{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_63598/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_63598","id":"gutenberg_63598","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/63598","summary":null,"tags":["Category: Philosophy & Ethics","Logic"],"text":"THE ESSENTIALS OF LOGIC\nbeing\nTEN LECTURES ON JUDGMENT AND INFERENCE\n\nby\n\nBERNARD BOSANQUET\nFORMERLY FELLOW OF UNIVERSITY COLLEGE, OXFORD\n\nMACMILLAN AND CO.\nLONDON AND NEW YORK\n1895\n\nThe right of Translation is reserved\n\nRichard Clay & Sons, Limited,\nLondon & Bungay.\n\nTranscriber's Note: Footnotes have been placed under the paragraphs to\nwhich they relate. A few added footnotes and additions to Bosanquet's\nfootnotes, giving the equivalents of Greek words in the text, are in\nsquare brackets. Bosanquet's marginal notes have been used as\nsubheadings. Page numbers from the original are in braces {}.\n\n\n\n\n\n{v}\n\nPREFACE\n\nIn this course of lectures I have attempted to carry out, under\nthe freer conditions of the University Extension system, a purpose\nconceived many years ago at Oxford. It was suggested to me by the\nanswer of a friend, engaged like myself from time to time in teaching\nelementary Logic, to the question which I put to him, \u201cWhat do you aim\nat in teaching Logic to beginners? What do you think can reasonably be\nhoped for?\u201d \u201cIf the men could learn what an Inference is, it would be\nsomething,\u201d was the reply.\n\nThe course of lectures which I now publish was projected in the spirit\nthus indicated. Though only the two last discourses deal explicitly\nwith Inference, yet those which precede them contribute, I hope, no\nless essentially, to explain the nature of that single development\nwhich in some stages we call Judgment, and in others Inference. So far\nas I could see, the attempt to go to the heart of the subject, however\nimperfectly executed, was appreciated by the students, and was rewarded\nwith a serious attention which would not have been commanded by the\ntrivialities of formal Logic, although more entertaining and less\nabstruse.\n\nThe details of traditional terminology may be found in Jevons\u2019s\n_Elementary Lessons in Logic_ (Macmillan). Those {vi} who desire to\npursue the study more in the sense of the present work, may be referred\nabove all to Bradley\u2019s _Principles of Logic_, and also to Lotze\u2019s\n_Logic_ (E. Tr.), and to Sigwart\u2019s great work on Logic, the English\ntranslation of which, just completed, opens a storehouse of knowledge\nand robust good sense to the English student. My own larger _Logic_\nexpresses _in extenso_ the views which these lectures set out in a\nshorter form.\n\nI hope it will be admitted by my critics that this experiment, whether\nsuccessful or unsuccessful, was worth making, and that except in the\nUniversity Extension system, it could not easily have been made.\n\nBernard Bosanquet.\nLondon, January 1895.\n\n\n\n\n{vii}\n\nCONTENTS\n\nLECTURE I   THE PROBLEM OF LOGIC\n\n1.  Difficulty of the Science                      1\n\n2.  The Problem stated                             3\n\n3.  World as Idea                                  4\n\n4.  \u201cWorld\u201d                                        5\n\n5.  The Animal\u2019s World                             6\n\n6.  The World as \u201cObjective\u201d                       7\n    i.   Common sense                              8\n    ii.  Common-sense Theory                       8\n    iii. Philosophic Theory                       11\n\n7.  Our separate \u201cWorlds\u201d                         14\n\n8.  Subjective Idealism                           19\n\n\nLECTURE II   JUDGMENT AS THE CONSCIOUSNESS OF A WORLD\n\n1.  Defect of Subjective Idealism                 21\n\n2.  The World as Knowledge                        22\n\n3.  Knowledge is in the form of Judgment          23\n    a.  Necessary                                 23\n    b.  Universal                                 26\n    c.  Constructive                              27\n\n4.  The Continuous Affirmation of Waking\n    Consciousness                                 33\n\n5.  Comparison with World as Will                 37\n\n6.  Distribution of Attention                     40\n\n{viii}\n\nLECTURE III   THE RELATION OF LOGIC TO KNOWLEDGE\n\n1.  Meaning of \u201cForm\u201d                             42\n\n2.  Form of Knowledge dependent on Content        49\n\n3.  The Relation of Part and Whole as Form\n    determined by Content                         54\n\n4.  Nature of Knowledge                           58\n\n5.  Conclusion                                    59\n\n\nLECTURE IV   TYPES OF JUDGMENT, AND THE GENERAL\n             CONDITIONS INVOLVED IN ASSERTION\n\n1.  Correspondence between Types of Judgment\n    and Nature of Objects as Knowledge            61\n    _a_.  Impersonal Judgment                     61\n    _b_.  Perceptive Judgment                     62\n    _c_.  Proper Names in Judgment                64\n    _d_.  Abstract Judgment                       65\n\n\n2.  The General Definition of Judgment            66\n    i.   What is implied in claiming Truth        67\n    ii.  By what means the claim is made          69\n    iii. The kind of Ideas which can claim Truth  74\n         _a_. Idea as Psychical Presentation      74\n         _b_. Idea as Identical Reference         74\n\n\nLECTURE V   THE PROPOSITION AND THE NAME\n\n1.  Judgment translated into Language             80\n\n2.  Proposition and Sentence                      82\n\n3.  Difference between Proposition and Judgment   82\n\n4.  \u201cParts of Speech\u201d                             85\n\n5.  Denotation and Connotation                    88\n\n6.  Have Proper Names Connotation?                91\n\n7.  Inverse Ratio of Connotation and Denotation   94\n\n{ix}\n\nLECTURE VI   PARTS OF THE JUDGMENT, AND ITS UNITY\n\n1.  Parts of the Judgment                         98\n\n2.  Copula                                        99\n\n3.  Are Subject and Predicate necessary?         100\n\n4.  Two Ideas or Things                          101\n    a.  Two Ideas                                102\n        i.  Mental Transition                    102\n        ii. Absence of Assertion                 103\n    b.  Two Things                               104\n\n5.  Distinction between Subject and Predicate    107\n\n\nLECTURE VII   THE CATEGORICAL AND THE HYPOTHETICAL\n              JUDGMENTS\n\n1.  Some Criticisms on the ordinary scheme of\n    Judgment                                     112\n    a.  Why we need a Scheme                     112\n    b.  The Common Scheme                        113\n\n2.  Which Judgments are Categorical?             116\n    (1)  The \u201cParticular\u201d Judgment               116\n         a.  Natural Meaning                     116\n         b.  Limited Meaning                     117\n    (2)  \u201cSingular\u201d Judgment                     118\n    (3)  \u201cUniversal\u201d Judgment                    119\n    (4)  \u201cHypothetical\u201d Judgment                 121\n    (5)  \u201cDisjunctive\u201d Judgment                  123\n\n\nLECTURE VIII   NEGATION, AND OPPOSITION OF JUDGMENTS\n\n1.  Distinction between Contrary and Contradictory\n    Opposition                                   126\n\n2.  Contrary Negation                            128\n\n3.  Why use Negation?                            130\n\n4.  Stage of Significant Negation; Combination\n    of Contrary and Contradictory                132\n\n5.  Negative Judgment expressing Fact            134\n\n6.  Operation of the Denied Idea                 135\n\n{x}\n\nLECTURE IX   INFERENCE AND THE SYLLOGISTIC FORMS\n\n1.  Inference in General                         137\n\n2.  Conditions of the Possibility of Inference   139\n\n3.  System the ultimate condition of Inference   140\n\n4.  Immediate Inference                          141\n\n5.  Number of Instances                          142\n\n6.  Figures of Syllogism, illustrating Progress\n    from Guess-work to Demonstration             146\n\n\nLECTURE X   INDUCTION, DEDUCTION, AND CAUSATION\n\n1.  Induction                                    151\n    a.  By simple Enumeration                    151\n    b.  Enumeration always has a Ground          152\n    c.  Perfect Induction                        152\n    d.  System                                   153\n    e.  Analogy as Step towards System           155\n    f.  Negative Instance                        158\n    g.  Classification and Generalisation        159\n    h.  Hypothesis                               161\n\n2.  Deduction                                    162\n    a.  Subsumption                              163\n    b.  Construction                             163\n\n3.  Causation                                    164\n\n4.  The Postulate of Knowledge                   165\n\n5.  Conclusion                                   166\n\n\n\n\n{1}\n\nLECTURE I   THE PROBLEM OF LOGIC\n\n_Difficulty of the science_\n\n1. There is no science more difficult than that on which we are\nentering in these lectures. It is worth while to discuss the nature of\nthis difficulty. It is a question of interest rather than of intricacy.\nAll sciences have, perhaps, much the same possibilities of broad theory\nand subtle analysis. But Logic stands alone in the difficulty with\nwhich the student sustains his persuasion that its point of view is\nworth applying.\n\nIn most other sciences, even in the philosophical sciences, there\nis a continual stimulus to sense-perception, to curiosity, to human\ninterest. The learner is called upon to dissect animals or plants,\nto undertake delicate manipulations with beautifully contrived\ninstruments, to acquaint himself with the history of nations, with\nthe genesis of worlds, with strange and novel speculations upon the\nnature of space, or with the industry and well-being of various classes\namong mankind at the present day. And these elements of novelty, these\nstimulations of sense-perception or of practical interest, carry us\nforward imperceptibly, and sustain our {2} eagerness to analyse and\ncombine in theoretic completeness the novel matter thus constantly\nimpinging upon us.\n\nIn Philosophy, and more especially in Logic, we can promise little\nor nothing of this kind. The teacher of Philosophy, from Socrates\ndownwards, has talked about common things, things already familiar\nto his hearers. And although he calls upon them to think of these\nthings in a peculiar way, and from an unaccustomed point of view, yet\nit is likely to be felt that he is demanding a new effort, without\nsupplying a new interest. And it is a common experience, that after a\ntime the mind rebels against this artificial attitude, which fatigues\nwithout instructing, if we have accustomed ourselves to understand by\ninstruction the accumulation of new sense-perceptions and the extension\nof historical or scientific vision over a wider superficial area.\n\nNow this I cannot help, and I will not disguise. In Philosophy, and\nin Logic above all, it must be so. The whole point and meaning of the\nstudy is that in it we re-traverse familiar ground, and survey it by\nunfamiliar processes. We do not, except accidentally, so much as widen\nour mental horizon. For those who care to understand, to trace the\nconnecting principles and functions that permeate our intellectual\nworld, there is indeed an interest of a peculiar kind. But even\nexperienced students will occasionally feel the strain of attending to\ndifficult distinctions, entirely without the excitement of novelty in\nsense-perception or of a practical bearing upon human life. It is this\nthat makes Logic probably the hardest of all the sciences.\n\n{3} _The problem stated_\n\n2. We cannot hope to vanquish this difficulty unless we face it boldly\nfrom the first. There are in the old-fashioned Logic-books tricks and\npuzzles, fallacies and repartees, which can in some degree be made\namusing; but of these I do not intend to speak. The course by which\nalone I can hope honestly to awaken a true logical interest among\nany who may be quite unfamiliar with the subject, is to approach the\nmatter descriptively, and try to set before you fully and fairly what\nthe problem is which the process of knowledge has to meet. And then\nit may be possible to claim a genuine theoretical curiosity--none the\nless genuine that it may be tinged with a sympathy for man\u2019s common\nbirthright of intelligence--for the detailed explanation of the means\nby which this problem is solved from day to day. Such an explanation is\nthe science of Logic.\n\nThe problem may be thus introduced. Several of those present have,\nI believe, attended a previous course of lectures on Psychology.