimate as long as the new elements are logically substitutable 
 for the original elements ; as long, that is, as the new are equivalent 
 to, included in, or implied in those they replace ; but in this case, 
 they are not. ' He spoke at great length ' does not necessarily 
 imply that he was tedious; nor does 'She found it' necessarily 
 imply that she was looking for it. Such fallacies may be termed 
 fallacies of the Illicit Ratio. 
 
 The third Minor Canon of Explication permits us to replace 
 any term in a postulate by a term that is, for the purpose of the 
 argument, equivalent to, included in, or implied in the replaced 
 term ; and we have seen that the fallacious substitution of a term 
 that purports to be substitutable under this Canon, but is not, 
 constitutes the fallacies, already examined, of the undistributed
 
 THE ILLICIT TERM 397 
 
 middle, the illicit processes, and the qnaternio tcrminorum. This 
 erroneous substitution constitutes also other fallacies, of which 
 Traditional Logic knows nothing, since it knows nothing of the 
 valid argument of which the fallacy is a perversion. If the roof 
 is waterproof, we may safely infer that it is proof against rain ; 
 but we may not infer from this postulate that it is proof against 
 snow; for snow is not, for the purpose of the argument, equivalent 
 to, or included in rain. If a body floats in olive oil, we may 
 safely infer that it will float in water, for water is, for the purpose 
 of this argument, implied in olive oil ; but if the same body will 
 burn when soaked in olive oil, it does not follow that it will burn 
 when soaked in water, for water is not, for the purpose of this 
 argument, implied in olive oil. If timothy and foxtail and cocks- 
 foot grow in this meadow, we may safely infer that couch also will 
 grow there ; but though timothy and foxtail and cocksfoot make 
 good hay, we may not from this postulate infer that couch makes 
 good hay ; for couch, which is implied in the other grasses for the 
 purpose of the first argument, is not implied in them for the 
 purpose of the second. These fallacies may be termed Fallacies 
 of the Illicit Term. 
 
 It will be seen that these fallacies, while they are due to be 
 noticed here, are properly fallacies of neglect of the purpose of 
 the argument ; and might have been dealt with, as similar fallacies 
 have been dealt with, on a previous page. Many fallacies can, in 
 fact, be referred to more than one class. 
 
 The second Canon of Explication allows us to infer, from any 
 postulate, all the conditions that are necessary to the postulate. 
 No fallacy arises from failure to take advantage of the privilege a 
 rule allows us ; but fallacy may, in this case, arise from taking, for 
 a necessary condition, one that is not necessary. If she saw him 
 do it, she must have been there when he did it ; but this postulate 
 does not necessarily imply, though it may be erroneously taken to 
 imply, ' He must have seen her watching him.' If there is no 
 honey in the comb, it will not do to infer that all the honey it 
 contained has been extracted. It may be brood-comb, and may 
 never have contained honey. If the school did not earn the 
 grant, it would be fallacious to argue that the teaching must have 
 been inefficient ; for that would be to assume what is not in the 
 postulate, that inefficient teaching is a necessary condition of not 
 earning the grant. If the fine details do not appear in this photo-
 
 398 A NEW LOGIC 
 
 graphic print, it would be fallacious to argue that the negative must 
 have been under-exposed ; for this is to assume, what is not in the 
 postulate, that under-exposure is a necessary condition of want 
 of fine detail. 'He has just taken the medicine' implies, as a 
 necessarv condition, 'The medicine glass is empty,' but 'The 
 medicine glass is empty ' does not imply ' He has just taken 
 the medicine.' He may have thrown it out of the window. 
 Fallacies of this sub-class also are unknown to Traditional 
 Logic; for this Logic knows nothing of the argument of which 
 thev are fallacies. We may call these Fallacies of the False 
 Condition. 
 
 The fourth Minor Canon of Explication allov/s us to deny any 
 proposition in which the Ratio of the postulate is replaced by a 
 Ratio that is, for the purpose of the argument, inconsistent with 
 the Ratio of the postulate. Care must be taken that the ratios 
 really are inconsistent, or the inference may be fallacious. If he 
 lives, we are justified in denying that he died; for the ratios are 
 inconsistent for the purpose of the argument ; but if he lived, we 
 cannot safely deny that he died ; for, for the purpose of this 
 argument, these Ratios are not inconsistent. If the ship foundered 
 at sea, we may safely deny that she arrived in port from her last 
 voyage ; but we may not deny that she ever arrived in port, nor 
 that she was seaworthy, nor that she was well navigated ; for 
 none of these Ratios is inconsistent with the Ratio that she 
 foundered. She may have been sunk by collision with a derelict, 
 or by the explosion of something in her cargo. If stones sink in 
 water, we may safely deny that they float in water ; but we cannot 
 safely deny that they are moved by w-ater ; for this Ratio is not, 
 for the purpose of the argument, inconsistent with the Ratio of 
 the postulate. Such fallacies are denials of the Consistent 
 Ratio. 
 
 The fifth Minor Canon of Explication permits us to deny any pro- 
 position in which a term of the postulate is replaced by one which 
 is, for the purpose of the argument, inconsistent with the displaced 
 term ; and again we must be careful that there is inconsistency, 
 or we may fall into fallacy. If he shot a brace of partridges, we 
 may safely deny that he shot nothing, for these terms are incon- 
 sistent ; but if he shot a brace of partridges, we may not, on the 
 ground of this postulate, deny that he shot a brace of hares, or of 
 pheasants : for hares and pheasants are not, for the purpose of
 
 FALLACIES OF ANALOGY 399 
 
 this argument, inconsistent with partridges. It may be that hard 
 words break no bones, but not on this account may we deny that 
 hard words break friendships ; for no bones are not inconsistent, 
 for the purpose of the argument, with friendships. Though 
 threatened men live long, we may not on that ground deny that 
 unthreatened men live long; for threatened men and unthreatened 
 men are not, for the purpose of this argument, inconsistent. Such 
 fallacies are denials of the Consistent Term. 
 
 The sixth Minor Canon of Explication allow us to deny any 
 proposition inconsistent with any condition necessary to the 
 postulate. We fall into fallacy if, on the ground of the postulate, 
 we deny a proposition that appears to be, but is not, inconsistent 
 with a necessary condition of the postulate. If he has typhoid 
 fever, we may safely deny that his temperature is normal in the 
 evening ; but it would be fallacious to deny that his temperature 
 was normal in some hour of the twenty-four. If the plant 
 languishes and is stunted, we may not on that account deny 
 that the soil is suitable ; since an unsuitable soil is not a necessary 
 condition to a languishing and stunted plant. It may be suffering 
 from drought, or infested with vermin. 
 
 All the fallacies of this class may be stigmatised by the term 
 non sequitiir, for in every case the conclusion is unwarranted by 
 the premisses. 
 
 Fallacies of Analogy. 
 
