THE LIBRARY 
 
 OF 
 
 THE UNIVERSITY 
 OF CALIFORNIA 
 
 LOS ANGELES 

 
 THE 
 
 ESSENTIALS OF LOGIC
 
 THE 
 
 ESSENTIALS OF LOGIC 
 
 BEING 
 
 TEN LECTURES ON JUDGMENT AND 
 
 INFERENCE 
 
 BY 
 
 BERNARD BOSANQUET 
 
 FORMERLY FELLOW OF UNIVERSITY COLLEGE, OXFORD 
 
 MACMILLAN AND CO., LIMITED 
 
 NEW YORK: THE MACMILLAN COMPANY 
 1897 
 
 All rights reserved
 
 First Edition, 1895. 
 Reprinted, 1897.
 
 U U L. 
 
 PREFACE 
 
 IN this course of lectures I have attempted to carry out r 
 under the freer conditions of the University Extension- 
 system, a purpose conceived many years ago at Oxford. It 
 was suggested to me by the answer of a friend, engaged 
 like myself from time to time in teaching elementary Logic, 
 to the question which I put to him, " What do you aim at 
 in teaching Logic to beginners ? What do you think can 
 reasonably be hoped for ? " " If the men could learn what 
 an Inference is, it would be something," was the reply. 
 
 The course of lectures which I now publish was projected 
 in the spirit thus indicated. Though only the two last 
 discourses deal explicitly with Inference, yet those which 
 precede them contribute, I hope, no less .essentially, to 
 explain the nature of that single development which in 
 some stages 'we call Judgment, and in others Inference. 
 So far as I could see, the attempt to go to the heart of the 
 subject, however imperfectly executed, was appreciated by 
 the students, and was rewarded with a serious attention 
 which would not have been commanded by the trivialitiea 
 of formal Logic, although more entertaining and less abstruse. 
 
 The details of traditional terminology may be found in 
 Jevons's Elementary Lessons in Logic (Macmillan). Those
 
 vi PREFACE 
 
 who desire to pursue the study more in the sense of the 
 present work, may be referred above all to Bradley's 
 Principles of Logic^ and also to Lotze's Logic (E. Tr.), and 
 to Sigwart's great work on Logic, the English translation 
 of which, just completed, opens a storehouse of knowledge 
 and robust good sense to the English student. My own 
 larger Logic expresses in extenso the views which these 
 lectures set out in a shorter form. 
 
 I hope it will be admitted by my critics that this ex- 
 periment, whether successful or unsuccessful, was worth 
 making, and that except in the University Extension system, 
 it could not easily have been made. 
 
 BERNARD BOSANQUET. 
 
 London, January 1895.
 
 CONTENTS 
 
 LECTURE I 
 
 THE PROBLEM OF LOGIC 
 
 PAGE 
 
 1. Difficulty of the Science ..... I 
 
 2. The Problem stated ...... 3 
 
 3. World as Idea ....... 4 
 
 4. "World" 5 
 
 5. The Animal's World ' . . . . . .6 
 
 6. The World as " Objective " ..... 7 
 
 L Common sense ...... 8 
 
 ii. Common-sense Theory . . . . .8 
 
 iii. Philosophic Theory . . . . . 1 1 
 
 7. Our separate "Worlds" . . . . .14 
 
 8. Subjective Idealism . . . . . 19 
 
 LECTURE II 
 JUDGMENT AS THE CONSCIOUSNESS OF A WORLD 
 
 1. Defect of Subjective Idealism . . . . .21 
 
 2. The World as Knowledge . . . . .22 
 
 3. Knowledge is in the form of Judgment . . 23 
 
 a. Necessary . ..... 23 
 
 /3. Universal . . . . . .26 
 
 7. Constructive . . . . . -27 
 
 4. The Continuous Affirmation of Waking Consciousness . 33 
 
 5. Comparison with World as Will . . . -37 
 
 6. Distribution of Attention . . . . 40
 
 viii CONTENTS 
 
 LECTURE III 
 
 THE RELATION OF LOGIC TO KNOWLEDGE 
 
 PAGE 
 
 1. Meaning of " Form " . ... 42 
 
 2. Form of Knowledge dependent on Content . . '49 
 
 3. The Relation of Part and Whole as Form determined by 
 
 Content ....... 54 
 
 4. Nature of Knowledge . . . . . 58 
 j>. Conclusion ....... 59 
 
 LECTURE IV 
 
 TYPES OF JUDGMENT, AND THE GENERAL CONDITIONS 
 INVOLVED IN ASSERTION 
 
 1. Correspondence between Types of Judgment and Nature of 
 
 Objects as Knowledge . . . .61 
 
 a. Impersonal Judgment . . . . .61 
 
 b. Perceptive Judgment . . . . .62 
 e. Proper Names in Judgment . . . .64 
 d. Abstract Judgment . . . . -65 
 
 2. The General Definition of Judgment . . . .66 
 
 i. What is implied in claiming Truth . . -67 
 
 ii. By what means the claim is made . . -69 
 
 iii. The kind of Ideas which can claim Truth . . 74 
 
 o. Idea as Psychical Presentation . . -74 
 
 . Idea as Identical Reference . . -74 
 
 LECTURE V 
 
 THE PROPOSITION AND THE NAME 
 
 1. Judgment translated into Language . . . .80 
 
 2. Proposition and Sentence . . . . .82 
 
 3. Difference between Proposition and Judgment . . 82 
 
 4. " Parts of Speech " ...... 85 
 
 5. Denotation and Connotation . . . . _ . 88 
 
 6. Have Proper Names Connotation ? . . . 91 
 
 7. Inverse Ratio of Connotation and Denotation . . -94
 
 CONTENTS ix 
 
 LECTURE VI 
 
 PARTS OF THE JUDGMENT, AND ITS UNITY 
 
 PAGE 
 
 1. Parts of the Judgment . . . . . -98 
 
 2. Copula ........ 99 
 
 3. Are Subject and Predicate necessary? .... 100 
 
 4. Two Ideas or Things ...... 101 
 
 a. Two Ideas ...... 102 
 
 i. Mental Transition . . . . .102 
 
 ii. Absence of Assertion . . . . .103 
 
 . Two Things ..... 104 
 
 5. Distinction between Subject and Predicate . . . 107 
 
 LECTURE VII 
 THE CATEGORICAL AND THE HYPOTHETICAL JUDGMENTS 
 
 1. Some Criticisms on the ordinary scheme of Judgment . . 112 
 
 a. Why we need a Scheme . . . .112 
 
 j8. The Common Scheme . . . . 113 
 
 2. Which Judgments are Categorical ? . . . .116 
 
 (1) The " Particular " Judgment .... 116 
 a. Natural Meaning . . . . .116 
 )8. Limited Meaning . . . . 1 1 7 
 
 (2) " Singular " Judgment . . . .118 
 
 (3) " Universal" Judgment .... 119 
 
 (4) "Hypothetical" Judgment .... 121 
 
 (5) "Disjunctive" Judgment .... 123 
 
 LECTURE VIII 
 NEGATION, AND OPPOSITION OF JUDGMENTS 
 
 1. Distinction between Contrary and Contradictory Opposition . 126 
 
 2. Contrary Negation . . . . . .128 
 
 3. Why use Negation ? ...... 130 
 
 4. Stage of Significant Negation ; Combination of Contrary and 
 
 Contradictory . . . . . 132 
 
 5. Negative Judgment expressing Fact . . . 134 
 
 6. Operation of the Denied Idea ..... 135
 
 x CONTENTS 
 
 LECTURE IX 
 
 INFERENCE AND THE SYLLOGISTIC FORMS 
 
 PAGE 
 
 1. Inference in General ...... 137 
 
 2. Conditions of the Possibility of Inference . . 139 
 
 3. System the ultimate condition of Inference . . .140 
 
 4. Immediate Inference ...... 141 
 
 5. Number of Instances ...... 142 
 
 6. Figures of Syllogism, illustrating Progress from Guess-work 
 
 to Demonstration ...... 146 
 
 LECTURE X 
 
 INDUCTION, DEDUCTION, AND CAUSATION 
 
 1. Induction ....... 151 
 
 a. By simple Enumeration . . . 151 
 
 b. Enumeration always has a Ground . . . 152 
 
 c. Perfect Induction . . . . 152 
 
 d. System ....... 153 
 
 e. Analogy as Step towards System . . 155 
 
 f. Negative Instance . . . . .158 
 
 g. Classification and Generalisation . . 159 
 h. Hypothesis . . . . . .161 
 
 2. Deduction . . . . . . .162 
 
 a. Subsumption . . . . . .163 
 
 b. Construction . . . . . .163 
 
 3. Causation ....... 164 
 
 4. The Postulate of Knowledge . . . . .165 
 
 5. Conclusion . . . . . . .166
 
 LECTURE I 
 
 THE PROBLEM OF LOGIC 
 
 i. THERE is no science more difficult than that on which Difficulty 
 we are entering in these lectures. It is worth while to science, 
 discuss the nature of this difficulty. It is a question of 
 interest rather than of intricacy. All sciences have, perhaps, 
 much the same possibilities of broad theory and subtle 
 analysis. But Logic stands alone in the difficulty with 
 which the student sustains his persuasion that its point of 
 view is worth applying. 
 
 In most other sciences, even in the philosophical sciences, 
 there is a continual stimulus to sense-perception, to curi- 
 osity, to human interest. The learner is called upon to dis- 
 sect animals or plants, to undertake delicate manipulations 
 with beautifully contrived instruments, to acquaint himself 
 with the history of nations, with the genesis of worlds, with 
 strange and novel speculations upon the nature of space, or 
 with the industry and well-being of various classes among 
 mankind at the present day. And these elements of 
 novelty, these stimulations of sense-perception or of practical 
 interest, carry us forward imperceptibly, and sustain our 
 
 B
 
 2 THE PROBLEM OF LOGIC LECT. 
 
 eagerness to analyse and combine in theoretic completeness 
 the novel matter thus constantly impinging upon us. 
 
 In Philosophy, and more especially in Logic, we can 
 promise little or nothing of this kind. The teacher of 
 Philosophy, from Socrates downwards, has talked about 
 common things, things already familiar to his hearers. And 
 although he calls upon them to think of these things in a 
 peculiar way, and from an unaccustomed point of view, yet 
 it is likely to be felt that he is demanding a new effort, with- 
 out supplying a new interest. And it is a common experience, 
 that after a time the mind rebels against this artificial 
 attitude, which fatigues without instructing, if we have 
 accustomed ourselves to understand by instruction the 
 accumulation of new sense-perceptions and the extension 
 of historical or scientific vision over a wider superficial 
 area. 
 
 Now this I cannot help, and I will not disguise. In 
 Philosophy, and in Logic above all, it must be so. The 
 whole point and meaning of the study is that in it we 
 re-traverse familiar ground, and survey it by unfamiliar 
 processes. We do not, except accidentally, so much as 
 widen our mental horizon. For those who care to under- 
 stand, to trace the connecting principles and functions that 
 permeate our intellectual world, there is indeed an interest 
 of a peculiar kind. But even experienced students will 
 occasionally feel the strain of attending to difficult dis- 
 tinctions, entirely without the excitement of novelty in sense- 
 perception or of a practical bearing upon human life. It 
 is this that makes Logic probably the hardest of all the 
 sciences.
 
 I LOGIC AND PSYCHOLOGY 
 
 2. We cannot hope to vanquish this difficulty unless we The 
 face it boldly from the first. There are in the old-fashioned 
 Logic-books tricks and puzzles, fallacies and repartees, which 
 can in some degree be made amusing ; but of these I do 
 not intend to speak. The course by which alone I can hope 
 honestly to awaken a true logical interest among any who 
 may be quite unfamiliar with the subject, is to approach the 
 matter descriptively, and try to set before you fully and 
 fairly what the problem is which the process of knowledge 
 has to meet. And then it may be possible to claim a genuine 
 theoretical curiosity none the less genuine that it may be 
 tinged with a sympathy for man's common birthright of 
 intelligence for the detailed explanation of the means by 
 which this problem is solved from day to day. Such an 
 explanation is the science of Logic. 
 
 The problem may be thus introduced. Several of those 
 present have, I believe, attended a previous course of 
 lectures on Psychology. They have learned, I presume, 
 to think of the mind as the course of consciousness, a 
 continuous connected presentation, more or less emphasising 
 within it various images, and groups of images and ideas, 
 which may be roughly said to act and re-act upon each other, 
 to cohere in systems, and to give rise to the perception of 
 self. This course of consciousness, including certain latent 
 elements, the existence of which it is necessary to assume, 
 is an individual mind, attached to a particular body, and so 
 far as we know, not separable from the actions and affections 
 of that body. What is the connection between such a 
 course of consciousness in any individual, and the world as 
 that individual knows and wills it ? This is the point at
 
 4 THE PROBLEM OF LOGIC LECT. 
 
 which Psychology passes into Logic. Psychology treats of 
 the course of ideas and feelings ; Logic of the mental con- 
 struction of reality. How does the course of my private 
 ideas and feelings contain in it, for me, a world of things 
 and persons which are not merely in my mind ? 
 
 World 3. Schopenhauer called his great work, The World as 
 
 Will and Idea. 1 Leaving out Will for the moment, let 
 us consider the world "as Idea." 
 
 " ' The world is my idea ; ' 2 this is a truth which holds 
 good for everything that lives and knows, though man alone 
 can bring it into reflective and abstract consciousness. If 
 he really does this, he has attained to philosophical wisdom. 
 It then becomes clear and certain to him that what he 
 knows is not a sun and an earth, but only an eye that sees 
 a sun, a hand that feels an earth; that the world which 
 surrounds him is there only as an idea, /. e. only in relation 
 to something else, the consciousness which is himself. If 
 any truth can be asserted a priori, it is this ; for it is the 
 expression of the most general form of all possible and think- 
 able experience : a form which is more general than time, 
 space, or causality, for they all pre-suppose it. 
 
 ****** 
 
 " No truth, therefore, is more certain, more independent 
 of all others, and less in need of proof than this, that all that 
 exists for knowledge, and, therefore, this whole world, is 
 only object in relation to subject, perception of a perceiver, 
 in a word, idea. This is obviously true of the past and the 
 future, as well as of the present, of what is farthest off, as of 
 
 1 E. Tr. (Trubner, 1883). 
 * Schopenhauer, op. cit., beginning.
 
 I A "WORLD" 5 
 
 what is near ; for it is true of time and space themselves, 
 in which alone these distinctions arise. All that in any 
 way belongs or can belong to the world is inevitably thus 
 conditioned through the subject and exists only for the 
 subject. The world is idea." 
 
 The world, then, for each of us, exists in the medium of 
 our mind. It is a sort of building, of which the materials 
 are our ideas and perceptions. 
 
 4. So much for "idea." What do we mean by "world"? The 
 A succession of images passing before us, or rather making wor ' 
 up our consciousness, like a dream, is not a world. The 
 term is very expressive ; it is a favourite word in Shakespeare. 
 When the courtier says 
 
 " Hereafter, in a better world than this, 
 I shall desire more love and knowledge of you," 
 
 he does not mean, as I used to think, " in heaven " ; he 
 means in a better condition of social affairs. In "mad 
 world, mad kings, mad composition," the term means 
 more especially the set of political and family connections 
 within which extraordinary reversals of behaviour have just 
 taken place. Often we use the expression, with a qualifying 
 epithet, to indicate some particular sphere of connected 
 action, " the ecclesiastical world," " the political world," and 
 so forth. Always there seems to be implied the notion of a 
 set of things or persons bound together by some common 
 quality which enables them to act upon each other, and 
 to constitute what is technically termed a " whole," The 
 " world "par excellence, then, ought to mean the one con- 
 nected set of things and persons which we all recognise
 
 6 THE PROBLEM OF LOGIC LEcf. 
 
 and refer to as the same, and as including ourselves along 
 with all who use the word in the same sense. 
 
 Then the " world as idea " means no less than this, that 
 the system of things and persons which surrounds all of us, 
 and which each of us speaks of and refers to as the same 
 for every one, exists for each of us as something built up in 
 his own mind the mind attached to his own body and 
 out of the material of his own mind. 
 
 The 5. Let us illustrate this building up by thinking of the 
 
 world. world, our surroundings, as an animal must be aware of it. 
 The lowest beginnings of sight, for example, give no colour 
 and no shape. An animal in this stage can, probably, only 
 just take warning if a dark object comes between him and 
 the light. Therefore he cannot have the ordered visual 
 image of space definitely stretching away all round him, 
 which is the primary basis of our idea of a world. He can 
 move, no doubt, but there is nothing to make us suppose 
 that he records and co-ordinates the results of his move- 
 ments into anything like that permanent order of objects 
 which must be constructed in some way by a human being 
 even though born blind. Succession, we might say, is 
 much more powerful with animals than co-existence; but 
 we should have to guard ourselves against supposing that 
 this was what we mean by succession, that is, a process 
 definitely recognised as in time, with a connection of some 
 reasonable kind between its phases. For the most part with 
 animals out of sight is out of mind ; if so, the present is not 
 interpreted, enlarged, and arranged with reference to what 
 is not present in time or space by them as it is by us. And 
 therefore the consciousness of a single system of things,
 
 t WHAT "A WORLD" IMPLIES 7 
 
 permanent, and distinct from the momentary presentations 
 of the senses, cannot, in all probability, grow up for them. 
 If so, they have no real world, but only a dream world, 1 /. e. 
 a world not contrasted with the stream of presentation, nor 
 taken as the common theatre of all actions and events. 
 This difference between the world of an animal and that of 
 a human being, is a rough measure of what man does by 
 mental or intellectual construction in making his world. 
 
 6. We have now got the idea of a " world," as a system The world 
 of things and persons connected together, taken to be the ^ e 
 same for oneself at different times and for different minds 
 at the same time, yet existing, for oneself, in the medium of 
 one's individual consciousness. 
 
 We see at once that we cannot stop here. We have 
 really got a contradiction. If the parts of our world are 
 connected with each other, they are not merely dependent 
 upon us, that is, upon the changes of our consciousness. 
 And we all take them to be independent of us, in the sense 
 that we do not suppose the presence or absence of our 
 perception to make any difference to the work! except by 
 the continuance or cessation of our perception of it or of its 
 parts. This is the state of mind in which we practically 
 live, philosophers and all. I do not really take notice of 
 any difference in mode of existence between the wall in 
 front of me, which I see, and the wall behind me, which I 
 
 1 The character of the sensory powers, which are strongest in many 
 animals, contributes to this conclusion. Mr. F. H. Bradley is sure 
 that his dog's system of logic, if he had one, would run, " What exists 
 smells; what does not smell is nothing." The sense of smell can 
 scarcely give rise to the idea of a world of objects. It has hardly any 
 capacity of structural discernment.
 
 8 THE PROBLEM OF LOGIC LECT. 
 
 do not see. While you are in this lecture-hall, if you think 
 of your rooms at home, you think of them as they look, that 
 is, as they would look if you were there to see them. How 
 else, indeed, could you think of them ? This is practically 
 necessary, and therefore, for practical purposes, true. 
 
 But if you take it as a theory, omitting the hypothetical 
 factor, "if I was there to see," you go wrong. You then 
 treat your world as being, outside your consciousness, the 
 same that it is inside your consciousness, without allowing 
 for the withdrawal of your consciousness. You are then on 
 the way to think that the world, as you see, /iear, and feel it, 
 is outside your mind, and that the sight, hearing, feeling, 
 and the ideas born of them, are inside your mind as a sort 
 of faint and imperfect copy of the world which you then call 
 "external," in the sense of outside the mind, 
 
 i. The first position was that of common sense. The 
 second is that of common-sense theory. Common sense is 
 quite justified. It says, " Things affect each other, but the 
 mere presence and absence of our perception does not affect 
 them." For practical purposes we must treat them as 
 being, when unapprehended by our minds, just the same as 
 when apprehended by our minds. This is the first idea or 
 rather postulate for it is not a theoretical idea of objec- 
 tivity. Objective = "independent of our consciousness for 
 practical purposes." 
 
 ii. In describing the second position as that of common- 
 sense theory I do not refer to the doctrine of any regular 
 school of philosophers. There was a Scotch school of 
 philosophy the school of Reid in the eighteenth century 
 commonly called the common-sense school. I will say
 
 I COMMON-SENSE THEORY 9 
 
 below how I think this school was related to the position 
 which I am now describing. But my present purpose is to 
 hit off the simple theory of reality which common-sense 
 people make for themselves when they reflect. Now this 
 theory, in which we all live except when we make a special 
 effort, accepts the distinction between things and the mind. 
 For example, it defines truth as the conformity of ideas to 
 objects. That means something of this kind : the ideas are 
 inside our heads, and the objects are outside our heads. 
 If we are to have knowledge, the objects have to be repre- 
 sented inside our heads, and they get in through the senses. 
 And then you have two similar forms of the world, one 
 outside our heads, which is real, and another like it but less 
 perfect and without solidity or causal power, inside our 
 heads, which is ideal or mental. This is what I call the 
 common-sense theory of the Objective. Like common sense, 
 it assumes that there is a world which the withdrawal of our 
 individual consciousness does not affect, but which persists 
 and acts all the same. Unlike common sense, it lays down 
 an assertion as to the nature of this world, viz. that it is, 
 apart from our consciousness, the same as it is for our con- 
 sciousness. The world in consciousness, it assumes, is 
 subjective, the world out of consciousness is objective, and 
 the former is an imperfect copy of the latter in a feebler 
 material. 
 
 The schools of common-sense philosophy, such as are 
 represented by Locke and Reid, are not quite so simple- 
 minded as the reflection of ordinary common sense, because 
 every systematic thinker sees at once that the question stares 
 him in the face, " If the world outside the mind is copied
 
 i6 THE PROBLEM OF LOGIC LECT. 
 
 by the world inside the mind, how can we ever know whether 
 the copy conforms to the original ? " We are by the hypo- 
 thesis inside the mind; whatever has passed through the 
 senses is inside the mind. We cannot as at present advised 
 get at anything outside the senses or outside the mind. In 
 face of this question, the common-sense philosophies have 
 two courses open. They may start from the idea of things 
 outside the mind, but admit that in passing through the 
 senses the things are in some partial respects transformed 
 as for instance, that they acquire colour, sound, and smell in 
 passing through the senses this is what Locke says. Or 
 again, still starting from the idea of things outside the mind, 
 they may simply assert that perception is of such a nature 
 that it gives us things as they really are. The former was 
 the view of Locke, the latter that of Reid. This latter view 
 obviously might pass into the most extreme idealism, and 
 its interpretation, if it does not so pass, is exceedingly 
 difficult. 
 
 But whatever may have been the view of the historical 
 "common-sense school," 1 the common-sense theory which 
 we all make for ourselves involves a separation between the 
 mind and reality. The objective world is the world as inde- 
 pendent of mind, and independent of mind means existing 
 and acting outside mind, exactly, or almost exactly, as it 
 seems to exist and act before the mind. 
 
 Now this is an absolute cul-de-sac. If the objective is that 
 which is outside perception, the objective is out of our 
 reach, and the world of our perception can never be objec- 
 tive. This is the pass to which we are brought by taking 
 1 See Seth, Scottish Philosophy (Blackwood, 1885).
 
 1 PHILOSOPHICAL THEORY It 
 
 common sense as the guide of theory and not as its 
 material. 
 
 iii. There is no way out but by retracing our steps, and Philoso- 
 avoiding a false turn which we took in passing from common 
 sense to common-sense theory. It was quite true that the 
 world is unaffected by the withdrawal of my individual per- 
 ception and consciousness (except in so far as I acted qua 
 bodily thing in the world) ; but it does not follow from this 
 that if it becomes the object of a consciousness in me, it can 
 be so otherwise than as presented within that consciousness. 
 We must distinguish between the idea that the objective is 
 outside consciousness and therefore not in consciousness, 
 and the idea that the objective can be in the individual con- 
 sciousness, but identified with something beyond the individ- 
 ual consciousness. It may be that consciousness is capable 
 of containing a world, not as a copy of a ready-made original, 
 but as something which it makes for itself by a necessary 
 process, and which refers beyond this finite and momentary 
 consciousness. 
 
 According to these ideas, the objective is, shortly stated, 
 whatever we are obliged to think. This, though it is in our 
 thought, is not considered merely as our thought, or as a 
 train of images or whole of presentation in our minds. That 
 is an artificial point of view, the point of view of psychology, 
 and we must carefully avoid starting from it. But know- 
 ledge refers beyond its mental self, and has no limitation in 
 time or in kind except its own necessity. Thus, I am forced 
 to think, by a certain context of ideas and perceptions, that 
 there is now a fire burning in my study at home. This 
 judgment is not barred by the fact that my mind, as a
 
 12 THE PROBLEM OF LOGIC LECT. 
 
 function attached to my body, is here three miles away. The 
 thought is objective for me, so long as I am obliged to think 
 it. My presence in or absence from the room where the fire 
 is burning has no effect on the question, except as it fur- 
 nishes me with evidence one way or the other. Not only 
 absence in space is no obstacle, but succession in time is no 
 obstacle. My thought, which is here and now, refers con- 
 fidently to what has happened in long intervals of time, if 
 the necessity of consistency obliges it to do so. Thus if I 
 go back to my room and find the fire out and the room very 
 cold, I infer without hesitation to certain acts and events 
 which are needed to explain this state of things. And inter- 
 pretations or explanations of this kind make up my world, 
 which is for me in my thought, but is presented as more than 
 my thought, and cannot be a world at all unless it is more 
 than in my thought. It is in as far as my thought con- 
 structs and presents a world which is more than my momen- 
 tary psychical state, that my thought, and the world as 
 presented to me in it, is objective. The world is not a set 
 of my ideas, but it is a set of objects and relations of which 
 I frame an idea, and the existence of which has no meaning 
 for me except as presented in the idea which I frame. We 
 are not to think of (i) Ideas, and (ii) Things which they 
 represent ; the ideas, taken as parts of a world, are the 
 things. 
 
 We begin to see, then, how the nature of knowledge 
 meets the puzzle which I stated above. How, I asked, can 
 a connected " world," whose parts act on one another quite 
 independently of my perception, be in my individual mind ? 
 I answer that it does not follow, because the world is for me
 
 I MEANING OF "OUTSIDE" 13 
 
 only in my presentation, that my presentation is the only 
 thing which goes on in the world. "What I am obliged to 
 think " may represent a real development depending on laws 
 and a system which is not confined to my individual course 
 of consciousness. The " objective " in this sense is for Logic 
 an assumption, or rather a fact to be analysed. We do not 
 attempt to prove its existence, except in the sense of calling 
 attention to its nature in detail. It will be seen that " out- 
 side the mind" ceases, on this view of objectivity, to have 
 meaning as regards anything that can be related to us. 
 " Outside " is a relation of bodies to one another ; but 
 everything, about which we can so much as ask a question, 
 is so far inside the mind, /. e. given in its continuum of 
 presentation or idea. 
 
 I will recapitulate the three conceptions of the " objective." 
 
 (1) According to practical "common sense " the objective 
 is independent of our consciousness in the sense that the 
 presence or absence of our consciousness makes no differ- 
 ence to the operation of things upon each other. 
 
 (2) According to " common-sense theory " the objective is 
 independent of our consciousness in the sense that the pre- 
 sence or absence of our consciousness makes no difference 
 in the mode of being of things (viz. that the world in 
 consciousness approaches objectivity by resembling or re- 
 producing a similar and quite objective world outside 
 consciousness). 
 
 (3) According to philosophical theory the objective is 
 independent of our consciousness in the sense that it is what 
 we are constrained to think in order to make our conscious- 
 ness consistent w'ith itself. " What we are constrained to
 
 14 THE PROBLEM OF LOGIC LECT. 
 
 think " is not confined, in its reference^ to our thought, or to 
 thought at all. 
 
 7. Thus, for the purposes of Logic, we must turn our 
 usual ideas upside down. We must try to imagine some- 
 thing of this kind. We have all seen a circular panorama. 
 Each one of us, we must think, is shut up alone inside such 
 a panorama, which is movable and flexible, and follows him 
 wherever he goes. The things and persons depicted in it 
 move and act upon one another ; but all this is in the pano- 
 rama, and not beyond it. The individual cannot get outside 
 this encircling scenery, and no one else can get inside it. 
 Apart from it, prior to it, we have no self; it is indeed the 
 stuff of which oneself is made. Is every one's panorama 
 exactly the same? No, they are not exactly the same. 
 They are formed round different centres, each person differ- 
 ing from all the others by individual qualities, and by his 
 position towards the points and processes which determine 
 his picture. For and here is the remarkable point every 
 one of us has painted for himself the picture within which he 
 is shut up, and he is perpetually painting and re-painting it, 
 not by copying from some original, but by arranging and 
 completing confused images and tints that are always appear- 
 ing magically on his canvas. Now this magical panorama, 
 from which the individual cannot escape, and the laws of 
 which are the laws of his experience, is simply his own mind 
 regarded as a content or a world. His own body and mind, 
 regarded as things, are within the panorama, just as other 
 people's bodies and minds are. The whole world, for each 
 of us, is our course of consciousness, in so far as this is 
 regarded as a system of objects which we are obliged to
 
 I MIND AND WORLD 15 
 
 think. Not, in so far as it really is a. system, for an onlooker, 
 say for a psychologist. For no doubt every child's mind, 
 and every animal's mind, is a working system of presenta- 
 tions, which a psychologist may study and analyse from 
 without. Consciousness is consciousness of a world only in 
 so far as it presents a system, a whole of objects, acting on 
 one another, and therefore independent of the presence or 
 absence of the consciousness which presents them. 
 
 I take another very rough metaphor to explain this curious 
 contrast between my mind as a working system, observable 
 from without, and belonging to my individual body dis- 
 tinguishable from the thirty or forty quite different minds 
 belonging to the thirty or forty persons in this room and 
 my mind as a continuum of presentations which includes, 
 as objects, itself, and all the other minds in the room, and 
 the whole world so far as I have any conscious relation to 
 it whatever. 
 
 All of us are familiar with the appearance of a microscope 
 ready adjusted for use, with its little lamp, its mirror and 
 illuminating apparatus under the stage, with a specimen 
 on the stage under the object-glass, its object-glass and its 
 eye-piece. Any one who understands the working of a 
 microscope finds this a most suggestive spectacle. He 
 follows in his imagination the light as it comes from the 
 lamp to the mirror, through the illuminating lenses, through 
 the transparent specimen, through perhaps a dozen lenses 
 arranged as an object-glass within an inch of distance, 
 through the eye-piece and into the observer's eye. Give him 
 the parts, lenses, prisms, and mirrors into his hands, and he 
 will test them all, and tell you exactly how they work. This
 
 16 THE PROBLEM OF LOGIC LECT. 
 
 scientific onlooker may be compared to the psychologist 
 looking at another man's mind. He sees it as a thing 
 among other things, a working system of parts. 
 
 But there is one thing that the mere onlooker cannot see. 
 He cannot see the object. That can only be seen by look- 
 ing through the tube. And every one has felt, I should 
 think, the magical transformation, suggestive of looking 
 through another man's eye and mind, which occurs when 
 you put your eye to the eye-piece of an optical instrument. 
 The outside world of other objects, the tube, the stage, the 
 mirror, the bystanders, the external light, all disappear, and 
 you see nothing but the field of vision and whatever dis- 
 tinctly pictured structure may be displayed within it. The 
 observer who looks through the tube may be compared with 
 each one of us as he contemplates his own world of know- 
 ledge and perception. This is a thing that no one else can 
 ever do. 
 
 The metaphor, indeed, breaks down, in so far as each of 
 us is able to observe the history and character of his own 
 mind as an object within the field of presentation which is 
 before his mind. Of course such a metaphor must break 
 down at some point. But it remains true that the mind, 
 while directly observing its field of objects, cannot observe 
 its own peculiarities, and when turned, as we say, upon 
 itself, is still observing only a part of itself. It remains true 
 that my mind contains the whole presented world for me, 
 and is merely one among thousands of similar mind-things 
 for you. 
 