\nThey have learned, I presume, to think of the mind as the course of\nconsciousness, a continuous connected presentation, more or less\nemphasising within it various images, and groups of images and ideas,\nwhich may be roughly said to act and re-act upon each other, to cohere\nin systems, and to give rise to the perception of self. This course\nof consciousness, including certain latent elements, the existence\nof which it is necessary to assume, is an individual mind, attached\nto a particular body, and so far as we know, not separable from the\nactions and affections of that body. What is the connection between\nsuch a course of consciousness in any individual, and the world as\nthat individual knows and wills it? This is the point at {4} which\nPsychology passes into Logic. Psychology treats of the course of ideas\nand feelings; Logic of the mental construction of reality. How does the\ncourse of my private ideas and feelings contain in it, for me, a world\nof things and persons which are _not merely in my mind_?\n\n_World as Idea_\n\n3. Schopenhauer called his great work, _The World as Will and\nIdea_. [1] Leaving out Will for the moment, let us consider the world\n\u201cas Idea.\u201d\n\n  \u201c\u2018The world is my idea;\u2019 [2] this is a truth which holds\n  good for everything that lives and knows, though man alone\n  can bring it into reflective and abstract consciousness. If\n  he really does this, he has attained to philosophical wisdom.\n  It then becomes clear and certain to him that what he knows\n  is not a sun and an earth, but only an eye that sees a sun,\n  a hand that feels an earth; that the world which surrounds\n  him is there only as an idea, _i.e._ only in relation to\n  something else, the consciousness which is himself. If any\n  truth can be asserted _a priori_, it is this; for it is the\n  expression of the most general form of all possible and\n  thinkable experience: a form which is more general than\n  time, space, or causality, for they all pre-suppose it.\n\n  .....\n\n  \u201cNo truth, therefore, is more certain, more independent of\n  all others, and less in need of proof than this, that all that\n  exists for knowledge, and, therefore, this whole world, is\n  only object in relation to subject, perception of a perceiver,\n  in a word, idea. This is obviously true of the past and the\n  future, as well as of the present, of what is farthest off, as\n  of {5} what is near; for it is true of time and space\n  themselves, in which alone these distinctions arise. All that\n  in any way belongs or can belong to the world is inevitably\n  thus conditioned through the subject and exists only for the\n  subject. The world is idea.\u201d\n\n[1] E. Tr. (Trubner, 1883).\n\n[2] Schopenhauer, _op. cit._ beginning.\n\nThe world, then, for each of us, exists in the medium of our mind.\nIt is a sort of building, of which the materials are our ideas and\nperceptions.\n\n_The \u201cworld\u201d_\n\n4. So much for \u201cidea.\u201d What do we mean by \u201cworld\u201d? A succession of\nimages passing before us, or rather making up our consciousness, like a\ndream, is not a world. The term is very expressive; it is a favourite\nword in Shakespeare. When the courtier says \u2014\n\n  \u201cHereafter, in a better world than this,\n  I shall desire more love and knowledge of you,\u201d\n\nhe does not mean, as I used to think, \u201cin heaven\u201d; he means in a\nbetter condition of social affairs. In \u201cmad world, mad kings, mad\ncomposition,\u201d the term means more especially the set of political and\nfamily connections within which extraordinary reversals of behaviour\nhave just taken place. Often we use the expression, with a qualifying\nepithet, to indicate some particular sphere of connected action, \u201cthe\necclesiastical world,\u201d \u201cthe political world,\u201d and so forth. Always\nthere seems to be implied the notion of a set of things or persons\nbound together by some common quality which enables them to act upon\neach other, and to constitute what is technically termed a \u201cwhole.\u201d\n_The_ \u201cworld\u201d _par excellence_, then, ought to mean the one connected\nset of things and persons which we all recognise {6} and refer to as\nthe same, and as including ourselves along with all who use the word in\nthe same sense.\n\nThen the \u201cworld as idea\u201d means no less than this, that the system of\nthings and persons which surrounds all of us, and which each of us\nspeaks of and refers to as the same for every one, exists for each of\nus as something built up in his own mind--the mind attached to his own\nbody--and out of the material of his own mind.\n\n_The animal\u2019s world_\n\n5. Let us illustrate this building up by thinking of the world, our\nsurroundings, as an animal must be aware of it. The lowest beginnings\nof sight, for example, give no colour and no shape. An animal in this\nstage can, probably, only just take warning if a dark object comes\nbetween him and the light. Therefore he cannot have the ordered visual\nimage of space definitely stretching away all round him, which is the\nprimary basis of our idea of a world. He can move, no doubt, but there\nis nothing to make us suppose that he records and co-ordinates the\nresults of his movements into anything like that permanent order of\nobjects which must be constructed in some way by a human being even\nthough born blind. Succession, we might say, is much more powerful\nwith animals than co-existence; but we should have to guard ourselves\nagainst supposing that this was what we mean by succession, that is,\na process definitely recognised as in time, with a connection of some\nreasonable kind between its phases. For the most part with animals\nout of sight is out of mind; if so, the present is not interpreted,\nenlarged, and arranged with reference to what is not present in time\nor space by them as it is by us. And therefore the consciousness of a\nsingle system of things, {7} permanent, and distinct from the momentary\npresentations of the senses, cannot, in all probability, grow up for\nthem. If so, they have no real world, but only a dream world, [1]\n_i.e._ a world not contrasted with the stream of presentation, nor\ntaken as the common theatre of all actions and events. This difference\nbetween the world of an animal and that of a human being, is a rough\nmeasure of what man does by mental or intellectual construction in\nmaking his world.\n\n[1] The character of the sensory powers, which are strongest in\nmany animals, contributes to this conclusion. Mr. F.H. Bradley\nis sure that his dog\u2019s system of logic, if he had one, would\nrun, \u201cWhat exists smells; what does not smell is nothing.\u201d The\nsense of smell can scarcely give rise to the idea of a world of\nobjects. It has hardly any capacity of structural discernment.\n\n_The world as objective_\n\n6. We have now got the idea of a \u201cworld,\u201d as a system of things and\npersons connected together, taken to be the same for oneself at\ndifferent times and for different minds at the same time, yet existing,\nfor oneself, in the medium of one\u2019s individual consciousness.\n\nWe see at once that we cannot stop here. We have really got a\ncontradiction. If the parts of our world are connected with each other,\nthey are not merely dependent upon us, that is, upon the changes of our\nconsciousness. And we all take them to be independent of us, in the\nsense that we do not suppose the presence or absence of our perception\nto make any difference to the world except by the continuance or\ncessation of our perception of it or of its parts. This is the state\nof mind in which we practically live, philosophers and all. I do not\nreally take notice of any difference in mode of existence between the\nwall in front of me, which I see, and the wall behind me, which I {8}\ndo not see. While you are in this lecture-hall, if you think of your\nrooms at home, you think of them as they look, that is, as they would\nlook if you were there to see them. How else, indeed, could you think\nof them? This is practically necessary, and therefore, for practical\npurposes, true.\n\nBut if you take it as a theory, omitting the hypothetical factor,\n\u201cif I was there to see,\u201d you go wrong. You then treat your world\nas being, outside your consciousness, the same that it is inside\nyour consciousness, without allowing for the withdrawal of your\nconsciousness. You are then on the way to think that the world, _as\nyou see, hear, and feel it_, is outside your mind, and that the sight,\nhearing, feeling, and the ideas born of them, are inside your mind as\na sort of faint and imperfect _copy_ of the world which you then call\n\u201cexternal,\u201d _in the sense of outside the mind_.\n\n_Common sense_\n\ni. The first position was that of common sense. The second is that\nof common-sense theory. Common sense is quite justified. It says,\n\u201cThings affect each other, but the mere presence and absence of our\nperception does not affect them.\u201d For practical purposes we must\ntreat them as being, when unapprehended by our minds, just the same\nas when apprehended by our minds. This is the first idea or rather\npostulate--for it is not a theoretical idea--of objectivity. Objective\n= \u201cindependent of our consciousness for practical purposes.\u201d\n\n_Common-sense theory_\n\nii. In describing the second position as that of common-sense theory\nI do not refer to the doctrine of any regular school of philosophers.\nThere was a Scotch school of philosophy--the school of Reid in the\neighteenth century--commonly called the common-sense school. I will say\n{9} below how I think this school was related to the position which\nI am now describing. But my present purpose is to hit off the simple\ntheory of reality which common-sense people make for themselves when\nthey reflect. Now this theory, in which we all live except when we make\na special effort, accepts the distinction between things and the mind.\nFor example, it defines truth as the conformity of ideas to objects.\nThat means something of this kind: the ideas are inside our heads,\nand the objects are outside our heads. If we are to have knowledge,\nthe objects have to be represented inside our heads, and they get in\nthrough the senses. And then you have two similar forms of the world,\none outside our heads, which is real, and another like it but less\nperfect and without solidity or causal power, inside our heads, which\nis ideal or mental. This is what I call the common-sense theory of the\nObjective. Like common sense, it assumes that there is a world which\nthe withdrawal of our individual consciousness does not affect, but\nwhich persists and acts all the same. Unlike common sense, it lays down\nan assertion as to the nature of this world, viz. that it is, apart\nfrom our consciousness, the same as it is for our consciousness. The\nworld in consciousness, it assumes, is subjective, the world out of\nconsciousness is objective, and the former is an imperfect copy of the\nlatter in a feebler material.\n\nThe schools of common-sense philosophy, such as are represented by\nLocke and Reid, are not quite so simple-minded as the reflection of\nordinary common sense, because every systematic thinker sees at once\nthat the question stares him in the face, \u201cIf the world outside the\nmind is copied {10} by the world inside the mind, how can we ever know\nwhether the copy conforms to the original?\u201d We are by the hypothesis\ninside the mind; whatever has passed through the senses is inside the\nmind. We cannot as at present advised get at anything outside the\nsenses or outside the mind. In face of this question, the common-sense\nphilosophies have two courses open. They may start from the idea of\nthings outside the mind, but admit that in passing through the senses\nthe things are in some partial respects transformed--as for instance,\nthat they acquire colour, sound, and smell in passing through the\nsenses--this is what Locke says. Or again, still starting from the idea\nof things outside the mind, they may simply assert that perception\nis of such a nature that it gives us things as they really are. The\nformer was the view of Locke, the latter that of Reid. This latter\nview obviously might pass into the most extreme idealism, and its\ninterpretation, if it does not so pass, is exceedingly difficult.\n\nBut whatever may have been the view of the historical \u201ccommon-sense\nschool,\u201d [1] the common-sense theory which we all make for ourselves\ninvolves a separation between the mind and reality. The objective world\nis the world as independent of mind, and independent of mind means\nexisting and acting outside mind, exactly, or almost exactly, as it\nseems to exist and act before the mind.\n\n[1] See Seth, _Scottish Philosophy_ (Blackwood, 1885).\n\nNow this is an absolute _cul-de-sac_. If the objective is that which is\noutside perception, the objective is out of our reach, and the world of\nour perception can never be objective. This is the pass to which we are\nbrought by taking {11} common sense as the guide of theory and not as\nits material.