 In literary or qualitative Analogy, the chief fallacy is that 
 assimilation of the terms of the compared relations which has 
 been explained to be beyond the province of Analogy. The 
 temptation to this error does not beset us in forming quantitative 
 analogies. No one supposes that, since the ratio of 3 to 6 is the 
 same as the ratio of 8 to 16, therefore three is the same as eight ; 
 but it is not at all unusual for qualitative Analogy to be confused 
 with Inference. If I say that a band is as good as a meal to a 
 marching regiment, I may be met by the reply that that is 
 nonsense, because the soldiers cannot eat the music. The asser- 
 tion that the pike is the shark of the river, may be met by the 
 reply that this cannot be so, for the pike is underhung, while the 
 shark is overhung. Such replies evince ignorance of the nature 
 and purpose of Analogy. They suppose that comparison of ratios
 
 400 A NEW LOGIC 
 
 carries with it comparison of the terms of the ratios. These 
 instances arc comparable with the attempt of many logicians to 
 assimilate Analogy to Induction ; or rather, to make it a kind of 
 Induction. 
 
 We have seen how difficult it is, in literary or qualitative 
 Analogy, to avoid some assimilation of the terms of the compared 
 relations ; and how, in comparing the stillness of the harmless 
 child to that of the harmless mouse, we feel that the Analogy 
 is more appropriate than would be comparison with the still- 
 ness of death, or the stillness of the air before a storm. Some 
 comparison of the terms, as well as of the ratios, is unavoidable, 
 we found, in literar}- Analogy ; and is not only unavoidable, but 
 appropriate and satisfying. Wherein, then, lies the fallacy ? It 
 lies in this : when Byron says the Assyrian came down like a wolf 
 on the fold, we understand him to suggest that the Assyrian 
 partook of the rapacity and savagery of the wolf; but this 
 suggestion is made, not as an inference from our previous know- 
 ledge, but as an addition to it. There is no reference here to 
 constancy in experience ; and consequently no Induction. There 
 is no substitution of one proposition for another which implies it ; 
 and consequently no Deduction. All that is put forward is a 
 suggestion. It is not a positive assertion : it is not a conclusion : 
 it is a covert assertion, or semi-assertion, that the Assyrian has the 
 detestable and terrifying qualities of the wolf. There is no fallacy 
 in making the suggestion : but to take the suggestion for proof, 
 that would be fallacious. If we turn the suggestion into an argu- 
 ment, and conclude that since the Assyrian came down like a wolf 
 on the fold, therefore he is as savage as a wolf, then we perpetrate 
 a fallacy ; but so long as we receive the suggestion as a mere 
 suggestion, it is not fallacious. 
 
 Quantitative analogy is fallacious when the ratios compared 
 
 o CIO. 
 
 and discerned to be alike, are in fact not alike. - = is a 
 
 3 359 
 
 fallacious analogy. "The ratio between the homologous sides of 
 similar triangles is equal to the ratio between their areas " is a 
 fallacious quantitative analogy. This application of analogy is 
 equally fallacious when like ratios are taken to be unlike, as when 
 triangles on the same base and between the same parallels are 
 allowed to be of different areas, or when the odds of 15 to 12 are 
 chosen in preference to odds of 25 to 20.
 
 PARADOX 401 
 
 Fallacies are invalid arguments having a specious appearance 
 of validity. There are arguments that have a superficial appear- 
 ance of fallacy, and yet are valid ; and this is the most appropriate 
 place in which to notice them. A Paradox is an apparent incon- 
 sistency that is not a real inconsistency. To say that the hare 
 beats the tortoise in a race, is a paradox. It is, on the face of it, 
 inconsistent with the llcetness of the hare and the slowness of the 
 tortoise. An asymptote is a paradox. It is a line that continually 
 approaches a straight line, but never reaches it. That a bird 
 could not fly unless it was heavier than air, is a paradox. It 
 states an apparent inconsistency that is not a real inconsistency. 
 
 The following is a complete enumeration of Fallacies : — 
 
 I. Fallacies in Dictione. 
 
 Equivocation. 
 
 Bivocation. 
 
 Amphiboly. 
 
 Fallacies of Punctuation. 
 
 Fallacies of Emphasis. 
 
 II. Fallacies extra Dictionem. 
 
 Fallacies of Confusion of the Modes of Reasoning. 
 Confusion of Induction with Deduction. 
 Confusion of Induction with Analogy. 
 Confusion of Deduction with Analogy. 
 
 Fallacies of Empirical Reasoning or Induction. 
 Jumping to a Conclusion. 
 The Accident. 
 Non Idem pro Eodem. 
 Indiscrimination. 
 The Previous Question. 
 
 Fallacies of Inference or Deduction. 
 Contradiction in Terms. 
 Neglect of the Purpose of the Argument. 
 I^noratio Elcnchi. 
 Fallacies of Exceeding the Postulate. 
 
 The F'allacy of the Consequent. 
 
 The False Reciprocal. 
 
 N-L. D D
 
 402 A NEW LOGIC 
 
 The Illicit Ratio. 
 The Illicit Term. 
 The False Condition. 
 Denial of a Consistent Ratio. 
 Denial of a Consistent Term. 
 Denial of a Condition. 
 
 Fallacies of Analogy. 
 
 Assimilation of the Terms of the sub-relations. 
 Assimilation of Unlike Ratios. 
 Discrimination of Like Ratios.
 
 CHAPTER XXVI 
 
 FAULTS OF THE EXISTING SYSTEMS OF LOGIC 
 
 From time to time in the course of this book, I have called 
 attention to errors and defects that seem to me to exist in the 
 scheme of Traditional Logic, in the scheme of Induction, and in 
 Modern Logic. Lest, however, there should be any misunder- 
 standing as to the nature or the extent of my disagreement with 
 them, it seems advisable to summarise here the more important 
 of the topics to which this disagreement extends. The promul- 
 gator of what purports to be new, is under obligation to make 
 clear in what the novelty consists ; and, irrespective of this 
 obligation, it is germane to my purpose, of superseding Tradi- 
 tional Logic and Inductive Logic by a Logic that pretends to be 
 more complete and more accurate, and Modern Logic by one that 
 pretends to be more intelligible if less profound, to collect 
 together what seem to me to be the main errors and defects of 
 my predecessors, and expose them in all their naked deformity. 
 When I am told, as no doubt I shall be told, that my system of 
 Logic is wrong from top to bottom, and from beginning to end, I 
 must bear the accusation with what equanimity I can summon ; 
 but I wish to forestall, if I can, the charge that my differences 
 from pre-existing systems of Logic have been anticipated ; that 
 they are of trifling importance ; or that they are mere verbal 
 modifications. 
 
 In the first place, I regard it as a defect in existing systems of 
 Logic, that its nature, purpose, and scope are left by them in 
 doubt. No two logicians agree as to what Logic is, what it 
 purports to treat of, or how far its range extends. They do not 
 agree as to whether it is a Science or an Art. Those who regard 
 it as a Science do not agree as to the nature of its subject-matter ; 
 those who regard it as an Art are not agreed as to what it does. 
 