 Thus, I repeat, the world for each of us is our course of 
 consciousness, looked at in that way in which it presents a
 
 I CORRESPONDING WORLDS 17 
 
 systematic, organised picture of inter-acting objects, not in 
 that way in which it is a stream of ideas and feelings, taking 
 place in our several heads. In the former point of view it 
 is the world as our idea ; in the latter point of view it is 
 simply the consciousness attached to our body. We might 
 soon puzzle ourselves with the contradictions which arise if 
 we fail to distinguish these points of view. In one sense 
 my mind is in my head, in the other sense my head is in my 
 mind. In the one sense I am in space, in the other sense 
 space is in me. Just so, however rough the metaphor, from 
 one point of view the microscope is one among a host of things 
 seen from the outside ; from the other point of view all that 
 we see is in the microscope, which is itself not seen at all. 
 
 It is in this latter sense that our mental equipment is 
 looked at, when it is regarded as knowledge ; and it is in 
 this sense that it forms a panorama which absolutely shuts 
 in every one of us into his own circle of ideas. (It is not 
 implied, we should carefully observe, that his ideas or experi- 
 ence are in any way secondary to his self, or separable from 
 it, or an adjective of it.) Then how does it happen ^that our 
 separate worlds, the panoramas which we construct, do not 
 contradict one another? 
 
 The answer is, that they correspond. It is this conception 
 from which we must start in Logic. We must learn to 
 regard our separate worlds of knowledge as something con- 
 structed by definite processes, and corresponding to each 
 other in consequence of the common nature of these pro- 
 cesses. We know that we begin apart. We begin in fact, 
 though not conscious of our limits, with feelings and fancies 
 and unorganised experiences which give us little or no 
 
 c
 
 1 8 THE PROBLEM OF LOGIC LECT. 
 
 common ground and power of co-operation with other 
 people. But as the constructive process advances, the corre- 
 spondence between our worlds is widened and deepened, 
 and the greater proportion of what we are obliged to think 
 is in harmony with what other people are obliged to think. 
 Now of course this would not be so unless reality, the whole 
 actual system in which we find ourselves, were self-consistent. 
 But more than that, it would not be so unless the nature of 
 intelligence were the same in every mind. It is this common 
 nature of intelligence, together with its differentiated adapta- 
 tions to reality, that we have to deal with in Logic. 
 
 Thus the separate worlds, in which we are all shut up, 
 must be considered as corresponding so far as they are 
 objective, that is, so far as they approach what we are ulti- 
 mately obliged to think. I say "corresponding," because 
 that is the term which expresses the relation between systems 
 which represent the same thing by the same rules, but with 
 different starting-points. Drawings in perspective of the 
 same building from different points of view are such corre- 
 sponding systems; the parts represented answer each to 
 each, but the same part is near or large in one drawing, and 
 distant and small in another ; not, however, by chance, but 
 as a definite consequence of the same laws. Our separate 
 worlds may be compared to such drawings : the things in 
 them are identified by their relations and functions, so that 
 we can understand each other, i. e. make identical references, 
 though my drawing be taken from the east, and yours from 
 the west. The things do not look quite the same in our 
 different worlds ; besides being taken from different stand- 
 points, both drawings are imperfect and incorrect. But so
 
 i SUBJECTIVE IDEALISM 1$ 
 
 long as we can make out the correspondence, we have a 
 basis for co-operation and for discussion. Logic shows us 
 the principles and processes by which, under the given 
 influences, these drawings are constructed. 
 
 8. If we merely hold to the doctrine of separate worlds, Subjective 
 without insisting upon their correspondence with each other c 
 and with reality, we fall back into the position of subjective 
 idealism, which is a natural completion of common-sense 
 theory, when, instead of turning round to retrace its path, it 
 runs deeper into the cul-de-sac. It is a very obvious reflec- 
 tion, that each of us is shut up within his own mind, and 
 much easier to grasp than the reason for assuming a real 
 system which appears differently, though correspondingly, in 
 the centres of consciousness which are ourselves. We 
 cannot get at anything but in terms of consciousness ; how 
 can we justify the assumption that our consciousness of a 
 world of objects is rooted in reality, e.g. that objects may 
 rightly be treated as persisting and inter-acting when our 
 personal consciousness is withdrawn? And if we once 
 doubt this, then why should we assume that our ideas need 
 be or tend to be consistent with themselves and each other, 
 as for the time they apparently are ? 
 
 Subjective Idealism necessarily arises if the common- 
 sense theory of two worlds, the real outside the mind, and 
 the ideal, copying it, within the mind, is pushed to its con- 
 clusion. The real, outside the mind, being inaccessible, 
 falls away. The arguments of this Idealism, as Hume said, 
 " admit of no answer and produce no conviction." * But I 
 
 1 Vol. iv. p. 176 (ed. of 1854), Inquiry concerning Human 
 Understanding, sect. 12.
 
 20 THE PROBLEM OF LOGIC LECT. I 
 
 mention the idea, because I do not think that any one can 
 really understand the problem of Logic, or indeed of science 
 in general, without having thoroughly thought himself into 
 the difficulty of Subjective Idealism. It is necessary to be 
 wholly dissatisfied with common-sense theory, and with the 
 notion of a ready-made world set up for us to copy in the 
 mind, before the logical analysis of intellectual construction 
 can have interest or meaning for us. And to produce this 
 dissatisfaction is the value of Subjective Idealism.
 
 LECTURE II 
 ''JUDGMENT" AS THE CONSCIOUSNESS OF A WORLD 
 
 i. THE last lecture was devoted to explaining the dis- Defect of 
 tinction between the stream of presentations and the world 
 as it is for knowledge. I ended by calling attention to the 
 theory known as " Subjective Idealism." This, I said, has 
 the merit of forcing upon us the question, " How do we get 
 from mind to reality ? How do we get from subjective to 
 objective ? " For we have always to remember that our 
 knowledge is within consciousness, though it may refer 
 outside it. 
 
 On the other hand, Subjective Idealism has the defect of 
 confounding the very distinction which we took so much 
 trouble to make plain. Its essence lies in ascribing to the 
 world of knowledge properties which are only true of the 
 stream of presentation. It is quite true that the actual 
 presentations of this room, which each of us has in his head 
 at this moment, are all different from each other, and 
 different from any which we have had before, and shall ever 
 have again. Every minute, every second, they differ ; they 
 are perishing existences, wholly mental, and each of them 
 when past is irrecoverably gone. That is the property of a 
 presentation within the course of consciousness. It is a 
 particular perishing existence.
 
 22 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 But Subjective Idealism says, " Because these mental 
 existences are particular perishing existences, and all know- 
 ledge consists in them as its medium, therefore the object 
 of knowledge is nothing beyond these mental facts, and is 
 not rooted in a permanent system 1 independent of our 
 mental connections." Here we must check the inference, 
 and reply, "No, it does not follow. The presentations 
 which themselves come and go may refer to something in 
 common, and through them all we may become aware of 
 something that is not wholly in any of them." In other 
 words, there is in Knowledge no passage from subjective to 
 objective, but only a development of the objective. 
 
 2. Therefore we say, coming closer to our subject, that 
 " Knowledge is the medium in which our world, as an inter- 
 related whole, 2 exists for us." This is more than saying that 
 it exists in mind or presentation, because the mere course of 
 consciousness need not amount to Knowledge. A world, 
 that is, a system of things acting on one another, could not 
 exist merely in the course of our ideas. But Knowledge, we 
 said, is the mental construction of reality. It consists of 
 what we are obliged to assert in thought, and because we 
 are all obliged to think assertorily according to the same 
 methods, the results of our thinking form corresponding 
 systems systems that correspond alike to each other and 
 to reality. (I may be asked, does not this agreement of 
 
 1 Our estimate of Berkeley's view must depend on the degree in 
 which we judge him to have identified the Deity with, or separated 
 Him from, a permanent and universal system. The statement in the 
 text applies fairly to Hume. 
 
 2 The words italicised make a reservation in favour of feeling, which 
 has its own form of reality, but is not relational.
 
 ii KNOWLEDGE IS A JUDGMENT 23 
 
 our knowledge depend on the agreement of the physical 
 stimuli supplied to us by nature, as well as on the homo- 
 geneousness of our intelligences ? The answer is, that these 
 stimuli, or nature, have no priority in Knowledge. Their 
 identity is merely a case or consequence of the identity of 
 our experience as a whole. We are regarding nature as a 
 system developed in experience, not as an unknown some- 
 what behind it. To suppose that solid or extended existence 
 somehow comes before and accounts for everything else, is 
 a form of the common-sense theory we have dismissed. 
 Knowledge and Truth have their limitations as forms of 
 Reality, but an appeal to solidity or extension will not 
 furnish the required supplementation.) 
 
 3. All that we have been saying about Knowledge is Know- 
 
 i -,-r ledge is in 
 
 summed up in the sentence, " Knowledge is a judgment, t he form of 
 
 an affirmation." We need not trouble ourselves yet about J ud S ment - 
 negation. We all know what affirmative assertion is, and 
 it is near enough for the present to say that all knowledge 
 is judgment in the sense of affirmative assertion. 
 
 I will explain how we sum up all we have said of know- 
 ledge by calling it a judgment. 
 
 Judgment or affirmation always implies three properties, 
 though they are not always recognised. 
 
 It is (a) necessary, (/3) universal, and (y) constructive. 
 
 (a) Judgment is necessary. In saying this, we express all Judgment 
 that we said about the objectivity of the world in know- m 
 ledge. " Objective " meant, we concluded, what we are 
 obliged to think. And judgment is necessary, because it 
 expresses what we are obliged to think; obliged, that is, 
 not as we are obliged to feel pain, as an unexplained and
 
 24 "JUDGMENT," CONSCIOUSNESS OF A WORLD I.ECT. 
 
 isolated fact, but obliged by a necessity operative within 
 the movement of our consciousness, though not, of course, 
 theoretically recognised as necessity in common thinking. 
 Thus, in the simplest phases of Judgment, necessity does 
 begin to approach the kind of necessity by which we feel 
 pain or are visited by persistent irrational associations. 
 
 We can trace an explicit sense of necessity in any 
 scientific matter, or in any doubtful and complex matters in 
 which we are aware of our own reflections. We constantly 
 hear and read such phrases as, " I am unable to resist the 
 conclusion " ; "I am forced to believe " ; "I am driven to 
 think " ; "I have no alternative but to suppose." These 
 are every-day phrases in controversy and in theoretical dis- 
 cussion. And what they all mean is just what was insisted 
 on in the last lecture ; the objective or real for us is what 
 we are obliged to think. Given our perceptive state and our 
 mental equipment, the judgment follows. 
 
 In trivial or simple judgments this necessity is harder to 
 observe within consciousness, and approaches more and 
 more to the mere constraint exercised upon us by physical 
 reality. In a judgment of mere sensuous comparison, such 
 as a " colour-match," the necessity is not that of an intel- 
 lectual system, but almost that of a feeling which we cannot 
 dispel. The chief intellectual labour is here negative, and 
 consists in precautions to remove all disturbing influences, 
 both mental and material, so as to let the perception operate 
 freely on the mind. But yet here is necessity ; we never for 
 a moment think that we can modify the result ; our aim is 
 simply to distinguish from all others the particular strand of 
 necessity by which we desire to be guided.
 
 n NECESSITY 25 
 
 It is easy for an observer to detect intellectual necessity 
 in judgment, even where the judging subject is wholly un- 
 reflective. If you contradict an obvious judgment made by 
 an uneducated man, he will no doubt be quite unable to 
 point out the intellectual necessity which constrains him to 
 it, /. e. to argue in support of it ; but he will be bewildered 
 and probably indignant, which shows that, unknown to him- 
 self, his whole intellectual existence is really impeached by 
 impeachment of a necessary conclusion from it. Many 
 people cannot see the difference between impeaching their 
 argument and impeaching their veracity ; and this confusion 
 arises, I presume, from a just feeling that their whole mind 
 is on its trial in the one case as in the other, although they 
 do not distinguish between the forms of its action which 
 are concerned. We are told, indeed, in formal logic, that 
 ordinary statements of fact do not claim necessity ; but this 
 merely arises from confining necessity to explicit necessity 
 expressed in a special grammatical form. 
 
 But, it may be objected, we do not always feel that every 
 trivial judgment emanates from and so implicates our whole 
 mental constitution and equipment. If I say to a friend, 
 " I saw you at Charing Cross yesterday," and he says, " No, 
 you could not, for I was out of town," then, unless I was 
 very certain indeed, I should admit having made a mistake, 
 and think no more about the matter. That only means, 
 (i) that the unity of the mind is not thoroughly complete 
 there are many more or less detached systems in the mind, 
 and one of them may not be very deeply inwrought in the 
 whole intellectual frame ; and (2) the necessity of thought 
 may itself modify the certainty of the facj^&^L-L Jajow that 
 
 ;f-li
 
 26 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 a mistake of identity is quite a common thing, and this 
 knowledge co-operates with my friend's denial. 
 
 But in any perceptive judgment, however unimportant its 
 immediate content, if it is clear and persistent, a contra- 
 diction is a most serious thing. There is a well-known form 
 of bewilderment connected with the judgment of direction ; 
 if you forget or do not know of a turn that you have taken, 
 and come out, for example, on familiar ground from the 
 North when you think you are coming on it from the South, 
 so that objects have the reverse position of what you ex- 
 pected, then, supposing that you cannot explain the contra- 
 diction, the result is sometimes a very grave perplexity ; 
 some men are quite unhinged by it for the moment, and 
 a psychologist in France l has given it a new name, " Vertigo 
 of Direction." This again shows how your whole intel- 
 lectual nature is staked upon the most trifling perception, 
 and if you seem to be forced to a flat contradiction even in 
 the simplest judgment you are almost " beside yourself." 
 
 (/3) Judgment is universal. There are different senses of 
 " universal " as of " necessary." We are now speaking only 
 in the widest sense, in which universality is a property of all 
 judgment whatever. If we assume that all our intellectual 
 natures are the same, then to be universal is a mere con- 
 sequence of being necessary. I not only feel that my 
 judgment is inevitable for me, but I never think of doubting 
 that, given the same materials, it is obligatory for every other 
 intelligent being. If some one disagrees with a judgment 
 of mine, I try to put the case before him as it is in my 
 mind. And I am absolutely sure that if I could do so, he 
 i M. Binet. See Mind, x. 156.
 
 II UNIVERSALITY 27 
 
 would be obliged to judge as I do. If it were not so, we 
 should never think of arguing. We should simply say, 
 "Perhaps his mind is differently constituted from mine," 
 as, in fact, with reference to special sets of dominant ideas, 
 and to special provinces of experience, we often do say. 
 But these we regard as hindrances, imperfections, accidents. 
 We do not doubt that the system of reason is active in him 
 as in us. 
 
 And thus, as reason is essentially a system, the universal- 
 ity of judgment involves something more. We not only 
 think that our judgment is obligatory upon every one else, 
 in as far as they have the same materials, but we think that 
 it must be consistent with the judgments of all other persons, 
 just as much as with our own. If it is inconsistent with 
 any other judgment, we think that one of the two must be 
 wrong; that is, we will not admit the possibility that the 
 real world, as others construct it, is out of harmony with the 
 real world as we construct it. 
 
 Thus knowledge, being judgment, is necessary and 
 universal, and in the widest sense this is true of all 
 judgments. 
 
 (y) These are two properties of the Judgment, but they Judgment 
 do not tell us what it is. We shall of course examine its 
 nature more fully in the later lectures. At present we need 
 only think of it as affirmation. This may be simply de- 
 scribed as "pronouncing the interpretation of our percep- 
 tions to form one system with the data of our perceptions." 
 We may at once admit the distinction between data and 
 interpretation to be only relative. Its relativity is the 
 consequence of the constructed or so to speak artificial
 
 28 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 character of our real world. We can get at no data un- 
 qualified by judgment. 
 
 We may take as an example our perception of things in 
 space. How much of what we see is given in present 
 sense-perception ? This is a question to which there is no 
 definite answer. We do not know what the presentations 
 of vision were like before we had learnt to see as a fully 
 conscious human being sees. We have no right to assume, 
 that after we have learned to see in this way the actual 
 sense-presentation remains the same as it was in a different 
 stage of our visual education. We can give no precise 
 meaning in the way of a time-limit to the presentness of 
 perception. But we know this much, that it takes a long 
 time and many kinds of experience to learn to see as an 
 educated human being sees, and that this acquired capacity 
 is never at a stand-still, but is always being extended or 
 diminished according to the vitality, growth, or atrophy of 
 our apperceptive masses. There is always a certain element 
 of amplification or interpretation, which by experience or 
 attentive introspection we can eliminate from the data 
 apparently forced upon us by reality, although these 
 data themselves are modified through and through both 
 by habitual interpretation, and by the very defining at- 
 tention which aims at eliminating all amplification from 
 them. 
 
 But yet the whole of sense-perception has a peculiar 
 quality in being present. Artificial though it is, it yet, 
 relatively speaking, contains an irreducible datum. It is 
 distinguishable from everything which is not present. It is 
 pervaded by something which we cannot reduce to Intel-
 
 II INTERPRETATION 29 
 
 lectual relation, though if we withdrew from it all that is 
 relation, the apparent datum would be gone. 
 
 Now Knowledge is the affirmation or judgment which 
 identifies the constructive interpretation of our present per- 
 ception with the reality which present perception forces upon 
 us. This is clear enough to begin with, but will have to 
 be modified below to suit the more circuitous or mediate 
 types of Judgment. 
 
 I take two examples, one from sight and one from sound. 
 
 Here is a table. In common language we should all say, 
 " We see that is a table." The expression is quite correct, 
 because human seeing is a judgment. But yet, if you were 
 asked to reduce your perception to terms of sight pure and 
 simple I mean of visual sensation why, unless you were 
 an analytic psychologist or a very skilful artist, you would 
 not be able to do it. To speak of one point only, you 
 would have to eliminate the attribute of depth and distance. 
 That is all, so far as mere vision is concerned, your theory 
 and your interpretation. The problem for an artist is to 
 get back, at his high plane of perceptive power, to what in 
 theory would be the lower plane. He has to re-translate 
 his perception of a thing in space into a flat coloured surface. 
 The difference between his flat picture and a real object in 
 space is a rough measure of the difference made by inter- 
 pretation or implication in the datum of sense-perception 
 when we say, judging by sight only, "That is a table." 
 All the experiences of touch and motion, from which we 
 have learned to perceive the solidity of the object, are, 
 theoretically speaking, put into the judgment by us. They 
 are not given by the eye alone, although we cannot now
 
 30 "JUDGMENT," CONSCIOUSNESS OF A WORLD LEG*. 
 
 separate them from that which is given by the eye alone. 
 For the artist's flat picture, which I used as an illustration, 
 is not a stage in our visual education. Our visual education 
 has proceeded pari passu with our education by touch and 
 motion ; and we saw objects in space as solids, long before 
 we reflected that for the eye alone a coloured surface would 
 naturally appear as flat. 1 
 
 But this impossibility of getting at an original datum only 
 shows how entirely we are right in saying that our world is 
 constructed by judgment. For the process of interpretative 
 amplification passes quite continuously from the unconscious 
 to the conscious ; and every definitely expressed judgment, 
 though perfectly homogeneous with the processes which 
 have qualified its datum, and though it may fall wholly 
 within the maximum of what in ordinary parlance we should 
 call a simple given perception, contains an identification of 
 some ideal element, enlargement, or interpretation, with 
 that relatively given element which reveals itself through a 
 peculiar quality of presentness pervading the "given" 
 perception. 
 
 In the example " That is a table," the unity of judgment is 
 so well shown that the identification becomes almost unreal. 
 In fact, we never judge except to satisfy an interest, and so 
 simple a judgment used as an example, apart from any 
 context which could explain the need for it, has an air of 
 unreality. You may hear a child make such a judgment 
 
 1 The view that depth is a visual datum in the same sense as breadth 
 seems to me in flagrant contradiction with experience. But for our 
 present purpose the question is only one of degree, as no one maintains 
 that either depth or breadth are seen without education as an adult sees 
 them.
 
 it INTERPRETATION 3i 
 
 constantly in the sheer pleasure of recognition. An adult 
 would never make it explicitly unless in some particular 
 context ; but it is made, as I shall maintain below, by the 
 mere glance of his eye which takes in the table as a real 
 object in a real world of space. Its appearance to the eye 
 is in this case the datum, while the interpretation consists 
 in construing this appearance as a solid individual existence 
 in space. 
 
 We will look at an example in which the discrimination 
 of elements is easier. Take the affirmation, "That is a 
 cab," assuming it to be made from merely hearing a sound. 
 In this we can much more nearly separate the datum or 
 minimum of sense from our enlargement or interpretation 
 of it, and we know that our interpretation is liable to be 
 wrong; that is to say, the reality into which we ought to 
 construe the sound may be some other kind of vehicle, and 
 not a cab. Now compare this with the affirmation, " That 
 (which I see) is a cab." This judgment of sight-perception, 
 though its terms are more inextricably interwoven, has just 
 the same elements in it as the judgment of sound-perception, 
 "That (which I hear) is a cab." In the sound-perception 
 the structure is quite plain. A particular complex quality 
 in the sound suggests as its objective explanation, what is 
 perfectly distinguishable from it in thought, the movement 
 of a cab on a particular kind of pavement. The quality of 
 the sound, its roughness, loudness, increase and decrease, 
 all form points of connection with the sound of a cab as 
 we know it, and with the speed, weight, etc. of such a 
 vehicle. But it is quite easy to consider the sound in itself 
 apart from its interpretation, and we sometimes feel the
 
 32 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 interpretation to be more immediate, and sometimes more 
 inferential. We sometimes say, " I hear a cab," just as we 
 say, "I see one," but in case of sound we more often 
 perhaps say, "That sounds like " such and such a thing, 
 which indicates a doubt, and the beginning of conscious 
 inference. 
 
 Thus we see how continuous is the mental construction 
 of reality. From our unreflective education in seeing, hear- 
 ing, and touching, to the explicit judgment of the trained 
 observer, which in its turn passes readily into inference, 
 there is no definite break. Once the idea of reality, or of 
 a world, is applied in practice (I do not say reflectively 
 grasped), there is no further difficulty in principle throughout 
 the whole process of its construction. 
 
 We may then sum up so far : our knowledge, or our 
 world in knowledge, exists for us as a judgment, that is, as 
 an affirmation in which our present perception is amplified 
 by an ideal interpretation which is identified with it. This 
 interpretation or enlargement claims necessity or universality, 
 and is therefore objective as our world, /. e. is what we are 
 obliged to think, and what we are all obliged to think. The 
 whole system in process of construction, viz. our present 
 perception as extended by interpretation, is what we mean 
 by reality, only with a reservation in favour of forms 
 of experience which are not intellectual at all. Every 
 judgment then affirms something to be real, and therefore 
 affirms reality to be defined, in part, by that something. 
 Knowledge exists in the form of affirmations about reality. 
 And our world as existing for us in the medium of knowledge 
 consists, for us, of a standing affirmation about reality.
 
 II WAKING CONSCIOUSNESS 33 
 
 4. This standing affirmation about reality maybe described Continu- 
 in other words as " the continuous affirmative judgment of the at j on O f 
 
 waking consciousness." In the common logic-books you will waki "g 
 
 . conscious- 
 
 find judgment treated only as the " proposition," that is, as an ness. 
 
 assertion made in language. That is a very convenient way 
 of treating the judgment, and is not false, if you remember 
 that the proposition, that is, the assertory sentence, is rather 
 a translation of the judgment than the judgment itself. But 
 the judgment expressed in a proposition is always some one 
 definite assertion, with a limited subject and predicate. 
 We shall speak of the judgment in this sense the usual 
 sense later. But to-day I want to describe the judgment 
 in a more extended sense, that is, as co-extensive with the 
 waking human consciousness, so far as aware of a world. 
 
 If judgment consists in the extension of our perceptions 
 by an interpretation considered as equally real with their 
 content, it clearly is not confined to the particular facts and 
 truths which from time to time we utter in language. And 
 more than this, everything that we do definitely utter, im- 
 plies a great deal which is not definitely uttered. If I say, 
 " I have to catch the train at Sloane Square to go down to 
 Essex Hall," I only mention the reality of one train, one 
 square, and one building. But my assertion shades off into 
 innumerable facts, the equal reality of which as elements in 
 my world is necessary to make this judgment intelligible and 
 true. It implies the real existence of the underground rail- 
 way, which implies that of London, and therefore that of 
 the surface of our globe in a certain definite order, and of 
 the civilised world. It implies the reality of this building 
 and of the meetings which we hold in it, of the University 
 
 D
 
 34 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 Extension system, and of my own life and habits as enabling 
 me to take part in the work of that system. Only a part of 
 this is in the focus of my attention as I judge; but the 
 whole is a continuous context, the parts of which are in- 
 separable ; and although I do not affirm the whole of it in so 
 many words, when I say that I am coming down here by 
 train this evening, yet if any part of it was not affirmed the 
 rest would, so to speak, fall to pieces, /. e. would lose relations 
 in the absence of which its meaning would be destroyed. 
 Other detached parts of one's life and knowledge may seem 
 to be separable from the content of such a judgment ; but 
 on looking closely we see that this is not the case. So long 
 as we are awake, our whole world is conceived as real, and 
 forms for us a single immense affirmation, which hangs from 
 present perception, and shares its constraining power. My 
 present perception is the illuminated spot, and shades off 
 gradually into the rest which forms the background, receiving 
 from this background its organised systematic individuality, 
 while impressing upon it a relation to its own sensuous pre- 
 sentness. We have only to reflect, in order to illustrate this 
 connection, on the way in which the idea of London forms 
 a determining background for the present perception of this 
 room, while on the other hand it is perceived by us as real 
 in our presentation of this room. 
 
 And indeed the simplest example of what I am pointing 
 out is the arrangement of objects and places in space. The 
 visual picture which each of us forms of this room is 
 certainly an affirmative judgment. It is a judgment because 
 it consists of ideas affirmed as true of reality. As we look 
 round, all the distances of the objects and the walls from
 
 il SENSE-PERCEPTION 34 
 
 each other, and their shapes and position, seem to be im- 
 printed on our minds without an effort. But really they are 
 conclusions from long education in the art of seeing and 
 from the experience of the other senses. They are an en- 
 largement or interpretation of sense-perception, taken as real, 
 /. e. as forming a system which is one with the content of 
 sense-perception, and touches us through sense-perception, 
 and therefore they exist for us in the form of Judgment. 
 And, as I described before, our whole world, both of things 
 in space and of our own history and circumstances, is also 
 affirmed as the background implied in this picture. That 
 is to say, it is all connected together, it is all taken as equally 
 real, and it is all vouched for by its connection with what is 
 given to us in perception. What do we mean by saying 
 that the Antipodes are real, and implied in my perception of 
 this room ? We mean that they are an element, necessary 
 to educated thought, in the same system with which I am in 
 contact at this moment by sight, touch, and hearing, the 
 system of reality. And though I may not have explicitly 
 thoughts of them since entering the room till now, yet, if 
 they were no part of my affirmed system of ideas, my per- 
 ception of anything in space would be quite different from 
 what it is. 
 
 This sense of necessary connection is confined, I think, to 
 our waking consciousness. Of course there are degrees 
 between waking and dreaming ; but I should be inclined to 
 set up the presence or absence of judgment as a very fair 
 test of those degrees. We say that a man is awake in as far 
 as he is aware (i.) of a reality which is not his mere course 
 of consciousness, and (ii.) of the same reality of which other
 
 36 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 people are aware ; /. e. in as far as he identifies his present 
 perception with a reality, and that the real reality. It is 
 said that surprise, i. e. the sense of conflict between expecta- 
 tion and the reality, is absent in dreams, and in a very 
 remarkable passage ^Eschylus identifies the life of the savage 
 in his (imaginary) primitive state with a dream-life, considered 
 as a life of sensuous presentation, in which the interpretative 
 judgment of perception was absent. With extraordinary 
 profoundness, in portraying this all but animal existence, he 
 strikes out all those relations to the objective world by which 
 man forms for himself a system that goes beyond the present, 
 so as to leave the stream of presentation without any back- 
 ground of organised reality. 1 
 
 1 I quote from Mrs. Browning's Translation of the Prometheus Bound, 
 which seems close enough for the present purpose. 
 
 " And let me tell you, not as taunting men, 
 But teaching you the intention of my gifts, 
 How first, beholding, they beheld in vain, 
 And hearing, heard not, but, like shapes in dreams, 
 Mixed all things wildly down the tedious time, 
 Nor knew to build a house against the sun 
 With wicketed sides, nor any woodwork knew, 
 But lived, like silly ants, beneath the ground, 
 In hollow caves unsunned. There came to them 
 No steadfast sign of winter, nor of spring 
 Flower-perfumed, nor of summer full of fruit, 
 But blindly and lawlessly they did all things, 
 Until I taught them how the stars do rise 
 And set in mystery, and devised for them 
 Number, the inducer of philosophies, 
 The synthesis of letters, and besides, 
 The artificer of all things, Memory, 
 That sweet muse-mother." Pr., v. 445, ff. 
 
 The expression "seeing saw not, and hearing heard not" appears to 
 suggest the contrast of presentation and objective perception.
 
 ii INSANITY 37 
 
 It may be asked, " Why should not a man form for himself 
 a system which interprets his own perception, but is discre- 
 pant from the system of every one else ? Should we in that 
 case count him as awake ? " Yes, he would be awake, but 
 he would be mad. Suppose, being a common man, he 
 interprets all his perceptions into a system which makes him 
 out to be King of England ; in such a case he cannot be 
 set down as dreaming, because he is alleging a connection 
 which goes beyond his present perception, and has, osten- 
 sibly, been propounded as an interpretation of it into a 
 systematic order of things. He has in short a world, but he 
 has broken away from the world, and therefore we pronounce 
 him mad. A completely new vision of life may cause a man 
 to be thought mad. 1 
 
 The whole world, then, of our waking 2 consciousness may 
 be treated as a single connected predicate affirmed as an 
 enlargement of present perception. All that we take to be 
 real is by the mere fact of being so taken, brought within an 
 affirmative judgment. 
 
 5. To further illustrate the relation of what, in our perma- Compari- 
 nent judgment, is distinctly thought, what is dimly thought, 
 and what is implied, let us look for a moment at what we 
 may call " the world as will." This is not the doctrine of 
 Schopenhauer in his work, The World as Will and Idea, 
 
 1 See Browning's Epistle of Karshish. 
 
 2 I do not mean to say that judgment and consciousness of a world 
 can be wholly absent in dreams, and often no doubt they are distinctly 
 present. But in those dreams, in my own experience the normal ones, 
 which leave behind a mere impression that unrecognisable images have 
 passed before the mind, judgment and the sense of reality must surely 
 have all but disappeared. I am inclined to think that dreams are very 
 much rationalised in recollection and description.
 
 38 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 although the two conceptions have something in common. 
 His is a metaphysical doctrine, in which he says that the 
 fundamental reality of the Universe must be conceived as 
 Will. We have nothing to do with that. We are speaking 
 merely of what the world is for us, and for us it is not only 
 a system of reality but a system of purposes. Our world of 
 will is a permanent factor of our waking consciousness, just 
 as much as our world of knowledge. Now our will is made 
 up of a great number of purposes, more or less connected 
 together, just as our knowledge is made up of a great number 
 of provinces and regions more or less connected together. 
 And just as in our knowledge at any moment much is clear, 
 much is dim, much is implied, and the whole forms a 
 continuous context, so it is with our purposes. 
 
 When, for example, one stands looking at a picture, one's 
 immediate conscious purpose is to study the picture. One 
 also entertains dimly or by force of habit the purpose to 
 remain standing, which is a curious though common instance 
 of will. We do not attend to the purpose of walking or 
 standing, yet we only walk or stand (in normal conditions of 
 mind) as long as we will to do so. If we go to sleep or 
 faint, we shall fall down. Purpose, like judgment, is confined 
 to the waking consciousness. 
 