\n\n_Philosophical theory._\n\niii. There is no way out but by retracing our steps, and avoiding a\nfalse turn which we took in passing from common sense to common-sense\ntheory. It was quite true that the world is unaffected by the\nwithdrawal of my individual perception and consciousness (except in so\nfar as I acted _qua_ bodily thing in the world); but it does not follow\nfrom this that _if_ it becomes the object of a consciousness in me,\nit can be so otherwise than as presented within that consciousness.\nWe must distinguish between the idea that the objective is outside\nconsciousness and therefore not in consciousness, and the idea that\nthe objective can be in the individual consciousness, but identified\nwith something beyond the individual consciousness. It may be that\nconsciousness is capable of containing a world, not as a copy of a\nready-made original, but as something which it makes for itself by a\nnecessary process, and which refers beyond this finite and momentary\nconsciousness.\n\nAccording to these ideas, the objective is, shortly stated, whatever\nwe are obliged to think. This, though it is _in_ our thought, is not\nconsidered merely _as_ our thought, or as a train of images or whole\nof presentation in our minds. That is an artificial point of view, the\npoint of view of psychology, and we must carefully avoid starting from\nit. But knowledge refers beyond its mental self, and has no limitation\nin time or in kind except its own necessity. Thus, I am forced to\nthink, by a certain context of ideas and perceptions, that there is\nnow a fire burning in my study at home. This judgment is not barred\nby the fact that my mind, as a {12} function attached to my body, is\nhere three miles away. The thought is objective for me, so long as I am\nobliged to think it. My presence in or absence from the room where the\nfire is burning has no effect on the question, except as it furnishes\nme with evidence one way or the other. Not only absence in space is no\nobstacle, but succession in time is no obstacle. My thought, which _is_\nhere and now, refers confidently to what has happened in long intervals\nof time, if the necessity of consistency obliges it to do so. Thus if\nI go back to my room and find the fire out and the room very cold, I\ninfer without hesitation to certain acts and events which are needed\nto explain this state of things. And interpretations or explanations\nof this kind make up my world, which is for me in my thought, but is\npresented as more than my thought, and cannot be a world at all unless\nit is more than in my thought. It is in as far as my thought constructs\nand presents a world which is more than my momentary psychical state,\nthat my thought, and the world as presented to me in it, is objective.\nThe world is not a set of my ideas, but it is a set of objects and\nrelations of which I frame an idea, and the existence of which has no\nmeaning for me except as presented in the idea which 1 frame. We are\nnot to think of (i) Ideas, and (ii) Things which they represent; the\nideas, taken as parts of a world, _are_ the things.\n\nWe begin to see, then, how the nature of knowledge meets the puzzle\nwhich I stated above. How, I asked, can a connected \u201cworld,\u201d whose\nparts act on one another quite independently of my perception, be in\nmy individual mind? I answer that it does not follow, because the\nworld _is for me_ {13} only in my presentation, that my presentation\nis the only thing which goes on in the world. \u201cWhat I am obliged to\nthink\u201d may represent a real development depending on laws and a system\nwhich is not confined to my individual course of consciousness. The\n\u201cobjective\u201d in this sense is for Logic an assumption, or rather a fact\nto be analysed. We do not attempt to prove its existence, except in the\nsense of calling attention to its nature in detail. It will be seen\nthat \u201coutside the mind\u201d ceases, on this view of objectivity, to have\nmeaning as regards anything that can be related to us. \u201cOutside\u201d is a\nrelation of bodies to one another; but everything, about which we can\nso much as ask a question, is so far inside the mind, _i.e._ given in\nits continuum of presentation or idea.\n\nI will recapitulate the three conceptions of the \u201cobjective.\u201d\n\n(1) According to practical \u201ccommon sense\u201d the objective is independent\nof our consciousness in the sense that the presence or absence of our\nconsciousness makes no difference to the operation of things upon each\nother.\n\n(2) According to \u201ccommon-sense theory\u201d the objective is independent\nof our consciousness in the sense that the presence or absence of our\nconsciousness makes no difference in the mode of being of things (viz.\nthat the world in consciousness approaches objectivity by resembling or\nreproducing a similar and quite objective world outside consciousness).\n\n(3) According to philosophical theory the objective is independent of\nour consciousness in the sense that it is what we are constrained to\nthink in order to make our consciousness consistent with itself. \u201cWhat\nwe are constrained to {14} think\u201d is not confined, in its _reference_\nto our thought, or to thought at all.\n\n_Our separate worlds._\n\n7. Thus, for the purposes of Logic, we must turn our usual ideas upside\ndown. We must try to imagine something of this kind. We have all seen\na circular panorama. Each one of us, we must think, is shut up alone\ninside such a panorama, which is movable and flexible, and follows him\nwherever he goes. The things and persons depicted in it move and act\nupon one another; but all this is in the panorama, and not beyond it.\nThe individual cannot get outside this encircling scenery, and no one\nelse can get inside it. Apart from it, prior to it, we have no self; it\nis indeed the stuff of which oneself is made. Is every one\u2019s panorama\nexactly the same? No, they are not exactly the same. They are formed\nround different centres, each person differing from all the others\nby individual qualities, and by his position towards the points and\nprocesses which determine his picture. For--and here is the remarkable\npoint--every one of us has painted for himself the picture within\nwhich he is shut up, and he is perpetually painting and re-painting\nit, not by copying from some original, but by arranging and completing\nconfused images and tints that are always appearing magically on his\ncanvas. Now this magical panorama, from which the individual cannot\nescape, and the laws of which are the laws of his experience, is simply\nhis own mind regarded as a content or a world. His own body and mind,\nregarded as things, are within the panorama, just as other people\u2019s\nbodies and minds are. The whole world, for each of us, _is_ our course\nof consciousness, in so far as this is regarded as a system of objects\nwhich we are obliged to {15} think. Not, in so far as it really _is_\na system, for an onlooker, say for a psychologist. For no doubt\nevery child\u2019s mind, and every animal\u2019s mind, _is_ a working system\nof presentations, which a psychologist may study and analyse from\nwithout. Consciousness is consciousness of a world only in so far as\nit _presents_ a system, a whole of objects, acting on one another, and\ntherefore independent of the presence or absence of the consciousness\nwhich presents them.\n\nI take another very rough metaphor to explain this curious contrast\nbetween my mind as a working system, observable from without, and\nbelonging to my individual body--distinguishable from the thirty or\nforty quite different minds belonging to the thirty or forty persons in\nthis room--and my mind as a continuum of presentations which includes,\nas objects, itself, and all the other minds in the room, and the whole\nworld so far as I have any conscious relation to it whatever.\n\nAll of us are familiar with the appearance of a microscope ready\nadjusted for use, with its little lamp, its mirror and illuminating\napparatus under the stage, with a specimen on the stage under the\nobject-glass, its object-glass and its eye-piece. Any one who\nunderstands the working of a microscope finds this a most suggestive\nspectacle. He follows in his imagination the light as it comes from\nthe lamp to the mirror, through the illuminating lenses, through the\ntransparent specimen, through perhaps a dozen lenses arranged as an\nobject-glass within an inch of distance, through the eye-piece and\ninto the observer\u2019s eye. Give him the parts, lenses, prisms, and\nmirrors into his hands, and he will test them all, and tell you exactly\nhow they work. This {16} scientific onlooker may be compared to the\npsychologist looking at another man\u2019s mind. He sees it as a thing among\nother things, a working system of parts.\n\nBut there is one thing that the mere onlooker cannot see. He cannot\nsee the object. That can only be seen by looking through the tube.\nAnd every one has felt, I should think, the magical transformation,\nsuggestive of looking through another man\u2019s eye and mind, which occurs\nwhen you put your eye to the eye-piece of an optical instrument. The\noutside world of other objects, the tube, the stage, the mirror, the\nbystanders, the external light, all disappear, and you see nothing but\nthe field of vision and whatever distinctly pictured structure may\nbe displayed within it. The observer who looks through the tube may\nbe compared with each one of us as he contemplates his own world of\nknowledge and perception. This is a thing that no one else can ever do.\n\nThe metaphor, indeed, breaks down, in so far as each of us is able to\nobserve the history and character of his own mind as an object within\nthe field of presentation which is before his mind. Of course such a\nmetaphor must break down at some point. But it remains true that the\nmind, while directly observing its field of objects, cannot observe its\nown peculiarities, and when turned, as we say, upon itself, is still\nobserving only a part of itself. It remains true that my mind contains\nthe whole presented world for me and is merely one among thousands of\nsimilar mind-things for you.\n\nThus, I repeat, the world for each of us is our course of\nconsciousness, looked at in that way in which it presents a {17}\nsystematic, organised picture of inter-acting objects, not in that way\nin which it is a stream of ideas and feelings, taking place in our\nseveral heads. In the former point of view it is the world as our idea;\nin the latter point of view it is simply the consciousness attached to\nour body. We might soon puzzle ourselves with the contradictions which\narise if we fail to distinguish these points of view. In one sense my\nmind is in my head, in the other sense my head is in my mind. In the\none sense I am in space, in the other sense space is in me. Just so,\nhowever rough the metaphor, from one point of view the microscope is\none among a host of things seen from the outside; from the other point\nof view all that we see is in the microscope, which is itself not seen\nat all.\n\nIt is in this latter sense that our mental equipment is looked at, when\nit is regarded as knowledge; and it is in this sense that it forms a\npanorama which absolutely shuts in every one of us into his own circle\nof ideas. (It is not implied, we should carefully observe, that his\nideas or experience are in any way secondary to his self, or separable\nfrom it, or an adjective of it.) Then how does it happen that our\nseparate worlds, the panoramas which we construct, do not contradict\none another?\n\nThe answer is, that they _correspond_. It is this conception from\nwhich we must start in Logic. We must learn to regard our separate\nworlds of knowledge; as something constructed by definite processes,\nand corresponding to each other in consequence of the common nature\nof these processes. We know that we begin apart. We begin in fact,\nthough not conscious of our limits, with feelings and fancies and\nunorganised experiences which give us little or no {18} common ground\nand power of co-operation with other people. But as the constructive\nprocess advances, the correspondence between our worlds is widened\nand deepened, and the greater proportion of what we are obliged to\nthink is in harmony with what other people are obliged to think. Now\nof course this would not be so unless reality, the whole actual system\nin which we find ourselves, were self-consistent. But more than that,\nit would not be so unless the nature of intelligence were the same in\nevery mind. It is this common nature of intelligence, together with its\ndifferentiated adaptations to reality, that we have to deal with in\nLogic.