 No logician up to the present time, except Spencer, who, to 
 use an Hibernicism, was not a logician, has recognised that 
 logical processes are not two, but three, or has admitted Analogy, 
 properly so called, to a place among reasoning processes. The 
 
 D D 2
 
 404 A NEW LOGIC 
 
 two processes — Deduction and Induction — that they do admit, 
 are not clearly or completely distinguished by any logician, nor 
 has the proper distinction between them ever been identified. No 
 logician but Hamilton, and he only dubiously and incompletely, 
 has recognised that Deduction has no function except to explicate 
 the implications of propositions. Every logician regards the 
 syollogism as a means of proceeding from the known to the 
 unknown — a means of discovering fact ; every logician takes for 
 granted that Induction, or part of Induction, is an application of 
 the syllogism, speaks of the Inductive syllogism, or considers that 
 Induction is reached by syllogistic reasoning. It has never 
 hitherto been made clear that Deduction is nothing more than 
 inference from postulates, whose truth or falsity is immaterial to 
 the argument ; and though it has been recognised by some 
 logicians, in some connections, that Induction is based on 
 propositions that are materially true, the Universal of Induction, 
 as a relation found in experience to be constant, has never been 
 clearly or consistently distinguished from the Universal of 
 Deduction, which is a general rule postulated for the purpose of 
 the argument. The whole of the secular Scholastic discussion of 
 Universals proceeded upon the assumption that the Universal of 
 Deductive reasoning must be true, or ought to be true, in fact. 
 The assumption of Modern Logic, that every proposition refers to 
 reality, or Reality, is a crude attempt to settle the question by 
 dogmatic assertion. As far as it is possible to understand the 
 mysterious and involved phraseology of Modern Logic, new 
 Identity is old Universal writ differently. In short, in Traditional 
 Logic, in Inductive Logic, and in Modern Logic, Deduction, 
 Induction and Analogy are all muddled up together, and endless 
 confusion results. A conspicuous example of this confusion is the 
 riddle oi the petitio principii in the syllogism, which Aristotle and 
 all his successors have tried to solve ; which every one of them 
 has failed to solve ; and which must remain insoluble until the 
 argument from postulates is clearly distinguished from the argu- 
 ment from fact. 
 
 As Logic makes no clear distinction between Deductive 
 reasoning and Inductive reasoning — between the argiimentum 
 ex postulato, and the argiimentum in materia, — it is not to be expected 
 that it will distinguish between the two "imports," or modes or 
 degrees of reference to externality, of propositions, on which the
 
 THE PURPOSE OF THE ARGUMENT 405 
 
 distinction between the two modes of reasoning rests. Nor does 
 Logic make this distinction. On the contrary, Modern Logic 
 asseverates with wearisome iteration that the reference of every 
 proposition is to Reahty, thereby necessarily implying, if Modern 
 Logic did but know it, that the whole range of Mathematical 
 Physics, and of higher Mathematics, is impossible and has no 
 existence. 
 
 Another damning defect of Logic as hitherto expounded, is its 
 failure to refer to the purpose of its argument. No previous 
 writer on Logic known to mc, recognises that the purpose of an 
 argument is vital to its validity, or that an argument may be 
 fully and completely valid for one purpose, and utterly false and 
 invalid for another. When some adumbration of the importance 
 of the purpose of the argument does reach the minds of logicians, 
 it is straightway lost in speculations about the 'essence' of the 
 Subject. That 'essential' means, in this connection, 'material 
 to the purpose of the argument,' and cannot, in this connection, 
 mean anything else, has never dawned upon their minds. If it is 
 of the ' essence ' of China clay to be a mineral, I do not see 
 how this essential quality can be made non-essential by a decision 
 of the Court of Appeal ; but whether China clay is or is not a 
 mineral for the purpose of a lease of minerals, is very properly 
 within the function of the Court to determine. 
 
 Traditional Logic is defective both as to the propositions it 
 excludes, and as to those it includes. Those it excludes on the 
 strange ground that they are ' verbal,' as if every proposition were 
 not verbal, are those alone whose predicate is identical with the 
 Subject, or is a part of the Subject. Propositions that are 
 meaningless because their terms are meaningless or contradictory, 
 are not formally excluded from Traditional Logic. The range of 
 propositions included by Traditional Logic is absurdly limited. 
 By ignoring the Problem, or Incomplete proposition. Logic 
 excludes itself from the proper conduct of Inductive reasoning, 
 and prevents itself from appreciating the true nature of that kind 
 of reasoning. By excluding the Modals that it recognises as 
 Modals, Logic convicts itself of folly, and condemns itself to 
 uselessness. By admitting that form of Modal that it does not 
 recognise to be Modal, Logic exhibits a blindness that may be 
 paralleled within its own limits, but scarcely exists outside of 
 them. The Analogical proposition, which is the foundation of
 
 4o6 A NEW LOGIC 
 
 an extensive and important mode of reasoning, is no more known 
 to Logic than is the mode of reasoning itself. 
 
 Logic analyses the proposition into its constituents ; and 
 analyses it wrongly. The analysis is so manifestly and glaringly 
 erroneous, that no logical mind could countenance it for a day ; 
 }-et not only is Traditional Logic contented with it ; not only does 
 every logician with the exception of Aristotle himself, insist upon 
 it ; but Modern Logic, as far as Modern Logic can be understood, 
 adopts and homologates it. 
 
 The Logical doctrine, that the Copula is the sole form of Ratio 
 that can form the basis of argument, is so widely discordant with 
 truth, that the contrary would be much nearer the mark. With 
 marvellous perverseness of ingenuity, Logic has chosen, for its 
 foundations, expressions that are every one of them ambiguous. 
 The copula is ambiguous; the 'All' of the Universal Affirmative 
 is ambiguous ; the ' some ' of the Particular proposition has 
 twenty or thirty meanings ; the * either ' of the hypothetical 
 proposition is ambiguous; 'the Predicate' is ambiguous ; the 
 classical example of the Universal proposition ' All men are 
 mortal ' is doubly, trebly, and quadruply ambiguous. 
 
 By virtue of a confusion, the like of which can scarcely be 
 discovered outside of Logical doctrine, Logic contrives to confound 
 the meanings of the copula with the varieties of the Subject. The 
 Subject must be an individual, a class, or a quality ; therefore, 
 says Logic, the Copula cannot express anything but the inclusion 
 of an indivitlual, or part of a class, in a class, or the attribution of 
 a quality to an individual, or a class, or part of a class. This is 
 a fallacy so ingeniously contrived, that it is difficult to find a place 
 for it among the long list of fallacies, so many of the Canons of 
 reasoning does it violate. It may be conveniently relegated to 
 that class of fallacies described by Jevons, as an argument *of so 
 loose and inconsequent a character that no one can discover any 
 cogency in it.' 
 