 But further ; the purpose which one entertains in standing 
 to look at a picture is not really an isolated pin-point of will. 
 It is uppermost in the mind at the moment in which we 
 carry it out, but it is only the uppermost stratum, or perhaps 
 rather the present point attained upon a definite road, within 
 an intricate formation or network of purposes, which taken 
 together constitute the world of will. The purpose of looking
 
 II THE CONTEXT OF PURPOSE 39 
 
 at a picture shades off into the more general purpose of 
 learning to take pleasure in what is good of its kind, which 
 is again set in a certain place within the conception of our 
 life and the way in which we desire to spend it, and our 
 purposes throughout every particular day are fitted into one 
 another, and give a particular setting and colour to each 
 other, and to each particular day, and week, and year. 
 
 Now less or more of all this may be clearly in the mind 
 when we are carrying out a particular momentary aim. But 
 it is quite certain that in a human life the particular moment- 
 ary aim derives its significance from this background of 
 other purposes ; and, if they were to fall away, the distinct 
 momentary purpose would change its character and become 
 quite a feeble and empty thing. 
 
 Thus we have, in our world of will, a parallel case which 
 illustrates the nature of our world of knowledge. There is 
 the clear will to look at the picture, the dim will to continue 
 standing, and the implied will to carry out certain general 
 aims, and follow a certain routine or course of life, which 
 gives the momentary purpose its entire setting and back- 
 ground. 
 
 I have spoken of the will in order to illustrate the 
 judgment, because the dim and implied elements are 
 perhaps more easy to observe in the case of the will. 
 Almost all our- common waking life is carried on by actions 
 such as walking and sitting, which we hardly know that we 
 will, but which we could not do if we did not will them. 
 And also the greater part of our life is rather within a sphere 
 of will which has become objective for us in our profession, 
 interests, and ideals, than a perpetual active choice between
 
 40 "JUDGMENT," CONSCIOUSNESS OF A WORLD LECT. 
 
 alternatives such as brings the act of volition before us in 
 the most striking way. Just so it is with judgment. Our 
 speaking and writing is a very small part of our judging, 
 just as our conscious choice between alternatives l is a very 
 small part of our willing. 
 
 Distribu- 6. Thus the world of knowledge and the world of will 
 tention. *~ must eac ^ ^ tnem be regarded as a continuum for the waking 
 consciousness. Whenever we are awake, we are judging ; 
 whenever we are awake we are willing. The distribution of 
 attention in these two worlds is very closely analogous. In 
 both, it is impossible to attend to our whole world at the 
 same moment. But in both, our world is taken as being 
 a single connected system ; and therefore (i.) attention 
 shades off gradually from the momentary focus of illumin- 
 ation into less and less intensity over the other parts of the 
 continuous judgment or purpose ; but (ii.) that which is in 
 the focus of attention depends for its quality upon that 
 which is less distinctly or not at all in the focus of attention. 
 And as attention diminishes in intensity, the implication of 
 reality does not diminish with it. In other words, in spite 
 of the inequality of attention, the reality of our whole world 
 is implied in the reality of which at any moment we are 
 distinctly aware. But being distinctly aware of reality is 
 another name for judgment. 
 
 Now the common logical judgments which we shall have 
 to analyse and classify are simply those parts of this con- 
 tinuous affirmation of consciousness which are from time 
 
 1 I do not for a moment suggest that our "conscious choice" is 
 ultimately different in kind from our habitual persistence in a course 
 of life. I only take it as an instance in which we fully attend to 
 our volition.
 
 II THE EXPLICIT JUDGMENT 41 
 
 to time separately made distinct. Each of them therefore 
 must be regarded as a partial expression of the nature of 
 reality, and the subject will always be Reality in one form, 
 and the predicate reality in another form. The ultimate 
 and complete judgment would be the whole of Reality 
 predicated of itself. All our logical judgments are such 
 portions and fragments of this judgment as we can grasp 
 at the moment. Some of these gather up in a system 
 whole provinces of reality, others merely enlarge, interpret, 
 or analyse the content of a very simple sense-perception. 
 We shall not go far wrong in practice if we start from this 
 judgment of Perception as the fundamental kind of Judg- 
 ment. The real subject in Judgment is always Reality in 
 some particular datum or qualification, and the tendency 
 of Judgment is always to be a definition of Reality. We 
 see the parts of Judgment most clearly in such thoughts as 
 "This is blue"; "This is a flower"; "That light is the 
 rising sun"; "That sound is the surf on a sandy shore." 
 In these we can plainly distinguish the element of presenta- 
 tion and the interpretative construction or analytic synthesis 
 which is by the judgment identified with it.
 
 LECTURE III 
 
 THE RELATION OF LOGIC TO KNOWLEDGE 
 
 Meaning of i. I SPOKE of the whole world, which we take to be real, 
 rm * as presented to us in the shape of a continuous judgment. 
 It is the task of Logic to analyse the structure of this 
 Judgment, the parts of which are Judgments. 
 
 The first thing is then to consider what sort of properties 
 of Judgments we attend to in Logic. It is commonly said 
 that Logic is a formal science ; that is, that it deals with 
 the form, and not with the content or matter of knowledge. 
 
 This word "form" is always meeting us in philosophy. 
 " Species " is Latin for form, as tldog and t'^c'a are Greek for 
 form. The form of any object primarily means its appear- 
 ance, that which the mind can carry away, while the object 
 as a physical reality, as material, remains where it was. It 
 need not mean shape as opposed to colour; that is a 
 narrower usage. The Greek opinion was no doubt rooted 
 in some such notion as that in knowing or remembering a 
 thing the mind possessed its form or image without its 
 matter. Thus the form came to stand for the knowable 
 shape or structure which makes a thing what it is, and by 
 which we recognise it when we see it. This was its species 
 or its idea, the " image," as it is used in the phrase, " Let us 
 make man in our own image." So in any work of the hands
 
 LECT. in FORM 43 
 
 of man, the form was the shape given by the workman, and 
 came out of his mind, while the matter was the stuff or 
 material out of which the thing was made. 
 
 The moment we contemplate a classification of the 
 sciences, we see that this is a purely relative distinction. 
 There is no matter without form. If it was in this deep 
 sense without form, it would be without properties, and so 
 incapable of acting or being acted upon. In a knife the 
 matter is steel, the form is the shape of the blade. But the 
 qualities of steel again depend, we must suppose, upon a 
 certain character and arrangement in its particles, and this 
 is, as Bacon would have called it, the form of steel. But 
 taken as purely relative, the distinction is good prima fade. 
 Steel has its own form, but the knife has its form, and the 
 matter steel can take many other forms besides that of a 
 knife. Marble has its own form, its definable properties as 
 marble (chemical and mechanical), but in a statue, marble 
 is the matter, and the form is the shape given by the 
 sculptor. 
 
 Now applying this distinction to knowledge in general, 
 we see that all science is formal, and therefore it is no dis- 
 tinction to say that Logic is a formal science. Geometry 
 is a formal science ; even molecular physics is a formal 
 science. All science is formal, because all science consists 
 in tracing out the universal characteristics of things, the 
 structure that makes them what they are. 
 
 The particular "form," then, with which a science deals 
 is simply the kind of properties that come under the point 
 of view from which that science in particular looks at things. 
 But a very general science is more emphatically formal than
 
 44 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 a very special science. That is to say, it deals with proper- 
 ties which are presented in some degree by everything ; and 
 so in every object a great multitude of properties are dis- 
 regarded by it, are treated by it as matter and not as form. 
 In this sense Logic is emphatically "formal," though not 
 nearly so formal as it is often supposed to be. The subject- 
 matter of Logic, then, is Knowledge qua Knowledge, or the 
 form of knowledge ; that is, the properties which are possessed 
 by objects or ideas in so far as they are members of the world 
 of knowledge. And it is quite essential to distinguish the 
 form of knowledge in this sense from its matter or content. 
 The " matter " of knowledge is the whole region of facts 
 dealt with by science and perception. If Logic dealt with 
 this in the way in which knowledge deals with it, /'. e. simply 
 as a process of acquiring and organising experience, then 
 Logic would simply be another name for the whole range 
 of science, history, and perception. Then there would be 
 no distinction between logic and science or common sense, 
 and in trying to ascertain, say, the wave-length of red light, 
 or the cab-fare from Chelsea to Essex Hall, we should be 
 investigating a logical problem. But we see at once that 
 this is not what we mean by studying knowledge as know- 
 ledge. Science or common sense aims at a particular 
 answer to each problem of this kind. Logic aims at under- 
 standing the type and principles both of the problem and 
 of its answer. The details of the particular answer are the 
 " matter of fact." The type and principles which are found 
 in all such particular answers may be regarded as the form 
 of fact, /'. e. that which makes the fact a fact in knowledge. 
 Jevons appears to me to make a terrible blunder at this
 
 in LOGIC AND SCIENCE 45 
 
 point. He says l " One name which has been given to 
 Logic, namely the Science of Sciences, very aptly describes 
 the all-extensive power of logical principles. The cultivators 
 of special branches of knowledge appear to have been fully 
 aware of the allegiance they owe to the highest of the 
 sciences, for they have usually given names implying this 
 allegiance. The very name of Logic occurs as part of 
 nearly all the names adopted for the sciences, which are 
 often vulgarly called the ' ologies,' but are really the ' logics/ 
 the ' o ' being only a connecting vowel or part of the previous 
 word. Thus geology is logic applied to explain the forma- 
 tion of the earth's crust ; biology is logic applied to the 
 phenomena of life ; psychology is logic applied to the nature 
 of the mind ; and the same is the case with physiology, 
 entomology, zoology, teratology, morphology, anthropology, 
 theology, ecclesiology, thalattology, and the rest. Each 
 science is thus distinctly confessed to be a special logic. 
 The name of Logic itself is derived from the common Greek 
 word Xoyoe, which usually means word, or the sign and 
 outward manifestation of any inward thought. But the 
 same word was also used to denote the inward thought or 
 reasoning of which words are the expression, and it is thus 
 probably that later Greek writers on reasoning were led to 
 call their science 7ri<mjpj Xoytd), or logical science, also 
 re'xi'J? Xoyt/a;, or logical art. The adjective Aoyu'/;, being 
 used alone, soon came to be the name of the science, just 
 as Mathematic, Rhetoric, and other names ending in 'ic* 
 were originally adjectives, but have been converted into 
 substantives." 
 
 1 Elementary Lessons, p. 6.
 
 46 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 This account of the connection between the name 
 " Logic " and the terminations of the names of the sciences 
 appears precisely wrong. Whatever may have been the 
 exact meaning of the expression "Logic," or "Logical 
 curriculum," 1 or " art," or " science " when first employed, 
 there can be no doubt that the word logical had a substan- 
 tive reference to that about which the science or teaching 
 in question was to treat. The term "logic," therefore, 
 corresponds not to the syllables " logy " in such a word as 
 " Zoology," but to the syllables " Zoo," which indicate the 
 province of the special science, and not its character as a 
 science. Zoology means connected discourse (Xo'yoc) about 
 living creatures. Logic meant a curriculum, or science or 
 art dealing with connected discourse. The phrase " Science 
 of Sciences," rightly interpreted, has the same meaning. It 
 does not mean that Logic is a Science which comprises all 
 the special sciences, but that Logic is a Science dealing with 
 those general properties and relations which all sciences qua 
 sciences have in common, but omitting, as from its point of 
 view matter and not form, the particular details of content 
 by which every science answers the particular questions 
 which it asks. It is wild, and most mischievous, to say that 
 " every science is a special logic," or that " biology is Logic 
 applied to the phenomena of life." This confusion destroys 
 the whole disinterestedness which is necessary to true scien- 
 tific Logic, and causes the logical student always to have 
 his eye on puzzles, and special methods, and interferences 
 by which he may teach the student of science how to per- 
 form the concrete labour of research. We quite admit that 
 1 irpay/j.d.Tfia. See Prantl, i. 545.
 
 Ill KNOWLEDGE AS KNOWLEDGE 4? 
 
 a looker-on may sometimes see more of the game, and no 
 wise investigator would contemn a priori the suggestions 
 of a student like Goethe, or Mill, or Lotze, because their 
 author was not exclusively engaged in the observation of 
 nature. But all this is secondary. The idea that Logic is 
 a judge of scientific results, able to pass sentence, in virtue 
 of some general criterion, upon their validity and invalidity, 
 arises from a deep-lying misconception of the nature of 
 truth which naturally allies itself with the above confusion 
 between Logic and the special sciences. 
 
 Therefore the relation between content or matter of 
 knowledge, and the form which is its general characteristic 
 as knowledge, is of this kind. We can either study the 
 objects of knowledge directly as we perceive them, or in- 
 directly, as examples of the way in which we know. As 
 studied for their own sake, they are regarded as the matter 
 or content in which the general form of knowledge finds 
 individual realisation. In botany, for instance, we have a 
 large number of actual plants classified and explained in 
 their relation to one another. A botanist is interested 
 directly in the affinities and evolution of these plants, and 
 in the principles of biology which underlie their history. 
 He pushes his researches further and further into the in- 
 dividual matters that come to light, without, as a rule, more 
 than a passing reflection upon the abstract nature of the 
 methods which he is creating as his work proceeds. He 
 classifies, explains, observes, experiments, theorises, gener- 
 alises, to the best of his power, solely in order to grasp and 
 render intelligible the region of concrete fact that lies before 
 him. Now while his particular results and discoveries con-
 
 48 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 stitute the " form " or knowable properties of the plant-world 
 as the object of botanical science, the science which inquires 
 into the general nature of knowledge must treat these par- 
 ticular results as " mere matter " as something with which 
 it is not directly concerned, any more than the art which 
 makes a statue is primarily and directly concerned with the 
 chemical and mechanical properties of marble. The " form " 
 or knowable properties with which the general science of 
 knowledge is directly concerned, consists in those methods 
 and processes which the man of science, developing the 
 modes in which common sense naturally works, constructs 
 unconsciously as he goes along. Thus, not the nature 
 and affinities of the plant-world, but classification, explan- 
 ation, observation, experiment, theory, are the phenomena 
 in virtue of which the organised structure of botanical 
 science participates in the form of knowledge, and its 
 objects become, in these respects, objects of logical 
 theory. 
 
 Hence some properties and relations of objects, being the 
 form or knowable structure of the concrete objects as a 
 special department of nature, correspond to the mere 
 matter, stuff, or content of Knowledge in general, while 
 other properties and relations of objects, being their form 
 or knowable structure as entering into a world of reality 
 displayed to our intelligence, correspond to the form of 
 Knowledge as treated of by a general inquiry into its 
 characteristics, which we call Logic. It is just as the 
 qualities or "forms" of the different metals of which knives 
 can be made are mere matter or irrelevant detail when we 
 are discussing the general " form " or quality of a good knife,
 
 in FORM AND MATTER 49 
 
 whatever its material. A reservation on this head appears 
 in the following section. 
 
 2. For the form of Knowledge depends in some de- Form of 
 gree upon its matter. It is very important to realise this i e d ge <j e . 
 truth ; for if Logic is swamped by being identified with the P endent n 
 whole range of special sciences, it is killed by being emptied 
 of all adaptation to living intelligence. What is called 
 Formal Logic par excellence, in all its shapes, whether anti- 
 quated as in Hamilton's or Thomson's Formal Laws of 
 Thought, or freshly worked out on a symbolic basis as by 
 Boole and others, has, it appears to me, this initial defect, 
 when considered as a general theory of Logic. As a contribu- 
 tion to such a theory, every method which will work un- 
 doubtedly has its place, and indicates and depends upon 
 some characteristic of real thought. But in the central 
 theory itself, and especially in so short an account of it as 
 must be attempted in these lectures, I should be inclined to 
 condemn all attempts to employ symbols for anything more 
 than the most passing illustration of points in logical pro- 
 cesses. All such attempts, I must maintain, share with the 
 old-fashioned laws of Identity, Contradiction, and Excluded 
 Middle the initial fallacy of representing a judgment by 
 something which is not and cannot be in any way an 
 adequate symbol of one. If, in order to get at the pure 
 form of Knowledge, we restrict ourselves to very abstract 
 characteristics in which all knowledge appears, very roughly 
 speaking, to agree, and which can be symbolized for working 
 purposes by combinations of signs which have not the 
 essential properties of ideal contents, then we have ab initio 
 substituted for the judgment something which is a very 
 
 I
 
 50 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 abstract corollary from the nature of judgment, and may or 
 not for certain purposes and within certain limits be a fair 
 representative of it. We cannot and must not exclude from 
 the form of Knowledge its modifications according to 
 "matter," and its nature as existing only in "matter." 
 
 In fact, the peculiar "form" of everything depends in 
 some degree on its " matter." A statue in marble is a little 
 differently treated if it is copied in bronze. A knife is 
 properly made of steel ; you can only make a bad one of 
 iron, or copper, or flint, and you cannot make one at all of 
 wax. Different matters will more or less take the same 
 form, but only within certain limits. So it is in Knowledge. 
 The nature of objects as Knowledge for we must remember 
 that "form" in our sense is not something put into the 
 " matter," something alien or indifferent to it, but is simply 
 its own inmost character revealed by the structural relations 
 in which it is found capable of standing l depends on the 
 way in which their parts are connected together. 
 
 Let us compare, for example, the use of number in 
 understanding objects of different kinds. 
 
 Suppose there are four books in a heap on the table. 
 This heap of books is the object. We desire to conceive 
 it as a whole consisting of parts. In order to do so we 
 simply count them " one, two, three, four books." If one is 
 taken away, there is one less to count ; if one is added, there 
 is one more. But the books themselves, as books, are not 
 
 1 The example of the marble statue may seem to contradict this idea ; 
 and no doubt the indifference of matter to form is a question of degree. 
 But the feeling for material is a most important element in fine art ; 
 and in knowledge there is only a relative distinction between formal 
 and material relations.
 
 Ill NUMBER AS A FORM 51 
 
 altered by taking away one from them or adding one to 
 them. They are parts indifferent to each other, forming 
 a heap which is sufficiently analysed or synthesised by 
 counting its parts. 
 
 But now instead of four books in a heap, let us think of 
 the four sides of a square. Of course we can count them, 
 as we counted the books ; but we have not conceived the 
 nature of the square by counting its sides. That does not 
 distinguish it from four straight lines drawn anyhow in 
 space. In order to appreciate what a square is, we must 
 consider that the sides are equal straight lines, put together 
 in a particular way so as to make a figure with four right 
 angles ; we must distinguish it from a figure with four equal 
 sides, but its angles not right angles, and from a four-sided 
 figure with right angles, but with only its opposite sides 
 equal ; and note that if we shorten up one side into nothing, 
 the square becomes a triangle, with altogether different 
 properties from those of a square ; if we put in another side 
 it becomes a pentagon, and so on. 
 
 These two things, the heap of books and the square, are 
 prima fade objects of perception. We commonly speak of 
 a diagram on a blackboard or in a book as " a square " if 
 we have reason to take it as approximately exact, and as 
 intended for a square. But on looking closer, we soon see 
 that the " matter," or individual attributes, of each of these 
 objects of our apprehension demands a different form of 
 knowledge from that necessary to the other. The judgment 
 " This heap of books has four books in it " is a judgment of 
 enumerative perception. The judgment " The square has 
 four sides " is a judgment of systematic necessity.
 
 52 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 Why did we not keep the two judgments in the same 
 logical shape ? Why did we say " This heap " and " The 
 square " ? Why did we not say " this " in both propositions, 
 or "the" in both propositions? Because the different 
 "matter" demands this difference of form. Let us try. 
 " The heap of books has four books in it." Probably we 
 interpret this proposition to mean just the same as if we had 
 said " This heap." That is owing to the fact that the judg- 
 ment naturally occurs to us in its right form. But if we 
 interpret " The heap " on the analogy of our interpretation 
 of " The square," our judgment will have become false. 
 
 It will have come to mean " Every heap of books has four 
 books in it," and a judgment of perception will not bear this 
 enlargement. The subject is composite, and one, the most 
 essential of its elements, is destroyed by the change from 
 "this "to "the." 
 
 Let us try again. Let us say "This square has four 
 sides." That is not exactly false, but it is ridiculous. 
 Every square must have four sides, and by saying "this 
 square " we strongly imply that foursidedness is a relation of 
 which we are aware chiefly, if not exclusively, in the object 
 attended to in the moment of judging, simply through the 
 apprehension of that moment. By this implication the form 
 of the judgment abandons and all but denies the character 
 of systematic necessity which its content naturally demands. 
 It is like saying, "It appears to me that in the present 
 instance two and two make four." The number of sides in 
 a square, then, is not a mere fact of perception, while the 
 number of books in a heap is in such a fact. 
 
 But you may answer by suggesting the case that an un-
 
 in LOWER AND HIGHER FORM 53 
 
 instructed person say a child, with a square figure before 
 him, and having heard the name square applied to figures 
 generally resembling that figure, may simply observe the 
 number of sides, without knowing any of the geometrical 
 properties connected with it ; will he not then be right in 
 saying, " This square has four sides " ? 
 
 Certainly not. In that case he has no right to call it a 
 square. It would only be a name he had picked up without 
 knowing what it meant. All he has the right to say would 
 be, " This object " or " This figure has four sides." That 
 would be a consistent judgment of mere perception, true as 
 far as it went. It is always possible to apprehend the more 
 complex objects of knowledge in the simpler forms ; but 
 then they are not apprehended adequately, not as complex 
 objects. It is also possible to apply very complex forms of 
 knowledge to very simple objects. Most truths that can be 
 laid down quite in the abstract about a human mind could 
 also be applied in some sense or other to any speck of pro- 
 toplasm, or to any pebble on the seashore. And every 
 simple form of knowledge is always being pushed on, by its 
 own defects and inconsistencies, in the direction of more 
 complex forms. 
 
 So far I have been trying to show that objects are capable 
 of being different in their nature as knowledge as well as in 
 their individual properties ; and that their different natures 
 as knowledge depend on the way in which their parts are 
 connected together. We took two objects of knowledge, 
 and found that the mode of connection between the parts 
 required two quite different kinds of judgment to express 
 them. Let us look at the reason of this.
 
 $4 THE RELATION OF LOGIC TO KNOWLEDGE LECt. 
 
 The rek- 3- The relation of Part and Whole is a form of the 
 Part and re l at i n f Identity and Difference. Every Judgment 
 Whole. expresses the unity of some parts in a whole, or of some 
 differences in an Identity. This is the meaning of " con- 
 struction " in knowledge. We saw that knowledge exists in 
 judgment as a construction (taking this to include main- 
 tenance) of reality. 
 
 The expression whole and parts may be used in a strict or 
 in a lax sense. 
 
 In a strict sense it means a whole of quantity, that is, a 
 whole considered as made up by the addition of parts of the 
 same kind, as a foot is made up of twelve inches. In this 
 sense the whole is the sum of the parts. And even in this 
 sense the whole is represented within every part by an 
 identity of quality that runs through them all. Otherwise 
 there would be nothing to earmark them as belonging to 
 the particular whole or kind of whole in question. Parts of 
 length make up a whole of length, parts of weight a whole 
 of weight, parts of intensity a whole of intensity, in so far as 
 a whole of intensity is quantitative, which is not a perfectly 
 easy question. Wholes like these are " Sums " or " Totals" 
 The relation of whole to part in this sense is a very simple 
 case of the relation of differences in an identity, but for that 
 very reason is not the easiest case to appreciate. The rela- 
 tion is so simple that it is apt to pass unnoticed, and in 
 dealing with numerical computation we are apt to forget 
 that in application to any concrete problem the numbers 
 must be numbers of something having a common quality, 
 and that the nature of this something may affect the result 
 as related to real fact, though not as a conclusion from pure
 
 Ill KINDS OF WHOLES 55 
 
 numerical premisses. In a whole of pure number the indif- 
 ference of parts to whole reaches its maximum. The unit 
 remains absolutely the same, into whatever total of addition 
 it may enter. 
 
 In a whole of differentiated members, such as a square, 
 all this begins to be different. A side in a square possesses, 
 by the fact of being a side, very different relations and 
 properties from those of a straight line conceived in isolation. 
 In this case the whole is not made up merely by adding 
 the parts together. It is a geometrical whole, and its parts 
 are combined according to a special form of necessity 
 which is rooted in the nature of space. Speaking gener- 
 ally, the point is that parts must occupy certain perfectly 
 definite places as regards each other. You cannot make 
 a square by merely adding three right angles to one, nor 
 by taking a given straight line and adding three more 
 equal straight lines to its length. You must construct 
 in a definite way so as to fulfil definite conditions. The 
 identity shows itself in the different elements which make it 
 up, not as a mere repeated quality, but as a property of 
 contributing, each part in a distinctive way, to the nature of 
 the whole. Such an identity is not a mere total or sum, 
 though I imagine that its relations can be fully expressed in 
 terms of quantity, certain differentiated objects or concep- 
 tions being given (e. g. line and angle). 
 
 I take a further instance to put a sharp point upon this 
 
 distinction. The relation of whole and parts is nowhere 
 
 more perfect, short of a living mind, than in a work of art. 
 
 There is a very fine Turner landscape now l in the " Old 
 
 1 February 1892.
 
 56 THE RELATION OF LOGIC TO KNOWLEDGE LECT. 
 
 Masters" Exhibition at Burlington House the picture of 
 the two bridges at Walton-on-Thames. The picture is full 
 of detail figures, animals, trees, and a curving river-bed. 
 But I am told that if one attempts to cut out the smallest 
 appreciable fragment of all this detail, one will find that it 
 cannot be done without ruining the whole effect of the 
 picture. That means that the individual totality is so 
 welded together by the master's selective composition, that, 
 according to Aristotle's definition of a true " whole," if any 
 part is modified or removed the total is entirely altered, 
 "for that of which the presence or absence makes nov 
 difference is no true part of the whole." l 
 
 Of course, in saying that the part is thus essential to the 
 whole, it is implied that the whole reacts upon and trans- 
 figures the part. It is in and by this transformation that its 
 pervading identity makes itself felt throughout all the 
 elements by which it is constituted. As the picture would 
 be ruined if a little patch of colour were removed, so the 
 little patch of colour might be such as to be devoid of all 
 value if seen on a piece of paper by itself. I will give an 
 extreme instance, almost amounting to a tour deforce^ from 
 the art of poetry, in illustration of this principle. We 
 constantly hear and use in daily life the phrase, "It all 
 comes to the same thing in the end." Perhaps in the very 
 commonest speech we use it less fully, omitting the word 
 " thing " ; but the sentence as written above is a perfectly 
 familiar platitude, with no special import, nor grace of sound 
 or rhythm. Now, in one of the closing stanzas of Browning's 
 poem Any Wife to Any Husband, this sentence, only modified 
 1 Poetics, 8.
 
 in THE ESTHETIC WHOLE 57 
 
 by the substitution of "at" for "in," forms an entire 
 line. 1 And I think it will generally be felt that there are 
 few more stately and pathetic passages than this in modern 
 poetry. Both the rhythm and sonorousness of the whole 
 poem, and also its burden of ideal feeling, are communicated 
 to the line in question by the context in which it is framed. 
 Through the rhythm thus prescribed to it, and through 
 the characteristic emotion which it contributes to reveal, 
 the " whole " of the poem re-acts upon this part, and con- 
 fers upon it a quality which, apart from such a setting, 
 we should never have dreamed that it was capable of 
 possessing. 
 
 We are not here concerned with the peculiar " aesthetic " 
 nature of works of art, which makes them, although rational, 
 nevertheless unique individuals. I only adduced the above 
 examples to show, in unmistakable cases, what is actually 
 meant when we speak of " a whole " as constituted by a 
 pervading identity which exhibits itself in the congruous or 
 co-operating nature of all the constituent parts. In wholes 
 of a higher kind than the whole of mere quantity the parts 
 no longer repeat each other. They are not merely distinct, 
 
 1 In order to remind the reader of the effect of this passage it is 
 necessary to quote a few lines before and after 
 
 "Re-issue words and looks from the old mint, 
 Pass them afresh, no matter whose the print, 
 
 Image and superscription once they bore ! 
 Re-coin thyself and give it them to spend, 
 It all comes to the same thing at the end, 
 
 Since mine thou wast, mine art and mine shall be, 
 Faithful or faithless, sealing up the sum 
 Or lavish of my treasure, thou must come 
 
 Back to the heart's place here I keep for thee ! "
 
 58 THE RELATION OF LOGIC TO KNOWLEDGE LECt. 
 
 but different. Yet the common or continuous nature shows 
 itself within each of them. 
 
 The parts of a sum-total, taking them for convenience of 
 summation as equal parts, may be called units ; l the parts 
 of an abstract system, such as a geometrical figure, may be 
 called elements (I cannot answer for mathematical usage), 
 and the parts of a concrete system, an aesthetic product, a 
 mind, or a society, might be called members. 
 
 But every kind of whole is an identity, and its parts are 
 always differences within it. 
 
 Nature of 4- It will be well to sum up here what we have learnt of 
 the nature of knowledge in general, before passing to the 
 definition and classification of Judgment. 
 
 Knowledge is always Judgment. Judgment is construc- 
 tive, for us, of the real world. Constructing the real world 
 means interpreting or amplifying our present perception by 
 what we are obliged to think, which we take as all belonging 
 to a single system one with itself, and with what constrains 
 us in sense-perception, and objective in the sense that its 
 parts act on each other independently of our individual 
 apprehension, and that we are obliged to think them thus. 
 The process of construction is always that of exhibiting a 
 whole in its parts, /. e. an identity in its differences ; that is 
 to say, it is always both analytic and synthetic. -The objects 
 of knowledge differ in the mode of relation between their 
 
 1 A unit of measurement implies in addition that it has been equated 
 with some accepted standard. If I divide the length of my room into 
 thirty equal parts, each part is a "unit" in the sum-total ; but I have 
 not measured the room till I have equated one such part with a known 
 standard, and thus made it into a unit in the general system of length 
 equations.
 
 ill KNOWLEDGE A LIVING SYSTEM & 
 
 parts and the whole, and thus give rise to different types of 
 judgment and inference ; and this difference in the form of 
 knowledge is a difference in the content of Logic, which 
 deals with the objects of experience only from the point of 
 view of their properties as objects in an intellectual world. 
 
 5. I hope that these general lectures, which, as I am quite Conclu- 
 aware, have anticipated the treatment of many difficult sion> 
 questions which they have not attempted to solve, have 
 been successful in putting the problem of Logic before us 
 with some degree of vividness. If this problem were 
 thoroughly impressed upon our minds, I should say that 
 we had already gained something definite from this course 
 of study. The points which I desire to emphasise are 
 two. 
 
 (i) I hope that we have learned to realise the world of 
 our knowledge as a living growth, sustained by the energy of 
 our intelligence; and to understand that we do not start 
 with a ready-made world in common, but can only enter 
 upon the inheritance of science and civilisation as the result 
 of courage, labour, and reasonable perseverance ; and further, 
 that we retain this inheritance just as long as our endurance 
 and capacity hold out, and no longer. 
 
 And (2) I have attempted to make clear that this living 
 growth, our knowledge, is like the vegetable or animal world 
 in being composed of infinite minor systems, each and all of 
 which are at bottom the same function with corresponding 
 parts or elements, modified by adaption to the environment. 
 So that the task of analysing the form of judgment bears a 
 certain resemblance to that of analysing the forms of plants. 
 Just as from the single cell of the undifferentiated Alga, to
 
 60 THE RELATION OF LOGIC TO KNOWLEDGE LF.CT. in 
 
 the most highly organised flower or tree, we have the same 
 formation, with its characteristic functions and operations, so 
 from the undifferentiated judgment, which in linguistic form 
 resembles an ejaculation or interjection, to the reasonable 
 systems of exact or philosophical science, we find the same 
 systematic function with corresponding elements. 
 
 But the world of knowledge has a unity which the world 
 of organic individuals cannot claim ; and this whole system 
 of functions is itself, for our intelligence, approximately a 
 single function or system, corresponding in structure to 
 each of its individual parts, as though the plant world or 
 animal world were itself in turn a plant or animal. We 
 cannot hope to exhaust the shapes taken by the pervading 
 fundamental function of intelligence. We shall only attempt 
 to understand the analogies and differences between some 
 few of its leading types.
 