\n\nThus the separate worlds, in which we are all shut up, must be\nconsidered as corresponding so far as they are objective, that is, so\nfar as they approach what we are ultimately obliged to think. I say\n\u201ccorresponding,\u201d because that is the term which expresses the relation\nbetween systems which represent the same thing by the same rules,\nbut with different starting-points. Drawings in perspective of the\nsame building from different points of view are such corresponding\nsystems; the parts represented answer each to each, but the same part\nis near or large in one drawing, and distant and small in another; not,\nhowever, by chance, but as a definite consequence of the same laws.\nOur separate worlds may be compared to such drawings: the things in\nthem are identified by their relations and functions, so that we can\nunderstand each other, _i.e._ make identical references, though my\ndrawing be taken from the east, and yours from the west. The things do\nnot look quite the same in our different worlds; besides being taken\nfrom different standpoints, both drawings are imperfect and incorrect.\nBut so {19} long as we can make out the correspondence, we have a basis\nfor co-operation and for discussion. Logic shows us the principles and\nprocesses by which, under the given influences, these drawings are\nconstructed.\n\n_Subjective Idealism_\n\n8. If we merely hold to the doctrine of separate worlds, without\ninsisting upon their correspondence with each other and with reality,\nwe fall back into the position of subjective idealism, which is a\nnatural completion of common-sense theory, when, instead of turning\nround to retrace its path, it runs deeper into the _cul-de-sac_. It\nis a very obvious reflection, that each of us is shut up within his\nown mind, and much easier to grasp than the reason for assuming a\nreal system which appears differently, though correspondingly, in the\ncentres of consciousness which are ourselves. We cannot get at anything\nbut in terms of consciousness; how can we justify the assumption that\nour consciousness of a world of objects is rooted in reality, _e.g._,\nthat objects may rightly be treated as persisting and inter-acting\nwhen our personal consciousness is withdrawn? And if we once doubt\nthis, then why should we assume that our ideas need be or tend to\nbe consistent with themselves and each other, as for the time they\napparently are?\n\nSubjective Idealism necessarily arises if the common-sense theory of\ntwo worlds, the real outside the mind, and the ideal, copying it,\nwithin the mind, is pushed to its conclusion. The real, outside the\nmind, being inaccessible, falls away. The arguments of this Idealism,\nas Hume said, \u201cadmit of no answer and produce no conviction.\u201d [1]\nBut I {20} mention the idea, because I do not think that any one\ncan really understand the problem of Logic, or indeed of science in\ngeneral, without having thoroughly thought himself into the difficulty\nof Subjective Idealism. It is necessary to be wholly dissatisfied with\ncommon-sense theory, and with the notion of a ready-made world set up\nfor us to copy in the mind, before the logical analysis of intellectual\nconstruction can have interest or meaning for us. And to produce this\ndissatisfaction is the value of Subjective Idealism.\n\n[1] Vol. iv. p. 176 (ed. of 1854), _Inquiry concerning Human\nUnderstanding_, sect. 12.\n\n\n\n\n{21}\n\nLECTURE II   \u201cJUDGMENT\u201d AS THE CONSCIOUSNESS OF A WORLD\n\n_Defect of Subjective Idealism_\n\n1. The last lecture was devoted to explaining the distinction between\nthe stream of presentations and the world as it is for knowledge.\nI ended by calling attention to the theory known as \u201cSubjective\nIdealism.\u201d This, I said, has the merit of forcing upon us the question,\n\u201cHow do we get from mind to reality? How do we get from subjective to\nobjective?\u201d For we have always to remember that our knowledge _is_\nwithin consciousness, though it may _refer_ outside it.\n\nOn the other hand, Subjective Idealism has the _defect_ of confounding\nthe very distinction which we took so much trouble to make plain. Its\nessence lies in ascribing to the world of knowledge properties which\nare only true of the stream of presentation. It is quite true that the\nactual presentations of this room, which each of us has in his head\nat this moment, are all different from each other, and different from\nany which we have had before, and shall ever have again. Every minute,\nevery second, they differ; they are perishing existences, wholly\nmental, and each of them when past is irrecoverably gone. That is the\nproperty of a presentation within the course of consciousness. It is a\nparticular perishing existence.\n\n{22} But Subjective Idealism says, \u201cBecause these mental existences are\nparticular perishing existences, and all knowledge consists in them as\nits medium, therefore the object of knowledge is nothing beyond these\nmental facts, and is not rooted in a permanent system [1] independent\nof our mental connections.\u201d Here we must check the inference, and\nreply, \u201cNo, it does not follow. The presentations which themselves come\nand go may refer to something in common, and through them all we may\nbecome aware of something that is not wholly in any of them.\u201d In other\nwords, there is in Knowledge no passage _from_ subjective to objective,\nbut only a development of the objective.\n\n[1] Our estimate of Berkeley\u2019s view must depend on the degree\nin which we judge him to have identified the Deity with, or\nseparated Him from, a permanent and universal system. The\nstatement in the text applies fairly to Hume.\n\n_The world as_ Knowledge\n\n2. Therefore we say, coming closer to our subject, that \u201c_Knowledge_\nis the medium in which our world, _as an interrelated whole_, [1]\nexists for us.\u201d This is more than saying that it exists in mind or\npresentation, because the mere course of consciousness need not\namount to Knowledge. A world, that is, a system of things acting\non one another, could not exist merely in the course of our ideas.\nBut _Knowledge_, we said, is the mental construction of reality. It\nconsists of what we are obliged to assert in thought, and because we\nare all obliged to think assertorily according to the same methods,\nthe results of our thinking form corresponding systems--systems that\ncorrespond alike to each other and to reality. (I may be asked, does\nnot this agreement of {23} our knowledge depend on the agreement of\nthe physical stimuli supplied to us by nature, as well as on the\nhomogeneousness of our intelligences? The answer is, that these\nstimuli, or nature, have no priority in Knowledge. Their identity is\nmerely a case or consequence of the identity of our experience as a\nwhole. We are regarding nature as a system developed in experience, not\nas an unknown somewhat behind it. To suppose that solid or extended\nexistence somehow comes before and accounts for everything else, is a\nform of the common-sense theory we have dismissed. Knowledge and Truth\nhave their limitations as forms of Reality, but an appeal to solidity\nor extension will not furnish the required supplementation.)\n\n[1] The words italicised make a reservation in favour of\nfeeling, which has its own form of reality, but is not\nrelational.\n\n_Knowledge is in the form of Judgement_\n\n3. All that we have been saying about Knowledge is summed up in the\nsentence, \u201cKnowledge is a judgment, an affirmation.\u201d We need not\ntrouble ourselves yet about negation. We all know what affirmative\nassertion is, and it is near enough for the present to say that all\nknowledge is judgment in the sense of affirmative assertion.\n\nI will explain how we sum up all we have said of knowledge by calling\nit a judgment.\n\nJudgment or affirmation always implies three properties, though they\nare not always recognised.\n\nIt is (a) necessary, (b) universal, and (c) constructive.\n\n_Judgment necessary_\n\n(a) Judgment is necessary. In saying this, we express all that we said\nabout the objectivity of the world in knowledge. \u201cObjective\u201d meant, we\nconcluded, what we are obliged to think. And judgment is necessary,\nbecause it expresses what we are obliged to think; obliged, that is,\nnot as we are obliged to feel pain, as an unexplained and {24} isolated\nfact, but obliged by a necessity operative within the movement of our\nconsciousness, though not, of course, theoretically recognised as\nnecessity in common thinking. Thus, in the simplest phases of Judgment,\nnecessity does begin to approach the kind of necessity by which we feel\npain or are visited by persistent irrational associations.\n\nWe can trace an explicit sense of necessity in any scientific matter,\nor in any doubtful and complex matters in which we are aware of our own\nreflections. We constantly hear and read such phrases as, \u201cI am unable\nto resist the conclusion\u201d; \u201cI am forced to believe\u201d; \u201cI am driven to\nthink\u201d; \u201cI have no alternative but to suppose.\u201d These are every-day\nphrases in controversy and in theoretical discussion. And what they all\nmean is just what was insisted on in the last lecture; the objective or\nreal for us is what we are obliged to think. Given our perceptive state\nand our mental equipment, the judgment follows.\n\nIn trivial or simple judgments this necessity is harder to observe\nwithin consciousness, and approaches more and more to the mere\nconstraint exercised upon us by physical reality. In a judgment of\nmere sensuous comparison, such as a \u201ccolour-match,\u201d the necessity is\nnot that of an intellectual system, but almost that of a feeling which\nwe cannot dispel. The chief intellectual labour is here negative, and\nconsists in precautions to remove all disturbing influences, both\nmental and material, so as to let the perception operate freely on the\nmind. But yet here _is_ necessity; we never for a moment think that we\ncan modify the result; our aim is simply to distinguish from all others\nthe particular strand of necessity by which we desire to be guided.\n\n{25} It is easy for an observer to detect intellectual necessity in\njudgment, even where the judging subject is wholly unreflective. If\nyou contradict an obvious judgment made by an uneducated man, he will\nno doubt be quite unable to point out the intellectual necessity\nwhich constrains him to it, _i.e._ to argue in support of it; but he\nwill be bewildered and probably indignant, which shows that, unknown\nto himself, his whole intellectual existence is really impeached by\nimpeachment of a necessary conclusion from it. Many people cannot see\nthe difference between impeaching their argument and impeaching their\nveracity; and this confusion arises, I presume, from a just feeling\nthat their whole mind is on its trial in the one case as in the other,\nalthough they do not distinguish between the forms of its action which\nare concerned. We are told, indeed, in formal logic, that ordinary\nstatements of fact do not claim necessity; but this merely arises\nfrom confining necessity to explicit necessity expressed in a special\ngrammatical form.\n\nBut, it may be objected, we do not always feel that every trivial\njudgment emanates from and so implicates our whole mental constitution\nand equipment. If I say to a friend, \u201cI saw you at Charing Cross\nyesterday,\u201d and he says, \u201cNo, you could not, for I was out of town,\u201d\nthen, unless I was very certain indeed, I should admit having made a\nmistake, and think no more about the matter. That only means, (1) that\nthe unity of the mind is not thoroughly complete--there are many more\nor less detached systems in the mind, and one of them may not be very\ndeeply inwrought in the whole intellectual frame; and (2) the necessity\nof thought may itself modify the certainty of the fact, _e.g._ I know\nthat {26} a mistake of identity is quite a common thing, and this\nknowledge co-operates with my friend\u2019s denial.\n\nBut in any perceptive judgment, however unimportant its immediate\ncontent, if it is clear and persistent, a contradiction is a most\nserious thing. There is a well-known form of bewilderment connected\nwith the judgment of direction; if you forget or do not know of a turn\nthat you have taken, and come out, for example, on familiar ground from\nthe North when you think you are coming on it from the South, so that\nobjects have the reverse position of what you expected, then, supposing\nthat you cannot explain the contradiction, the result is sometimes\na very grave perplexity; some men are quite unhinged by it for the\nmoment, and a psychologist in France [1] has given it a new name,\n\u201cVertigo of Direction.\u201d This again shows how your whole intellectual\nnature is staked upon the most trifling perception, and if you seem to\nbe forced to a flat contradiction even in the simplest judgment you are\nalmost \u201cbeside yourself.