 The discussion on the connotation of terms, that finds a place 
 in every text-book published since the researches of the Port Royal 
 logicians, is superfluous and misleading. It implies that terms 
 may be understood in connotation ; in fact, they never are so 
 understood in Traditional Logic, or hardly ever. In that Logic, 
 every term must be * distributed ' or ' undistributed,' that is to say, 
 it must be understood in denotation.
 
 QUANTITY AND QUALITY 407 
 
 Logic divides all propositions into Universal and Particular; 
 and the whole doctrine of the syllogism depends on the distinction. 
 Yet most logicians so define the Particular proposition as to include 
 it among Universals. 
 
 In supposing that Classification must, or ought to, proceed 
 dichotomously, Traditional Logic is as wrong as it is in almost 
 everything else — as wrong as it is, for instance, in supposing that 
 there is any important difference between what it calls Natural 
 Classification and other classifications. Logic confuses Generalisa- 
 tion with Induction and with Classification, and consequently fails 
 to appreciate the true nature of either. 
 
 In its treatment of Quantity and Quality, Traditional Logic is 
 deficient to the point of ineptitude. It considers that quantity is 
 inherent in the whole proposition ; whereas, in fact, it inheres in 
 the terms only. Not only does Logic ignore by far the most 
 of the many common and familiar quantities about which we 
 reason all day long; but it practically denies their existence. 
 Perhaps the most astounding defect in all Traditional Logic is its 
 blindness to the fact that quantities, other than the ' distributive ' 
 and the ' non-distributive,' can be expressed in the Object-term, 
 and are, in fact, as often, and as usefully expressed in the Object- 
 term as in the Subject. That All men are mortal, is a proposition 
 that Logic can appreciate ; that it can admit into its sacred 
 precincts; and on which it can exercise all the complicated and 
 useful operations of its art ; but that Mortality is an attribute of 
 all men, is a proposition so strange, so bizarre, so unheard of, so 
 monstrous, that neither Traditional Logic, nor any other Logic that 
 has been formulated until now, even recognises the possibility of 
 its existence. In the whole two thousand and odd years of its 
 existence. Logic has never discovered that a property that all men 
 possess, may be possessed by them all. An inference so startling, 
 so amazing, is far, far beyond the range of Logic, and beyond its 
 power to effect. Logic admits, as a logical proposition, 'AH the 
 men in the house were sportsmen,' and * All the game on the estate 
 were pheasants,' and it might admit, with a little demur, perhaps, 
 that ' All the wine in the house was claret ' ; but that the house 
 contained all the sportsmen, that the sportsmen shot all the 
 pheasants on the estate, and drank all the wine in the house, — 
 these are not logical propositions. To Logic, they are not proposi- 
 tions at all. No logician seems to have conceived the possibility
 
 4o8 A NEW LOGIC 
 
 that such propositions can exist or be constructed, for certainly, 
 no book on Loj^ic makes any allusion to propositions constructed 
 on this plan. It is not that such propositions have been examined 
 by logicians and rejected. For Logic they have no existence. That 
 the Object-term of a proposition, as well as the Subject, can 
 express any quantity but the technical, conventional, and largely 
 imaginary * distributive ' quantity of Traditional Logic, seems 
 never, in the course of two thousand years, to have occurred to 
 any logician. Traditional Logic stands within a chalk line drawn 
 on the floor, and declares that the chalk line is a twenty-foot wall, 
 that is not merely insurmountable, but that is also opaque to the 
 vision ! 
 
 Of the eight classes of particular quantities in daily use, and 
 of the many quantities included in these classes. Logic knows 
 nothing. That any one could wish to reason of few, many, most, 
 nearly all, scarcely any, this, that, the other, each, any, the rest ; 
 or that, if he did so wish, his desire could be satisfied, seems never 
 to have occurred to Logic. Of the scores of negative propositions 
 known to common discourse and in daily use, Logic knows of five 
 only, and practically limits its purview to two — the E and O 
 propositions. To the rest it resolutely shuts its eyes. Of the 
 thousands of forms of propositions that are used in daily discourse, 
 and enter into the reasonings of practical men, as well as of 
 logicians outside their books. Logic knows of four only — A, E, I, 
 and O — and gravely declares that no more than these four exist, 
 or at least, that if there are any besides, none but these four can 
 enter into argument. 
 
 We look to the logician as our authority on propositions, just 
 as we look to the zoologist as our authority on animals, and to 
 the botanist as our authority on vegetables. If a logician or a 
 botanist were to be told, by a zoologist, that there are but four 
 forms of animals — cats, dogs, blackbeetles, and oysters — what 
 would they think of him ? what would they say ? Would they 
 not say ' We, with our limited experience, know of hundreds of 
 forms of animals — cows, horses, goats, birds, fishes, creeping, 
 flying, jumping, and swimming things innumerable. You, as an 
 expert, must know of hundreds of forms for every one that is 
 known to us, and do you say there are only four ? Either you 
 are joking, or you are bereft of your senses.' If a logician and a 
 zoologist were to be told by a botanist that there are only four
 
 FORMS OF PROPOSITIONS 409 
 
 forms of vegetables — oaks, palms, peas, and potatoes — what would 
 they think of him, and what would they say? Would they not 
 say * We, who have never paid any attention to vegetables, know 
 of hundreds more forms than this. In every garden, in every 
 country walk, we see scores for every one you have enumerated. 
 You, with your wider experience, and your expert knowledge, must 
 be acquainted with innumerable forms that are unknown to us. 
 Either you are joking, or your friends must be advised to look 
 after you.' But when the zoologist and the botanist go to the 
 logician, and ask him how many forms of propositions there are, 
 and are told by him that there are but four, they receive the 
 statement with unquestioning submission. Aristotle said so ; and 
 if he said so, it must be so. In spite of their daily experience of cow 
 propositions and horse propositions ; in spite of their experience, 
 in every house and garden, in every country walk, and on every 
 occasion of human intercourse, of hundreds of propositions besides 
 the A, E, I, and O of Traditional Logic ; they accept the assurance 
 of logicians with a faith, that it would be a libel on the intelligence 
 of children to call child-like. It is the most astounding instance of 
 the power of authority to blind the eyes and deafen the ears to 
 plain, insistent, and clamorous fact, that the history of the world 
 can show. Truly says Bacon, * The mind . . . has become 
 possessed with corrupted doctrines, and filled with the vainest 
 idols. The art of Logic . . . has tended more to confirm errors, 
 than to disclose truth.' 
 
 According to Traditional Logic, the combinations of propositions 
 into triplets in the form of the syllogism, amount in all to sixty- 
 four. In fact, if all quantities of both Subject- and Object-term, 
 and all combinations of the negative in Ratio and Terms, are 
 taken into account, the triple combinations run into thousands of 
 millions. The proportion of sixty-four to thousands of millions 
 represents, therefore, the degree of adequacy of Traditional Logic 
 in its own small department of Inference alone, leaving out of 
 account the vast field of Inference that it does not pretend to 
 explore, and the still greater field of Induction and Analogy. 
 