 LECTURE IV 
 
 TYPES OF JUDGMENT AND THE GENERAL CONDITIONS 
 INVOLVED IN ASSERTION 
 
 i. THE question of correspondence between the types of Cone- 
 Judgment and the orders of Knowledge was really antici- 
 
 pated in discussing the relation between the content and tyP es of 
 the form of knowledge. We saw that the content or matter and nature 
 
 known determines on the whole the form or method of S*** 8 
 
 as Know- 
 
 knowledge by which it can be known. ledge. 
 
 I give a few cases of this correspondence, not professing 
 to complete the list. We should accustom ourselves to 
 think of these forms as constituting a progression in the 
 sense that each of them betrays a reference to an ideal of 
 knowledge which in itself it is unable to fulfil, and therefore 
 inevitably suggests some further or divergent form. And 
 the defect by which the forms contradict the ideal, is felt by 
 us as a defect in their grasp of reality, in their presentation 
 of real connections. 
 
 a. We think of the judgment as predicating an ideal "Imper- 
 content of a subject indicated in present perception. But judg men t 
 there are judgments which scarcely have an immediate 
 subject at all, such as "How hot!" "Bad!" "It hurts!" 
 In the judgments thus represented the true subject is some
 
 62 TYPES OF JUDGMENT LECT. 
 
 undefined aspect of the given complex presentation. Of 
 course the words which we use are not an absolutely safe 
 guide to the judgment they may be merely an abbreviation. 
 But there are typical judgments of this kind in which we 
 merely mean to connect some namable content with that 
 which can only be defined as the focus of attention at the 
 moment. Such judgments might be called predications of 
 mere quality. The only link by which they bind their parts 
 into a whole is a feeling referred to our momentary surround- 
 ings. A mere quality, if not defined or analysed, or a 
 feeling of pleasure or pain, is the sort of object which can 
 be expressed in such a judgment. 
 
 Perceptive &> Then we have the very wide sphere of perceptive 
 Judgment, judgment, which we may most conveniently confine to 
 judgments which have in the subject elements analogous to 
 "This," "Here," "Now." Such particles as these indicate 
 an effort to distinguish elements within the complex pre- 
 sented. They have no content beyond the reference to 
 presentation, and, in "here" and "now," an implication 
 that the present is taken in a particular kind of continuum. 
 Otherwise they mean nothing more or other than is meant 
 by pointing with the finger. We may or may not help out 
 a "subject" of this kind by definite ideas attached to it as 
 conditions of the judgment. If we do, we are already on 
 the road to a new form of knowledge, incompatible with the 
 judgment of perception. For so long as we keep a demon- 
 strative, spatial or temporal, reference in the thought, the 
 subject of judgment is not cut loose from our personal focus 
 of presentation. And as the existence of such a focus is 
 undeniable, we are secure against criticism so far as the
 
 iv PERCEPTION AND OBSERVATION 63 
 
 content of the subject is concerned. But if we begin to 
 specify it, we do so at our peril. 
 
 Such judgments as these have been called "Analytic 
 judgments of sense." l The term is not generally accepted 
 in this meaning, but is conveniently illustrative of the nature 
 of these judgments. It is intended to imply that they are a 
 breaking up and reconstruction of what, in our usual loose 
 way of talking, is said to be given in sense-perception. 
 They remain on the whole within the complex of "that 
 which " is presented. 
 
 From the point of view which we have taken, such judg- 
 ments are not confined to what we think it worth while 
 to say, but are the essence of every orderly and objective 
 perception of the world around us. In a waking human 
 consciousness nothing is unaffirmed. 
 
 We have no other term than perception to express the 
 process which is employed in scientific observation and 
 experiment. But it is plain that so soon as the judgment 
 that refers to "This" is modified through the inevitable 
 demand for qualification by exact ideas " This hurts me," 
 "What hurts you?" "This old sprain, at the pace we are 
 walking" a conflict of elements has arisen within the 
 judgment. And as commonplace perception passes into 
 scientific observation, the qualifying ideas, on which truth 
 and relevancy depend, dwarf the importance of the " this," 
 and ultimately oust it altogether. That is a simple case in 
 which the ideal of knowledge and the nature of reality oper- 
 ate within the judgment to split asunder its primitive form. 
 The subject as expressed by a pure demonstrative refuses to 
 * Mr. F. H. Bradley, Principle of Logic, p. 48.
 
 64 TYPES OF JUDGMENT LECT. 
 
 take account either of truth, /. e. consistency with knowledge 
 as a whole, or of relevancy, /. e. consistency with the relation 
 involved in the particular predication that may be in question. 
 Our commonplace perception halts between these two ex- 
 tremes. It deals with the world of individual objects and 
 persons, which, being already systematised according to our 
 current observations and interests, has, so long as we keep 
 to its order, a sufficient degree of truth and- relevancy for 
 the needs of daily life. Thus if I say, " This book will do 
 as a desk to write upon," the truth of the qualification 
 " book " (/'. e. the reality of the subject) is assumed on the 
 ground of the facility of recognising a well-known " thing," 
 while the relevancy of the qualification "book" is not 
 questioned, because we accept an individual thing as an 
 object of habitual interest qua individual, and do not demand 
 that whenever it is named those properties alone should 
 be indicated which are relevant to the purpose for which 
 it is named. The "thing" is a current coin of popular 
 thought, and makes common perception workable without 
 straining after a special relevancy in the subject of every 
 predication. Such special relevancy leads ultimately to the 
 ideal of definition, in which subject and predicate are 
 adequate to each other and necessarily connected. A 
 definitory judgment drops the demonstrative and relies on 
 qualifying ideas alone. It is therefore an abstract universal 
 Judgment, while the Judgment of Perception, so long as it 
 retains the demonstrative, is a Singular Judgment. 
 Proper c. But a very curious example of a divergence or half-way 
 
 house in Knowledge is that form of the singular Judgment 
 in which the subject is a proper name, A proper name is
 
 IV THE INDIVIDUAL 65 
 
 designative and not definitory. It may be described as a 
 generalised demonstrative pronoun a demonstrative pro- 
 noun which has the same particular reference in the mouth 
 of every one who uses it, and beyond the given present of 
 time. 
 
 iSo the reference of a proper name is a good example 
 onwhat we called a universal or an identity. That which is 
 referred to by such a name is a person or thing whose 
 existence is extended in time and its parts bound together 
 by/ some continuous quality an individual person or thing 
 and the whole of this individuality is referred to in whatever 
 is affirmed about it. Thus the reference of such a name is 
 Universal, not as including more than one individual, but as 
 /including in the identity of the individual numberless differ- 
 ences the acts, events, and relations that make up its 
 history and situation. 
 
 What kinds of things are called by Proper Names, and 
 why ? This question is akin to the doctrine of Connotation 
 and Denotation, which will be discussed in the next lecture. 
 It is a very good problem to think over beforehand, noting 
 especially the limiting cases, in which either some people give 
 proper names to things to which other people do not give 
 them, or some things are given proper names while other 
 things of the same general kind are not. These judgments, 
 which are both Singular and Universal, may perhaps be 
 called for distinction's sake " Individual " Judgments. 
 
 d. The demonstrative perception may also be replaced by Abstract 
 a more or less complete analysis or definition. -* u gme 
 
 Within this province Definition of a concrete whole is 
 one extreme, e.g. "Human Society is a system of wills"; 
 
 F
 
 66 TYPES OF JUDGMENT LECT. 
 
 that of an abstract whole the other extreme, "12 
 There are all degrees, between these two, in the amount of 
 modification which the parts undergo by belonging to the 
 whole. There are also all sorts of incomplete definitions, 
 expressing merely the effects of single conditions out of 
 those which go to make up a whole. These form the 
 abstract universal judgments of the exact sciences, such as, 
 "If water is heated to 212 Fahr. under one atmosphere it 
 boils." In all these cases some idea, " abstract " as being 
 cut loose from the focus of present perception, whether 
 abstract or concrete in its content, replaces the demonstrative 
 of the judgment which is a perception. These are the 
 judgments which in the ordinary logical classification rank 
 as universal. 
 
 The gene- 2. It was quite right of us to consider some types of judg- 
 
 tioifof m ~ ment before trying to define it generally. It is hopeless to 
 
 Judgment, understand a definition unless the object to be defined is 
 
 tolerably familiar. We have said a great deal about know- 
 
 ledge and about judgment as the organ or medium of know- 
 
 ledge. Now we want to study particular judgments in their 
 
 parts and working, and observe how they perform their 
 
 function of constructing reality. 
 
 Now, for our purpose, we may take the clearest cases of 
 judgment, viz. the meanings of propositions. 
 
 The distinctive character of Judgment as contrasted with 
 every other act of mind is that it claims to be true, *'. e. 
 pre-supposes the distinction between truth and falsity. 
 
 First, we have to consider what is implied in claiming 
 truth. 
 
 Secondly, by what means truth is claimed in Judgment.
 
 iv TRUTH 67 
 
 Thirdly, the nature of the ideas for which alone truth can 
 be claimed. 
 
 (i.) Claiming truth implies the distinction between truth What is 
 and falsity. I do not say, "between truth and falsehood," chJming 
 because falsehood includes a lie, and a lie is not, prima facie, truth. 
 an error or falsity of knowledge. It is, as may be said of a 
 question, altogether addressed to another person, and has 
 no existence as a distinct species within knowledge. Thus 
 a lie is called by Plato " falsehood in words " ; the term 
 " falsehood in the mind " he reserves for ignorance or error, 
 which he treats as the worst of the two, which from an 
 intellectual point of view it plainly is. 
 
 No distinction between truth and falsity can exist unless, 
 in the act or state which claims truth, there is a reference to 
 something outside psychical occurrence in the course of 
 ideas. Falsity or error are relations that imply existences 
 which, having reality of one kind, claim in addition to this 
 another kind of reality which they have not. In fact, all 
 things that are called false, are called so because they claim 
 a place or property which they do not possess. They must 
 exist, in order to be false. It is in the non-fulfilment, by 
 their existence, of some claim or pretension which it sug- 
 gests, that falsity consists. And so it is in the fulfilment of 
 such a claim that truth has a meaning. A false coin exists 
 as a piece of metal ; it is false because it pretends to a place 
 in the monetary system which its properties or history 1 
 contradict. 
 
 As the claim to be true is made by every judgment in its 
 
 1 For it is, I suppose, technically false, even if over value, if not 
 coined by those who have the exclusive legal right to coin..
 
 68 TYPES OF JUDGMENT LECT. 
 
 form, there can be no judgment without some recognition of 
 a difference between psychical occurrences and the system 
 of reality. That is to say, there is no judgment unless the 
 judging mind is more or less aware that it is possible to 
 have an idea which is not in accordance with reality. 
 
 Thus, if an animal has no real world distinct from his 
 train of mental images, if, that is, and just because, these 
 are his world directly, and without discord, he cannot judge. 
 The question is, e. g. when he seems disappointed, whether 
 the pleasant image l simply disappears and a less pleasant 
 image takes its place, or whether the erroneous image was 
 distinguished as an element in " a mere idea," which could 
 be retained and compared with the systematised perceptions 
 which force it out, as an idea with reality. 
 
 We must all of us have seen a dog show signs of pleasure 
 when he notices preparations for a walk, and then express the 
 extreme of unhappiness when the walk is not taken at all, or 
 he is left at home. People interpret these phenomena very 
 carelessly. They say " he thought that he was going to be 
 taken out." If he did "think that, etc," then he made a 
 judgment. This would imply that he distinguishes between 
 the images suggested to his mind, and the reality of their 
 content as the future event of going out, and knew that he 
 might have the one without the other following. But of 
 
 3 It will be observed that we are not treating the mental images as 
 being taken for such by the primitive mind. It is just in as far as they 
 are not yet taken for such that they are merely such. Mr. James says 
 that the first sensation is for the child the universe {Psychology, II. 7). 
 But it is a universe in which all is equally mere fact, and there is no 
 distinction of truth and falsehood, or reality and unreality. That can 
 only come when an existent is found to be a fraud.
 
 IV CAPABLE OF BEING DENIED 69 
 
 course it is quite possible that the dog has no distinct 
 expectation of something different from his present images, 
 but merely derives pleasure from them, which he expresses, 
 and suffers and expresses pain when they are replaced by 
 something else. It is here, no doubt, in the conflict of 
 suggestion and perception, that judgment originates. 
 
 On the other hand, animals, especially domestic animals, 
 do seem to use the imperative, which perhaps implies that 
 they know what they want, and have it definitely contrasted 
 with their present ideas as something to be realised. 
 
 However this may be, the claim of truth marks the mini- 
 mum of Judgment. There can be no judgment until we 
 distinguish psychical fact from the reference to Reality. A 
 mere mental fact as such is not true or false. In other 
 words, there is no judgment unless there is something that, 
 formally speaking, is capable of being denied. When your 
 dog sees you go to the front door, he may have an image 
 of hunting a rabbit suggested to his mind, but so far 
 there is nothing that can be denied. If he has the image, 
 of course he has. There is nothing that can be denied 
 until the meaning of this image is treated as a further 
 fact beyond the image itself, in a system independent of the 
 momentary consciousness in his mind. Then it is possible 
 to say, " No, the fact does not correspond to your idea," /. e. 
 what we are ultimately obliged to think as a system is incon- 
 sistent with the idea as you affirmed it of the same system. 
 
 (ii.) The first thing then in Judgment is that we must By what 
 have a world of reality distinguished from the course of our 
 
 ideas. Thereupon the claim to truth is actually made by trut , h is 
 
 made. 
 attaching the meaning of an idea to some point in the real
 
 70 TYPES OF JUDGMENT LficT. 
 
 world. This can only be done where an identity is recog- 
 nised between reality and our meaning. 
 
 Thus (keeping to the Judgment of Perception) I say, 
 "This table is made of oak." This table is given in 
 perception already qualified by numberless judgments ; 
 it is a point in the continuous system or tissue which 
 we take as reality. Among its qualities it has a certain 
 grain and colour in the wood. I know the colour and 
 grain of oak-wood, and if they are the same as those of the 
 table, then the meaning or content " made of oak " coalesces 
 with this point in reality, and instead of merely saying, 
 " This table is made of wood that has such and such a 
 grain and colour," I am able to say " This table is made 
 of oak-wood." 
 
 This example shows the true distinction between the 
 Logical Subject and Predicate. The fact is, that the ulti- 
 mate subject in Judgment is always Reality. Of course the 
 logical subject may be quite different from the grammatical 
 subject. Some kinds of words cannot in strict grammar be 
 made subjects of a sentence, though they can represent a 
 logical subject quite-well : e. g. " Now is the time." " Here 
 is the right place." Adverbs, I suppose, cannot be gram- 
 matical subjects. But in these sentences they stand for the 
 logical subjects, certain points in the perceptive series. 
 
 The true logical subject then is always reality, however 
 much disguised by qualifications or conditions. The logical 
 predicate is always the meaning of an idea ; and the claim 
 to be true consists in the affirmation of the meaning as be- 
 longing to the tissue of reality at the point indicated by the 
 subject. The connection is always made by identity of
 
 IV IDENTITY IN JUDGMENT 71 
 
 content at the point where the idea joins the reality, so that 
 the judgment always appears as a revelation of something 
 which is in reality. It simply develops, accents, or gives 
 accuracy to a recognised quality of the real. This is easily 
 seen in cases of simple quality e. g. " This colour is sky- 
 blue." The colour is given, and the judgment merely iden- 
 tifies it with sky-blue, and so reveals another element 
 belonging to its identity, the element of being seen in the 
 sky on a clear day. 
 
 The analysis is not quite so easy when there is a concrete 
 subject like a person ; for how can there be an identity 
 between a person and a fact ? " A. B. passed me in the 
 street this afternoon." Between what elements is the 
 identity in this case ? It is between him, as an individual 
 whom I know by sight in other places, and him as he 
 appeared this afternoon in particular surroundings. His 
 identity already extends through a great many different par- 
 ticulars of time and place, and this judgment merely recog- 
 nises one more particular as included in the same continuous 
 history. " He in this context belongs to him in a former 
 context." In this simple case the operative identity is 
 probably that of my friend's personal appearance ; but the 
 judgment is not merely about that but about his whole 
 personality, of which his personal appearance is merely 
 taken as a sign. 
 
 Any assertion which is incredible because the identical 
 quality is wanting will illustrate the required structure. 
 There is a story commented on by Thackeray in one of his 
 occasional papers, which implied that the Duke of Wellington 
 took home note-paper from a club to which he did not
 
 72 TYPES OF JUDGMENT LECT. 
 
 belong. (Thackeray gives the true explanation of the fact 
 on which the suggestion was founded.) The identity con- 
 cerned in this case would be that of character. Can we find 
 an identity between the character involved in a piece of 
 meanness like that suggested and the character of the Duke 
 of Wellington ? No ; and prima fade therefore the judg- 
 ment is false. The identity which should bind it together 
 breaks it in two. But yet, again : supposing the external 
 evidence to be strong enough, we may have to accept a fact 
 which conflicts with a man's character as we conceive it. 
 That is so : in such a case one kind of identity appears to 
 contradict the other. I may think that I saw a man with 
 my own eyes, doing something which wholly contradicts his 
 character as I judge it. Then there is a conflict between 
 identity in personal appearance and identity in character, 
 and we have to criticise the two estimates of identity /. e. to 
 refer them both to our general system of knowledge, and to 
 accept the connection which can be best adapted to that 
 system. 
 
 We have got, then, as the active elements in Judgment a 
 Subject in Reality, the meaning of an idea, and an identity 
 between them. 
 
 Is this enough ? Have we the peculiar act of affirmation 
 wherever we have these conditions ? 
 
 This is not the question by what elements of language the 
 judgment is rendered. We shall speak of that in the next 
 lecture. The question is now, simply, "Is a significant 
 idea, referred to reality, always an assertion ? " 
 
 The first answer seems to be that such an idea is always 
 in an assertion, but need not constitute the whole of an
 
 iv IDEA AND AFFIRMATION 73 
 
 assertion. If we think of a subject in judgment which is 
 represented by a relative sentence, it seems clear that any 
 idea which can stand a predicate can also form a part of a 
 subject. " The exhibition which it is proposed to hold at 
 Chicago in 1893 " has in effect just the same elements of 
 meaning, and just the same reference to a point in our 
 world of reality as if the sentence ran, "It is proposed to 
 hold an exhibition at Chicago in 1893." In common par- 
 lance we should say, that in the former case we entertain an 
 idea or conceive or represent it while in the latter case 
 we affirm it. 
 
 But if we go on to say that the former kind of sentence 
 as truly represents the nature of thought as the latter, then 
 it seems that we are mistaken. Even language does not 
 admit such a clause to the rank of an independent sentence. 
 
 If we insist on considering it in its isolation, we probably 
 eke it out in thought by an unarticulated affirmation such as 
 that which constitutes an impersonal judgment; in other 
 words, we affirm it to belong to reality under some condition 
 which remains unspecified. Thus the linguistic form of the 
 relative clause, as also the separate existence of the spoken 
 or written word, produces an illusion which has governed 
 the greater part of logical theory so far as concerns the 
 separation between concept and judgment, /. e. between 
 entertaining ideas and affirming them in reality. In our 
 waking life, all thought is judgment, every idea is referred to 
 reality, and in being so referred, is ultimately affirmed of 
 reality. The separation of elements in the texture of Judg- 
 ment into Subjects and Predicates which, as separated, are 
 conceived as possible Subjects and Predicates, is therefore
 
 74 
 
 TYPES OF JUDGMENT 
 
 LF.cf. 
 
 claim 
 
 theoretical and ideal, an analysis of a living tissue, not an 
 enumeration of loose bricks out of which something is 
 about to be built up. 
 The kind (iii.) " Idea " has two principal meanings. 
 
 (") A P s y chical presentation and 
 
 (/3) An identical reference. 
 
 This distinction is the same as that between our course 
 of ideas and our world of knowledge. We must try now 
 to define it more accurately. 
 
 (a) An idea as a psychical presentation is strictly a par- 
 ticular. Every moment of consciousness is full of a given 
 complex of presentation which passes away and can never be 
 repeated without some difference. For this purpose a repre- 
 sentation is just the same as a presentation ; is, in fact, a 
 presentation. Its detail at any given moment is filled in by 
 the influence of the moment, and it can never occur again 
 with precisely the same elements of detail as before. If we 
 use the term " idea " in this sense, as a momentary particular 
 mental state, it is nonsense to speak of having the same idea 
 twice, or of referring it to a reality other than our mental life. 
 The idea in this sense is a psychical image. We cannot 
 illustrate this usage by any recognisable part of our mental 
 furniture, for every such part which can be described and 
 indicated by a general name, is something more than a 
 psychical image. We can only say that that which at any 
 moment we have in consciousness, when our waking per- 
 ception encounters reality, is such an idea, and so too is 
 the image supplied by memory, when considered simply 
 as a datum, a fact, in our mental history. 
 
 (/3) To get at the other sense of " idea " we should think
 
 IV MEANING 7; 
 
 of the meaning of a word ; a very simple case is that of a 
 proper name. What is the meaning of " St. Paul's Cathedral 
 in London"? No two people who have seen it have 
 carried away precisely the same hnage of it in their minds, 
 nor does memory, when it represents the Cathedral to each 
 of them, supply the same image in every detail and associ- 
 ation twice over to the same person, nor do we for a 
 moment think that such an image ts the Cathedral. 1 Yet 
 we neither doubt that the name means something, and that 
 the same to all those who employ it, nor that it means the 
 same to each of them at one time that it did at every other 
 time. The psychical images which formed the first vision 
 of it are dead and gone for ever, and so, after every occasion 
 on which it has been remembered, are those in which that 
 memory was evoked. The essence of the idea does not lie 
 in the peculiarities of any one of their varying presentations, 
 but in the identical reference that runs through them all, 
 and to which they all serve as material, and the content of 
 this reference is the object of our thought. 
 
 In order to distinguish and employ this reference it is 
 necessary that there should be a symbol for it, and so long 
 as it brings us to the object which is the centre of the 
 entire system, this symbol may vary within considerable 
 limits. 
 
 The commonest and most secure means of reference is 
 
 1 When we are actually looking at the Cathedral, we say, " That is 
 the Cathedral." Does not this mean that we take our momentary 
 image, to which we point, to be the reality of the Cathedral ? Not 
 precisely so. It is the "that," not our definite predication about it, 
 which makes us so confident. The " that " is identified by our judgment, 
 but goes beyond it.
 
 76 TYPES OF JUDGMENT LECT. 
 
 the word or name. 1 So confident are we in the "conven- 
 tional " or artificially adapted character of this mark or sign 
 of reference, that we are inclined to treat it as absolutely 
 unvarying on every occasion of utterance. But of course 
 it is not unvarying. It differs in sound every time it is 
 spoken, and in context and appearance every time we see 
 it in a written shape. Our reliance upon it as identical 
 throughout depends on the fact that it has a recognisable 
 character to which its variations are irrelevant, and which 
 practically crushes out these variations from our attention. 
 Unless we are on the look-out for mispronunciations or 
 misprints, they do not interfere at all with our attention to 
 the main reference of words. We know that it is almost 
 impossible to detect misprints so long as one reads a book 
 with attention to its meaning. This then is a fair parallel 
 to the distinction which we are considering between two 
 kinds of ideas. If the momentary sound or look of a word 
 is analogous to idea as psychical presentation, " the word " 
 as a permanent possession of our knowledge is analogous 
 to the idea as a reference to an object in our systematic 
 world, and is the normal instrument of such a reference. 
 But either with the word or without it there may be a 
 symbol of another kind. Any psychical image that falls 
 within certain limits may appear as the momentary vehicle 
 of the constant reference to an object. Just as in recog- 
 nising the reference of a word we omit to notice the accent 
 and loudness with which it is pronounced, or the quality of 
 the paper on which it is printed, just so in recognising the 
 
 1 "A name is a sound which has significance according to con- 
 vention," i. e. according to rational agreement. Ar. de Intcrp. 16 a 19.
 
 IV IDENTICAL REFERENCE 77 
 
 reference of a psychical image our attention fails to note 
 its momentary context, colouring, and detail. If it includes 
 something that definitely belongs to a systematic object in 
 our world of objects, that is enough, unless counteracted by 
 cross references, to effect the suggestion we require, and 
 that, and nothing else, arrests our attention for the moment. 
 When I think of St. Paul's Cathedral, it may be the west 
 front, or the dome seen from the outside, or the gallery seen 
 from the inside, that happens to occur to my mind ; and 
 further, that which does occur to me occurs in a particular 
 form or colouring, dictated by the condition of my memory 
 and attention at the moment. But these peculiarities are 
 dwarfed by the meaning, and unless I consider them for 
 psychological purposes, I do not know that they are there. 
 It is the typical element only, the element which points 
 to the common reference in which my interest centres, 
 that forms the content of the idea in this sense, taken 
 not as a transient feature of the mental complex, but as 
 definitely suggesting a constant object in our constructed 
 world. And it suggests this object because it, the typical 
 element, is a common point that links together the various 
 cases and the various presentations in which the object is 
 given to us. In this sense it is a universal or an identity. 
 
 How can this conception of a logical idea be applied to 
 a perfectly simple presentation ? It would be impossible so 
 to apply it, but there does not seem to be such a thing as 
 a simple presentation in the sense of a presentation that has 
 no connection as a universal with anything else. In the 
 image of a particular blue colour, we cannot indeed separate 
 out what makes it blue from what makes it the particular
 
 78 TYPES OF JUDGMENT LECT. 
 
 shade of blue that it is. But nevertheless its blueness 
 makes it a symbol to us of blue in general, and when so 
 thought of, crushes out of sight all the visible peculiarities 
 that attend every spatial surface. We understand perfectly 
 well that the colour is blue, and that in saying this we have 
 gone beyond the limits of the momentary image, and have 
 referred something in it as a universal quality to our world 
 of objects. An idea, in this sense, is both less and more 
 than a psychical image. It contains less, but stands for 
 more. It includes only what is central and characteristic 
 in the detail of each mental presentation, and therefore 
 omits much. But it is not taken as a mental presentation 
 at all, but as a content belonging to a systematic world of 
 objects independent of my thought, and therefore stands for 
 something which is not mere psychical image. 
 
 If therefore we are asked to display it as an image, as 
 something fixed in a permanent outline, however pale or 
 meagre, we cannot do so. It is not an abstract image, but 
 a concrete habit or tendency. It can only be displayed in 
 the judgment, that is, in a concrete case of reference to 
 reality. Apart from this, it is a mere abstraction of analysis, 
 a tendency to operate in a certain way upon certain psychical 
 presentations. Psychically speaking, it is when realised in 
 judgment a process more or less systematic, extending 
 through time, and dealing with momentary presentations 
 as its material. In other words, we may describe it as a 
 selective rule, shown by its working, but not consciously 
 before the mind for if it were, it would no longer be an 
 idea, but an idea of an idea. 
 
 Every judgment, whether made with language or without^
 
 IV TRUTH DEMANDS MEANING 79 
 
 is an instance of such an idea, which may be called a 
 symbolic idea as distinct from a psychical image; "sym- 
 bolic " because the mental units or images involved are not 
 as such taken as the whole of the object for which they 
 stand, but are in a secondary sense, as the word in a 
 primary sense, symbols or vehicles only. 
 
 Such ideas can have truth claimed for them, because they 
 have a reference beyond their mental existence. They 
 point to an object in a system of permanent objects, and 
 that to which they point may or may not suit the relation 
 which they claim for it. Therefore the judgment can only 
 be made by help of symbolic ideas. Mere mental facts, 
 occurrences in my mental history, taken as such, cannot 
 enter into judgment. When we judge about them, as in the 
 last sentence, they are not themselves subject or predicate, 
 but are referred to, like any other facts, by help of a 
 selective process dealing with our current mental images of 
 them. We shall not be far wrong then, if in every judgment, 
 under whatever disguises it may assume, we look for ele- 
 ments analogous to those which are manifest in the simple 
 perceptive judgment, " This is green," or " That is a horse." 
 The relation between these and more elaborate forms of 
 affirmation, such as the abstract judgment of science, has 
 partly been indicated in the earlier portion of this lecture. 
 The general definition of judgment has therefore been 
 sufficiently suggested on p. 72. Judgment is the reference 
 of a significant idea to a subject in reality, by means of an 
 identity of content between them.
 
 LECTURE V 
 
 THE PROPOSITION AND THE NAME 
 
 Judgment i. JUDGMENT expressed in words is a Proposition. Must 
 _ Judgment be expressed in words ? We have assumed that 
 
 guage, this need not be so. Mill l says of Inference that "it is an 
 operation which usually takes place by means of words, and 
 in complicated cases can take place in no other way." The 
 same is true of Judgment. 
 
 We may say in general that words are not needed, when 
 thinking about objects by help of pictorial images will do 
 the work demanded of the mind, /. e. when perfectly in- 
 dividualised connections in space and time are in question. 
 Mr. Stout 2 gives chess-playing as an example. With the 
 board before him, even an ordinary player does not need 
 words to describe to himself the move which he is about 
 to make. 
 
 Words are needed when we have to attend to the general 
 plan of any system, as in thinking about organisms with 
 reference to their type, or about political relations about 
 anything, that is, which is not of such a nature that the 
 members of the idea can be symbolised in pictorial form. 
 It would be difficult, for example, to comprehend the 
 respiration of plants under a symbolic picture-idea drawn 
 
 1 Logic, vol. I. c. i., init. * In Mind, no. 62.
 
 LECT. v WHAT IS A WORD? Si 
 
 from the respiration of the higher animals. The relations 
 which constitute a common element between the two pro- 
 cesses do not include the movements, feelings, and visible 
 changes in the circulatory fluid from which our image of 
 animal respiration is chiefly drawn ; and we could hardly 
 frame a pictorial idea that would duly insist on the chemical 
 and organic conditions on which the common element of 
 the process depends. In a case of this kind the word is the 
 symbol which enables us to hold together in a coherent 
 system, though not in a single image, the relations which 
 make up the content of our thought. 
 
 "Words" may be of many different kinds spoken, 
 written, indicated by deaf and dumb signs ; all of these are 
 derived from the word as it is in speech, although writing 
 and printing become practically independent of sound, and 
 we read, like the deaf and dumb alphabet, directly by the 
 eye. Then there may be any kind of conventional signals 
 either for letters, words, or sentences, and any kind of cipher 
 or memoria technica either for private or for general use 
 in these the " conventional " nature of language reaches its 
 climax, and the relation to a natural growth of speech has 
 disappeared. And finally there are all forms of picture- 
 writing, which need not, so far as its intrinsic nature goes, 
 have any connection with speech at all, and which seems 
 to form a direct transition between picture-thinking and 
 thinking through the written sign. 
 
 All these must be considered under the head of language, 
 as a fixed system or signs for meanings, before we can 
 ultimately pronounce that we think without words. 
 
 Every Judgment, however, can b.e expressed in words, 
 
 G
 
 82 THE PROPOSITION AND THE NAME LECT. 
 
 though not every Judgment need be so expressed or can 
 readily be so. 
 
 Proposi- 2. A Judgment expressed in words is a Proposition, which 
 sentence * s one k mc * ^ sentence - A command question or wish is a 
 sentence but not a proposition. A detached relative clause l 
 is not even a complete sentence. The meaning of the 
 imperative and the question seems to include some act of 
 w/7// the meaning of a proposition is always given out 
 simply for fact or truth. We need not consider any 
 sentence that has no meaning at all. 
 
 Difference 3- Almost all English logicians speak of the Proposition and 
 not ^ tne Judgment. 2 This does not matter, so long as we 
 
 tion and are agreed about what they mean. They must mean the pro- 
 Judgment. . . . . . , 
 
 position as understood, and this is what we call the judgment. 
 
 In order to make this distinction clear, let us consider the 
 proposition as it reaches us from without, that is to say, 
 either as spoken or as written. The words, the parts of such 
 a proposition, as we hear or read them, are separate and 
 successive either in time alone, or in time and space. 
 Further, the mere sounds or signs can be mastered apart 
 from the meaning. You can repeat them or copy them 
 without understanding them in the least, as e.g. in the case 
 of a proposition in an unknown language. So far, the pro- 
 position has not become a judgment, and I do not suppose 
 that any logician would admit that it deserved the name 
 even of a proposition. But if not, then we must not con- 
 fuse the attributes which it has before it becomes a pro- 
 position with those which it has after. 
 