\u201d\n\n[1] M. Binet. See _Mind_, x. 156.\n\n_Judgment universal_\n\n(b) Judgment is universal. There are different senses of \u201cuniversal\u201d as\nof \u201cnecessary.\u201d We are now speaking only in the widest sense, in which\nuniversality is a property of all judgment whatever. If we assume that\nall our intellectual natures are the same, then to be universal is a\nmere consequence of being necessary. I not only feel that my judgment\nis inevitable for me, but I never think of doubting that, given the\nsame materials, it is obligatory for every other intelligent being.\nIf some one disagrees with a judgment of mine, I try to put the case\nbefore him as it is in my mind. And I am absolutely sure that if I\ncould do so, he {27} would be obliged to judge as I do. If it were not\nso, we should never think of arguing. We should simply say, \u201cPerhaps\nhis mind is differently constituted from mine,\u201d as, in fact, with\nreference to special sets of dominant ideas, and to special provinces\nof experience, we often do say. But these we regard as hindrances,\nimperfections, accidents. We do not doubt that the system of reason is\nactive in him as in us.\n\nAnd thus, as reason is essentially a system, the universality of\njudgment involves something more. We not only think that our judgment\nis obligatory upon every one else, in as far as they have the same\nmaterials, but we think that it must be _consistent with_ the\njudgments of all other persons, just as much as with our own. If it\nis inconsistent with any other judgment, we think that one of the two\nmust be wrong; that is, we will not admit the possibility that the real\nworld, as others construct it, is out of harmony with the real world as\nwe construct it.\n\nThus knowledge, being judgment, is necessary and universal, and in the\nwidest sense this is true of all judgments.\n\n_Judgment is constructive_\n\n(c) These are two properties of the Judgment, but they do not tell us\nwhat it is. We shall of course examine its nature more fully in the\nlater lectures. At present we need only think of it as affirmation.\nThis may be simply described as \u201cpronouncing the interpretation of our\nperceptions to form one system with the data of our perceptions.\u201d We\nmay at once admit the distinction between _data_ and interpretation to\nbe only relative. Its relativity is the consequence of the constructed\nor so to speak artificial {28} character of our real world. We can get\nat no data unqualified by judgment.\n\nWe may take as an example our perception of things in space. How\nmuch of what we see is given in present sense-perception? This is a\nquestion to which there is no definite answer. We do not know what\nthe presentations of vision were like before we had learnt to see as\na fully conscious human being sees. We have no right to assume, that\nafter we have learned to see in this way the actual sense-presentation\nremains the same as it was in a different stage of our visual\neducation. We can give no precise meaning in the way of a time-limit\nto the _presentness_ of perception. But we know this much, that it\ntakes a long time and many kinds of experience to learn to see as an\neducated human being sees, and that this acquired capacity is never at\na stand-still, but is always being extended or diminished according to\nthe vitality, growth, or atrophy of our apperceptive masses. There is\nalways a certain element of amplification or interpretation, which by\nexperience, or attentive introspection we can eliminate from the data,\napparently forced upon us by reality, although these data themselves\nare modified through and through both by habitual interpretation,\nand by the very defining attention which aims at eliminating all\namplification from them.\n\nBut yet the whole of sense-perception has a peculiar quality in being\n_present_. Artificial though it is, it yet, relatively speaking,\ncontains an irreducible datum. It is distinguishable from everything\nwhich is not present. It is pervaded by something which we cannot\nreduce to {29} intellectual relation, though if we withdrew from it all\nthat is relation, the apparent datum would be gone.\n\nNow Knowledge is the affirmation or judgment which identifies the\nconstructive interpretation of our present perception with the reality\nwhich present perception forces upon us. This is clear enough to begin\nwith, but will have to be modified below to suit the more circuitous or\nmediate types of Judgment.\n\nI take two examples, one from sight and one from sound.\n\nHere is a table. In common language we should all say, \u201cWe see that\nis a table.\u201d The expression is quite correct, because human seeing\nis a judgment. But yet, if you were asked to reduce your perception\nto terms of sight pure and simple--I mean of visual sensation--why,\nunless you were an analytic psychologist or a very skilful artist,\nyou would not be able to do it. To speak of one point only, you would\nhave to eliminate the attribute of depth and distance. That is all, so\nfar as mere vision is concerned, your theory and your interpretation.\nThe problem for an artist is to get back, at his high plane of\nperceptive power, to what in theory would be the lower plane. He has to\nre-translate his perception of a thing in space into a flat coloured\nsurface. The difference between his flat picture and a real object in\nspace is a rough measure of the difference made by interpretation or\nimplication in the datum of sense-perception when we say, judging by\nsight only, \u201cThat is a table.\u201d All the experiences of touch and motion,\nfrom which we have learned to perceive the solidity of the object, are,\ntheoretically speaking, put into the judgment by us. They are not given\nby the eye alone, although we cannot now {30} separate them from that\nwhich is given by the eye alone. For the artist\u2019s flat picture, which\nI used as an illustration, is not a stage in our visual education.\nOur visual education has proceeded _pari passu_ with our education by\ntouch and motion; and we saw objects in space as solids, long before\nwe reflected that for the eye alone a coloured surface would naturally\nappear as flat. [1]\n\n[1] The view that depth is a visual datum in the same sense as\nbreadth seems to me in flagrant contradiction with experience.\nBut for our present purpose the question is only one of degree,\nas no one maintains, that either depth or breadth are seen\nwithout education as an adult sees them.\n\nBut this impossibility of getting at an original datum only shows\nhow entirely we are right in saying that our world is constructed\nby judgment. For the process of interpretative amplification passes\nquite continuously from the unconscious to the conscious; and every\ndefinitely expressed judgment, though perfectly homogeneous with the\nprocesses which have qualified its datum, and though it may fall\nwholly within the maximum of what in ordinary parlance we should call\na simple given perception, contains an identification of some ideal\nelement, enlargement, or interpretation, with that relatively given\nelement which reveals itself through a peculiar quality of presentness\npervading the \u201cgiven\u201d perception.\n\nIn the example \u201cThat is a table,\u201d the unity of judgment is so well\nshown that the identification becomes almost unreal. In fact, we never\njudge except to satisfy an interest and so simple a judgment used as an\nexample, apart from any context which could explain the need for it,\nhas an air of unreality. You may hear a child make such a judgment {31}\nconstantly in the sheer pleasure of recognition. An adult would never\nmake it explicitly unless in some particular context; but it is made,\nas I shall maintain below, by the mere glance of his eye which takes in\nthe table as a real object in a real world of space. Its appearance to\nthe eye is in this case the datum, while the interpretation consists in\nconstruing this appearance as a solid individual existence in space.\n\nWe will look at an example in which the discrimination of elements is\neasier. Take the affirmation, \u201cThat is a cab,\u201d assuming it to be made\nfrom merely hearing a sound. In this we can much more nearly separate\nthe datum or minimum of sense from our enlargement or interpretation\nof it, and we know that our interpretation is liable to be wrong;\nthat is to say, the reality into which we ought to construe the sound\nmay be some other kind of vehicle, and not a cab. Now compare this\nwith the affirmation, \u201cThat (which I see) is a cab.\u201d This judgment of\nsight-perception, though its terms are more inextricably interwoven,\nhas just the same elements in it as the judgment of sound-perception,\n\u201cThat (which I hear) is a cab.\u201d In the sound-perception the structure\nis quite plain. A particular complex quality in the sound suggests as\nits objective explanation, what is perfectly distinguishable from it in\nthought, the movement of a cab on a particular kind of pavement. The\nquality of the sound, its roughness, loudness, increase and decrease,\nall form points of connection with the sound of a cab as we know it,\nand with the speed, weight, etc. of such a vehicle. But it is quite\neasy to consider the sound in itself apart from its interpretation, and\nwe sometimes feel the {32} interpretation to be more immediate, and\nsometimes more inferential. We sometimes say, \u201cI hear a cab,\u201d just as\nwe say, \u201cI see one,\u201d but in case of sound we more often perhaps say,\n\u201cThat sounds like--\u201d such and such a thing, which indicates a doubt,\nand the beginning of conscious inference.\n\nThus we see how continuous is the mental construction of reality.\nFrom our unreflective education in seeing, hearing, and touching, to\nthe explicit judgment of the trained observer, which in its turn\npasses readily into inference, there is no definite break. Once the\nidea of reality, or of a world, is applied in practice (I do not say\nreflectively grasped), there is no further difficulty in principle\nthroughout the whole process of its construction.\n\nWe may then sum up so far: our knowledge, or our world in knowledge,\nexists for us as a judgment, that is, as an affirmation in which our\npresent perception is amplified by an ideal interpretation which is\nidentified with it. This interpretation or enlargement claims necessity\nor universality, and is therefore objective as our world, _i.e._ is\nwhat we are _obliged_ to think, and what we are _all_ obliged to\nthink. The whole system in process of construction, viz. our present\nperception as extended by interpretation, is what we mean by reality,\nonly with a reservation in favour of forms of experience which are\nnot intellectual at all. Every judgment then affirms something to be\nreal, and therefore affirms reality to be defined, in part, by that\nsomething. Knowledge exists in the form of affirmations about reality.\nAnd our world as existing for us in the medium of knowledge consists,\nfor us, of a standing affirmation about reality.\n\n{33} _Continuous affirmation of waking consciousness_\n\n4. This standing affirmation about reality may be described in\nother words as \u201cthe continuous affirmative judgment of the waking\nconsciousness.\u201d In the common logic-books you will find judgment\ntreated only as the \u201cproposition,\u201d that is, as an assertion made in\nlanguage. That is a very convenient way of treating the judgment,\nand is not false, if you remember that the proposition, that is, the\nassertory sentence, is rather a translation of the judgment than the\njudgment itself. But the judgment expressed in a proposition is always\nsome one definite assertion, with a limited subject and predicate. We\nshall speak of the judgment in this sense--the usual sense--later. But\nto-day I want to describe the judgment in a more extended sense, that\nis, as co-extensive with the waking human consciousness, so far as\naware of a world.\n\nIf Judgment consists in the extension of our perceptions by an\ninterpretation considered as equally real with their content, it\nclearly is not confined to the particular facts and truths which from\ntime to time we utter in language. And more than this, everything that\nwe do definitely utter, implies a great deal which is not definitely\nuttered. If I say, \u201cI have to catch the train at Sloane Square to go\ndown to Essex Hall,\u201d I only mention the reality of one train, one\nsquare, and one building. But my assertion shades off into innumerable\nfacts, the equal reality of which as elements in my world is necessary\nto make this judgment intelligible and true. It implies the real\nexistence of the underground railway, which implies that of London, and\ntherefore that of the surface of our globe in a certain definite order,\nand of the civilised world. It implies the reality of this building and\nof the meetings which we hold in it, of the University {34} Extension\nsystem, and of my own life and habits as enabling me to take part in\nthe work of that system. Only a part of this is in the focus of my\nattention as I judge; but the whole is a continuous context, the parts\nof which are inseparable; and although I do not affirm the whole of it\nin so many words, when I say that I am coming down here by train this\nevening, yet if any part of it was not affirmed the rest would, so to\nspeak, fall to pieces, _i.e._ would lose relations in the absence of\nwhich its meaning would be destroyed. Other detached parts of one\u2019s\nlife and knowledge may seem to be separable from the content of such\na judgment; but on looking closely we see that this is not the case.