 Of the vast field of Empirical reasoning; of the solution of 
 Problems ; of Hypothesis and Conjecture ; Traditional Logic knows 
 nothing. Inductive Logic confuses Empirical reasoning with 
 Inference, with Generalisation, and with Analogy, and so does 
 Modern Logic.
 
 410 A NEW LOGIC 
 
 According to some of its exponents, Traditional Logic is the 
 Art of Reasoning ; but they lay down no general rules for the 
 employment of this art. The only semblance of rules available 
 are the Laws of Thought, the Dictum de omni et nullo, and the 
 Canons of the Syllogism. 
 
 The Laws of Thought are not Laws of Thought. If they are 
 laws at all, they are laws of Things, the objects of thought. As 
 * verbal ' propositions, which they are, Logic tells us they convey 
 no information, and that we learn nothing from them. It is a 
 relief to find myself at last in agreement with Traditional Logic 
 on one matter. The Laws of Thought tell us nothing. They 
 convey to us no information. We learn nothing from them. 
 They are bald truisms, that fail to attain to the dignity even of 
 platitudes. 
 
 The Canons of the Syllogism are not general Canons of 
 Reasoning. They are Canons of an insignificantly small part 
 of reasoning ; and even as applicable to this part, they are 
 incorrect and misleading. 
 
 The Dictum de omni et nullo is a truism no less bald, no less 
 empty, than the so-called Laws of Thought. It asserts, or it 
 should assert, if properly stated, that what is predicated of every 
 member of a class is predicated of each and any member of that 
 class. Why, of course it is. The meanings of Every, Any, and 
 Each, are so closely alike, that it requires some skill to distinguish 
 them ; and to say that what is true of every one is true of each 
 and of any one, satisfies completely the description of a ' verbal ' 
 proposition. To say that what is true of every one is true of each 
 one, is to say what is true ; but to imagine that it can be erected 
 into a general principle of reasoning, and be made the basis of 
 any reasoning process that is more than the restatement, in other 
 words, of part of a general proposition, is a notion too crazy to 
 enter the mind of any one but a logician. 
 
 The Laws of Thought and the Dictum are acknowledged and 
 proclaimed to be the foundation and substructure on which the 
 whole fabric of Traditional Logic rests. They are worshipped 
 with unquestioning reverence by all Logicians; and the best 
 that can be said for them is that they arc empty and silly truisms. 
 These be thy Gods, O Israel ! 
 
 The Immediate Inferences of Traditional Logic are four in 
 number. Of these, one is, without doubt, illegitimate and erroneous.
 
 INFERENCE 411 
 
 The others are of doubtful validity, and of still more doubtful 
 utility. Of the eij:(ht classes that actually exist of Immediate 
 Inferences; of the indefinitely numerous multitude of Inferences 
 that are included in these eight classes, all valid, and all in 
 frequent use, Traditional Logic knows no more than I know of 
 the configuration of the surface of the other side of the moon, 
 or of the mental process by which logicians persuade themselves 
 that the Laws of Thought and the Dictum de omni are of any 
 importance. Traditional Logic can no more infer from ' She 
 saw him do it' to 'She was there when he did it' than it can 
 infer from ' He designed a sundial ' to ' He was conversant with 
 Astronomy and Geometr}-.' All that Traditional Logic can obtain 
 from these postulates is * Some person who saw him do it was 
 she,' ' Some person who did not design a sundial was not he,' 
 and ' It was not he that did not design a sundial.' Whether these 
 inferences compare in elegance and value with the first two, the 
 reader must judge. 
 
 As for Mediate Inference, the crowning achievement of 
 Traditional Logic, to which this Logic owes its enormous 
 prestige, it is applicable to a small proportion only of Compound 
 propositions ; from the small proportion to which it is applicable 
 it can extract but one, or at most two, of the multitudes they 
 may contain ; it is not self-evidently valid, but needs, in most 
 cases, an awkward, cumbrous, and complicated process of reduction 
 to make it appear so ; its rules are faulty ; and it cannot be applied 
 without a knowledge of the barbarous mnemonic verses. And 
 this clumsy and inefficient process, of extremely limited applica- 
 tion, and still more limited utility, is the crown and flower of 
 Traditional Logic ; its pride and its glory ; its one title to the 
 reverence and applause that mankind have, for two thousand 
 years, so freely and lavishly bestowed upon it. Never, in the 
 long history of man, has kudos been obtained so cheaply. 
 
 Of Analogy, in the strict Aristotelian sense, which is a valid, 
 telling, useful, and frequently employed mode of reasoning, 
 nothing is known by any system of Logic hitherto devised, though 
 Spencer, who was not a logician, recognised its use and value. 
 If logicians mention it at all, they either confuse it with Empirical 
 Reasoning, or they fail to appreciate that it is a mode of reasoning 
 at all. 
 
 The reasonings of Mathematics have no part or lot in any
 
 412 A NEW LOGIC 
 
 scheme of Logic hitherto propounded ; or, if they have, they are 
 misappreciated, and taken to be examples of syllogistic reasoning, 
 which they very seldom are. The understood doctrine that 
 Mathematical reasoning is so different from other reasoning, that 
 Logic need take no heed of it, seems to me merely another 
 instance of the passion of logicians for hedging themselves about 
 with conventional, unnecessary, and unreasoning restrictions, and 
 for excluding from Logic what properly belongs to it. 
 
 Finally, the fallacies ?';; didione of Aristotle are not, strictly 
 speaking, fallacies at all, and the fallacies extra dictionem are, in 
 Traditional Logic, illogical excrescences. Logicians do not 
 enumerate or recognise by any means all the fallacies that may 
 be perpetrated. One whole class of Fallacies — the fallacies of 
 confusion of the mode of argument — is almost confined to books 
 on Logic, and is cherished by logicians as their own peculiar pet. 
 Traditional Logic lays down no rules by which the fallacies that 
 it does enumerate may be avoided, nor are its fallacies extra 
 dictionem breaches of any of its rules. A more illogical position it 
 would be difficult to invent. When a man has fallen into a pit, 
 it does not help him much to tell him the name of the pit ; but 
 this is all the aid that Logic, whether Traditional, Inductive, or 
 Modern, affords him. It seems to me that the least any one, who 
 professes and calls himself a logician, can do for the wandering 
 reasoner, is to stake out his route, and to put up notice boards, 
 inscribed ' Danger ! Beware of fallacy ! Keep to the right.' 
 But Logic, as hitherto taught, does nothing of this. All it does 
 is to say to the unwary reasoner, who has fallen into a fallacy and 
 broken his shins, ' My poor friend, it will comfort you to know 
 that the fallacy into which you are fallen is called z^/iom^^o elenchi. 
 There are plenty more fallacies farther along your path. I cannot 
 tell you how to avoid them ; for this you must trust to your own 
 natural acuteness ; but I will not leave you altogether without 
 assistance. Here, suffering stranger, is a list of their names, or at 
 any rate, of the names of some of them. Whenever you find 
 yourself an object of scorn from having fallen into another pit, 
 it will console you to find, in this list, the name of the pit into 
 which you have fallen.' 
 