 1 See above, Lect. IV. 
 
 2 So Mill, Venn, Jevons, Bain (see his note, p. 80).
 
 V HOW WE UNDERSTAND 83 
 
 Further, in understanding a proposition, or in construing 
 a sentence into a proposition (if the sentence only becomes 
 a proposition when understood), there are many degrees. I 
 read upon a postcard, "A meeting will be held on Saturday 
 next by the Women's Liberal Association, to discuss the 
 taxation of ground-rents." The meaning of such a sentence 
 takes time to grasp, and if the words are read aloud to us, 
 must of necessity be apprehended by degrees. We under- 
 stand very quickly that a meeting is to be held next 
 Saturday. This understanding is already a judgment. It 
 is something quite different from merely repeating the words 
 which we read. It consists in realising them as meanings, 
 and bringing these meanings together into a connected idea, 
 and affirming this idea to belong to our real world. The 
 meanings are not separate, outside one another, as the words 
 are when we first hear or read them. They enter into each 
 other, modify each other, and become parts of an ideal 
 whole. This gradual apprehension of a sentence recalls to 
 one the boyish amusement of melting down bits of lead in a 
 ladle. At first the pieces all lie about, rigid and out of 
 contact; but as they begin to be fused a fluid system is 
 formed in which they give up their rigidity and independ- 
 ence, and enter into the closest possible contact, so that 
 their movements and position determine each other. But 
 still some parts, like words not yet grasped, remain hard and 
 separate, and it is only when the melting is complete that 
 this isolation is destroyed, and there are no longer detached 
 fragments, but a fluid body such that all its parts are in the 
 closest connection with one another. 
 
 Thus then in understanding a sentence we have a judg-
 
 84 THE PROPOSITION AND THE NAME I.ECT. 
 
 ment from the first. The rest of the process of understand- 
 ing consists in completing the content of this judgment by 
 fusing with it the meanings of the words not yet apprehended ; 
 and in the completeness with which this is effected there will 
 always be great differences of degree between different 
 minds, and also between the same mind at different times. 
 Some of us attach a complete and distinct meaning to the 
 words " Women's Liberal Association " ; some of us do not 
 know, or have forgotten, exactly what it is, and what are its 
 aims and history. All of us have some conception of the 
 purpose described as " taxation of ground rents," but the 
 phrase conveys a perfectly definite scheme hardly to one in 
 a thousand readers. Nevertheless, in so far as we have some 
 symbolic idea which refers to this place or context in the 
 world of objects, the content of this idea enters into and 
 modifies the total meaning which in apprehending the 
 sentence before us we affirm of reality. The heard or 
 written proposition (or sentence, if it is not a proposition 
 till understood) serves as an instrument by which we build 
 up in our intellectual world a sort of plan or scheme of 
 connected meanings, and also, not subsequently but con- 
 currently with this work of building, affirm the whole content 
 thus being put together to be true of reality. Then we have 
 what I call a Judgment. It is not that the words are neces- 
 sarily forgotten ; they, or at least the principal significant 
 terms, are probably still in the mind as guides and symbols ; 
 but yet a constructive work has been done; a complex 
 experience has been called up and analysed, and its parts 
 fitted together in a certain definite order by the operation of 
 universal ideas or meanings, each of which is a system play-
 
 v THE SENTENCE IS THE UNIT 85 
 
 ing into other systems ; and the whole thus realised has been 
 added as an extension to the significance of the continuous 
 judgment which forms our waking consciousness. The in- 
 convenience of the term " proposition " is that it tends to 
 confuse the heard or written sentence in its separate words 
 with the proposition as apprehended and intellectually 
 affirmed. And these two things have quite different 
 characteristics. 
 
 4. Thus we must be very careful how we apply the con- Parts of 
 ception of "parts of speech." The grammatical analysis P eeCt> 
 which classifies words as substantives, adjectives, adverbs, 
 verbs, and the like, is not to be taken as telling us what 
 words are by themselves, but just the opposite, viz. what 
 they do when employed in a significant sentence. They 
 are studied separately for convenience in attending to them, 
 as we may study the wheels and pistons of an engine ; but 
 the work which gives them their names can only be done 
 when they are together. This truth is often expressed by 
 saying that " the sentence is the unit of language," /. e. a 
 word taken by itself cannot have a complete meaning 
 unless it is a verb, or used with verbal force, for a verb is 
 an unanalysed sentence. If any one uses a substantive or 
 adverb by itself, we think that he has not finished his sen- 
 tence, and no meaning is conveyed to our minds. We ask 
 him, "Well, what about it ? " The same is true, as we saw, 
 of a relative clause. If we read in a newspaper such a 
 clause as this, "The epidemic of influenza, which has 
 appeared in England for three successive seasons," followed 
 by a full stop, we should infer, without hesitation, that some 
 words had dropped out by accident. Of course such a
 
 86 THE PROPOSITION AND THE NAME LECT. 
 
 combination of words would make us think something, but 
 the meaning which we might ascribe to it would be con- 
 jectural; we should necessarily complete the thought for 
 ourselves by some affirmation some relation to reality 
 while recognising that no such relation was given in the 
 clause as we read it. Nothing less than a sentence, or, 
 omitting the wish and the command, nothing less than a 
 proposition, conveys a meaning in which the mind can 
 acquiesce as not requiring to be supplemented conjecturally. 
 There are traces in language that indicate the sentence to 
 have been historically prior to the word. I question whether 
 the word could be certainly distinguished within the sen- 
 tence in early languages that have not been reduced to 
 writing. The tendency of reflective analysis, as in grammar 
 and dictionaries, is to give it a more and more artificial 
 isolation. The Greeks did not separate their words in 
 writing, and they wrote down the change in a terminal con- 
 sonant produced by the initial letter of the next word, just 
 as if it was within a compound word. Nor had they really 
 any current term co-extensive with our " word." Where we 
 should say "the word 'horse'" they most commonly use 
 the neuter article " the " followed by the word in question 
 as if in quotation-marks (" the ' horse ' "). In defining noun 
 and verb, Aristotle has no simple class name like " word " 
 to employ as a common element of the definition, but uses 
 the curious description " a portion of discourse, of which no 
 part has a meaning by itself." 
 
 Of course, single words often stand as signs for proposi- 
 tions. It is interesting to note the pregnant meaning of a 
 single word in the mouth of a child, Thus " stool " was
 
 V TWO PARTS OF LOGIC 87 
 
 used to mean "(i) Where is my stool? (2) My stool is 
 broken ; (3) Lift me on to the stool ; (4) Here is a stool." l 
 There is in this an interesting conflict of form and meaning, 
 owing to the child of European race having at command 
 only "parts of speech." In a less analytical language he 
 might have at command a sound corresponding to a sentence 
 rather than to a "noun substantive." 
 
 The verb of inflected languages, 2 such as Greek or Latin, 
 in which the " nominative case " need not be supplied even 
 by a pronoun, is the type for us of a sentence not yet 
 broken up. 
 
 The bearing of this truth on Logic is to make us treat 
 it in two parts and not in three. We do not treat of 
 Name, Proposition, Syllogism, or of Concept, Judgment, 
 Inference, but only of the two latter parts. The name or 
 concept has no reality in living language or living thought, 
 except when referred to its place in a proposition or judg- 
 ment. We ought not to think of propositions as built up 
 by putting words or names together, but of words or names 
 as distinguished though not separable elements in proposi- 
 tions. Aristotle takes the simple and straightforward view. 
 " A term is the element into which a proposition is broken 
 up, such as subject and predicate." 3 Of course different 
 languages separate the parts of the proposition very differently, 
 
 1 Preyer, quoted in Hoffding. Psych., 176. 
 
 2 In German and English, though the verb is inflected, custom forbids 
 it to stand without the pronoun. 
 
 3 Anal, prior., 2^b, 16. The opposite view seems to be expressed 
 in the beginning of the trepl 'Epyurjj'ei'as, that the separate word corre- 
 sponds to the separate idea. I have attempted to explain this as an 
 illusion, p. 73, above.
 
 88 
 
 THE PROPOSITION AND THE NAME 
 
 LECT. 
 
 Dcnota- 
 
 Connota- 
 tion. 
 
 and uneducated people hardly separate them at all. 
 Formal Logic breaks down the grammatical meaning of 
 " name," so far as to treat as a " logical name " any com- 
 plex words that can stand as Subject or Predicate in a 
 Proposition (e. g. a relative clause). 
 
 5. The doctrine of the meaning of names has suffered 
 ^ rom ^ ie ^ r relation to propositions not being borne in mind. 
 Mill's discussion l is very sensible, but, as always, very care- 
 less of strict system. More especially it seems a pity to 
 state the question as if it concerned a division of names 
 into Connotative and Non-connotative ; because in this way 
 we from the first let go of the idea that the meaning of a 
 name has necessarily two aspects, 2 and we almost bind our- 
 selves to make out that there are some non-connotative 
 names. It is better to consider this latter subject on its 
 merits. Mill says that an ordinary significant name such 
 as "man" "signifies the subjects directly, the attributes 
 indirectly; it denotes the subjects, and implies or involves 
 or indicates, or, as we shall say henceforth, connotes^ the 
 attributes." In short, the denotation of a name consists of 
 the things to which it rt/plies, the connotation consists of 
 the properties which it wplies. The denotation is made 
 up of individuals and the connotation of attributes. Deno- 
 tation is also called Extension, especially if we are speaking 
 of Concepts rather than of names. Connotation is then 
 called Intension. In the German writers it is more usual 
 to say that the Extension or Area (Umfang) consists not 
 of the individuals, but of the species that are contained in 
 
 1 Logic, Bk. I. c. ii. 5. Cf. Venn, 174 and 183, and Bain, 48. 
 2 See Bradley, p. 155.
 
 V OBJECTS AND ATTRIBUTES 89 
 
 the meaning of a general name. They oppose it to Con- 
 tent (In/ialf), corresponding to our "Connotation." Thus 
 the "Area" of "rose" would not be the individual roses in 
 the world, but rather all the species of rose in the world 
 (Rosa Canina, Rosa Rubiginosa, etc.). This raises a diffi- 
 culty as to the denotation of a specific name, but perhaps 
 represents the actual process of thought, in the case of a 
 generic name, better than that which Mill adopts. The 
 difference is not important. 
 
 Well, then, according to Mill, when we say, "The 
 Marshal Niel is a yellow rose," we refer directly to a 
 group of real or possible objects, and we mean that all 
 these individual objects are yellow roses. The attributes 
 are only mentioned by the way, or implied. So Dr. Venn 
 says that the denotation is real, and the connotation is 
 notional. 
 
 But there is another side to this question. The objects 
 may be what you mean, but the attributes seem to be the 
 meaning, for how can you (especially on Mill's theory of 
 the proposition) refer to any objects except through these 
 attributes, unless indeed you can point to them with your 
 finger ? And so again it seems, especially if we consider 
 Mill's account of predication, as if the Connotation were 
 the primary meaning and the Denotation the secondary 
 meaning. The Connotation determines the Denotation ; 
 and if we " define " the meaning of the name it is the 
 Connotation that we state. And so Mill tells us two or 
 three pages further on, that whenever the names given to 
 objects have properly any meaning, the meaning resides not 
 in what they denote, but in what they connote. In short,
 
 90 THE PROPOSITION AND THE NAME LECT. 
 
 the denotation of a general name is simply the meaning of 
 its plural, or of its singular, in that sense in which it implies 
 a plural, while the connotation is the meaning per se, not 
 considered in its instances. 
 
 It is clear then that every name has these two kinds of 
 meaning first, a content, and then instances, whether pos- 
 sible or actual, of the content ; and the two are obviously 
 inseparable, although they are distinguishable. Ultimately, 
 indeed, the denotation itself is an attribute, and so part of 
 the connotation. It is one of the attributes of man to be 
 a unit in the plurality men, *'. e. to be "a man." It may 
 be said that some names have no plural. If so, these 
 would be non-denotative rather than non-connotative, but in 
 fact this is not true. The content of a significant name can 
 always, unless hindered by a special convention (see below 
 on proper names), be prima facie regarded, in respect of 
 its actual embodiment, as a unit against other possible 
 units. Granting that there may be an object, which accord- 
 ing to our knowledge can only be real as an isolated case, 
 the very consideration of it as such a case is enough to 
 distinguish its existence, whether real or possible, from its 
 content. Thus, as a real or possible existence, the object 
 is ipso facto considered in the light of a particular, and as 
 capable of entering into a plurality. But its nature or con- 
 tent, the meaning of its name, cannot enter into a plurality. 
 Two meanings, two connotations, are alternative and irre- 
 concilable. Denotation and connotation are thus simply 
 the particular, or particulars, which embody or are thought 
 of as embodying a content, and the single or universal 
 content itself.
 
 V MERE IDENTITY 91 
 
 6. Therefore I think that Mill is wrong, when he goes Have Pro 
 on, " The only names of objects which connote nothing are 
 Proper Names, and these have, strictly speaking, no signifi- tion ? 
 cation." * If the name has no signification, for what reason, 
 or by what means, is it attached to a person or a place ? 
 You may say that it is only a conventional mark. But a 
 mark which has power to select from all objects in the 
 world, and bring to our minds, a particular absent object, is 
 surely a significant mark. Granted that it is conventional, 
 yet by what mechanism, and for what purpose, does the 
 convention operate? 
 
 Mill's point, however, is quite clear. To be told the 
 name of a person or object does not inform us of his or its 
 attributes. Directly, it only warns us by what sign the same 
 person or object will be recognisable in language again. 2 If 
 a name is changed, the new name tells us nothing different 
 from the old, 3 whereas if an object that was called vegetable 
 is now called animal, our conception of it is radically trans- 
 formed. A name expresses the continued identity of an 
 object, and this implies only a historical continuity of attri- 
 butes and relations, and no constant attribute whatever. 
 
 1 Cf. Venn, 183 ff, and Bradley, 156. 
 
 2 We cannot make it a distinctive mark of proper names that they 
 recur in different and quite disconnected meanings, because the words 
 which are used as general names have this same property. Nor can we 
 say that a proper name is not used in the same sense of more than one 
 object. Family names and national names make this plainly untrue. 
 Through these, and names typically employed, there is a clear gradation 
 from proper to general names. 
 
 3 The case of marriage may be urged. But a lady's change of name 
 does not by itself indicate marriage. It is a mere fact, which may have 
 various explanations. The change of title (from "Miss "to "Mrs.") 
 is more significant, but it is not a change of name.
 
 92 THE PROPOSITION AND THE NAME LECT. 
 
 Thus i proper name is a contradiction in terms. 1 A 
 name should have a meaning. But a meaning cannot be 
 proper that is, particular. The name-word is therefore 
 like a demonstrative pronoun, if this were attached, by a 
 special convention, to one identifiable object only. It 
 acquires meaning, but its meaning is an ever-growing contra- 
 diction with its usage. The meaning is necessarily general, 
 the usage is ex hypothesi particular. 
 
 This convention of usage, which prevents a proper name 
 from becoming general, i. e. from being cut loose and used 
 simply for its meaning, is always on the point of breaking 
 down. 2 Christian names usually indicate sex ; family names, 
 though now with little certainty, descent and relationship. 
 There are germs of a general meaning within the several 
 usages of names ; while a Solon, a Croesus, a Christian, a 
 Mahometan, have become purely general names cut loose 
 from all unique reference. Still in a proper name, as such, 
 we have no right to build on any general meaning. Recog- 
 nition is its only purpose ; and the law permits, it has been 
 said, that a man should have one name for Mondays, 
 Wednesdays, and Fridays, and another for Tuesdays, Thurs- 
 days, and Saturdays. The essence of a name is a reference 
 to unique identity; it employs meaning only to establish 
 identity. 
 
 What kinds of things have proper names given, then? 
 Always things individually known to the people who give 
 
 1 So, from the complementary point of view, is a general name. A 
 name, it may be urged, is meant to designate a particular thing or 
 things. And this a name with a true "meaning " cannot do. 
 
 8 See note on last page.
 
 v NAMES IN HISTORY 93 
 
 the name, and interesting to them for some reason beyond 
 generic or specific qualities. Pet animals have names, 
 when other animals of the same kind have not. The 
 peasants throughout England use names, it is said, for all 
 the fields, although strangers are not usually acquainted 
 with them. 
 
 A Proper Name, then, has a connotation, but not a 
 fixed general connotation. It is attached to a unique 
 individual, and connotes whatever may be involved in 
 his identity, or is instrumental in bringing it before the 
 mind. 
 
 When we think of history, the importance of proper 
 names becomes very great. This is the characteristic logical 
 difference between history and science. "England" and 
 " France " are proper names, names of individual existences 
 in contact with our world of perception, not scientific ab- 
 stractions. Even the words, " 1892 A.D.," are partly of the 
 nature of a proper name. They say nothing merely general 
 or abstract about this year ; they assign the year a name by 
 counting forwards from a unique point in the series of years, 
 itself designated by the name of a historical personage. 
 Everything that is simply distinguished by its place in the 
 series of events in space and time is in some degree a proper 
 name. Thus we could not identify the French Revolution 
 by mere scientific definition. It is known by its proper 
 name, as a unique event, in a particular place and time. 
 When thus identified it may have all kinds of general ideas 
 attached to it. It would be hard to show that " Our earth," 
 " Our solar system " are not proper names, in virtue of their 
 uniqueness.
 
 94 
 
 THE PROPOSITION AND THE NAME 
 
 LfcCf. 
 
 Inverse 
 ratio of 
 Connota- 
 tion, and 
 Denota- 
 tion. 
 
 7. It has sometimes been said that Connotation is in 
 inverse ratio l to Denotation. Mill explains the fact upon 
 which any such idea rests. 2 If we arrange things in classes, 
 such that the one class includes the other e.g. Species 
 " Buttercup," Genus " Ranunculus," Order " Ranunculacese," 
 of course the genus will contain many species besides the 
 one mentioned, and the order many genera besides the one 
 mentioned. The object of the arrangement is that they 
 should do so, and thus bring out the graduated natural 
 affinities which prevail in the world. Thus the denotation 
 of the genus-name is larger than that 3 of the species, and 
 the denotation of the order-name is larger than that of the 
 genus-name. 
 
 But further, in such an arrangement the genus can 
 contain only the attributes which are common to all the 
 species, and the order can contain only the attributes 
 which are common to all the genera; so the genus-name 
 implies fewer attributes (less connotation) than any one 
 species-name under it, and the order-name implies fewer 
 attributes (less connotation) than any one genus-name 
 under it. 
 
 That is the fact which suggests the conception of Denota- 
 tion and Connotation as varying inversely. 
 
 But in any case it would not be right to speak thus 
 mathematically of an inverse ratio, because there is no 
 meaning in a numerical comparison of attributes and indi- 
 
 1 See Venn, p. 1 74, for reference to Hamilton. Venn points out the 
 fallacy. 
 
 2 Logic, Bk. I. ch. vii. 5. 
 
 3 Or "than the species," if we take the denotation as made up of 
 species.
 
 V ABSTRACTION CRITICISED 9$ 
 
 viduals, and the addition of one attribute will exclude some- 
 times more and sometimes fewer individuals. 1 
 
 And there are more important objections to the whole 
 idea of a corresponding gradation in these two kinds of 
 meaning. The idea of abstraction thus implied is altogether 
 wrong. The meaning of a genus-name does not omit the 
 properties in which the species differ. If it did, it would 
 omit nearly all properties. What happens is that the genus- 
 idea represents the general plan on which the species are 
 built, but provides for each of the parts that constitute the 
 whole, varying in the specific cases within certain limits. 
 Thus in the Ranunculacese some species have no petals. 
 But we do not omit the character " petals " from the genus- 
 idea. We state the general plan so far as this element is 
 concerned as " Petals five or more ; rarely none." This is 
 read by a botanist to mean that in some groups the petals 
 tend to be aborted, and sometimes are actually missing. In 
 a symbolic representation of the genus-idea such a property 
 may stand as A, and its various specific forms as Ai, Az, 
 A3, etc. There is nothing to prevent these specific phases 
 approaching and sometimes reaching zero. No doubt if 
 the classification is pursued in the direction of " universals " 
 containing fewer and fewer properties, it is possible to arrive 
 at concepts which appear to have a larger denotation and a 
 smaller connotation than those "below "them. "Ranun- 
 culaceae," "Dicotyledons," "Plants," "Organisms." 
 
 But this is only because we choose to form our system by 
 that process of abstraction which consists in leaving out 
 properties. E. g. comparing Frenchmen with men in general, 
 1 See Jevons, p. 40.
 
 96 THE PROPOSITION AND THE NAME LECT. 
 
 we assume that " Frenchman " indicates () all the qualities 
 of humanity as such, and (/3) the qualities of French humanity 
 in addition to these. But is this so in fact? Humanity, 
 considered as a wider, and therefore as a deeper, idea, may 
 have more content, as well as more area, than Frenchmanity. 
 We do not really, in thinking of humanity, omit from our 
 schematic thought all references to qualities of Greek, Jew, 
 English, and German, and their bearing and interaction 
 upon one another. It is only that we have been drilled to 
 assume a certain neatness in the pyramidal arrangement by 
 which we vainly try to reduce the meaning of a great idea to 
 something that has no system and no inter-relation of parts, 
 but approaches as near as possible in fixity to the character 
 of a definite image, though far removed from such a character 
 in the impossibility of bringing it before the mind. 
 
 So we can only say, " the greater the denotation the less 
 the connotation," and vice versa, in as far as we arrange 
 ideas by progressive abstraction in the sense of progressive 
 omission. But it is not the only way of regarding them. 
 Things may develop new inter-relations as their number 
 increases. Has the community, as Mr. Bradley asks, less 
 meaning than the individual person? But we must not 
 consider the community, would be the answer; we must 
 simply consider the relation of an idea of one individual to 
 any idea that applies to many individuals. This is simply 
 to rule out those relations that arise within progressively 
 larger wholes. We can do so, if we think the exclusion 
 necessary in the interests of logical purity, but it is only by 
 doing so that we can maintain the traditional view of conno- 
 tation and denotation. It is worth while to think out the
 
 v MAN AND ANIMAL 97 
 
 matter for ourselves in relation to such familiar ideas as 
 those of man and animal. It is plain that the idea of 
 " animal " cannot omit all reference to intelligence, but must 
 in some way allow for the different phases of this property 
 which run throughout the animal kingdom, and only find 
 a climax in man. And it is plain also, that even if intelli- 
 gence were wholly omitted, this would not leave behind, as 
 in a simple stratification, properties in which the whole 
 animal kingdom was the same. Man's animality is modified 
 throughout in a way corresponding to his rationality, so that 
 no general idea could be framed including him and other 
 animals, simply by collecting properties which are the same 
 and omitting those which are different. The idea of " man " 
 really becomes richer when considered in the light of a 
 comparison l with the rest of the animal world. Our great 
 systems of natural classification, representing affinities 
 graduated by descent, are what give the view which we 
 have criticised a certain objective importance. But they 
 do not establish it as an exclusive logical doctrine. 
 
 1 If we insist on throwing the whole of this comparison, in explicit 
 shape, into the complete idea of man, then the progress to the idea 
 "animal" can add nothing; even so, however, it loses nothing, but 
 simply becomes the same set of relations, looked at, so to speak, from 
 the other end. 
 
 11
 
 LECTURE VI 
 
 PARTS OF THE JUDGMENT, AND ITS UNITY 
 
 Parts of i. THE result of taking the Judgment as one with the 
 ment & ' ^ >TO P sl ^ on nas been to assume that its parts were the same 
 as those of the Proposition ; l and moreover the same as 
 those of the Proposition in a very artificial form, viz. as 
 analysed into three separable elements, "Subject," "Predi- 
 cate," " Copula," commonly represented in the examples 
 of the text-books by Substantive, Adjective or Substantive, 
 and the Verb " is." 
 
 For the operation of Formal Logic it is almost necessary 
 to have these parts, because it is requisite to transpose the 
 terms (as in Conversion) without changing their meaning, 2 
 and to get rid of tenses, which do not belong to Scientific 
 Judgment, and are very troublesome in Formal Inference. 
 
 Thus in Formal Logic we prefer the shape of sentence 
 " Gold is lustrous " to " Gold glitters," and " The bridge is 
 
 1 This assumption involves (see Lecture V.) a confusion between the 
 Proposition as thoroughly understood, and the Proposition as a series 
 of partially significant sounds or signs. For obvious reasons, this 
 confusion is very readily made. 
 
 2 If the ' ' predicate " is a Substantive, this presents no difficulty ; 
 and if it is an Adjective, it can be done by a little straining of grammar, 
 or the insertion of "thing" or "things." With a verb it is more 
 clumsy.
 
 LECT. vi COPULA NOT A LINK 99 
 
 cracked " to " There is a crack in the bridge." And prac- 
 tically all propositions can be thrown into this shape, which 
 is convenient for comparing them. The educational value 
 of elementary formal logic consists chiefly, I am convinced, 
 in the exercise of paraphrasing poetical or rhetorical asser- 
 tions into this typical shape, with the least possible sacrifice 
 of meaning. The commonest mistakes in the work of 
 beginners, within my experience as a teacher, consist 
 in failures to interpret rightly the sentence given for 
 analysis. 
 
 But this type is not really ultimate. The judgment can 
 be conveyed without a grammatical subject, and without 
 the verb " is " indeed without any grammatical verb at all. 
 On the whole this agrees with Mill's view in the chapter 
 "Of Propositions." 1 He points out ( i) that we really 
 need nothing but the Subject and Predicate, and that the 
 copula is a mere sign of their connection as Subject and 
 Predicate. He does not, however, discuss the case in which 
 the grammatical Subject is absent. 
 
 2. In analysing the Judgment as an act of thought we Copula, 
 may begin by dismissing the separate Copula. It has no 
 separate existence in thought corresponding to its separate 
 place in the typical proposition of Formal Logic. It has 
 come to be considered separately, because the abstract verb 
 "is" is used in our languages as a sign of the complete 
 enunciation. But there is not in the Judgment any separate 
 significant idea any third idea coming in between the 
 Subject and Predicate of Judgment. We should try to 
 think of the Copula not as a link, separable and always 
 1 Mill's Logic, Bk. I. ch. iv.
 
 ioo TARTS OF THE JUDGMENT, AND ITS UNITY LECT. 
 
 intrinsically the same, 1 connecting two distinct things. We 
 should think of it rather as the grip with which the parts 
 of a single complex whole cohere with one another, differing 
 according to the nature of the whole and the inter-depend- 
 ence of its parts. Benno Erdmann 2 has strikingly expressed 
 this point of view by saying, that in the Judgment, " The 
 dead ride fast," the Subject is " the dead," the Predicate 
 "fast riding," and the Copula "the fast riding of the dead" 
 In other words, the Copula is simply the Judgment con- 
 sidered exclusively as a cohesion between parts of a complex 
 idea, the individual connection between which can only be 
 indicated by supplying the idea of those parts themselves. 
 
 Arc Sub- 3. The explicit Predicate is more necessary than the 
 ject and ,. .. <-, , . 
 
 Predicate explicit Subject. 
 
 necessary? -\y e have spoken of Judgments expressed by one word, 
 "Fire!" "Thieves!" etc., and also of impersonal Proposi- 
 tions, " It is raining," " It is thawing." These two classes 
 of Judgments show hardly any explicit Subject at all. But 
 we could not assert anything without a Predicate that 
 would be to assert without asserting anything in particular. 
 
 As these Judgments have, roughly speaking, a Predicate 
 and no Subject, I do not think it convenient to call them, 
 with Dr. Venn, existential judgments. It is true that they 
 refer to reality, but their peculiarity is in not referring to a 
 distinct subject. And when used for definite and complex 
 assertions they become very artificial, e.g, "There is a 
 
 1 In a comic Logic, with pictures, meant to stimulate dull minds at 
 a University, I have seen the Copula represented as the coupling-link 
 between two railway carriages. This is an excellent type of the way 
 in which we should not think of it. 
 
 2 Logik, p. 189.
 
 vr SUBJECT UNNECESSARY 101 
 
 British Constitution by which our liberties are guaranteed." 
 Instead of organising the content of the Judgment, such a 
 form of assertion simply tosses the whole of it into the 
 Predicate in a single mass. 
 
 The question is only one of words ; but it appears to me 
 more convenient to reserve the term Existential judgments 
 for those highly artificial assertions which actually employ 
 the Predicate "exist "or " existence," e. g. "Matter exists." 
 These are at the opposite end of the scale from those last- 
 mentioned, and are the nearest approach to Judgment with 
 Subject and no Predicate. That is to say, their Predicate 
 is the generalised abstract form of predication l without any 
 special content the kind and degree of existence asserted 
 being understood from the context. 
 
 Except, however, in the case of these peculiarly abstract 
 and reflective assertions, it must be laid down that a pre- 
 dicated content is necessary to judgment, while an explicit 
 subject of predication is unnecessary. 
 
 4. If it is possible, in some cases, to throw the whole Two Ideas 
 content of judgment into the predicate, this rather disposes OI 
 us to criticise the notion that there must be two distinct 
 matters, objects, ideas, or contents, in every judgment. 
 The notion in question has two forms. 
 
 It is thought that the Judgment consists in putting two 
 ideas together, 2 or, 
 
 1 Expressed in Greek by the word corresponding to "is," used with 
 an accent, which does not belong to it in its ordinary use. He is good 
 = aya.e6s fffri ; lie exists = ?<TT. 
 
 2 For this conception, see Hamilton's Lectures on Logic, \. 22J, and 
 for a criticism on it, Mill's Logic, Bk. I. ch. v., init. Mr. Venn seems 
 to incline to Hamilton's view, but I do not feel sure that he intends to
 
 102 PARTS OF THE JUDGMENT, AND ITS UNITY LECT. 
 
 That the Judgment consists in comparing two or more 
 things. 1 
 
 Two Ideas. (a) The notion of "two ideas "has two principal diffi- 
 culties. 
 
 Notion of (i-) In its simplest shape the notion of " two ideas " in- 
 ti^rfit volves the great blunder which I explained in Lecture IV. 
 
 pure and - It suggests that the parts of Judgment are separate and 
 simple. . , . , 
 
 successive psychical states, and that the Judgment consists 
 
 in a change from the one to the other. Herbert Spencer, 
 as I understand him, considers every relation to be appre- 
 hended as a mental change or passage from one idea to 
 another. This view would degrade logical connection into 
 mere psychical transition. I do not say that there is no 
 psychical transition in Judgment. I do say that psychical 
 transition is not enough to make a Judgment. The parts 
 of Judgment, as we saw in the last lecture, do not succeed 
 one another separately like the parts of a sentence. The 
 relation between Subject and Predicate is not a relation 
 between mental states, but is itself the content of a single 
 though continuous mental state. Mill has rightly touched 
 on this point. "When I say that fire causes heat, do I 
 mean that my idea of fire causes my idea of heat ?" 2 and so 
 on. The fact is that " Fire-causing-heat " is itself the single 
 content or meaning represented in my symbolic idea ; it is 
 not a succession of psychical states in my mind, or a passage 
 from the idea of fire to the idea of causing heat. 
 
 discuss the question in the form in which it is referred to in the text. 
 See his Empirical Logic, pp. 210 and 21 1. 
 
 1 See Jevons, pp. 6l-2; and Mill, Bk. I. ch. iii., init.; and ch. iv., 
 init. 
 
 2 Logic, Bk. I. ch. v. I.
 
 VI SUBJECT MUST BE REALITY 103 
 
 (ii.) But further, understanding now that the Judgment is Absence of 
 composed of a single ideal content, and is not a transition 
 from one mental state to another, there is still a difficulty 
 in the conception that its component elements are nothing 
 but ideas. If the Subject in Judgment is no more than an 
 ideal content, how, by what means, does the Judgment 
 claim to be true of Reality ? " The Subject cannot belong 
 to the content or fall within it, for in that case it would be 
 the idea attributed to itself." 1 If the Subject were only a 
 part of an ideal content it would not claim to be true of 
 Reality, and where it appears to be only an ideal content 
 there is much dispute in what sense the Judgment does 
 claim to be true of Reality. " Violations of a law of nature 
 are impossible." " The three angles of a triangle are equal 
 to two right angles." " All trespassers will be prosecuted." 
 In these Judgments we should find it hard to make out that 
 the Subjects are real things corresponding to our ideas. And 
 yet, if they are not, how can the Judgment attach itself to 
 Reality ? This is the difficult question of the distinction 
 between the categorical and the hypothetical Judgment, and 
 we shall have to return to it. In the meantime, we must 
 adhere to our judgment of perception as the true underlying 
 type. The Subject is here not an idea, but is the given 
 reality, this or t/iat, and the Judgment is not a conjunction 
 of two ideas, but is present reality qualified by an idea. 
 We say, " It is very hot," meaning that heat, the general 
 quality embodied for us in an ideal content, is true of 
 forms one tissue with the surroundings which here and 
 now press upon our attention. Or again, "This is red," 
 1 Bradley's Principles of Logic, p. 14.
 