\nSo long as we are awake, our whole world is conceived as real, and\nforms for us a single immense affirmation, which hangs from present\nperception, and shares its constraining power. My present perception\nis the illuminated spot, and shades off gradually into the rest which\nforms the background, receiving from this background its organised\nsystematic individuality, while impressing upon it a relation to\nits own sensuous presentness. We have only to reflect, in order to\nillustrate this connection, on the way in which the idea of London\nforms a determining background for the present perception of this\nroom, while on the other hand it is perceived by us as real in our\npresentation of this room.\n\nAnd indeed the simplest example of what I am pointing out is the\narrangement of objects and places in space. The visual picture which\neach of us forms of this room is certainly an affirmative judgment. It\nis a judgment because it consists of ideas affirmed as true of reality.\nAs we look round, all the distances of the objects and the walls from\n{35} each other, and their shapes and position, seem to be imprinted on\nour minds without an effort. But really they are conclusions from long\neducation in the art of seeing and from the experience of the other\nsenses. They are an enlargement or interpretation of sense-perception,\ntaken as real, _i.e._ as forming a system which is one with the\ncontent of sense-perception, and touches us through sense-perception,\nand therefore they exist for us in the form of Judgment. And, as I\ndescribed before, our whole world, both of things in space and of our\nown history and circumstances, is also affirmed as the background\nimplied in this picture. That is to say, it is all connected together,\nit is all taken as equally real, and it is all vouched for by its\nconnection with what is given to us in perception. What do we mean by\nsaying that the Antipodes are real, and implied in my perception of\nthis room? We mean that they are an element, necessary to educated\nthought, in the same system with which I am in contact at this moment\nby sight, touch, and hearing, the system of reality. And though I may\nnot have explicitly thoughts of them since entering the room till now,\nyet, if they were no part of my affirmed system of ideas, my perception\nof anything in space would be quite different from what it is.\n\nThis sense of necessary connection is confined, I think, to our\n_waking_ consciousness. Of course there are degrees between waking and\ndreaming; but I should be inclined to set up the presence or absence\nof judgment as a very fair test of those degrees. We say that a man\nis _awake_ in as far as he is aware (i) of a reality which is not his\nmere course of consciousness, and (ii.) of the same reality of which\nother {36} people are aware; _i.e._ in as far as he identifies his\npresent perception with a reality, and that the real reality. It is\nsaid that surprise, _i.e._ the sense of conflict between expectation\nand the reality, is absent In dreams, and in a very remarkable passage\nAeschylus identifies the life of the savage in his (imaginary)\nprimitive state with a dream-life, considered as a life of sensuous\npresentation, in which the interpretative judgment of perception was\nabsent. With extraordinary profoundness, in portraying this all but\nanimal existence, he strikes out all those relations to the objective\nworld by which man forms for himself a system that goes beyond the\npresent, so as to leave the stream of presentation without any\nbackground of organised reality. [1]\n\n[1] I quote from Mrs. Browning\u2019s Translation of the _Prometheus\nBound_, which seems close enough for the present purpose.\n\n  \u201cAnd let me tell you, not as taunting men,\n  But teaching you the intention of my gifts,\n  How first, _beholding, they beheld in vain.\n  And hearing, heard not, but, like shapes in dreams_,\n  Mixed all things wildly down the tedious time,\n  Nor knew to build a house against the sun\n  With wicketed sides, nor any woodwork knew,\n  But lived, like silly ants, beneath the ground,\n  In hollow caves unsunned. There came to them\n  No steadfast sign of winter, nor of spring\n  Flower-perfumed, nor of summer full of fruit.\n  But blindly and lawlessly they did all things,\n  Until I taught them how the stars do rise\n  And set in mystery, and devised for them\n  Number, the inducer of philosophies.\n  The synthesis of letters, and besides,\n  The artificer of all things, Memory,\n  That sweet muse-mother.\u201d _Pr_., v. 445, ff.\n\nThe expression \u201cseeing saw not, and hearing heard not\u201d appears to\nsuggest the contrast of presentation and objective perception.\n\n{37} It may be asked, \u201cWhy should not a man form for himself a system\nwhich interprets his own perception, but is discrepant from the system\nof every one else? Should we in that case count him as awake?\u201d Yes, he\nwould be awake, but he would be mad. Suppose, being a common man, he\ninterprets all his perceptions into a system which makes him out to\nbe King of England; in such a case he cannot be set down as dreaming,\nbecause he is alleging a connection which goes beyond his present\nperception, and has, ostensibly, been propounded as an interpretation\nof it into a systematic order of things. He has in short _a_ world, but\nhe has broken away from _the_ world, and therefore we pronounce him\nmad. A completely new vision of life may cause a man to be thought mad.\n[1]\n\n[1] See Browning\u2019s _Epistle of Karshish_.\n\nThe whole world, then, of our waking [1] consciousness may be treated\nas a single connected predicate affirmed as an enlargement of present\nperception. All that we take to be real is by the mere fact of being so\ntaken, brought within an affirmative judgment.\n\n[1] I do not mean to say that judgment and consciousness of\na world can be wholly absent in dreams, and often no doubt\nthey are distinctly present. But in those dreams, in my own\nexperience the normal ones, which leave behind a mere impression\nthat unrecognisable images have passed before the mind, judgment\nand the sense of reality must surely have all but disappeared. I\nam inclined to think that dreams are very much rationalised in\nrecollection and description.\n\n_Comparison with world as Will_\n\n5. To further illustrate the relation of what, in our permanent\njudgment, is distinctly thought, what is dimly thought, and what is\nimplied, let us look for a moment at what we may call \u201cthe world\nas will.\u201d This is _not_ the doctrine of Schopenhauer in his work,\n_The World as Will and Idea_, {38} although the two conceptions have\nsomething in common. His is a metaphysical doctrine, in which he says\nthat the fundamental reality of the Universe must be conceived as\nWill. We have nothing to do with that. We are speaking merely of what\nthe world is for us, and for us it is not only a system of reality\nbut a system of purposes. Our world of will is a permanent factor of\nour waking consciousness, just as much as our world of knowledge.\nNow our will is made up of a great number of purposes, more or less\nconnected together, just as our knowledge is made up of a great number\nof provinces and regions more or less connected together. And just as\nin our knowledge at any moment much is clear, much is dim, much is\nimplied, and the whole forms a continuous context, so it is with our\npurposes.\n\nWhen, for example, one stands looking at a picture, one\u2019s immediate\nconscious purpose is to study the picture. One also entertains dimly or\nby force of habit the purpose to remain standing, which is a curious\nthough common instance of will. We do not attend to the purpose of\nwalking or standing, yet we only walk or stand (in normal conditions\nof mind) as long as we will to do so. If we go to sleep or faint, we\nshall fall down. Purpose, like judgment, is confined to the waking\nconsciousness.\n\nBut further; the purpose which one entertains in standing to look at a\npicture is not really an isolated pin-point of will. It is uppermost\nin the mind at the moment in which we carry it out, but it is only the\nuppermost stratum, or perhaps rather the present point attained upon a\ndefinite road, within an intricate formation or network of purposes,\nwhich taken together constitute the world of will. The purpose of\nlooking {39} at a picture shades off into the more general purpose of\nlearning to take pleasure in what is good of its kind, which is again\nset in a certain place within the conception of our life and the way\nin which we desire to spend it, and our purposes throughout every\nparticular day are fitted into one another, and give a particular\nsetting and colour to each other, and to each particular day, and week,\nand year.\n\nNow less or more of all this may be clearly in the mind when we are\ncarrying out a particular momentary aim. But it is quite certain that\nin a human life the particular momentary aim derives its significance\nfrom this background of other purposes; and, if they were to fall away,\nthe distinct momentary purpose would change its character and become\nquite a feeble and empty thing.\n\nThus we have, in our world of will, a parallel case which illustrates\nthe nature of our world of knowledge. There is the clear will to look\nat the picture, the dim will to continue standing, and the implied will\nto carry out certain general aims, and follow a certain routine or\ncourse of life, which gives the momentary purpose its entire setting\nand background.\n\nI have spoken of the will in order to illustrate the judgment, because\nthe dim and implied elements are perhaps more easy to observe in the\ncase of the will. Almost all our common waking life is carried on by\nactions such as walking and sitting, which we hardly know that we\nwill, but which we could not do if we did not will them. And also the\ngreater part of our life is rather within a sphere of will which has\nbecome objective for us in our profession, interests, and ideals, than\na perpetual active choice between {40} alternatives such as brings the\nact of volition before us in the most striking way. Just so it is with\njudgment. Our speaking and writing is a very small part of our judging,\njust as our conscious choice between alternatives [1] is a very small\npart of our willing.\n\n[1] I do not for a moment suggest that our \u201cconscious choice\u201d is\nultimately different in kind from our habitual persistence in a\ncourse of life. I only take it as an instance in which we fully\nattend to our volition.\n\n_Distribution of Attention_\n\n6. Thus the world of knowledge and the world of will must each of them\nbe regarded as a _continuum_ for the waking consciousness. Whenever\nwe are awake, we are judging; whenever we are awake we are willing.\nThe distribution of attention in these two worlds is very closely\nanalogous. In both, it is impossible to attend to our whole world at\nthe same moment. But in both, our world is taken as being a single\nconnected system; and therefore (i.) attention shades off gradually\nfrom the momentary focus of illumination into less and less intensity\nover the other parts of the continuous judgment or purpose; but (ii.)\nthat which is _in_ the focus of attention depends for its quality upon\nthat which is less distinctly or not at all in the focus of attention.\nAnd as attention diminishes in intensity, the implication of reality\ndoes not diminish with it. In other words, in spite of the inequality\nof attention, the reality of our whole world is implied in the reality\nof which at any moment we are distinctly aware. But being distinctly\naware of reality is another name for judgment.