 If, in the foregoing pages, I have paid less attention, and given 
 less prominence, to the doctrines of Modern Logic than its votaries 
 may think it deserves, the fault is their own. Supposing it to be
 
 THE EMPEROR'S CLOTHES 413 
 
 a new departure, a divergence from Traditional Logic, and an 
 improvement on it, I was prepared to welcome Modern Logic 
 with open arms ; but I soon found reason to despise it ; for its 
 exponents are either incapable of expressing themselves intelli- 
 gibly, or they deliberately seek to impart to their writings a 
 spurious air of profundity, by the constant use of expressions that 
 are unintelligible. The reason I have not attacked Modern Logic 
 with the weapon of argument is the same reason that would 
 prevent me from attacking a London fog with a small-sword. 
 There is nothing tangible or palpable to attack. The only way to 
 dissipate a fog is to produce such a change in the atmosphere as 
 is incompatible with fog. If logicians can be induced to think 
 clearly ; to form crisp and definite notions in their minds ; to 
 express these notions in appropriate words, orderly arranged, and 
 duly punctuated ; and to refuse admission, as not pertaining to 
 Logic, or as fallacious, to any expressions that are flagrant and 
 wilful violations of these rules ; Modern Logic will be dissipated, 
 as fog is dissipated by sun and wind. It will die out, as men of 
 lowly organised type die out in the presence of high civilisation ; 
 because it finds itself in an intellectual and moral atmosphere 
 incompatible with its existence. When I observe the reverence 
 and awe with which some of the recent exponents of Traditional 
 Logic treat the lucubrations of Modern Logic, I am irresistibly 
 reminded of the story of the Emperor's clothes. They were 
 invisible, so said the clothiers who supplied them, to every one 
 who was unfit for his place, or was very stupid ; so every courtier, 
 and official, and officer of State, made haste to cut-do every other 
 in the loudness and lavishness of his praises ; and the whole 
 populace followed suit. It was, at last, a little child who cried 
 out ' Why, the Emperor has no clothes on ! ' At once the 
 populace took up the cry, and at length even the courtiers, who 
 were undoubtedly votaries of Traditional Logic, were obliged to 
 admit that they could see no clothes upon their Sovereign. In 
 Logic, I am a child; and when I seethe exponents of Traditional 
 Logic bowing down before Modern Logic, and doing homage to 
 it, I am irresistibly impelled to cry out 'The Emperor has no 
 clothes on ! ' 
 
 If there is any votary of Modern Logic who has sufficient faith 
 in his own doctrines to break a lance in their defence, let him 
 come out of the fog, and show himself and his doctrines in a clear
 
 414 A NEW LOGIC 
 
 light, and I shall be pleased to oblige him ; but I am under no 
 obligation to choke myself and blind myself by following him into 
 a region of obscurity and mystery, that I verily believe I could 
 recognise, but for the fog, as a thoroughfare, or a blind alley, 
 with which I have been familiar from childhood. 
 
 To the examination of logical doctrine contained in this book, I 
 have brought no academic equipment. I pretend to no scholarship 
 in Greek, to no scholastic learning. Any logician can trip me up 
 on knowledge of the pure text of Aristotle. I could not, without 
 the help of a text-book, reduce Bocardo to Barbara, or Fesapo 
 to Ferio, even if I were so curiously constituted as to wish 
 to perform the operation. The only qualifications I bring to 
 the task are ordinary common sense and a plentiful lack of 
 reverence for authority in general, and for Greek philosophy in 
 particular. The only weapons I am armed with, are the sling of 
 common sense, and a few smooth pebbles of fact from the brook 
 of experience. There is, however, a mode of argument, hitherto 
 unmentioned, that I may pray in aid of my attack upon Traditional 
 Logic. Darwin's doctrines were fiercely opposed by theologians 
 until it was found that, if Genesis is read aright, the doctrine of 
 the Origin of Species by Natural Selection can be found therein. 
 After that discover)', all went well with Darwin and his doctrines. 
 I suggest that if Aristotle is read aright, and understood in the 
 sense he intended, it will be found that my doctrines are in 
 harmony with his, and are potentially contained in his Organon. 
 In case there is any doctrine of mine that cannot be found in the 
 Organon, I submit that it was contained in those of his books 
 that have been lost, and have not come down to us ; and I defy 
 my critics to prove that it was not so contained. Moreover, if 
 there is anything in Aristotle inconsistent with the doctrines I 
 propound, then the passages in which these inconsistencies are 
 found, are not to be attributed to Aristotle, but have been inserted 
 by transcribers, either from carelessness, or for their own 
 nefarious purposes. This mode of argument is not, indeed, 
 taught in Aristotelian Logic ; but it is freely employed by those 
 who have been brought up in the Aristotelian atmosphere, and is 
 an argument of great power and efficacy. It sometimes goes by 
 the name of the Higher Criticism. 
 
 Here I terminate my review of the Logic of my predecessors, 
 and rny exposition of the New Logic. This New Logic may be
 
 THE END OF TRADITIONAL LOGIC 415 
 
 right or wrong, and I may or may not have been able to commend 
 it to the assent of my readers ; but of this I am sure — that the 
 Logic of Tradition can no longer stand before the world as a 
 complete, an accurate, or a valid scheme of doctrine. Its hour 
 is struck ; its sentence is delivered ; its doom is pronounced. The 
 handwriting is on the wall ; the enemy is at the gate; Aristotelian 
 Logic is weighed in the balances, and found wanting ; and its 
 kingdom is to be taken away, and given to one more worthy. In 
 vain will it struggle against the inevitable; in vain plead for a 
 longer existence. If it consults its own dignity, it will follow the 
 example of Socrates, and calmly lay down a life that is no longer 
 serviceable, and no longer ministers to the uses of man. To sink 
 into the position of Giant Pope and Giant Pagan in the immortal 
 allegory ; to sit unheeded by the wayside, threatening indifferent 
 wayfarers with penalties that it is powerless to enforce ; to cry 
 ' Unless you reason by the syllogism, your arguments have no 
 validity, your reasonings are unsound ' ; is a part unworthy of its 
 splendid history ; derogatory to its great traditions. Men and 
 women will continue in the future, as in the past, to reason 
 without employing the syllogism ; and, so reasoning, they will 
 continue in the future, as in the past, to survive, to prevail, to 
 increase and multiply exceedingly ; and they will justly adduce 
 their success as proof beyond cavil that their reasonings, on the 
 whole, are sound. Against fact, as against stupidity, even the 
 gods themselves fight in vain. But Aristotelian Logic, on its 
 deathbed, may look back on a life well spent. It has had a royal 
 career. It has dominated the minds of men for sixty generations 
 of the human race. It has received honour unprecedented, 
 and homage unrivalled. It has outlived dynasties, nations, 
 civilisations, and religions. It is older than the Papacy ; older 
 than Christianity itself. It is the oldest product of the human 
 intellect that exists in Europe ; and now it must submit to the 
 inexorable doom that, soon or late, overtakes all earthly things. 
 