 104 PARTS OF THE JUDGMENT, AND ITS UNITY LECT. 
 
 /. e. the content of the idea red is what my attention selects 
 and emphasises within the mass of detail presented to it in 
 its own unique focus which the pronoun " this " simply 
 points out as though with the finger. We shall find such 
 a structure underlying all the more artificial forms of 
 Judgment. 
 
 Two (/3) Thus it would seem that Jevons and Mill are much 
 
 nearer the real point when they say that the proposition has 
 to do with two Things, or with a Thing and a group of 
 Things. But we must notice in passing that Mill, 1 after 
 fighting hard against calling them Ideas, takes our breath 
 away by saying that they are states of consciousness. There 
 is, of course, a difficulty, which I will not try to deal with 
 now, in the fact that however much we refer to things, we 
 have nothing to work with intellectually but our ideas of 
 them, and in some types of Judgment the reference to real 
 things is difficult to trace. Mill further emphasises this by 
 showing, that what we assert in ordinary general Judgment is 
 co-existence of attributes. 2 " Now when we say, Man is 
 mortal, we mean that wherever these various mental and 
 physical phenomena (the attributes of man) are all found, 
 then we have assurance that the other physical and 
 mental phenomenon called death, will not fail to take place." 
 That is, no doubt, a very indirect way of referring to the 
 real things which we call men. Moreover, he treats all 
 conclusions in geometry and mechanics as hypothetical. 3 
 All this we shall have to return to, in order to reconcile it 
 with our doctrine ; which is apparently coincident with 
 
 1 Logic, Bk. I. cli. v. 5. - Ibid., 4. 
 
 3 Ibid., lik. II. ch. vi. 3,4.
 
 vi JUDGMENT AND COMPARISON 105 
 
 Mill's view in the place first alluded to, that the subject in 
 Judgment is always reality. 
 
 But our point at present is only the duality ascribed to 
 the Judgment by saying that it essentially deals with two 
 things or groups of things. Jevons even says l that every 
 Judgment is a comparison of two things though these 
 " things " are really, it would seem, groups of things. 2 We 
 thus have it impressed upon our minds that there is one 
 " thing " corresponding to the Subject-word (or clause) of 
 the Propositional sentence, and another " thing " corre- 
 sponding to the Predicate-word (or clause), and that these 
 are somehow separate, like two railway carriages, till we 
 bring them together by the coupling-link of the copula. 
 This is a very inconvenient way of looking at the 
 matter. It is not true that all Judgment is comparison, 
 in the proper and usual sense of the word. It is not 
 true that Judgment involves two things; two or more 
 things may be mentioned in a Judgment, but they cannot 
 correspond respectively to the Subject and Predicate. 
 It is a real Comparison if you say, " A.B. is taller than 
 CD.," but C.D. is here not a term in the Judgment. The 
 one person, A.B., is qualified by the ideal content " taller 
 than C.D.," and the idea of A.B. so qualified is referred to, 
 or discriminated within, perceptive reality. Comparison is 
 a rather complex process, and consists in a cross-reference 
 by which each of two objects is judged according to a 
 standard furnished by the other ; but this complex process 
 is not necessary to all Judgment, and cannot be expressed 
 with complete convenience in a single Judgment. And in 
 1 Elementary Lessons in Logic, p. 6l. - Ibid., p. 62.
 
 lo6 PARTS OF THE JUDGMENT, AND ITS UNITY LECT. 
 
 any case the two objects that enter into the comparison do 
 not correspond to two essential parts of Judgment. 
 
 It is far more simple and true to say that Judgment is 
 always the analysis and synthesis of elements in some one 
 thing or ideal content. " Gold is yellow " has not within it, 
 as Jevons says it has, 1 any direct comparison of gold with 
 other yellow substances. It simply drags to light the 
 property " yellow " as distinct within the complex of attributes 
 belonging to gold, while at the same time insisting that this 
 property this meaning of an idea belongs to, is of one 
 piece with, perceived reality in so far as gold is given in 
 such reality. The Judgment exhibits the content in its 
 parts. It breaks it up, and pronounces it to be all of one 
 tissue, by one and the same indivisible act. We should 
 practically have a much fairer chance of seeing clearly what 
 Judgment is if we began by considering it as not two things 
 or two terms but as one thing or one term drawn out into 
 elements by discriminating selection. Even if the paradox 
 that every " Thing " is a Judgment neglects some necessary 
 distinctions, I am convinced that we shall understand 
 Judgment much more clearly if we do our best to approach 
 it from this point of view. Whenever we look or listen, and 
 notice features and qualities in the perceptions that arrest the 
 eye and ear, we are rapidly and continuously judging. 
 " The fire is crackling," " The daylight is waning," " That 
 bookshelf is not full," " The window-curtain is twisted." In 
 none of these cases is there any separation other than an 
 intellectual distinction between the predicated content and 
 the perceived reality. The Judgment is simply a distinct 
 1 &( t dt,
 
 VI UNITY OF JUDGMENT 107 
 
 insistence on a quality within a certain focus of reality as 
 belonging to that reality. This is the fundamental nature 
 of Judgment. 
 
 Therefore, to draw our conclusion as to the Unity of the 
 Judgment, it is not a transition from one mental state to 
 another; the relation of which it consists is not between 
 ideas in it, but is the content of the idea which forms it. 
 Judgment is not primarily comparison between two things : 
 it is a thing or content displayed as possessing some definite 
 relation or quality within its identity. Every Judgment is 
 the content of one idea, but you may of course distinguish 
 relations between ideal elements within this idea. " Fire 
 causes heat " is a single content or idea, the nature of fare, 
 expanded into one of its properties. 
 
 5. But then, if the whole Judgment is a single content, Distinc- 
 what is the difference between Subject and Predicate, and is tweenSub- 
 
 it necessary to distinguish Subject from Predicate at all ? J ect ancl 
 
 Predicate. 
 If some Judgments can be made without explicit Subjects, 
 
 cannot all be made in that way ? 
 
 This suggestion is very useful as carrying on the simplest 
 type of Judgment throughout the whole theory of Judgment. 
 By a little torture of expression any Judgment can be 
 thrown into a form in which undefined Reality is the 
 general subject, and the whole mass of the Judgment is the 
 Predicate. " William Pitt was a great statesman " = " There 
 was a great statesman named William Pitt " ; " The three 
 angles of every triangle are equal to two right angles " = 
 " There are figures known as triangles with their three angles 
 equal to two right angles"; "All citizens are members of 
 a moral order " = " There is a moral order, including th$
 
 io8 PARTS OF THE JUDGMENT, AND ITS UNITY LECT. 
 
 relations of citizenship " ; " All trespassers will be pro- 
 secuted " = " Here are conditions which ensure the prosecu- 
 tion of possible trespassers." Or you might always put a 
 subject, "Reality is such that" "Reality is characterised 
 by." 
 
 Thus we see that, as we have said before, in every Judg- 
 ment the ultimate subject is Reality, the world in contact 
 with us as we have already qualified it by previous Judgment. 
 It is a less mistake to reject the Subject and Predicate in 
 the Judgment altogether, than to think that they are separate 
 things or ideas, and that in judging you pass or change from 
 one to the other. Always bear in mind that it is possible 
 to mass the whole Judgment as a single Predicate directly or 
 indirectly true of Reality. 
 
 Having said this much, to make the Unity of the Judg- 
 ment unmistakable, we may now safely distinguish between 
 the Subject and Predicate in the Judgment. And we shall 
 find the safest clue to be that the explicit Subject, when 
 there is one, marks the place at which, or the conditions 
 under which, Reality accepts the Predicate. The natural 
 Subject is concrete, and the Predicate abstract ; the Subject 
 real, and the Predicate ideal, but pronounced to be real. 
 The reason of this is that every Judgment is the connection 
 of parts in a whole, and to be a whole is the characteristic 
 of reality. In other words, the natural course of thought is 
 to define further what is already in great part defined, and 
 our real world is that which we have so far defined. The 
 isolated judgments of the text-books make it very hard to 
 grasp this, because you seem to begin anywhere for no 
 connected reason at all. But if we reflect on actual thought,
 
 vi USE OF SUBJECT AND PREDICATE 109 
 
 we find that, as Mr. Stout very cleverly says, we are always 
 developing a "subject" which is in our minds (in the 
 ordinary sense of a " subject of conversation "), and this 
 subject is some region or province of the world of reality. 
 
 Now the explicit Subject in Judgment or the grammatical 
 Subject in Proposition does not always set out the full 
 nature of this, but merely some mark or point in it which 
 we wish to insist upon. So that we may find in Judgment 
 almost anything serving as explicit Subject. Thus, as 
 Aristotle said quite plainly and sensibly, it is natural to say 
 "The horse is white," but we may have occasion to say 
 " This white is a horse " ; it depends on the way in which 
 the Subject comes into our minds. 1 Usually the Subject 
 will be what Dr. Venn calls the heavier term, /. e. the term 
 with more connotation. When there is no difference of 
 concreteness between parts and whole, the Judgment be- 
 comes reversible as in the equation 7 + 5 = 12. There is 
 no distinction here between Subject and Predicate. The 
 real underlying unity or Subject is the numerical system. 
 
 Therefore by recognising Subject and Predicate \ve repre- 
 sent the organisation of knowledge, and the connection of 
 inherence or consequence within the content of our know- 
 ledge. If we do not recognise this distinction we throw the 
 whole of Judgment into an undifferentiated mass of fact, run- 
 ning all assertion into the same mould, "It is the case that," 
 etc. One difficulty still remains. If the relation between 
 Subject and Predicate is within an idea, and not between 
 ideas that is, if the whole explicit content, Subject and 
 
 1 See Prof. Bain, p. 56, upon the Universe, and Universe of Dis- 
 course, /. e. the general subject which you have in your mind.
 
 lio PARTS OF THE JUDGMENT, AND ITS UNITY LECt. 
 
 Predicate together, can be regarded as predicated of reality, 
 why is the act of predication expressed by a verb, /. e. a 
 sign of activity within this content ? Why is a verb often if 
 not always the form of predication which connotes Subject 
 and Predicate? Not because it is a time-word. On the 
 contrary, we want to get rid of the tense in Logic. The 
 time of a Judgment ought to be determined only by the 
 special connection between Subject and Predicate, not by 
 tense, because tense is always subjective, merely relative to 
 the time of speaking, and is accidental to the content of 
 Judgment. Action seems nearer to what we want ; the verb 
 expresses both action and predicate. But the idea of action 
 again does not make a predication, and the verb " is " does 
 not really indicate action. Perhaps it is the demonstrative 
 element in a finite verb that makes it the vehicle of predi- 
 cation, i, e. in a finite verb you have a meaning referred by 
 a demonstrative element to something else. Originally the 
 meaning was always an action ; " is " of course meant 
 " breathes." But now the verb has lost vitality by wear and 
 tear, and only refers something to something else. The 
 puzzle is that the Judgment is not referred to us who make 
 it, but is expressed as if it was accomplished by something 
 outside us. That puzzle points to the essential eature 
 which we insisted on, viz. its objectivity ; in predication we 
 refer what is mentally our act to a subject that represents 
 the real world, not to ourselves at all. When I say " Glad- 
 stone comes to London this week," the verb which expresses 
 Gladstone's action also expresses that my real world in his 
 person accepts the qualification "coming to London this 
 week." Because of this objectivity of thought, I attribute to
 
 vt THE JUDGMENT OBJECTIVE in 
 
 the real world and not to myself the connection which is 
 presented to my mind, and so it takes its place as an act of 
 the real world. But I might throw the whole content into 
 the Predicate by saying, " The ideal content ' Gladstone 
 coming to London this week' is a predication true of 
 Reality." Thus though the distinction between Subject and 
 Predicate best exhibits the living structure of knowledge, we 
 must beware of the notion that two ideas or two things are 
 needed for Judgment.
 
 LECTURE VII l 
 
 THE CATEGORICAL AND HYPOTHETICAL CHARACTERS IN 
 JUDGMENT 
 
 Somecriti- i. WE will first consider why we want to examine the 
 ordinary & tyP es f Judgment, and then what arrangement of them best 
 scheme. fulfils our want. 
 
 Why we (a) If we attended purely to the propositions in common 
 
 arrange- use > we snou ld g et an unmanageable variety of forms, 
 
 menu though the reality of thought would be fairly represented. 
 
 We cannot quite do this ; we must try to select the forms 
 
 which for some reason are the most fundamental and 
 
 constant. 
 
 On the other hand, it is possible to think simply of what 
 is convenient in logical combination ; and then for working 
 with syllogistic Logic we get the well-known scheme of four 
 propositions, each with Subject and Predicate ; and for work- 
 ing with symbolic Logic we get the existential scheme in 
 which Subject and Predicate disappear, and " All S. are P." 
 turns into " There exists no S. which is not P." ; or we get 
 Jevons' Equational Logic, in which " All A is B " stands as 
 A = AB. Now every Judgment has a great many aspects, 
 
 1 Read Mill, ch. iv. (Bk. I.), on Propositions; Venn, Empirical Logic, 
 ch. ix., x. Cf. Knowledge and Reality, pp. 57-8; and Venn, p. 264. 
 Ordinary statement, Jevons, p. 60, ff. ; cf. p. 163.
 
 LECT. vii JUDGMENT AS EXPRESSION 113 
 
 being really a very complex systematic act of mind, and a 
 logical method can be founded on any of these aspects 
 which is sufficiently constant to stand for the Judgment. 
 You can take " All men are mortal " to mean " There are 
 no not-mortal men," or " Men = some mortals," or two or 
 three more meanings. The two former are artificial or formal 
 corollaries from the natural Judgment, representing it for 
 some purposes but omitting a great part of its natural mean- 
 ing. They tell you nothing about a relation of causality 
 between the content of man and the property mortal, and 
 they destroy all implication of existence in the Subject man. 
 
 What we want is neither to follow mere everyday language, 
 nor be guided by mere convenience of logical combination. 
 We want to look at the Judgment on its merits with refer- 
 ence to its power of expressing the principal kinds of our 
 experience, which in fact are constructed in the medium of 
 Judgment. The great kingdoms of intellectual experience 
 are Perception, History, and Science, and of these three, 
 Science, including Philosophy, is the form towards which all 
 knowledge presses on, and its judgment must therefore be 
 considered as the most complete type. 
 
 (ft) With this purpose in mind, let us look at the tra- The 
 ditional scheme, omitting the negative Judgments of which 
 we have not yet spoken. We may dismiss the Indefinite 
 Judgment " Men are mortal " as imperfect by not being 
 " quantified," and we have left, as Categorical Judgments, the 
 Particular Affirmative " Some men are mortal," the Universal 
 Affirmative " All men are mortal," and the Singular Affirma- 
 tive " Socrates is mortal." The Singular Affirmative, how- 
 ever, is not treated of any further under the old scheme, 
 
 i
 
 ii4 CATEGORICAL AND HYPOTHETICAL LECT. 
 
 because in it the Subject is taken in its full extent, and 
 therefore the Singular Affirmative Judgment is ranked with 
 the Universal Affirmative. So as Categorical Judgments 
 we have left the Particular Affirmative and the Universal 
 Affirmative. 
 
 Outside the account of the Categorical Judgment we find 
 the Hypothetical and Disjunctive Judgments touched on as 
 a sort of Appendix, standing as "Conditional." The his- 
 torical reason of this is, that they were not recognised by 
 Aristotle, and have never been incorporated in the diagram 
 of judgments employed in traditional Logic. Then on the 
 ordinary scheme we have 
 
 Categorical. Conditional. 
 
 Particular Universal Hypothetical Disjunctive 
 
 Judgments. Judgments, Judgments, 
 
 including 
 Singular 
 Judgments. 
 
 The defects of this scheme from our point of view are 
 
 (i.) Our Impersonal and Demonstrative Judgments are 
 omitted. They might be classed under the particular, which 
 also has an undefined element in the subject. 
 
 (ii.) The Singular Judgment (of which the chief instance 
 is the judgment with proper name) is rightly classed as 
 Universal, but yet is wrongly absorbed in the abstract 
 universal, from which it ought to be distinguished. 
 
 (iii.) In the treatment of the Universal Judgment there 
 are two defects 
 
 (i) The Collective Judgment, resulting from enumeration,
 
 vii CRITICISMS 115 
 
 direct or indirect, is not distinguished from the Generic 
 Judgment, resting on a connection of content or presumption 
 of causality. "All the 1 papers have been looked over" 
 should be distinguished from " All triangles have their three 
 angles equal to two right angles." 
 
 (2) The nature of the Universal Judgment is not examined 
 with a view to the distinction between Categorical and 
 Hypothetical. The common Logic does not go behind the 
 grammatical form, which on this point is not decisive. 
 
 (iv.) The Hypothetical Judgment 2 is said to consist of two 
 categorical propositions, or to be " complex" But of course 
 it is a simple judgment, prima fade expressing a relation of 
 reason and consequent. Its parts are not Judgments, for 
 they are not such as to stand alone. 
 
 (v.) The Disjunctive Judgment is often (e.g. by Mill and 
 Bain) said to be equivalent to two Hypothetical Judgments. 
 The strange thing is that both of these writers take the wrong 
 two. 3 If we allow conversion of a Hypothetical Judgment 
 two are enough, but of course they must be the two which 
 cannot be got from each other by conversion, viz. the two 
 beginning, " If A is B " and " If A is not B " respect- 
 ively. If we do not admit conversion we must have all 
 four. Let the disjunction be, "This signal light is either 
 red or green." In order to know this we must know not 
 
 1 "The" as here used indeed practically = "these," so that, by our 
 analysis, such a judgment has no claim to rank as a universal judgment. 
 It is difficult to find a plainly collective judgment which has not some 
 affinity to judgment with demonstrative pronoun or proper name. A 
 judgment in which "All M.P.'s" stands as subject, has affinity with 
 the latter. 
 
 3 Bain, p. 85 ; Jevons, p. 160. 
 
 8 Mill, ch. iv. ; Bain, p. 86.
 
 Ii6 CATEGORICAL AND HYPOTHETICAL I.ECT. 
 
 only that, " If it is red it is not green " (with its equivalent, 
 " If it is green it is not red "), but that, " If it is not red it 
 is green " (with its equivalent, " If it is not green it is red "). 
 The former by itself leaves open the possibility that it may 
 be not red or green, but blue or yellow ; the latter by itself 
 the possibility that when it is red it may also at the same 
 time be green. The former secures that the two terms 
 exclude each other; the latter, that, taken together, they 
 exclude all other predicates. 
 
 In any case, the disjunctive is more than any combination 
 of Hypothetical, and really tends to be Categorical, and 
 ought not to be claimed as Conditional. 
 
 Which are 2. We will now look at these Judgments in order, consider 
 their real meaning, and also ascertain the limits of the 
 Categorical Judgment, viz. that which affirms the existence 
 of its Subject, or in other words, asserts a fact. 
 
 The Tar- (i) The Particular Judgment of common Logic, "Some 
 
 Judgment. S. is P.," has different meanings according as it is understood 
 naturally, or tied down to be a result of enumeration. 
 
 In any case it is an imperfect, unscientific Judgment, in 
 which the mind cannot rest, because it has an undefined 
 limitation imposed upon the Subject. 
 
 Its natural (a) For the natural meaning, take the example, "Some 
 
 un ^' engines can drag a train at a mile a minute for a long 
 
 distance." 1 This does not mean a certain number of 
 
 engines, though of course they are a certain number. It 
 
 1 To be accurate, the Judgment would demand the insertion of precise 
 details about train, distance, and other matters. But this illustrates the 
 point of the text, because the assignment of such details would naturally 
 extend to the Subject, and then the " Some" would be displaced.
 
 vil PARTICULAR JUDGMENT 117 
 
 means certain engines of a particular make, not specified 
 in the Judgment. The Judgment is Categorical, because 
 the undefined reservation implies a reference to something 
 unanalysed, but merely touched or presented in experience. 
 If it was a mere idea it would have to be clear ; and if the 
 full description or definition were inserted, the Judgment 
 would cease to affirm the existence of the engines in 
 question. And the Judgment itself challenges this completion. 
 
 (ft) A more artificial meaning is to take the Judgment Anarrower 
 as not formed by imperfect description, but by imperfect 
 enumeration (understanding it almost wholly in denotation). 
 "Some Conservatives are in favour of women's suffrage." 
 This means or may mean that we have counted a certain 
 number, large or small, who are so, and we may or may 
 not know about the others. Thus understood, the Judgment 
 challenges complete enumeration; it contains of course the 
 elements of a fraction half, most, nine-tenths of, and 
 so on. 
 
 This again is Categorical ; not merely because it implies 
 counting, but because it implies counting units separately 
 given to experience. 
 
 The Particular Judgment does not include our Impersonal 
 and Demonstrative Judgments ; they are not classed in the 
 common text-books. But as referring to perception they 
 too are categorical and assert facts, whether they have ideas 
 to help out the perceptive reference or not. And there is 
 no reason against including them under the Particular 
 Judgment. The assertion, "This engine can drag a train a 
 mile a minute," is much the same kind of Judgment as, 
 " Some engines can, etc." Either of these would be false
 
 LECt. 
 
 if no such engines existed. These Judgments are of the 
 essence of perception. They have the connection of content 
 and the undefined complex of presentation struggling to- 
 gether in them. They assert fact. 
 
 Singular (2) The Singular Judgment of the common Logic is pretty 
 e ' much our Judgment with a proper name, which I call Indi- 
 vidual, and which, as we saw, is in part rightly called universal 
 because the Subject extends beyond perception, and the 
 Predicate follows the Subject. But it is a concrete or in- 
 dividual Universal, not an abstract Universal, and therefore 
 asserts the existence of its Subject. The reason why it is 
 taken to assert the reality of its Subject must be, I sup- 
 pose, that it can assert this, its Subject being a name for 
 an existence that has limited reality within the temporal 
 series, and cannot assert anything else, not having any 
 general fixed content or connotation which could imply a 
 general connection of Subject and Predicate. The general 
 connection of content which is so fatal to the asserting of 
 fact does not exist in this case. We see this in Mill's 
 instance. "The summit of Chimborazo is white." When 
 the Subject is a unique name with precise connotation, 
 " The centre of gravity of the material universe is variable," 
 then we are passing into the abstract Universal, and I think 
 we may take such a Judgment perhaps as one of the best 
 examples of a conjunction of categorical and hypothetical 
 meaning, /. e. of a connection of content ascribed to a Sub- 
 ject affirmed to exist. But usually one meaning or the other 
 is uppermost. 
 
 These Judgments, called Singular or Individual, corre- 
 spond to the region of history or narrative. The realities
 
 vii FROM CONCRETE TO ABSTRACT 119 
 
 with which they deal have their definite position in a single 
 system of time and space, and this is often made emphatic 
 by the use of tenses. But these change with the date 
 relative to the speaker, so that a Judgment with real tense 
 must once have been false, or must become false by 
 lapse of time. Thus the Judgment of fact may be not 
 absolutely true. Nothing is genuinely true which a change 
 of date can make false. The permanently true time-relations 
 between Subject and Predicate are determined by their 
 content, and the copula is not a tense, but a mere sign of 
 affirmation. The Singular as Categorical is sharply dis- 
 tinguished from the Abstract Universal, with which common 
 Logic classes it. 
 
 (3) Down to this point the judgment states a. fact. When Universal 
 we come to the ordinary universal affirmative, we see at once ^ gme 
 that it may express very different meanings. In its natural 
 meaning it strongly implies that its Subject has a particular 
 existence within the series of time and space, but hardly 
 asserts it. 
 
 Mill, for example, says " the objects are no longer individu- Import of 
 ally designated, they are pointed out only by their attributes ; " i 
 " most of them not known individually at all." That means 
 that the explicit Subject is not made of individuals. The 
 natural meaning is disputed ; I incline to think with Venn, 
 that the Subject is naturally taken more in Denotation (not 
 solely, which is unmeaning), and the Predicate more in 
 connotation. But clearly in literal form the Subject is 
 simply a significant idea, and its existence in things or events 
 is not affirmed though it may be strongly implied. Hamilton J 
 1 Lectures, vol. iii. p. 327.
 
 120 CATEGORICAL AND HYPOTHETICAL LECT. 
 
 says quite calmly " ' Rainy weather is wet weather ' is a 
 Categorical Proposition ; ' If it rains it will be wet ' is 
 Hypothetical." Between the two I can see no distinction 
 of meaning at all. 1 If indeed we take the Universal Affir- 
 mative in the pure sense of aggregate formed by enumeration, 
 and therefore finite, it may be said that we assert the exist- 
 ence of the individuals composing it ; but this is a very 
 unreal view of the meaning of the Judgment (though 
 suggested by its customary form), and even then it would be 
 hard to prove that we continue to think of the Subject as 
 individuals. This reference to a finite aggregate makes 
 the Collective Judgment or Judgment of Allness. It cannot 
 really exist in the case of a class like man, of unknown 
 extension, and is confined, at its widest, to such cases as 
 " All present Members of Parliament have to take a line on 
 the Irish question." This might be Categorical, but need 
 not be so. 
 
 Otherwise, the Universal Affirmative of common Logic is 
 literally Hypothetical, though in some cases it may strongly 
 imply the assertion of reality. Dr. Venn has discussed this 
 question. 2 He says the implication of existence is much 
 stronger with a single-word Subject than with a many-worded 
 Subject ; /. e, perhaps with a natural than with an artificial 
 conception. But in any case, the expressed bond with per- 
 ception is lost, and in pure form the Subject is a mere 
 abstract idea, so that the relations of content entirely 
 predominate over the implication of existence. 
 
 Thus the Universal Affirmative in its full meaning fairly 
 
 1 Contrast Jevons, Elementary Logic, p. 163. 
 3 Empirical Logic, pp. 258-9.
 
 vii ABSTRACT AND HYPOTHETICAL 121 
 
 represents the sciences of classification, combining a sub- 
 ordinate meaning of Allness or numerical totality with a 
 primary meaning of connotation of attributes or presumed 
 causality. When we say "All the Buttercup family have an 
 inferior corolla," of course we mean that there is a reason for 
 this. Often we omit the term all, as in " Heat is a mode of 
 motion." In doing this we wipe out the last trace of a reference 
 to individual objects, and we pass to the pure hypothetical 
 form which absolutely neglects the existence of objects. 
 
 (4) The simplest type of this Judgment is, if A is B it "Hypo- 
 is C. This Judgment corresponds to abstract science, but 
 it is only making explicit what was implied in the Universal 
 Affirmative. That expressed a presumption of causality, 
 this expresses a clear Reason and Consequent or scientific 
 necessity. The point of this form is (i.) that it drops all 
 reference to individual objects, (ii.) that it challenges you to 
 explain how the Subject-content is tied to the Predicate- 
 content. "Water boils at 212," is a statement we should 
 generally pass in so-called Categorical form, because it does 
 not challenge any great accuracy of connection. But " If 
 water boils, it is at a temperature of 212," puts us upon 
 asking, " Is the condition adequate ? " and we see at once 
 that we must at least say, " If water boils under pressure of 
 one atmosphere, it is at a temperature of 212,'' or else the 
 judgment is untrue. Of course we may apply the form 
 rightly or wrongly, as you may fill up your census paper 
 rightly or wrongly. We can only say that it calls upon you 
 to put in an adequate condition. Therefore I rather object 
 to the form " If A is, B is," because it adds very little to 
 the so-called Categorical shape.
 
 122 CATEGORICAL AND HYPOTHETICAL LECT. 
 
 We have now to ask how the Hypothetical Judgment 
 connects its content with reality, /. e. how it is a Judgment at 
 all ? And the same explanation must apply to so-called 
 Categorical Judgments, which can be thrown into this form 
 without change of meaning. 
 
 The point from which the explanation starts is taking 
 hypothesis as supposition. This is much more true, I think, 
 than connecting it with doubt. In Dr. Venn's Empirical 
 Logic the connection of Hypothetical Judgment and doubt 
 to my mind disfigures the whole treatment of the Scientific 
 Judgment. Supposition is distinct from affirmation that is 
 true but just because it is distinct from affirmation, it can- 
 not indicate doubt. It probably arose out of doubt, but as 
 a method of science it does not imply doubt, but only the 
 accurate limitation of attention. What doubt is there when 
 we judge " If equals be added to equals, the wholes are 
 equal " ? We are attending to one particular thread of the 
 nexus. 
 
 Hypothetical Judgment, then, is Judgment that starts from 
 a supposition. Every supposition is made upon a certain 
 basis of Reality. Take as an extreme case, " If you ask 
 permission of A. B., he will refuse it." This is a supposition 
 and its result, on the basis of the known character of A. B. 
 And the full judgment is " A. B. is of such a character, that, 
 supposing you ask him for permission, etc." The Hypo- 
 thetical Judgment may be true, as an assertion about A. B.'s 
 character, though you may never ask. 
 
 Here, then, is the clue to the analysis of all Abstract 
 Judgments. Like Perceptive Judgment, they affirm some- 
 thing of Reality, but they do this indirectly and not directly.
 
 Vil FACT AND TRUTH 123 
 
 Underlying them there is the implied Categorical Judgment, 
 " Reality has a character, such that, supposing so and so, 
 the consequence will be so and so." And if this implied 
 assertion is true, then the Hypothetical Judgment is true, 
 although its terms may be not only unreal, but impossible. 
 " If a microscopic object-lens with a focal length of T ^ in. 
 were used, its magnifying power with an A eye-piece would 
 be so many diameters." This is a mere matter of calcula- 
 tion, and is unquestionably true, depending upon the effects 
 of refraction upon the optical image. But I do not suppose 
 that such an object-lens could be made, or used. Does 
 such a Judgment, although true, express a fact? No, I 
 should say not, although common usage varies. I remember 
 a Pall Mall leading article which said, " It is an absolute 
 fact, that, if Mr. Gladstone had not done something the 
 Government would have committed some iniquity or other." 
 Is this what we call a fact ? We observe that the content 
 actually mentioned was never real at all. The implied 
 connection with reality is " There existed in reality a condi- 
 tion of things (unspecified) in which if Mr. Gladstone, etc., 
 etc." Are mathematical truths facts, and in what sense? 
 Abstract truth need not, and perhaps cannot express fact, 
 but implies fact indirectly. 
 
 (5) The Disjunctive Judgment "A is either B or C," is Disjunct- 
 again not a judgment of doubt but a mode of Knowledge. ^ e v* *=" 
 It may be taken as numerical ; then it gives rise to the 
 statement of Chances. But in its perfect form it is appro- 
 priate to the exposition of a content as a system, and it 
 may be taken as returning to the Categorical Judgment, 
 and combining it with the Hypothetical, because its
 
 124 
 
 content is naturally taken as an individual, being necessarily 
 concrete. 
 
 The peculiar point of the Disjunctive is that it makes 
 negation positively significant. 
 