\n\nNow the common logical judgments which we shall have to analyse\nand classify are simply those parts of this continuous affirmation\nof consciousness which are from time {41} to time separately made\ndistinct. Each of them therefore must be regarded as a partial\nexpression of the nature of reality, and the subject will always be\nReality in one form, and the predicate reality in another form. The\nultimate and complete judgment would be the whole of Reality predicated\nof itself. All our logical judgments are such portions and fragments\nof this judgment as we can grasp at the moment. Some of these gather\nup in a system whole provinces of reality, others merely enlarge,\ninterpret, or analyse the content of a very simple sense-perception.\nWe shall not go far wrong in practice if we start from this judgment\nof Perception as the fundamental kind of Judgment. The real subject in\nJudgment is always Reality in some particular datum or qualification,\nand the tendency of Judgment is always to be a definition of Reality.\nWe see the parts of Judgment most clearly in such thoughts as \u201cThis is\nblue\u201d; \u201cThis is a flower\u201d; \u201cThat light is the rising sun\u201d; \u201cThat sound\nis the surf on a sandy shore.\u201d In these we can plainly distinguish the\nelement of presentation and the interpretative construction or analytic\nsynthesis which is by the judgment identified with it.\n\n\n\n\n{42}\n\nLECTURE III   THE RELATION OF LOGIC TO KNOWLEDGE\n\n_Meaning of \u201cForm\u201d_\n\n1. I spoke of the whole world, which we take to be real, as presented\nto us in the shape of a continuous judgment. It is the task of Logic\nto analyse the structure of this Judgment, the parts of which are\nJudgments.\n\nThe first thing is then to consider what sort of properties of\nJudgments we attend to in Logic. It is commonly said that Logic is a\nformal science; that is, that it deals with the form, and not with the\ncontent or matter of knowledge.\n\nThis word \u201cform\u201d is always meeting us in philosophy. \u201cSpecies\u201d is Latin\nfor form, as \u03b5\u1f36\u03b4\u03bf\u03c2 and \u1f30\u03b4\u03b5\u03b1 [1] are Greek for form. The form of any\nobject primarily means its appearance, that which the mind can carry\naway, while the object as a physical reality, as material, remains\nwhere it was. It need not mean shape as opposed to colour; that is a\nnarrower usage. The Greek opinion was no doubt rooted in some such\nnotion as that in knowing or remembering a thing the mind possessed\nits form or image without its matter. Thus the form came to stand for\nthe knowable shape or structure which makes a thing what it is, and by\nwhich we recognise it when we see it. This was its species or its idea,\nthe \u201cimage,\u201d as it is used in the phrase, \u201cLet us make man in our own\nimage.\u201d So in any work of the hands {43} of man, the form was the shape\ngiven by the workman, and came out of his mind, while the matter was\nthe stuff or material out of which the thing was made.\n\n[1] [= \u201ceidos\u201d and \u201cidea\u201d. Tr.]\n\nThe moment we contemplate a classification of the sciences, we see\nthat this is a purely relative distinction. There is no matter without\nform. If it was in this deep sense without form, it would be without\nproperties, and so incapable of acting or being acted upon. In a\nknife the matter is steel, the form is the shape of the blade. But\nthe qualities of steel again depend, we must suppose, upon a certain\ncharacter and arrangement in its particles, and this is, as Bacon would\nhave called it, the _form_ of steel. But taken as purely relative,\nthe distinction is good _prima facie_. Steel has its own form, but\nthe knife has its form, and the matter steel can take many other\nforms besides that of a knife. Marble has its own form, its definable\nproperties as marble (chemical and mechanical), but in a statue, marble\nis the matter, and the form is the shape given by the sculptor.\n\nNow applying this distinction to knowledge in general, we see that\nall science is formal, and therefore it is no distinction to say that\nLogic is a formal science. Geometry is a formal science; even molecular\nphysics is a formal science. All science is formal, because all science\nconsists in tracing out the universal characteristics of things, the\nstructure that makes them what they are.\n\nThe particular \u201cform,\u201d then, with which a science deals is simply the\nkind of properties that come under the point of view from which that\nscience in particular looks at things. But a very general science is\nmore emphatically formal than {44} a very special science. That is to\nsay, it deals with properties which are presented in some degree by\neverything; and so in every object a great multitude of properties\nare disregarded by it, are treated by it as matter and not as form.\nIn this sense Logic is emphatically \u201cformal,\u201d though not nearly so\nformal as it is often supposed to be. The subject-matter of Logic,\nthen, is Knowledge _qua_ Knowledge, or the form of knowledge; that is,\nthe properties which are possessed by objects or ideas _in so far as\nthey are members of the world of knowledge_. And it is quite essential\nto distinguish the form of knowledge in this sense from its matter or\ncontent. The \u201cmatter\u201d of knowledge is the whole region of facts dealt\nwith by science and perception. If Logic dealt with this in the way in\nwhich knowledge deals with it, _i.e._ simply as a process of acquiring\nand organising experience, then Logic would simply be another name for\nthe whole range of science, history, and perception. Then there would\nbe no distinction between logic and science or common sense, and in\ntrying to ascertain, say, the wave-length of red light, or the cab-fare\nfrom Chelsea to Essex Hall, we should be investigating a logical\nproblem. But we see at once that this is not what we mean by studying\nknowledge as knowledge. Science or common sense aims at a particular\nanswer to each problem of this kind. Logic aims at understanding\nthe type and principles both of the problem and of its answer. The\ndetails of the particular answer are the \u201c_matter_ of fact.\u201d The type\nand principles which are found in all such particular answers may be\nregarded as the form of fact, _i.e._ that which makes the fact a fact\nin knowledge.\n\nJevons appears to me to make a terrible blunder at this {45} point. He\nsays [1]--\u201cOne name which has been given to Logic, namely the Science\nof Sciences, very aptly describes the all-extensive power of logical\nprinciples. The cultivators of special branches of knowledge appear\nto have been fully aware of the allegiance they owe to the highest\nof the sciences, for they have usually given names implying this\nallegiance. The very name of Logic occurs as part of nearly all the\nnames adopted for the sciences, which are often vulgarly called the\n\u2018ologies,\u2019 but are really the \u2018logics,\u2019 the \u2018o\u2019 being only a connecting\nvowel or part of the previous word. Thus geology is logic applied to\nexplain the formation of the earth\u2019s crust; biology is logic applied\nto the phenomena of life; psychology is logic applied to the nature\nof the mind; and the same is the case with physiology, entomology,\nzoology, teratology, morphology, anthropology, theology, ecclesiology,\nthalattology, and the rest. Each science is thus distinctly confessed\nto be a special logic. The name of Logic itself is derived from the\ncommon Greek word \u03bb\u03cc\u03b3\u03bf\u03c2, which usually means _word_, or the sign and\noutward manifestation of any inward thought. But the same word was\nalso used to denote the inward thought or reasoning of which words are\nthe expression, and it is thus probably that later Greek writers on\nreasoning were led to call their science \u1f10\u03c0\u03b9\u03c3\u03c4\u03ae\u03bc\u03b7 \u03bb\u03bf\u03b3\u03b9\u03ba\u03ae, or logical\nscience, also \u03c4\u03ad\u03c7\u03bd\u03b7 \u03bb\u03bf\u03b3\u03b9\u03ba\u03ae or logical art. [2] The adjective \u03bb\u03bf\u03b3\u03b9\u03ba\u03ae,\nbeing used alone, soon came to be the name of the science, just as\nMathematic, Rhetoric, and other names ending in \u2018ic\u2019 were originally\nadjectives, but have been converted into substantives.\u201d\n\n[1] _Elementary Lessons_, p. 6.\n\n[2] [= \u201clogos\u201d, \u201cepisteme logike\u201d, \u201ctechne logike\u201d and \u201clogike\u201d. Tr.]\n\n{46} This account of the connection between the name \u201cLogic\u201d and the\nterminations of the names of the sciences appears precisely wrong.\nWhatever may have been the exact meaning of the expression \u201cLogic,\u201d\nor \u201cLogical curriculum,\u201d [1] or \u201cart,\u201d or \u201cscience\u201d when first\nemployed, there can be no doubt that the word logical had a substantive\nreference to that about which the science or teaching in question\nwas to treat. The term \u201clogic,\u201d therefore, corresponds not to the\nsyllables \u201clogy\u201d in such a word as \u201cZoology,\u201d but to the syllables\n\u201cZoo,\u201d which indicate the province of the special science, and not\nits character as a science. Zoology means connected discourse (\u03bb\u03cc\u03b3\u03bf\u03c2)\nabout living creatures. Logic meant a curriculum, or science or art\ndealing with connected discourse. The phrase \u201cScience of Sciences,\u201d\nrightly interpreted, has the same meaning. It does not mean that Logic\nis a Science which comprises all the special sciences, but that Logic\nis a Science dealing with those general properties and relations which\nall sciences _qua_ sciences have in common, but omitting, as from its\npoint of view matter and not form, the particular details of content by\nwhich every science answers the particular questions which it asks. It\nis wild, and most mischievous, to say that \u201cevery science is a special\nlogic,\u201d or that \u201cbiology is Logic applied to the phenomena of life.\u201d\nThis confusion destroys the whole disinterestedness which is necessary\nto true scientific Logic, and causes the logical student always to have\nhis eye on puzzles, and special methods, and interferences by which he\nmay teach the student of science how to perform the concrete labour\nof research. We quite admit that {47} a looker-on may _sometimes_ see\nmore of the game, and no wise investigator would contemn _a priori_\nthe suggestions of a student like Goethe, or Mill, or Lotze, because\ntheir author was not exclusively engaged in the observation of\nnature. But all this is secondary. The idea that Logic is a judge of\nscientific results, able to pass sentence, in virtue of some general\ncriterion, upon their validity and invalidity, arises from a deep-lying\nmisconception of the nature of truth which naturally allies itself with\nthe above confusion between Logic and the special sciences.\n\n[1] \u03c0\u03c1\u03b1\u03b3\u03bc\u03ac\u03c4\u03b5\u03b9\u03b1 [= pragmateia Tr.]. See Prantl, i. 545.\n\nTherefore the relation between content or matter of knowledge, and\nthe form which is its general characteristic as knowledge, is of\nthis kind. We can either study the objects of knowledge directly as\nwe perceive them, or indirectly, as examples of the way in which we\nknow. As studied for their own sake, they are regarded as the matter\nor content in which the general form of knowledge finds individual\nrealisation. In botany, for instance, we have a large number of actual\nplants classified and explained in their relation to one another.\nA botanist is interested directly in the affinities and evolution\nof these plants, and in the principles of biology which underlie\ntheir history. He pushes his researches further and further into\nthe individual matters that come to light, without, as a rule, more\nthan a passing reflection upon the abstract nature of the methods\nwhich he is creating as his work proceeds. He classifies, explains,\nobserves, experiments, theorises, generalises, to the best of his\npower, solely in order to grasp and render intelligible the region of\nconcrete fact that lies before him. Now while his particular results\nand discoveries {48} constitute the \u201cform\u201d or knowable properties of\nthe plant-world _as the object of botanical science_, the science\nwhich inquires into the general nature of knowledge must treat these\nparticular results as \u201cmere matter\u201d--as something with which it is\nnot directly concerned, any more than the art which makes a statue\nis primarily and directly concerned with the chemical and mechanical\nproperties of marble. The \u201cform\u201d or knowable properties with which the\ngeneral science of knowledge is directly concerned, consists in those\nmethods and processes which the man of science, developing the modes\nin which common sense naturally works, constructs unconsciously as he\ngoes along. Thus, not the nature and affinities of the plant-world,\nbut classification, explanation, observation, experiment, theory, are\nthe phenomena in virtue of which the organised structure of botanical\nscience participates in the form of knowledge, and its objects become,\nin these respects, objects of logical theory.