 That spell upon the minds of men 
 Breaks, never to unite again. 
 
 Pallida mors ccquo pulsat pede pauperum tahcrnas, Regtimque turres. 
 Its fight is fought ; its race is run ; may it rest for ever in peace !
 
 APPENDIX 
 
 A CLASSIFICATION OF SCIENCES 
 
 A CHAPTER on the Classification of the Sciences is included in 
 some books on Logic ; and the reader is inclined to wonder how 
 it got there, and what it is doing there. It appears to have no 
 connection with Logic, except as an essay in classification and an 
 example of classification ; and classification is itself no integral 
 part of Traditional Logic. The classification of the Sciences has, 
 however, with Logic a connection that must, I suppose, have been 
 inarticulately present to the minds of those logicians who have 
 included a classification of sciences in their books on Logic ; but 
 a connection they neither explain nor refer to. 
 
 Early in this book it was asserted that words have been devised, 
 
 or have grown, in response to the needs that have been felt to 
 
 express mental states in words ; and similarly, we may be sure 
 
 that if there are different ways of reasoning about things, it is 
 
 because things have presented themselves in different aspects, or 
 
 as of different natures, which have elicited these different ways of 
 
 reasoning about them. As Science is organised Knowledge, and 
 
 as Knowledge is acquired largely by reasoning, there is a prima 
 
 facie likelihood that the different kinds of Science may correspond 
 
 with the different kinds of reasoning; and on inquiry we find that 
 
 this is so. We find that Sciences may be divided into three main 
 
 kinds, which correspond with the three modes of reasoning, and 
 
 correspond also with the three varieties of subject-matter of these 
 
 modes of reasoning. 
 
 The subject-matter of Inductive Reasoning is observed fact, the 
 
 fruit of experience : the subject-matter of Deductive Reasoning is 
 
 postulated quasi-fact, the fruit of imagination : the subject-matter 
 
 . of Analogy is relation ; and correspondingly we find that there are 
 
 three main groups or classes of Sciences, similarly characterised. 
 
 The Inductive Sciences have for their subject-matter facts of 
 experience; and treat these facts primarily and mainly by Inductive 
 Reasoning. 
 
 N.L. E E
 
 4i8 A NEW LOGIC 
 
 The Deductive Sciences have for their subject-matter postulated 
 quasi-fact ; and treat this postulated matter primarily and mainly 
 by Deductive Reasoning. 
 
 The Sciences of Relations have for their subject-matter relations ; 
 and treat these relations mainly by Analogical Reasoning. 
 
 Since, however, all knowledge is relative, it follows that rela- 
 tions, and reasoning about relations, cannot be excluded from the 
 first two classes of Sciences. Since observation and knowledge of 
 fact are frequently defective, it follows that they are often supple- 
 mented by postulation to fill the gaps, and that Inductive Science 
 must often pray in aid the services of Deductive reasoning. The 
 postulated quasi-facts of Deduction are derived from experience, 
 in that they are experiences from which some factors are postu- 
 lated away ; and since knowledge of relations is gained from 
 experience, it follows that Analogical reasoning is based ultimately 
 on observed fact. The inter-relations of the different classes of 
 Sciences are, therefore, numerous and close : but in spite of this, 
 they are distinguishable in their main features, and constitute what 
 our forefathers would have called Natural Kinds. 
 
 Inductive Sciences treat of facts observed ; and these facts may 
 be mental or non-mental, which gives us the first division of this 
 group of Sciences. 
 
 Mental facts may be regarded simpliciter, in and for themselves, 
 and without further reference : so regarded they are the subject- 
 matter of Psychology. Or they may be regarded, not simpliciter, 
 but with reference to extra-mental facts, real or postulated, with 
 which they correspond. If the mental fact thus regarded is the 
 process of establishing mental relations, the Science is Logic ; if 
 the mental fact is not the process of establishing mental relations, 
 but the established relations, then the Science is Epistemology. 
 
 Non-mental facts of observation are divisible into two broadly 
 distinguished classes — Material bodies and Modes of Motion. 
 Each of these forms the subject-matter of a large group of 
 Sciences. 
 
 Material bodies are divisible into Living and not-Living ; the 
 former being the subject-matter of the Biological sciences, the 
 latter of the first group of Physical sciences. The Biological 
 sciences are well characterised, and their limits are not often con- 
 fused ; but the term Physical Science is by no means well defined. 
 It includes, in fact, three different groups of Sciences that are well
 
 APPENDIX 
 
 419 
 
 distinguished from one another, of which the Sciences having not- 
 living natural material bodies for their subject-matter, constitute 
 the first. This group of Sciences includes Astronomy, Geology, 
 Oceanology, Mineralogy, Metallurgy, Crystallology, Chemistry, 
 and so forth, all easily distinguished from the next group of 
 Physical Sciences, which includes : — 
 
 Sciences whose subject-matter consists of Modes of Motion as 
 observed facts. They are divisible primarily according as the 
 motion is Molar, Molecular, or Ethereal. To the first sub-group 
 belong Ballistics and Hydraulics ; to the second Molecular 
 Physics; and to the third the Sciences of Gravitation, Heat, 
 Light, Electricity and Magnetism, as ascertained from observation 
 and experiment. 
 
 This outline of the Inductive Sciences will scarcely be complete 
 without a further expansion of the Biological Sciences. The 
 obvious primary division is into Phytology and Zoology. Whether 
 Anthropology is included under Zoology, or forms a third class 
 of co-ordinate rank, is a matter of taste ; but in either case 
 Anthropolog\' is the fruitful mother of a large family of Sciences. 
 Individual man may be investigated, and knowledge gained and 
 systematised, as to his properties, his kinds, his constituents, his 
 relations, and so forth. He may be investigated as to his diseases, 
 his conduct, his history, and in many other respects. He may also 
 be regarded as massed together in communities, and then becomes 
 the subject-matter of Sociology in all its branches. Finally man 
 is a maker, and every one of the things he makes may be the 
 subject-matter of a science, and many products of man are in 
 fact subject-matters of several sciences each. He makes things 
 material, such as bridges and houses, subject-matters respec- 
 tively of the sciences of Engineering and Architecture ; and 
 he makes things immaterial, such as laws and propositions, the 
 subject-matters, respectively, of the sciences of Jurisprudence and 
 Logic. 
 