 " This signal light shows either red or green." Here we 
 have the categorical element, "This signal light shows 
 some colour," and on the top of this the two Hypothetical 
 Judgments, " If it shows red it does not show green," " If it 
 does not show red it does show green." You cannot make 
 it up out of the two Hypothetical Judgments alone ; they 
 do not give you the assertion that " it shows some colour." l 
 
 Does this state a fact ? I think it implies a fact much 
 more distinctly than the hypothetical does, but of course it 
 is a question whether an alternative can be called a fact. It 
 seems a precise expression of some kinds of reality, but it is 
 not a solid single momentary fact. It is very appropriate to 
 the objects of philosophy as the higher concrete science, 
 which are conceived as systems of facts bearing definite 
 relations to each other ; e. g. " Society is a structure of 
 individual characters, having positions which are not inter- 
 changeable." Taken all as a mass, they are conjunctively 
 connected, but taken in distinguishable relations they are 
 disjunctively related. A human being as such has some 
 position and no other, and this is ultimately determined by 
 
 1 The example in the text, chosen for its simplicity, may be objected 
 to as involving perceptive concreteness by the pronoun "this." You 
 can have a disjunction, it may be said, dealing with " the triangle" as 
 such ; and why should this be more " Categorical " than the assertion 
 that the triangle has its angles = three right angles ? Still, it might be 
 replied, the development of a single nature into a number of precise 
 and necessary alternatives, always gives it an implication of self- 
 completeness.
 
 VII FROM ABSTRACT TO CONCRETE 125 
 
 the nature of the social whole to which he belongs. He is 
 if this, nothing else, and if nothing else, then this. A more 
 artificial example, which illustrates the degree in which 
 actual abstract knowledge and purpose can be embodied by 
 man in machinery, is the interlocking system of points and 
 signals at a great railway station. I suppose that the essence 
 of such a system lies in arrangements for necessarily closing 
 every track to all but one at a time of any tracks which cross 
 it or converge into it. The track X receives trains from A, 
 B, C, D ; if the entrance for those from A is open, B, C, 
 and D are ipso facto closed ; if A, B, and C are closed, D 
 is open, and so on. This is a disjunction consciously and 
 purposely incorporated in material fact, and differs from a 
 Disjunctive Judgment only in so far as existence necessarily 
 differs from discursive thought. 
 
 The disjunction seems to complete the system of judg- 
 ments, including all the others in itself, and it is wrong in 
 principle to distinguish, e. g. between a hypothetical and 
 categorical disjunction, or to consider how a disjunction 
 can be denied. For disjunction in itself implies a kind of 
 individuality which is beyond mere fact and mere abstract 
 truth, though allied to both ; and all intelligible negation 
 is under, not of, a disjunction. Negation of a disjunction 
 would mean throwing aside the whole of some definite 
 group of thoughts as fallacious, and going back to begin 
 again with a judgment of the simplest kind. It amounts 
 to saying, " None of your distinctions touch the point ; you 
 must begin afresh,"
 
 LECTURE VIII 1 
 
 NEGATION, AND OPPOSITION OF JUDGMENTS 
 
 Distinc- i. THE only important point in the traditional diagram of 
 
 tween 6 " tne opposition of Judgments is the distinction between 
 Contrary contrary and contradictory opposition, the opposition, that 
 
 tradictory is, between A and E, and the opposition between A and O, 
 opposition. or E and L 
 
 In Contrary Opposition the one Judgment not only denies 
 the other, but goes on to deny or assert something more 
 besides. The mere grammatical shape " No man is mortal " 
 conceals this, but we easily see that it says more than is 
 necessary to deny the other, "All men are mortal." 
 
 In Contradictory Opposition, the one Judgment does 
 absolutely nothing more than is involved in destroying 
 the other. 
 
 The Contrary Negation has the advantage in positive, or 
 at least in definite import. 
 
 The Contradictory or pure Negation has the advantage in 
 the exhaustive disjunction which it involves. 
 
 This is plain if we reflect that Contrary Negation only 
 
 1 Read Bain, pp. 55-6, on "Negative Names and the Universe of 
 the Proposition," also on "Negative Propositions," p. 83 ff. ; Venn, 
 Empirical Logic, pp. 214 217; Jevons, Elementary Logic, ix., on 
 " Opposition of Propositions" ; Mill, ch. iv. 2.
 
 LECT. vin CONTRARY AND CONTRADICTORY 127 
 
 rests on the Law of Contradiction, " X is not both A and 
 not A." 
 
 Ordinary Diagram of Opposition of Judgments. 
 
 E 
 
 Contrary Opposition. 
 
 0. 
 
 '\. 
 
 ^ O 
 
 v . 
 
 
 
 Sub-contrary Opposition. 
 
 O 
 
 A = Universal Affirmative. All men are mortal. 
 E = Universal Negative. No men are mortal. 
 
 I = Particular Affirmative. Some men are mortal. 
 O = Particular Negative. Some men are not mortal. 
 
 Sub-contrary Opposition has no real meaning ; the judg- 
 ments so opposed are compatible. 
 
 It is not true both that " All M.P.'s are wise," and that 
 " No M.P.'s are wise," but both may be false ; while Con- 
 tradictory Negation implies the Law of Excluded Third or 
 excluded Middle, "X is either A or not A," the principle 
 of disjunction, or rather, the simplest case of it. It is not
 
 128 NEGATION, AND OPPOSITION OF JUDGMENTS I.KCT. 
 
 false both that " All M.P.'s are wise " and that " Some M.P.'s 
 are not wise." The point is, then, on the one hand, that in 
 Contradiction you can go from falsehood to truth, 1 while in 
 Contrariety you can only go from truth to falsehood ; but 
 also that in Contradiction the Affirmative and Negative are 
 not at all on a level in meaning, while in Contrariety they 
 are much more nearly so. Then if we leave out the relations 
 of mere plurality, of All and Some, which enable you to 
 get contrary negation in pure negative form in the common 
 Logic, we may say generally that in contrary negation some- 
 thing is asserted, and in contradictory negation taken quite 
 literally nothing is asserted, but we have a " bare denial," a 
 predicate is merely removed. In actual thought this can- 
 not be quite realised, because a bare denial is really mean- 
 ingless, and we always have in our mind some subject or 
 universe of discourse within which the denial is construed 
 definitely. But this definite construing is not justified by 
 the bare form of contradiction, which consists simply in 
 destroying a predication and not replacing it by another. 
 In as far as you replace it by another, defined or undefined, 
 you are going forward towards contrary negation. 
 Contrary 2. Thus, Contrary Negation in its essence is affirmation 
 ^gation. w j t ^ a ne g a ti ve intention, and we may take as a type of it in 
 this wider sense the affirmation of a positive character with 
 the intention of denying another positive character. E.g. 
 when you deny "This is a right-angled triangle " by asserting 
 " This is an equilateral triangle," you have typical contrary 
 negation. It is not really safe to speak of contraries ex- 
 cept with reference to judgments, intended to deny each 
 
 1 /. . Contradictory alternatives are exhaustive.
 
 Vin DIFFERENT AND CONTRARY 129 
 
 other; but it is common to speak of species of the same 
 genus as contraries or opposites, because the same thing 
 cannot be both. 1 
 
 We must therefore distinguish contrary from different. Of 
 course the same thing or content has many different quali- 
 ties, and even combines qualities that we are apt to call 
 contrary or opposite. But as Plato was fond of pointing 
 out, a thing cannot have different or opposing qualities in 
 the same relation, that is to say, belonging to the same sub- 
 ject under the same condition. The same thing may be 
 blue in one part of it and green in another, and the same 
 part of it may be blue by daylight and green by candlelight. 
 But the same surface cannot be blue and green at once by 
 the same light to the same eye looking in the same direction. 
 Different qualities become contrary when they claim to stand 
 in the same relation to the same subject. Right-angled 
 triangles and equilateral triangles do not deny each other if 
 we leave them in peace side by side. They are then merely 
 different species of the same genus, or different combinations 
 of the same angular space. But if you say, " This triangle is 
 right-angled," and I say "It is equilateral," then they deny 
 each other, and become true contraries. 
 
 Then the meaning of denial is always of the nature of 
 contrary denial. As we always speak and think within a 
 general subject or universe of discourse, it follows that every 
 denial substitutes some affirmation for the judgment which 
 it denies. The only judgments in which this is not the case 
 are those called by an unmeaning tradition Infinite Judg- 
 ments, /. e. judgments in which the negative predicate 
 1 Bain, p. 55 ff.
 
 130 NEGATION, AND OPPOSITION OF JUDGMENTS LECT. 
 
 includes every determination which has applicability to the 
 Subject. This is because the attribute denied has no appli- 
 cability to the Subject, and therefore all that has applicability 
 is undiscriminatingly affirmed, in other words, the judgment 
 has no meaning. " Virtue is not-square." This suggests 
 no definite positive quality applicable to virtue, and there- 
 fore is idle. You may safely analyse a significant negative 
 judgment, " A is not B " as = "A is not B but C," or as = " A 
 is X, which excludes B." For X may be undetermined, " a 
 colour not red." But then if the meaning is always affirma- 
 tive or positive, why do we ever use the negative form ? 
 Why use 3. In the first place, we use it because it indicates exclu- 
 Negation? s j on ^ an( j w j t ^ OU j- jj- we canno t distinguish between mere 
 
 differents on the one hand and contraries on the other. If 
 you ask me, " Are you going to Victoria, London Chatham 
 and Dover station ? " and I answer, " I am going to Victoria, 
 London Brighton and South Coast," that will not be satis- 
 factory to you, unless you happen to know beforehand that 
 these stations are so arranged that if you are at one you are 
 not at the other. They might be a single station used by 
 different companies, and called indifferently by the name of 
 either. To make it clear that the suggestion and the 
 answer are incompatible, I must say, "I am not going to 
 Victoria, London Chatham and Dover," and I may add or 
 not add, "I am going to Victoria, London Brighton and 
 South Coast." That tells you that the one predicate ex- 
 cludes the other, and that is the first reason why we use the 
 generalised form of exclusion, *'. e. negation. 
 
 But in the second place, it can give us more, and some- 
 thing absolutely necessary to our knowledge, and that is not
 
 Vm DOUBLE NEGATION 131 
 
 merely exclusion, but exhaustion. In literal form negation 
 is absolutely exhaustive, that is to say, contradictory. The 
 Judgment " A is not B " forms an exhaustive alternative to 
 the Judgment " A is B," so that no third case beyond these 
 two is possible, and therefore you can argue from the false- 
 hood of either to the truth of the other. Now this form is 
 potentially of immense value for knowledge, and all disjunc- 
 tion consists in applying it ; but as it stands in the abstract 
 it is worthless, because it is an empty form. "A is red 
 or not-red." If either of these is false the other is true. 
 But what do you gain by this ? You are not entitled to 
 put any positive meaning upon not-red ; if you do so you 
 slide into mere contrary negation, and the inference from 
 falsehood becomes a fallacy. Make an argument, "The 
 soul is red or not-red." "It is not-red .'. it is some other 
 colour than red." The argument is futile. We have con- 
 strued " not-red " as a positive contrary, and that being so, 
 the disjunction is no longer exhaustive. We had no right 
 to say that the soul is either red or some other colour ; the 
 law of Excluded Middle does not warrant that. 
 
 I pause to say that the proof of the exhaustiveness of 
 negation, /. e. that two negatives make an affirmative that if 
 A is not not-B, it follows that A is B is a disputed problem, 
 the problem known as double negation. How do you know 
 that what is not not-red must be red ? I take the law of 
 Excluded Middle simply as a definition of the bare form of 
 denial, or the distinction between this and not-this ; " not- 
 this" being the bare abstraction of the other than this. 
 Others say that every negation presupposes an affirmation ; 
 so " A is not-B " presupposes the affirmation " A is B," and
 
 132 NEGATION, AND OPPOSITION OF JUDGMENTS LECT. 
 
 Stage of 
 Significant 
 Negation. 
 Combin- 
 ation of 
 Contrary 
 and Con- 
 tradictory. 
 
 Different 
 Affirm- 
 ations. 
 
 Contrary 
 Opposi- 
 tion, ex- 
 clusive. 
 
 if you knock down the negative, the original affirmative is 
 left standing. Sigwart and B. Erdmann say this. I think 
 it monstrous. I do not believe that you must find an 
 affirmative standing before you can deny. 
 
 4. Well, then, the point we have reached is this. What 
 we mean in denial is always the contrary, something positive. 
 What we say in denial in other words, the literal form 
 which we use always approaches the contradictory, /'. e. is 
 pure exclusion. The Contrary of the diagram denies more 
 than it need, but still its form is that of exclusion. Now we 
 have seen that in denial, as used in common speech, we get 
 the benefit of both affirmation and exclusion, but in accurate 
 thought we want to do much more than this ; we want to 
 get the whole benefit of the negative form that is, to get 
 a positive meaning together with not only exclusion, but 
 exhaustion. 
 
 I will put the three cases in one example, beginning with 
 mere affirmations of different facts. 
 
 (1) " He goes by this train to-day." " He goes by that 
 train to-morrow." This conjunction, as simply stated, gives 
 no inference from the truth or falsehood of either statement 
 to the truth or falsehood of the other. 
 
 (2) "He goes by this train," and " He goes by that train," 
 with a meaning equivalent to "No, he goes by that." If 
 it is true that in the sense suggested by the context he 
 goes by this train, then it is not true that he goes by the 
 other, and if it is true, in the sense explained, that he 
 goes by the other, then he does not go by this. Each 
 excludes the other, but both may be excluded by a third 
 alternative. If it is not true that he goes by this train
 
 VIH THE POSITIVE NEGATION 133 
 
 nothing follows. There may be any number of trains he 
 might go by, or he might give up going ; /. e. your Universe 
 of discourse, your implicit meaning is not expressly limited. 
 If it is not true to say, " No, he goes by that " taking the 
 whole meaning together, and not separating its parts, for 
 this combination is essential to the " contrary " nothing 
 follows as to the truth of the other statement. He may not 
 be going at all, or may be going by some third train, or by 
 road. 
 
 But if you limit your Universe, or general subject, then 
 you can combine the value of contrary and contradictory 
 negation. Then you say, 
 
 (3) " He goes either by this train or by that." Then you Combined 
 can infer not only from " He goes by this train," that " He 
 
 does not go by that," but from "He does not go by this tradictory 
 train "to " He does go by that." 
 
 The alternative between "A is B" and "A is not-B " 
 remains exhaustive, but not-B has been given a positive 
 value, because we have limited the possibilities by definite 
 kntnvledge. The processes of accurate thinking and observ- 
 ation aim almost entirely at giving a positive value C to 
 not-B, and a positive value B to not-C, under a disjunction, 
 because it is then that you define exactly where and within 
 what conditions C which is not B passes into B which is 
 not C. Take the disjunction, " Sound is either musical or 
 noise." If the successive vibrations are of a uniform period 
 it is musical sound; if they are of irregular periods it is 
 noise. This is a disjunction which assumes the form, 
 
 A is either B or C. That is to say, If it is B it is not C,. 
 If it is not B it is C.
 
 134 NEGATION, AND OPPOSITION OF JUDGMENTS LECT. 
 
 Therefore I think that all " determination is negation " 
 of course, however, not bare negation, but significant nega- 
 tion ; the essence of it consists in correcting and confirming 
 our judgment of the nature of a positive phenomenon by 
 showing that //AST" when its condition ceases, just then some- 
 thing else begins, and when you have exhausted the whole 
 operation of the system of conditions in question, so that 
 from any one phase of their effects you can read off what it 
 is not but the others are, then you have almost all the know- 
 ledge we can get. The "Just-not" is the important point, 
 and this is only given by a positive negation within a definite 
 system. You want to explain or define the case in which A 
 becomes B. You want observation of not-B ; but almost 
 the whole world is formally or barely not-B, so that you are 
 lost in chaos. What you must do is to find the point 
 within A, where Aj which is B passes into A 2 which is C, 
 and that will give you the jusf-not-E which is the valuable 
 negative instance. 
 
 Negative 5. You will find it said that a Negative Judgment cannot 
 expressing express fact ; e. g. that a Judgment of Perception cannot be 
 fact. negative. This is worth reflecting upon ; I hope that what 
 
 has been said makes clear how far it is true. The bare form 
 of Negation is not adequate to fact ; it contains mere empti- 
 ness or ignorance ; we nowhere in our perception come 
 upon a mere " not-something." No doubt negation is in 
 this way more subjective than affirmation. But then as it 
 fills up in meaning, the denial becomes more and more on 
 a level with the affirmation, till at last in systematic know- 
 ledge both become double-edged every affirmative denies, 
 and every negative affirms. When a man who is both a
 
 Yin ANALYSIS OF NEGATION 135 
 
 musician and a physicist says, " this compound tone A is a 
 discord Y," he knows exactly how much of a discord, what 
 ratio of vibration makes it so much of a discord, how much 
 it would have to change to become a concord (X which is 
 not Y), and what change in the vibration ratio from a t to a 2 
 would be needed to make it a concord. To such knowledge 
 as this, the accurate negation is just as expressive as the 
 affirmation, and it does not matter whether he says "A is 
 Y," or " A is by so much not X." It becomes, as Venn 
 says, all but impossible to distinguish the affirmation from 
 the negation. No doubt affirmative terms come in at this 
 stage, though the meaning is negative. Observe in this 
 connection how we sometimes use the nearest word we can 
 think of, knowing that the negative gives the positive indi- 
 rectly " He was, I won't say insolent," meaning//^/ not or 
 " all but " insolent ; or again, "That was not right," rather 
 than saying bluntly "wrong." 
 
 6. Every significant negation " A is not B " can be analysed Operation 
 
 as "A is X which excludes B." Of course X may not be f *]? . de ' 
 
 _ ' med idea. 
 
 a distinct C ; e.g. we may be able to see that A is not red, 
 but we may not be able to make out for certain what 
 colour it is ; then the colour X is " an unknown colour 
 which excludes red." 
 
 How does the rejected idea operate in Judgment ? I 
 suppose it operates by suggesting a Judgment which as you 
 make it destroys some of its own characteristics. It is 
 really an expression of the confirmatory negative instance or 
 "just-not." Just when two parallel straight lines swing so 
 that they can meet,/'ktf then the two interior angles begin 
 to be less than two right angles, which tells us that the
 
 136 NEGATION, AND OPPOSITION OF JUDGMENTS 
 
 straight lines are ceasing to be parallel. Just in as much 
 as two straight lines begin to enclose a space we become 
 aware that one or other of them is not straight, so 
 that A in turning from Y to X turns pari J>assu from A t to 
 A 2 , and we are therefore justified in saying that A, when it 
 is Y, cannot be X. 
 
 This lecture may pave the way for Induction, by giving 
 some idea of the importance of the negative instance which 
 Bacon preached so assiduously. 
 
 In a real system of science the conceptions are negative 
 towards each other merely as denning each other. One of 
 them is not in itself more negative than another. Such a 
 conception, e.g., is that of a triangle compared with two 
 parallel straight lines which are cut by a third line. If the 
 parallels are swung so as to meet, they become a triangle 
 which gains in its third angle what the parallels lose on the 
 two interior angles, and the total of two right angles remains 
 the same. Thus in saying that parallels cut by a third 
 straight line cannot form a triangle, and that the three 
 angles of a triangle are equal to two right angles, we are 
 expressing the frontier which is at once the demarcation 
 between two sets of geometrical relations, and the positive 
 grasp or connection of the one with the other. The negation 
 is no bar to a positive continuity in the organism of the 
 science, but is essential to defining its nature and constituent 
 elements. This is the bearing of significant negation when 
 fully developed.
 
 LECTURE IX 1 
 
 INFERENCE AND THE SYLLOGISTIC FORMS 
 
 i. THE Problem of Inference is something of a paradox. Inference 
 Inference consists in asserting as fact or truth, on the ground m gen ' 
 of certain given facts or truths, something which is not 
 included in those data. We have not got inference unless 
 the conclusion, (i.) is necessary from the premisses, and (ii.) 
 goes beyond the premisses. To put the paradox quite 
 roughly we have not got inference unless the conclusion is 
 (i.) in the premisses, and (ii.) outside the premisses. This is 
 the problem which exercises Mill so much in the chapter, 
 " Function and Value of the Syllogism." We should notice 
 especially his 7, " the universal type of the reasoning 
 process." The point of it is to make the justice of inference 
 depend upon relations of content, which are judged of 
 by what he calls induction. That is quite right, but the 
 question still returns upon us, " What kind of relations of 
 content must we have, in order to realise the paradox of 
 Inference ? " This the " type of inference " rather shirks. 
 See Mill's remarks when he is brought face to face with 
 
 1 Read for Lectures IX. and X., Mill, Bk. II. ch. i., ii., iii. ; 
 Bk. III. ch. i. and ii. at least ; Venn, ch. xiv., xv. ; Jevons, Lessons, 
 xv. and xxiv. ; De Morgan's Budget of Paradoxes*
 
 138 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 Induction, Bk. III. ch. i. 2. An Inference, as he there 
 recognises, either does not hold at all, or it holds "in 
 all cases of a certain description," i.e. it depends on 
 universals. 
 
 I ought to warn you at once that though we may have 
 novelty in the conclusion of Inference (as in multiplication 
 of large numbers), the necessity is more essential than the 
 novelty. In fact, much of Inference consists in demonstrat- 
 ing the connection of matters that as facts are pretty familiar. 
 Of course, however, they are always modified in the process, 
 and in that sense there is always novelty. You obtain the 
 most vital idea of Inference by starting from the conclusion 
 as a suggestion, or even as an observation, and asking your- 
 self how it is proved, or explained, and treating the whole 
 process as a single mediate judgment, /. e. a reasoned 
 affirmation. Take the observation, " The tide at new and 
 full moon is exceptionally high." In scientific inference 
 this is filled out by a middle term. We may profitably think 
 of the " middle term," as the copula or grip which holds the 
 conclusion together, made explicit and definitely stated. 
 Thus the judgment pulls out like a telescope, exhibiting 
 fresh parts within it, as it passes into inference. " The tide 
 at new and full moon, being at these times the lunar tide plus 
 the solar tide, is exceptionally high." This is the sort of 
 inference which is really commonest in science. Such an 
 inference would no doubt give us the conclusion if we did 
 not know it by observation, but it happens in many cases 
 that we do know it by observation, and what the inference 
 gives us is the connection, which of course may enable us to 
 correct the observation.
 
 ;x IDENTITY IN INFERENCE 139 
 
 2. In the strictest formal sense there can be no inference Conditions 
 from particulars to particulars. When there seems to be sibility P of * 
 such inference, it is merely that the ground of inference Inference, 
 is not mentioned, sometimes because it is obvious, some- 
 times because it is not clearly specified in the mind. 
 Suppose we say, " Morley and Harcourt will go for Dis- 
 establishment, and I think, therefore, that Gladstone will." 
 I do not express any connecting link, merely because ever}' 
 one sees at once that I am inferring from the intentions of 
 some Liberal leaders to those of another. If the terms 
 are really particulars, " X is A, Y is B, Z is C," one is help- 
 less ; they do not point to anything further at all ; there is 
 no bridge from one to the other. 
 
 Inference cannot possibly take place except through the 
 medium of an identity or universal which acts as a bridge 
 from one case or relation to another. If each particular 
 was shut up within itself as in the letters taken as an instance 
 just now, you could never get from one which is given 
 to another which is not given, or to a connection not given 
 between two which are given. 
 
 Take the simplest conceivable case, which hardly amounts 
 to Inference, that of producing a given straight line. How 
 is it that this is possible ? Because the direction of the 
 straight line is universal and self-identical as against possible 
 directions in space, and it acts as a rule which carries you 
 beyond the given portion of it. This might fairly be called 
 an "immediate inference." So I presume that any curve 
 can be constructed out of a sufficient portion of the curve, 
 although, except with a circle, this is more than repeating 
 the same line over again. The content has a nature which
 
 140 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 is capable of prescribing its own continuation. A curve is 
 not a direction ; a truth which is a puzzle to the non- 
 mathematician it is a law of continuous change of direction. 
 
 System the 3. Ultimately the condition of inference is always a 
 ultimate A , . .,, , , _. . A , ,. , 
 
 condition s y stem - And it will help us in getting a vital notion of 
 
 of Infer- inference if we think, to begin with, of the interdependence 
 ence. 
 
 of relations in space in geometrical figures, or, to take 
 
 a commonplace example, in the adjustment of a Chinese 
 puzzle or a dissected map. Or any of the propositions about 
 the properties of triangles are a good example. How can 
 one property or attribute determine another, so that you can 
 say, " Given this, there must be that " ? This can only be 
 answered by pointing to the nature of a whole with parts, or 
 a system, which just means this, a group of relations or 
 properties or things so held together by a common nature 
 that you can judge from some of them what the others must 
 be. Not all systems admit of precise calculation and 
 demonstration, but wherever there is inference at all there is 
 at least an identity of content which may be more or less 
 developed into a precise relation between parts. For 
 example, we cannot construct geometrically the life and 
 character of an individual man ; we can argue from his 
 character to some extent, but the connection of facts in his 
 personal identity is all that we can infer for certain ; and 
 even this involves a certain context of facts, as in cir- 
 cumstantial evidence. Yet this simplest linking together of 
 occurrences by personal identity is enough to give very 
 startling inferences. Thackeray's story of the priest is a 
 good instance of inference from mere identity. "An old 
 abbe", talking among a party of intimate friends, happened
 
 IX LOWER LIMIT 141 
 
 to say, ' A priest has strange experiences ; why, ladies, my 
 first penitent was a murderer.' Upon this, the principal 
 nobleman of the neighbourhood enters the room. 'Ah, 
 Abbe, here you are ; do you know, ladies, I was the Abbe's 
 first penitent, and I promise you my confession astonished 
 him ! ' ' Here the inference depends solely on individual 
 identity, which is, as we saw, a kind of universal. 
 
 But in this case was there really an inference ? Does not 
 the conclusion fall inside the premisses ? It must in one 
 sense fall inside the premisses, or it is not true. But it does 
 not fall inside them until we have brought them into contact 
 by their point of identity and melted them down into the 
 same judgment. I admit that these inferences from indi- 
 vidual identity, assuming the terms not to be ambiguous, 
 are only just within the line of rational inference, but, as we 
 see in this case, they bring together the parts of a very 
 extended universal. What is the lower limit of inference ? 
 
 4. In the doctrine of immediate Inference common Logic Immediate 
 treats of Conversion and the Opposition of judgments. 
 
 Is a mere transposition of Subject and Predicate, where 
 the truth of the new judgment follows from that of the old, 
 an inference ? It is a matter of degree. 1 Does it give 
 anything new? "The Queen is a woman." "A woman 
 is the Queen." If we make a real difference between the 
 implications of a Subject and a Predicate, we seem to get 
 something new; but it is a point of little interest. Com- 
 
 1 The collective or general judgment, as commonly explained, cannot 
 be converted "simply," because the predicate is "wider" than the 
 subject, and the same rule is accepted for the relation of consequent to 
 antecedent* The aim of science, it might almost be said, is to get 
 beyond the kind of judgment to which this rule applies.
 
 H2 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 parison or Recognition are more like immediate inferences. 
 Comparison means that we do not let ourselves perceive 
 freely, but take a particular content as the means of ap- 
 perception of another content, /". e. as the medium through 
 which we look at it. I do not merely look at the second, 
 but I look at it with the first in my mind. And so far I 
 may be said to infer, without the form of proof, from data 
 of perception to a relation between them. "You are taller 
 than me," is a result obtained by considering your height 
 from the point of view of mine, or vice versa. Recognition 
 is somewhat similar. It is more than a mere perception, 
 because it implies reproduction of elements not given, and 
 an identification with them. I recognise this man as so- 
 and-so, /. e. I see he is identical with the person who did 
 so-and-so. It is a judgment, but it goes beyond the primary 
 judgment, "He is such and such," and is really inferred 
 from it. It is a matter of degree. Almost every Judgment 
 can be broken up into elements, and recognition fades 
 gradually into cognition we " recognise " an example of a 
 law, a right, a duty, an authority ; not that we knew if, the 
 special case, before, but that in analysing it we find a principle 
 which commands our assent, and with which we identify 
 the particular instance before us. 
 
 Number of 5- The difference between guess-work and demonstration 
 Instances. rests on tne difference between a detached quality or rela- 
 tion striking enough to suggest something to us, and a 
 system thoroughly known in its parts as depending on one 
 another. This is so even in recognising an individual 
 person ; it is necessary to know that the quality by which 
 you recognise him is one that no one else possesses, or else
 
 ix NUMBER OF INSTANCES *43 
 
 it is guess-work. Still more is this the case in attempting a 
 scientific connection. All scientific connection is really by 
 system as between the parts of the content. A quality is 
 often forced on our attention by being repeated a great 
 many times in some particular kind of occurrence, but as 
 long as we do not know its causal connection with the 
 properties and relations involved in the occurrence it is 
 only guess-work to treat them as essentially connected. 
 This is a matter very easy to confuse, and very important. 
 It is easy to confuse, because a number of instances does 
 help us really in inference, as it always insensibly gives us 
 an immense command of content ; that is to say, without 
 knowing it we correct and enlarge our idea of the probable 
 connection a little with every instance. So the connection 
 between the properties that strike us becomes much larger 
 and also more correct than it is to people who have only 
 seen a few instances. But this is because the instances are 
 all a little different, and so correct each other, and show 
 transitions from more obvious forms to less obvious forms 
 of the properties in question which lead us up to a true 
 understanding of them. If the instances were all exactly 
 the same they would not help us in this way, but our guess 
 would still be a guess, however many instances might have 
 suggested it. 
 
 I remember that a great many years ago I hardly believed 
 in the stone-age tools being really tools made by men. I 
 had only seen a few bad specimens, one or two of which I 
 still think were just accidentally broken flints which an old 
 country clergyman took for stone-age tools. This was to 
 me then a mere guess, viz. that the cutting shape proved
 
 144 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 the flints to have been made by men. And obviously, if I 
 had seen hundreds of specimens no better than these, I 
 should have treated it as a mere guess all the same. But 
 I happened to go to Salisbury, and there I saw the famous 
 Blackmore Museum, where there are not only hundreds of 
 specimens, but specimens arranged in series from the most 
 beautiful knives and arrow-heads to the rudest. There one's 
 eye caught the common look of them at once, the better 
 specimens helping one to interpret the worse, and the guess 
 was almost turned into a demonstration, because one's eyes 
 were opened to the sort of handwork which these things 
 exhibit, and to the way in which they are chipped and 
 flaked. 
 
 Now this very important operation of number of examples, 
 in helping the mind to an explanation, is always being con- 
 fused with the effect of mere repetition of examples, which 
 does not help you to an explanation, /*. e. a repetition in 
 which one tells you no more than another. But these mere 
 repetitions operate prima facie in a different way, viz. by 
 making you think there is an unkn&wn cause in favour of 
 the combination of properties which recurs, and lead up 
 to the old-fashioned perfect Induction and the doctrine of 
 chances, and not to demonstration. 1 
 
 On the road from guess-work to demonstration, and 
 generally assisted by great experience, we have skilful guess- 
 
 1 Ultimately the calculus of chances may be said to rest on the 
 same principle as Induction, in so far ai the repetition of examples 
 derives its force from the (unspecified) variety of contexts through which 
 this repetition shows a certain result to be persistent. But in such a 
 calculus the presumption from recurrence in such a variety of contexts is 
 only estimated, and not analysed.
 
 ix GUESS-WORK AND PROOF 145 
 
 work, the first stage of discovery. This depends on the 
 capacity for hitting upon qualities which are connected by 
 causation, though the connection remains to be proved. So 
 a countryman or a sailor gets to judge of the weather ; it is 
 not merely that he has seen so many instances, but he has 
 been taught by a great variety of instances to recognise the 
 essential points, and has formed probably a much more 
 complex judgment than he can put into words. So again a 
 doctor or a nurse can see how ill a patient is, though it 
 does not follow that they could always say why this appear- 
 ance goes with this degree of illness. In proportion as you 
 merely ^resume a causal connection, it is guess-work or pure 
 discovery. In as far as you can analyse a causal connection 
 it is demonstration or proof; and for Logic, discovery 
 cannot be treated apart from proof, except as skilful guess- 
 work. In as far as there is ground for the guess, so far it 
 approaches to proof; in as far as there is no ground, it 
 gives nothing for Logic to get hold of is mere caprice. A 
 good scientific guess really depends on a shrewd eye for the 
 essential points. I am not mathematician enough to give 
 the history of the discovery of Neptune by Leverrier and 
 Adams, " calculating a planet into existence by enormous 
 heaps of algebra," l but it must have begun as a guess. I 
 should suppose it was suggested before Adams and Leverrier 
 took it up, on the ground of the anomalous movements of 
 Uranus indicating an attraction unaccounted for by the 
 known solar system. And I suppose that this guess would 
 gradually grow into demonstration as it became clear that 
 nothing but a new planet would explain the anomalies of 
 1 De Morgan, Budget of Paradoxes, p. 53. 
 L
 
 I 4 6 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 the orbit of Uranus. And at last the calculators were able 
 to tell the telescopist almost exactly where to look for the 
 unknown planet. The proof in this case preceded the 
 observation or discovery by perception, and this makes it a 
 very dramatic example; but if the observation had come 
 earlier, it would not I suppose have dispensed with the 
 precise proof of Neptune's effect on Uranus, though it 
 might have made it easier. 
 
 Figures of 6. In illustration of this progress from guess-work to 
 ogism. sc ; ence) i j w ju gj ve an example of the three Aristotelian 
 figures of the Syllogism. I omit the fourth. I assume that 
 the heavier term, or the term most like a " thing," is fitted 
 to be the Subject, and the term more like an attribute to be 
 the Predicate. The syllogistic rules depend practically on 
 the fact that common Logic, following common speech and 
 thought, treats the Predicate as wider than the Subject, 
 which corresponds to Mill's view (also the common scien- 
 tific view), that the same effect may have several alternative 
 causes (not a compound cause, but different possible causes), 
 and that consequent is wider than antecedent. 2 It is this 
 assumption that prevents affirmative propositions from being 
 simply convertible, /'. e. prevents " All men are mortal " from 
 being identical with " All mortals are men," and but for it 
 there would be no difference of figure at all, as there is not 
 for inference by equation. 
 
 This progression is here merely meant to illustrate the 
 universal or systematic connection of particulars in process 
 of disengaging itself. But I do not say that the first 
 
 Cf. Plato's Republic, Bk. VI., end. 
 8 See p. 141, note,
 
 ix THE FIGURES 147 
 
 figure with a major premise is a natural form for all 
 arguments. 
 
 I take the scheme of the first three figures from Jevons, 
 and suggest their meaning as follows : 
 
 X denotes the major term, 
 middle term. 
 
 z 
 
 ,, ,, minor term. 
 
 
 ist Fig. 
 
 and Fig. 
 
 3 rd Fig. 
 
 Major Premise 
 
 ... Y X 
 
 ... X Y ... 
 
 Y X 
 
 Minor ,, 
 
 ... Z Y 
 
 ... Z Y ... 
 
 Y Z 
 
 Conclusion 
 
 ... Z X 
 
 ... Z X ... 
 
 Z X 
 
 Fig. 3. An observation and a guess. 
 Yesterday it rained in the evening. 
 All yesterday the smoke tended to sink. 
 
 / may be \ 
 
 .'. The smoke sinking ( . . )a sign of ram. 
 
 \is sometimes/ 
 
 The conclusion cannot be general in this figure, because 
 nothing general has been said in the premisses about the 
 subject of the conclusion. So it is very suitable for a mere 
 suggested connection given in a single content that of the 
 time "yesterday," implying moreover that both the points 
 in question have something to do with the state of the 
 atmosphere on that single day. 
 
 Fig. 2. A tentative justification. 
 
 Smoke that goes downwards is heavier than air 
 
 Particles of moisture are heavier than air. 
 
 .. Particles of moisture may be in the descending smoke. 
 
 A universal conclusion in this figure would be formally 
 bad. But we do not care for that, because we only mean 
 it to be tentative, and we do not draw a universal affirmative
 
 148 INFERENCE AND THE SYLLOGISTIC FORMS LECT. 
 
 conclusion. We express its badness by querying it, or by 
 saying "may be." The reason why it is formally bad is 
 that nothing general has been said in the premisses about 
 the middle term or reason, so that it is possible that the 
 two Subjects do not touch each other within it, ;'. e. that the 
 suggested special cause, moisture, is not connected with the 
 special effect, the sinking of the smoke. The general reason 
 "heavier than air" may include both special suggested 
 cause and special suggested effect without their touching. 
 Smoke and moisture may both sink in air, but for different 
 and unconnected reasons. Still, when a special cause is 
 suggested which is probably present in part, and which 
 would act in the way required by the general character of 
 the effect, there is a certain probability that it is the opera- 
 tive cause, subject to further analysis ; and the argument 
 has substantive value, though bad in form. The only good 
 arguments in this figure have negative conclusions, e.g. 
 
 Smoke that is heavier than air goes downwards. 
 
 Smoke on dry days does not go downwards. 
 
 .'. Smoke on dry days is not heavier than air. 
 
 This conclusion is formal, because the negative throws 
 the second Subject altogether outside the Predicate, and so 
 outside the first Subject. The one content always has a 
 characteristic which can never attach to the other, and 
 consequently it is clear that some genuine underlying 
 difference keeps them apart. Such an inference would 
 corroborate the suggestion previously obtained that the 
 presence of moisture was the active cause of the descending 
 smoke on days when rain was coming. 
 
 Fig. i. A completely reasoned judgment.
 
 ix MAJOR PREMISE 149 
 
 All particles that sink in the air in damp \veather more 
 than in dry, are loaded with moisture when they sink. 
 
 Smoke that descends before rain is an example of par- 
 ticles that sink in the air in damp weather more than in 
 dry. 
 
 /. Smoke that descends before rain is loaded with 
 moisture when it descends (and therefore its sinking is not 
 accidentally a sign of rain, but is really connected with 
 the cause of rain). 
 
 The major premise belongs only to this figure. In the 
 other it is mere tradition to call it so, and their two pre- 
 misses are the same in kind, and contribute equally to the 
 conclusion, and for that reason the affirmative conclusion 
 was not general or not formal. If your general conclusion 
 is to follow by mere form, you must show your principle 
 as explicitly covering your conclusion. But if you do this, 
 then of course you are charged with begging the question. 
 And, in a sense, that is what you mean to do, when you 
 set out to make your argument complete by its mere form. 
 If you have bona fide to construct a combination of your 
 data, you cannot predict whether the conclusion will take 
 this form or that form. Using a major premise meant, 
 " We have got a principle that covers the conclusion, and 
 so explains the case before us." Granting that the major 
 premise involves the minor premise and conclusion, that 
 is just the reason why it is imperative to express them. 
 The meaning of the Syllogism is that it analyses the whole 
 actual thought ; the fault is to suppose that novelty is the 
 point of inference. The Syllogism shows you how you 
 must understand either premise in order that it may cover
 
 ISO INFERENCE ANt> THE SYLLOGISTIC FORMS LECT. ix 
 
 the conclusion. Or, starting from the conclusion as a 
 current popular belief, or as an isolated observation or 
 suggestion by an individual observer (and this is practically 
 the way in which our science on any subject as a rule takes 
 its rise), the characteristic process through the three stages 
 described above consists in first noting the given circum- 
 stances under which, according to the prima facie belief 
 or observation, the conjunction in question takes place 
 (" yesterday," /'. e. " in the state of the atmosphere yester- 
 day ") ; secondly in analysing or considering those given 
 circumstances, to find within them something which looks 
 like a general property, a law, or causal operation, which 
 may attach the conjunction in question to the systematic 
 whole of our experience (the presence of something heavier 
 than air in the atmosphere) ; and thirdly, in the exhibition 
 of this ground or reason as a principle, in the light of which 
 the primary belief or observation (probably a good deal 
 modified) becomes a part of our systematic intelligible 
 world.
 
 LECTURE X 1 
 
 INDUCTION, DEDUCTION, AND CAUSATION 
 
 i. INDUCTION has always meant some process that starts Induction, 
 from instances ; the Greek word for it is used by Aristotle 
 both in his own Logic and in describing the method of 
 Socrates. It meant either "bringing up instance after 
 instance," or " carrying the hearer on by instances." And 
 still in speaking of Induction we think of some process that 
 consists in doing something with a number of instances. 
 But we find that this notion really breaks down, and the 
 contradiction between Mill and other writers (Jevons, ch. i.) 
 shows exactly how it breaks down. The question is whether 
 one experiment will establish an inductive truth. We will 
 review the meanings of the term, and show how they change. 
 
 (a) Induction by simple enumeration was what Bacon was Induction 
 always attacking, and saying, quite rightly, that it was not 
 scientific. It is the method which I stated in the Third ation. 
 Figure of the syllogism, almost a conversational method; 
 the mere beginning of observation. "I am sure the in- 
 fluenza is a serious illness ; all my friends who have had it 
 have been dreadfully pulled down." 
 
 1 Read N. Lockyer's Elements of Astronomy; Abney's Colour 
 Measurement ; Introduction to Bain on Induction ; Jevons's Elementary 
 Lessons on ** Observation and Experiment, " p. 228, and on Induction^ 
 p. 214 (about Mill).
 
 152 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 ABC have been seriously ill. 
 
 ABC have had influenza. 
 
 .'. Influenza is a serious illness. 
 
 Now this popular kind of inference, as Bacon says, " Pre- 
 carie concludit, et periculo exponitur ab instantia contra- 
 dictoria." Suppose you come across one slight case of 
 influenza, the conclusion is upset. This type of reasoning 
 really appeals to two quite opposite principles ; one the 
 principle of counting, which leads up to statistics and the 
 old-fashioned perfect Induction or the theory of chance, the 
 other the principle of scientific system. 
 
 Enumer- (b) In counting, we do not think of the reason why we 
 always has count > but there always is a reason, which is given in the 
 aground, nature of the whole whose parts we are counting. If I 
 count the members of this audience, it is because I want 
 to know how many units the whole audience consists of. I 
 do not ask why each unit is there ; counting is different 
 from scientific analysis ; but yet the connection between 
 whole and part is present in my reason for counting. So 
 really, though I only say, "One, two, three, four, etc.," 
 each unit demands a judgment, "This is one member 
 that makes two members, that makes three members," etc. 
 Counting is the construction of a total of units sharing a 
 common nature; measurement is a form of counting in 
 which the units are also referred to some other standard 
 besides the whole in question, e.g. the standard pound or 
 inch. 
 
 Perfect (c) Mere counting or " enumeration " only helps you in 
 
 lon ' induction by comparison with some other numerical result, 
 
 and, if imperfect, only to the extent of suggesting that there
 
 X NUMBER v. SYSTEM 153 
 
 is a common cause or there is not a common cause. E.g. 
 if you throw a six with one die fifty times running, you 
 infer that the die is probably loaded. This is because you 
 compare the result with that which you expect if the die 
 is fair, viz. a six once in every six throws. You infer that 
 there is a special cause favouring one side. The principle 
 is that ignorance is impartial. If you know no reason for 
 one case more than another, you take them as equal 
 fractions of reality; if results are not equal fractions of 
 reality, you infer a special reason favouring one case. 1 Pure 
 counting cannot help you in Induction in any way but this. 
 Perfect Induction simply means that the total is limited and 
 the limit is reached; you have counted 100 per cent, of 
 the possible cases, and the chance becomes certainty. The 
 result is a mere collective judgment. 
 
 (d) The principle of scientific system is quite a different System, 
 thing. Essentially, it has nothing to do with number or 
 with a generalised conclusion. It is merely this, " What is 
 once true is always true, and what is not true never was 
 true." The aim of scientific induction is to find out " What 
 is true," /. e. what is consistent with the given system. We 
 never doubt this principle ; if we did we could have no 
 science. If observation contradicts our best-established 
 scientific laws, and we cannot suppose an error in the 
 observation, we must infer that the law was wrongly, /'. e. 
 untruly stated. Therefore, as Mill says, one case is enough, 
 if you can find the truth about it. People object that you 
 cannot make a whole science out of one case, and there- 
 fore you must have a number of instances. That is a 
 1 See Lecture IX,, p. 144, note.
 
 *54 INDUCTION, DEDUCTION, AND CAUSATION LKCT. 
 
 practical point to be borne in mind, but it has no real 
 scientific meaning. " Instance " cannot be defined except 
 as one observation, which is a purely accidental limitation. 
 The point is, that you use your instances not by counting 
 cases of given terms, but by ascertaining what the terms 
 really are (/. e. modifying them), and what is their real con- 
 nection. This is the simple secret of Mill's struggle to base 
 scientific Induction, on Induction by simple Enumeration ; 
 the latter is not the evidence, but the beginning of eliciting 
 the evidence so that the Scientific Induction is far more 
 certain than that on which Mill bases it. Aristotle's statement 
 is the clearest and profoundest that has ever been made. 
 Aristotle, " Nor is it possible to obtain scientific knowledge by way 
 87' b. 28.' f sense-perception. For even if sense-perception reveals a 
 certain character in its object, yet we necessarily perceive 
 t/iis, here, and now. The universal, which is throughout all, 
 it is impossible to perceive ; for it is not a this-now ; if it 
 had been it would not have been universal, for what is 
 always and everywhere we call universal. Since then 
 demonstration (science) is universal, and such elements it 
 is impossible to perceive by sense, it is plain that we cannot 
 obtain scientific knowledge by way of sense. But it is clear 
 that even if we had been able to perceive by sense \e.g. 
 by measurement] that the three angles of a triangle are 
 equal to two right angles, we should still have had to search 
 for a demonstration, and should not, as some say, have 
 known it scientifically (without one); for we necessarily 
 perceive in particular cases only, but science comes by 
 knowing the universal. Wherefore if we could have been 
 on the moon, and seen the earth coming between it and the
 
 x THE UNIVERSAL *55 
 
 sun, we should not (by that mere perception) have known 
 the cause of the eclipse. Not but what by seeing this 
 frequently happen we should have grasped the universal, 
 and obtained a demonstration ; for the universal becomes 
 evident out of a plurality of particulars, and the universal 
 is valuable because it reveals the cause;" and again, 1 "And 
 that the search of science is for the middle term is made 
 plain in those cases in which the middle term is percep- 
 tible to sense. For we search where we have had no per- 
 ception, as for the reason (or middle term) of an eclipse, 
 to know if there is a reason or not. But if we had been 
 upon the moon, we should not have had to inquire if the 
 process (of an eclipse as such, and not some other kind 
 of darkness) takes place, or for what reason, but both 
 would have been plain at once. The perception would 
 have been, 'The earth is now coming between,' carrying 
 with it the obvious fact, ' The moon is now suffering an 
 eclipse,' and out of this the universal (connection) would 
 have arisen." 
 
 (e) I showed you a method on the way to this in the shape Analogy. 
 of Aristotle's second figure, which we may call analogy. 
 The plain sign of it is, that you give up counting the in- 
 stances and begin to weigh them, so that the attributes 
 which are predicates fall into the middle term or reason. 
 In the former inference about influenza we did not suppose 
 that you had any idea why influenza was a serious illness ; 
 but in analogy there is some suggestion of this kind, so that 
 the connection is examined into. Here at once you begin 
 to get suggested explanations and confirmation from the 
 1 Aristotle, An. Post., 90, a 24.
 
 156 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 system of knowledge. You cannot have analogy by merely 
 counting attributes. 
 
 I begin from Enumerative Suggestion drawn from observ- 
 ation of Butterflies. 
 
 1. Three species of genus x closely resemble three species 
 ofj. 
 
 2. The species of x would be protected by resembling y 
 (because y is distasteful to birds). 
 
 .'. The resemblance may be a "protective resemblance," 
 /". e. a resemblance brought about by survival of those thus 
 protected. 
 
 On this there naturally follows Analogy. 
 
 1. Protective resemblances naturally increase through 
 series of species from slighter to closer resemblances. 
 
 2. The resemblances in question increase in genus x 
 through series of species from slighter to closer resemblance 
 to_y. 
 
 .'. The resemblances in question show important signs of 
 being protective resemblances. 
 
 When we get thus far, a single syllogism will not really 
 represent the argument. It can only analyse with con- 
 venience a single step in inference. But . now we have 
 connected the reason of the resemblances with the whole 
 doctrine of natural selection, the gradual approximation of 
 the species is most striking, and we could set up a corro- 
 borative analogy on the basis of every feature and detail of 
 these resemblances, the tendency of which would be to 
 show that no cause or combination of causes other than 
 that suggested is likely to account for the observed re- 
 semblances.
 
 X USE OF VARYING CONDITIONS 157 
 
 I give a confirmatory negative analogy. 
 
 1. No protective resemblance can grow up where there 
 is no initial tendency to resemblance. 
 
 2. The non-resembling species in the genus x show no 
 initial tendency towards y. 
 
 .'. The non-resemblances observed are such as could not 
 produce protective resemblances. This is a formally bad 
 argument from two negative premisses justified by its positive 
 meaning, which implies that just where the alleged effect 
 ceases, the alleged cause ceases too. 
 
 If you look at the case in the Natural History Museum * 
 you see the normal Pierinae down one side, not approaching 
 Euploinae. They are the positive examples, negatively 
 confirming the explanation of those which do approach 
 Euploinae. These latter all start from some form which 
 varied slightly, by accident we presume, towards Euploinse, 
 and then this partially resembling series splits into three 
 sets, each leading up to a different and complete protective 
 resemblance. 
 
 I said mere number was no help in scientific Induction. 
 But do not these three sets of resemblances make a stranger 
 proof than any one would ? Yes, because we need a pre- 
 sumption against accident. You would not want this if 
 you could unveil what really happens in one case, but as 
 infinite conditions are operative in such matters, and it is 
 impossible to experiment accurately, 2 this cannot be done ; 
 
 1 These cases in the entrance-hall of the Natural History Museum 
 at South Kensington afford excellent practical illustrations of Inductive 
 Method. I strongly urge the London student to try his hand at 
 formulating them. 
 
 2 Ultimately, no experiments are absolutely accurate. There is
 
 158 INDUCTION, DEDUCTION, AND CAUSATION I.KCT. 
 
 and it might be said that one such resemblance was an 
 accident, /. e. that it was owing to causes independent of the 
 protection. But as the cases become more numerous it 
 becomes more improbable that different circumstances 
 produce the same effect, which would then be a mere 
 coincidence, in so many different cases. If, however, 
 we knew by positive and negative analysis what circum- 
 stance did produce the effect, this confirmation would be 
 useless. 
 
 Negative (/) In order to show exactly what circumstance produces 
 
 ice ' a given effect, a system must be brought to bear on the 
 
 phenomenon through negation. The only test of truth is 
 
 that it is that which enables you to organise your thought 
 
 and perception. 
 
 The first means of doing this is Observation, then Experi- 
 ment, then Classification and Hypothesis, which takes us 
 into Deduction. 
 
 Observation is inaccurate, until you begin to distinguish 
 what is connected from what is not connected. When you 
 do this, you are very near experiment, the use of which is to 
 introduce perfectly definite and measurable changes into 
 what you are observing. 1 There is no absolute distinction 
 between observation and experiment. Looking at a tissue 
 through a microscope is observation ; putting on a polari- 
 scope, though it changes the image altogether, is observation ; 
 if you warm the stage, or put an acid on the object, that, I 
 suppose, is experiment, because you interfere with the object 
 
 always an unexhausted background in which unsuspected causes of error 
 may be latent. 
 
 1 Jevons, loc. fit., esp. quot. from Herschel (p. 234).
 
 X THE NEGATIVE INSTANCE 15$ 
 
 itself. What should we say, for example, as to spectroscopic 
 analysis of the Sun's corona ? 
 
 The moment you begin accurate observation you get a 
 negative with positive value, which is really the converse by 
 negation of your positive observation, a! is b t ; b 2 (which is 
 just not-bi) is a-, (which is just not-a^. Thus the two may 
 be represented as the same judgment in positive and nega- 
 tive forms, which confirm one another. " Yellow is a com- 
 pound of red and green " in Experiment, " if, and as far as 
 you take away the red or the green you destroy the yellow." 
 That describes an experiment with the colour-box. I have 
 inverted the order in the conversions in compliance with the 
 rule of common Logic, that Predicate is wider than Subject ; 
 but in accurate matter it is a false rule, and very inconveni- 
 ent. The common rule means that a man who is drowned 
 is dead, but a man who is dead need not have been 
 drowned; but of course if he has the signs of death by 
 drowning then he has been drowned. 
 
 (g) Classification is a consequence of all systematic theory ; Classifica- 
 it is not a separate method of science. It is merely the Generalis- 
 arrangement of positive contents negatively related. No ation. 
 doubt where we have a kind of family relations between 
 individuals classification is more prominent, and in the 
 theory of continuous matter or operation, where individual- 
 ities are not remarkable e.g. in geometry it is less pro- 
 minent. But both are always there classification and theory. 
 Classification which expresses no theory is worthless, except 
 that intended for convenient reference, such as alphabetical 
 classification. 
 
 Under classification I may say a word on generalisation.
 
 160 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 The common idea of inference from many cases, because 
 they are many, to all cases of the same kind, is quite without 
 justification. The only genuine and fundamental law of 
 generalisation is "Once true always true." But this might 
 fail to suffice for our practical purposes, because it might 
 save its truth by abstraction. Let us take the example, 
 " Water is made of oxygen and hydrogen." If that is true 
 once, it is always true in the same sense. If you find some 
 fluid of a different composition which you are inclined to 
 call water, then you must identify or distinguish the two, 
 and this is a mere question of classification. Practically, 
 however, we could not get on unless our knowledge had 
 some degree of exhaustiveness, i. e. unless we knew roughly 
 that most of what we take for water will have the alleged 
 properties. But no Induction or analysis, however accurate, 
 can assure us against confusion and error, viz. assure us that 
 everything we take to be water will be made of oxygen and 
 hydrogen, nor that water will always be found on the earth. 
 I call this accurate analysis, which may be made in a single 
 instance only, and is the only perfectly scientific generalisa- 
 tion, generalisation by mere determination. Its classification 
 is hypothetical, /. e. in it the individuals are merely possible 
 individuals. 
 
 But this passes into another kind of generalisation, which 
 may be called generalisation by concrete system, as when 
 we attach scientific analysis to some extensive individual 
 reality, e.g. to the solar system or the race of man. Then 
 our judgments have a place in the real world, and our classi- 
 fication is categorical classification. The generalisation in 
 this case does not follow from the judgment being extended
 
 X MERE LIKENESS 161 
 
 over a great plurality of possible similar subjects, but from 
 the subject to which it applies having as an organised totality 
 a large place in the world; e.g. "The human race alone 
 gives moral interest to the history of our planet." These 
 judgments come by making explicit the reality which under- 
 lies such hypothetical judgments as "all men are capable 
 of morality." It means that we actually venture to assign 
 a place in the universe to the system we are speaking of. 
 Then, though it is an individual, and unique, its name has 
 a meaning, and is not a mere proper name. The solar 
 system is good instance. Judgments about it or parts of 
 it are universal but not purely hypothetical, and as our 
 knowledge of this kind increases it becomes even a little 
 exhaustive. 
 
 Generalisation by mere likeness or analogy, on the other 
 hand, is precarious. It is what popular theory has in its 
 mind in speaking of Induction, viz. a conclusion from a 
 truth to judgments concerning all similar cases, e. g. from 
 "Water is made of Oxygen and Hydrogen" to "All liquids 
 which we choose to take for water are made of Oxygen and 
 Hydrogen." No scientific method can possibly give us this 
 result. In as far as it has value it depends upon our guess- 
 ing rightly by analogy. It may be replied, "that the signs 
 of recognition are set down in the law or truth." Well, if 
 they are certain, generalisation by mere determination is 
 enough ; if they are doubtful, no induction can warrant your 
 judgment of them in particular cases. Practically, of course, 
 we get them right pretty often, although wrong very often. 
 
 (h) Hypothesis is merely supposition ; it consists in sug- Hypo- 
 gesting a fact as if it were real, when it is the only way of thesis> 
 
 M
 
 162 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 completing given facts into a consistent system. If the 
 hypothesis is proved that is a demonstration. It has been 
 said that " Facts are only familiar theories." If a bell rings 
 in the house, I say unhesitatingly, "Some one rang that 
 bell." Once in ten years it may be rung, not by a person, 
 but by some mechanical accident, in which case the "some 
 one " is a hypothesis, but one always treats it as a fact. The 
 only proof of a hypothesis is its being the only one that will 
 fit the facts, /. e. make our system of reality relatively self- 
 consistent. We believe many things we can never verify by 
 perception, e.g. the existence of the centre of the earth, or 
 that you have an idea in your minds ; and if we go to ulti- 
 mate analysis, perception itself involves hypothesis, and a 
 fortiori all experiment involves hypothesis. Every experi- 
 mental interference with nature involves some supposition 
 as to a possible connection which it is intended to confirm 
 or disprove. 
 
 2. Classification and hypothesis bring us into Deduction, 
 which is not really a separate kind of inference from Induc- 
 tion, but is a name given to science when it becomes syste- 
 matic, so that it goes from the whole to the parts, and not 
 from the parts to the whole. In Induction you are finding 
 out the system piecemeal, in Deduction you already have 
 the clue ; but the system, and the system only, is the ground 
 of inference in both. Induction is tentative because we do 
 not know the system completely. Their relation may be 
 fairly represented by the relation of the first figure of the 
 Syllogism to the second and third. The difference is merely 
 that in deduction we are sure of having knowledge which 
 covers the whole system. If a man observed, " The differ-
 
 x DEDUCTION 163 
 
 ence between the dark blood in the veins and the bright 
 blood in the arteries calls for explanation," that is the 
 beginning of Induction. If a man states the circulation 
 of the blood as an explanation, that is Deduction. Really 
 Induction is only a popular name for such Inference as 
 deals with numbers of instances. Mill's experimental 
 methods do not depend upon number of instances, but only 
 upon content ; they presuppose the instances already broken 
 up into conditions A, B, C, and consequents a, b, c. 
 
 I must distinguish subsumption and construction as two 
 forms of deduction. Only the former properly employs 
 Syllogism in the first figure. 
 
 (a) Subsumption is argument by subject and attribute ; Subsump- 
 /. e. when we do not know the system so as to construct the 
 detail, f. g. a man's character, and can only state in what 
 individual system the details occur. Then we really want 
 the major premise to lay down the properties of the system, 
 and all deduction can therefore be employed with a major 
 premise, e.g. a mathematical argument might ultimately 
 take the form, "space is such that two parallels cannot meet." 
 
 But (b} when the nature of the subject is very obvious, Construe- 
 and the combinations in it very definite, then the major tlon> 
 premise is superfluous, and adds nothing to the elements 
 of the combination. 
 
 "A to right of B, B to right of C. 
 . . A to right of C." 
 
 This is clear, but it is not formal ; as a syllogism it has four 
 terms. It is simply a construction in a series of which the 
 nature is obvious. And if you insert a major premise it 
 would be, " What is to the right of anything is to the right
 
 164 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 of that which the former is to the right of," and that is 
 simply the nature of the series implied in the inference 
 stated in an abstract form. "Inference is a construction 
 followed by an intuition." 1 The construction, I think, 
 however, must be a stage of the intuition. I am therefore 
 inclined to suggest that a factor of general insight into 
 principle is neglected in this definition, from which much 
 may undoubtedly be learned. 
 
 Causation. 3. I have said very little about causation. The fact is, 
 that in Logic the cause necessarily fades away into the 
 reason, that is, the explanation. If we follow Mill's account, 
 we see how this takes place. I will put the stages very 
 briefly. 
 
 Cause. (a) We start, no doubt, by thinking of a cause as a real 
 
 event in time, the priority of which is the condition of 
 another event, the effect. Pull the trigger cause and the 
 gun goes off effect. 
 
 Complete (b} The moment we look closer at it, we see that this will 
 lons> not do, and we begin to say with Mill, that the cause is the 
 antecedent which includes all the conditions of the effect. 
 The plurality of alternative causes breaks down, through the 
 conditions defining the effect. Pull the trigger ? yes, but 
 the cartridge must be in its place, the striker must be 
 straight, the cap must be in order, the powder must be dry 
 and chemically fit, and so on, and so on, till it becomes 
 pretty clear that the cause is a system of circumstances 
 which include the effect. 
 
 Law. (c) But then our troubles are not ended. Only the essen- 
 
 tial and invariable conditions enter into the cause, if the 
 1 Bradley, Principles of Logic, p. 235.
 
 x GROUND 165 
 
 cause is invariable. This begins to cut away the particular 
 circumstances of the case. You need not use the trigger, 
 nor even the cap ; you may ignite powder in many ways. 
 You may have many kinds of explosives. All that is 
 essential is to have an explosion of a certain force and 
 not too great rapidity. Then you will get this paradox. 
 What is merely essential to the effect, is always something 
 less than any combination of real " things " which will pro- 
 duce the effect, because every real thing has many properties 
 irrelevant to this particular effect. So, if the cause means 
 something real, as a material object is real, it cannot be 
 invariable and essential. If it is not something real, and is 
 essential, it fines down into a reason or law the antecedent 
 in a hypothetical judgment. 
 
 (</) We can only escape this by identifying both cause Ground, 
 and reason with the complete ground ; that is, the nature of system 
 
 a system of reality within which the cause and effect both with 
 
 known 
 lie. But even then, though the ground is real, it is not laws. 
 
 antecedent in time. We see, indeed, that the conditions of 
 an effect must be continuous through the effect. If the 
 process were taken as cut in two at any point, its connection 
 would be destroyed. If a cause and b effect were really 
 detached events, what difference could it make if, instead of 
 a, c preceded b ? 
 
 4. The postulate of Knowledge, then, is very badly stated Postulate 
 as Uniformity of Nature. That was due to the vulgar 
 notion of Inductive "generalisation." It must be stated in 
 two parts : first, " Once true always true ; " and secondly, 
 " Our truth is enough for us," that is, it covers enough of 
 the universe for our practical and theoretical needs. The
 
 166 INDUCTION, DEDUCTION, AND CAUSATION LECT. 
 
 two parts may be put together by saying, " The universe is 
 a rational system," taking rational to mean not only of such 
 a nature that it can be known by intelligence, but further of 
 such a nature that it can be known and handled by our 
 intelligence. 
 
 Con- 5. These lectures have been unavoidably descriptive 
 
 rather than thorough, and yet, as I warned you, descriptive 
 of properties which are in a sense not at all new, but quite 
 familiar, and even trite. You will not feel, at first, that the 
 full interest which I claimed for the science of knowledge, 
 really attaches to these dry relations of abstract thought. 
 You will get no permanent good unless you carry the study 
 forward for yourselves, and use these ideas as a clue to find 
 your bearings in the great world of knowledge. 
 
 And I would give you one hint about this. / do not 
 suggest that you should neglect philosophy but yet you 
 should remember that philosophy can tell you no new facts, 
 and can make no discoveries. All that it can tell you is the 
 significant connection of what you already know. And if 
 you know little or nothing, philosophy has little or nothing 
 to tell you. Plato says, " The synoptical man, the man who 
 has a conspectus of knowledge, is the philosopher ; and the 
 man who is not synoptical, who cannot see two subjects in 
 their relation, is no philosopher." By all means read good 
 logical books ; but also and more especially read good and 
 thorough systematic books on science, or history, or politics, 
 or fine art I do not mean on all of these subjects, but on 
 some, wherever your interest leads you. You cannot learn 
 the nature of inference, of systematic necessity, of the con- 
 struction of reality, by reading logic exclusively ; you must
 
 x THE PHILOSOPHIC SPIRIT 167 
 
 feel it and possess it by working in the world of concrete 
 knowledge. I give one example in passing. If you study 
 social questions, test for yourselves the value of statistics 
 i.e. sets of enumerative judgments. Consider what the 
 causal analysis of any problem demands ; remember that all 
 enumeration implies a ground or whole, on which its value 
 depends ; and contrast the exhaustive examination of an 
 instance thoroughly known, with the enumeration of thou- 
 sands of cases lumped under a general predicate. Determine 
 always to know the truth ; welcome all information and all 
 suggestion, but remember that truth is always systematic, 
 and that every judgment, when you scrutinise it, demands a ' 
 fuller and fuller connection with the structure of life. It is 
 not cleverness or learning that makes the philosopher ; it is 
 a certain spirit ; openness of mind, thoroughness of work, 
 and hatred of superficiality. Each of us, whatever his 
 opportunities, can become in a true sense, if he has the 
 real philosophic spirit, in Plato's magnificent words, "The 
 spectator of all time and of all existence." 
 
 THE END
 
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