 Deductive Sciences, like Deductive Reasoning, which they 
 mainly employ, have for their subject-matter, not observed facts, 
 but quasi-facts, postulated for the purpose of argument. These 
 quasi-facts are derived from observed facts by abstracting certain 
 qualities, and then postulating away the remainder, and there- 
 upon treating the abstracted qualities as if they existed in isolation 
 from their associates, with which, in experience, they are invariably
 
 420 A NEW LOGIC 
 
 combined. The things thus treated may be mental facts or 
 material facts ; and in the latter case may be material bodies, living 
 or not living, or modes of motion, molar, molecular, or ethereal. 
 Thus, we may postulate away from the complete mental equipment 
 of man, all mental qualities but desire for gain, industry, honesty, 
 and intelligence; and it is this abstract that forms the human 
 subject-matter of the deductive aspect of Political Economy. 
 From water we may postulate away all qualities but equi-pressure 
 and weight, and so form the subject-matter of hydrostatics and 
 hydrodynamics. From light we may postulate away all qualities 
 but those of radiating in straight lines, reflection, and refraction, 
 and so form the subject-matter of Geometrical Optics ; Statics 
 treats of levers postulated to be without weight or flexibility ; of 
 pulleys from which friction has been postulated away, and so on. 
 These form a third group of Physical Sciences, often called 
 Mathematical Physics, since their treatment is mainly numerically 
 quantitative. 
 
 The third primary group of Sciences are those which treat, for 
 the most part by Analogical reasoning, neither of mental facts 
 nor of material bodies, nor of modes of motion ; neither of observed 
 facts nor of postulated quasi-facts, but of relations ; and not of 
 relations between mental facts, material bodies or modes of 
 motion, but of relations alone, considered abstractedly. They are 
 divisible according to the relations of which they treat, and are 
 three in number. Space-relations form the subject-matter of the 
 Science of Geometry. Numerical relations form the subject- 
 matter of the Science of Mathematics. But since numbers are 
 known to us primarily in sequence — since when we count, we must 
 count serially — it is clear that numerical relations originate as 
 time-relations ; and Mathematics has its foundations in relations of 
 Time, as Geometry is the Science of relations of Space. A third 
 Science of relations has for its subject-matter the relations between 
 Subject and Object ; and this is Metaphysics. 
 
 Postulation is not limited to material bodies or to modes of motion. 
 It may be applied to relations of quantity also ; and such postu- 
 lated relations form the subject-matter of the Integral and other 
 Calculi. These are so connate with Mathematics that they are 
 usually, and no doubt rightly, considered branches or sub-sciences 
 of Mathematics ; though it is clear that, as their subject-matter 
 is postulated, they are, strictly speaking. Deductive Sciences. It
 
 APPENDIX 421 
 
 is merely a question of relative importance for the purpose in hand. 
 If the fact that the subject-matter consists of abstract relations 
 is, for an)' purpose, more important, then they are Mathematical 
 sciences. If the postulation of the subject-matter is, for any 
 purpose, more important than its nature as abstract relations, 
 then for that purpose they are Deductive Sciences. They are, in 
 fact, both Mathematical and Deductive. 
 
 To whichever class a Science may be relegated, it does not long 
 remain purely Inductive, purely Deductive, or purely Analogical 
 in its methods. As long as Inductive Science is content to 
 observe, to describe, to analyse, and to classify, it remains pure ; 
 but the mind of man is not long content with mere knowledge. 
 It demands explanation also ; and explanation, by which is meant 
 knowledge of causes, is not often to be had without the aid of 
 Deduction from hypothesis, that is to say from a postulate. More- 
 over, as soon as Inductive science becomes accurate, it must 
 become quantitative ; that is to say, it must speak in numbers, 
 and so pray in aid the science of relations. And further, whenever 
 investigation is pushed to its limit, it brings up against some 
 problem of Metaphysics, and so becomes involved with another 
 science of relations. 
 
 Deductive Science is the science of postulates ; but postulates 
 are themselves but fragments drawn from the stores of Experience. 
 A lever that is without weight is derived from levers actually used 
 in experience. The weight that is postulated away from it, is 
 weight that it has been found in experience to possess. The con- 
 clusions of Deduction are no sooner made than they are carried 
 across to Induction. They are compared with fact, and are 
 made the occasion of new investigation, which often results in the 
 revelation of facts previously unsuspected. 
 
 In general outline, the suggested classification is as follows : — 
 
 Mental Experiences — The Mental Sciences. 
 'Living — The Biological 
 Sciences. 
 Material Bodies I j^Qt living — Physical Sci- 
 
 [ ences (ist group). 
 
 Physical Sciences (2nd 
 group). Experimental 
 Physics. 
 
 N.L. F F 
 
 Inductive Sciences 
 Sciences of the^ 
 observed facts of 
 
 Modes of Motion ■
 
 422 
 
 A NEW LOGIC 
 
 Deductive Sciences. [ Material Bodies. — Physical Sciences (3rd 
 Sciences of postu- group). 
 
 lated quasi - fact Modes of Motion. — Mathematical Physics. 
 
 concerning I Relations — Integral and other Calculi. 
 
 . , _ . I Of Number — Mathematics. 
 
 Analogical Sciences. ) r^c c^ ^ 
 
 _ . ° -^ , . < Or Space — Geometry. 
 
 Sciences 01 Relations L^r o 1 • ^ j ^-.l- i. at j. u • 
 
 [ Of Subject and Object — Metaphysics. 
 
 The soundness of a classification, provided the rules of classifi- 
 cation are observed, depends on the purpose for which the 
 classification is required. For the purpose of a mere arrangement, 
 setting forth resemblances and differences, placing together those 
 that are, on the whole, most alike, and separating those that, on 
 the whole, are most unlike, this classification is submitted to be 
 sound ; but for the practical purposes of actual study, it is not 
 necessarily the best. In practice, Photology is studied as observed 
 fact and as postulated quasi-fact. Photometry is almost a pure 
 Inductive Science. Catoptrics is almost purely Deductive. Still, 
 Photology is always regarded as consisting of two sciences, 
 and Experimental Photology and Mathematical Photology are 
 distinguished in all University curricula. The same is the case 
 with the Sciences of which Heat, Electricity, and Magnetism 
 form the subject-matter. Chemistry also has its Deductive as 
 well as its Inductive aspect ; but as the Inductive science prepon- 
 derates greatly over the Deductive, the two Sciences have not 
 hitherto been separately considered. The time is at hand, how- 
 ever, when Experimental Chemistry will be as completely separated 
 from Deductive Chemistry as Experimental Mechanics is separated 
 from Statics and Dynamics. 
 
 As treating of postulated relations, the Calculi are Deductive 
 Sciences. As treating of relations mainly by Analogical reason- 
 ing, they are Analogical Sciences. Under which class they shall 
 be placed depends on the purpose of the classification ; and since 
 this purpose is usually that of determining their place in a cur- 
 riculum of study, they are usually relegated to Mathematics, to 
 which also their mode of treatment is most appropriate. 
 
 THE END. 
 
 BRADBUKY, ACNEW, & CO., LD., PRINTERS, I.O.NDON ANU TONBRIDGE.
 
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