\n\nHence some properties and relations of objects, being the form or\nknowable structure of the concrete objects as a special department of\nnature, correspond to the mere matter, stuff, or content of Knowledge\nin general, while other properties and relations of objects, being\ntheir form or knowable structure as entering into a world of reality\ndisplayed to our intelligence, correspond to the form of Knowledge as\ntreated of by a general inquiry into its characteristics, which we\ncall Logic. It is just as the qualities or \u201cforms\u201d of the different\nmetals of which knives can be made are mere matter or irrelevant detail\nwhen we are discussing the general \u201cform\u201d or quality of a good knife,\n{49} whatever its material. A reservation on this head appears in the\nfollowing section.\n\n_Form of Knowledge dependent on Content_\n\n2. For the form of Knowledge depends in some degree upon its matter.\nIt is very important to realise this truth; for if Logic is swamped\nby being identified with the whole range of special sciences, it is\nkilled by being emptied of all adaptation to living intelligence. What\nis called Formal Logic _par excellence_ in all its shapes, whether\nantiquated as in Hamilton\u2019s or Thomson\u2019s Formal Laws of Thought,\nor freshly worked out on a symbolic basis as by Boole and others,\nhas, it appears to me, this initial defect, _when considered as a\ngeneral theory of Logic_. As a contribution to such a theory, every\nmethod which will work undoubtedly has its place, and indicates and\ndepends upon some characteristic of real thought. But in the central\ntheory itself, and especially in so short an account of it as must\nbe attempted in these lectures, I should be inclined to condemn all\nattempts to employ symbols for anything more than the most passing\nillustration of points in logical processes. All such attempts, I must\nmaintain, share with the old-fashioned laws of Identity, Contradiction,\nand Excluded Middle the initial fallacy of representing a judgment\nby something which is not and cannot be in any way an adequate\nsymbol of one. If, in order to get at the pure form of Knowledge,\nwe restrict ourselves to very abstract characteristics in which all\nknowledge appears, very roughly speaking, to agree, and which can be\nsymbolized for working purposes by combinations of signs which have\nnot the essential properties of ideal contents, then we have _ab\ninitio_ substituted for the judgment something which is a very {50}\nabstract corollary from the nature of judgment, and may or not for\ncertain purposes and within certain limits be a fair representative\nof it. We cannot and must not exclude from the form of Knowledge its\nmodifications according to \u201cmatter,\u201d and its nature as existing only in\n\u201cmatter.\u201d\n\nIn fact, the peculiar \u201cform\u201d of _everything_ depends in some degree\non its \u201cmatter.\u201d A statue in marble is a little differently treated\nif it is copied in bronze. A knife is properly made of steel; you\ncan only make a bad one of iron, or copper, or flint, and you cannot\nmake one at all of wax. Different matters will more or less take the\nsame form, but only within certain limits. So it is in Knowledge. The\n_nature of objects as Knowledge_--for we _must_ remember that \u201cform\u201d\nin our sense is not something put into the \u201cmatter,\u201d something alien\nor indifferent to it, but is simply its own inmost character revealed\nby the structural relations in which it is found capable of standing\n[1]--depends on the way in which their parts are connected together.\n\n[1] The example of the marble statue may seem to contradict\nthis idea; and no doubt the indifference of matter to form is\na question of degree. But the feeling for material is a most\nimportant element in fine art; and in knowledge there is only a\nrelative distinction between formal and material relations.\n\nLet us compare, for example, the use of number in understanding objects\nof different kinds.\n\nSuppose there are four books in a heap on the table. This heap of\nbooks is the object. We desire to conceive it as a whole consisting\nof parts. In order to do so we simply _count_ them \u201cone, two, three,\n_four_ books.\u201d If one is taken away, there is one less to count; if\none is added, there is one more. But the books themselves, as books,\nare not {51} altered by taking away one from them or adding one to\nthem. They are parts indifferent to each other, forming a heap which is\nsufficiently analysed or synthesised by counting its parts.\n\nBut now instead of four books in a heap, let us think of the four\nsides of a square. Of course we _can_ count them, as we counted the\nbooks; but we have not conceived the nature of the square by counting\nits sides. That does not distinguish it from four straight lines drawn\nanyhow in space. In order to appreciate what a square is, we must\nconsider that the sides are _equal_ straight lines, put together in a\nparticular way so as to make a figure with four right angles; we must\ndistinguish it from a figure with four equal sides, but its angles not\nright angles, and from a four-sided figure with right angles, but with\nonly its opposite sides equal; and note that if we shorten up one side\ninto nothing, the square becomes a triangle, with altogether different\nproperties from those of a square; if we put in another side it becomes\na pentagon, and so on.\n\nThese two things, the heap of books and the square, are _prima\nfacie_ objects of perception. We commonly speak of a diagram on a\nblackboard or in a book as \u201ca square\u201d if we have reason to take it\nas approximately exact, and as intended for a square. But on looking\ncloser, we soon see that the \u201cmatter,\u201d or individual attributes, of\neach of these objects of our apprehension demands a different form of\nknowledge from that necessary to the other. The judgment \u201c_This_ heap\nof books has four books in it\u201d is a judgment of enumerative perception.\nThe judgment \u201c_The_ square has four sides\u201d is a judgment of systematic\nnecessity.\n\n{52} Why did we not keep the two judgments in the same logical shape?\nWhy did we say \u201c_This_ heap\u201d and \u201c_The_ square\u201d? Why did we not say\n\u201cthis\u201d in both propositions, or \u201cthe\u201d in both propositions? Because\nthe different \u201cmatter\u201d demands this difference of form. Let us try.\n\u201cThe heap of books has four books in it.\u201d Probably we interpret this\nproposition to mean just the same as if we had said \u201cThis heap.\u201d That\nis owing to the fact that the judgment naturally occurs to us in its\nright form. But if we interpret \u201cThe heap\u201d on the analogy of our\ninterpretation of \u201cThe square,\u201d our judgment will have become false.\n\nIt will have come to mean \u201cEvery heap of books has four books in it,\u201d\nand a judgment of perception will not bear this enlargement. The\nsubject is composite, and one, the most essential of its elements, is\ndestroyed by the change from \u201cthis\u201d to \u201cthe.\u201d\n\nLet us try again. Let us say \u201cThis square has four sides.\u201d That is\nnot exactly false, but it is ridiculous. Every square must have four\nsides, and by saying \u201cthis square\u201d we strongly imply that foursidedness\nis a relation of which we are aware chiefly, if not exclusively, in\nthe object attended to in the moment of judging, simply through the\napprehension of that moment. By this implication the form of the\njudgment abandons and all but denies the character of systematic\nnecessity which its content naturally demands. It is like saying, \u201cIt\nappears to me that in the present instance two and two make four.\u201d The\nnumber of sides in a square, then, is not a mere fact of perception,\nwhile the number of books in a heap is such a fact.\n\nBut you may answer by suggesting the case that an {53} uninstructed\nperson--say a child, with a square figure before him, and having heard\nthe name square applied to figures generally resembling that figure,\nmay simply observe the number of sides, without knowing any of the\ngeometrical properties connected with it; will he not then be right in\nsaying, \u201cThis square has four sides\u201d?\n\nCertainly not. In that case he has no right to call it a square.\nIt would only be a name he had picked up without knowing what it\nmeant. All he has the right to say would be, \u201cThis object\u201d or \u201cThis\nfigure has four sides.\u201d That would be a consistent judgment of mere\nperception, true as far as it went. It is always possible to apprehend\nthe more complex objects of knowledge in the simpler forms; but then\nthey are not apprehended adequately, not _as_ complex objects. It is\nalso possible to apply very complex forms of knowledge to very simple\nobjects. Most truths that can be laid down quite in the abstract about\na human mind could also be applied in some sense or other to any speck\nof protoplasm, or to any pebble on the seashore. And every simple\nform of knowledge is always being pushed on, by its own defects and\ninconsistencies, in the direction of more complex forms.\n\nSo far I have been trying to show that objects are capable of being\ndifferent in their nature as knowledge as well as in their individual\nproperties; and that their different natures as knowledge depend on the\nway in which their parts are connected together. We took two objects\nof knowledge, and found that the mode of connection between the parts\nrequired two quite different kinds of judgment to express them. Let us\nlook at the reason of this.\n\n{54} _The relation of Part and Whole_\n\n3. The relation of Part and Whole is a form of the relation of Identity\nand Difference. Every Judgment expresses the unity of some parts in a\nwhole, or of some differences in an Identity. This is the meaning of\n\u201cconstruction\u201d in knowledge. We saw that knowledge exists in judgment\nas a construction (taking this to include maintenance) of reality.\n\nThe expression whole and parts may be used in a strict or in a lax\nsense.\n\nIn a strict sense it means a whole of quantity, that is, a whole\nconsidered as made up by the addition of parts of the same kind, as a\nfoot is made up of twelve inches. In this sense the whole is the sum of\nthe parts. And even in this sense the whole is represented within every\npart by an identity of quality that runs through them all. Otherwise\nthere would be nothing to earmark them as belonging to the particular\nwhole or kind of whole in question. Parts of length make up a whole\nof length, parts of weight a whole of weight, parts of intensity a\nwhole of intensity, in so far as a whole of intensity is quantitative,\nwhich is not a perfectly easy question. Wholes like these are \u201c_Sums_\u201d\nor \u201c_Totals_\u201d. The relation of whole to part in this sense is a very\nsimple case of the relation of differences in an identity, but for\nthat very reason is not the easiest case to appreciate. The relation\nis so simple that it is apt to pass unnoticed, and in dealing with\nnumerical computation we are apt to forget that in application to any\nconcrete problem the numbers must be numbers of something having a\ncommon quality, and that the nature of this something may affect the\nresult as related to real fact, though not as a conclusion from pure\n{55} numerical premisses. In a whole of pure number the indifference\nof parts to whole reaches its maximum. The unit remains absolutely the\nsame, into whatever total of addition it may enter.\n\nIn a whole of differentiated members, such as a square, all this begins\nto be different. A side in a square possesses, by the fact of being a\nside, very different relations and properties from those of a straight\nline conceived in isolation. In this case the whole is not made up\nmerely by adding the parts together. It is a geometrical whole, and its\nparts are combined according to a special form of necessity which is\nrooted in the nature of space. Speaking generally, the point is that\nparts must occupy certain perfectly definite places as regards each\nother. You cannot make a square by merely adding three right angles to\none, nor by taking a given straight line and adding three more equal\nstraight lines to its length. You must construct in a definite way so\nas to fulfil definite conditions. The identity shows itself in the\ndifferent elements which make it up, not as a mere repeated quality,\nbut as a property of contributing, each part in a distinctive way, to\nthe nature of the whole. Such an identity is not a mere total or sum,\nthough I imagine that its relations can be fully expressed in terms of\nquantity, certain differentiated objects or conceptions being given\n(_e.g._ line and angle).\n\nI take a further instance to put a sharp point upon this distinction.\nThe relation of whole and parts is nowhere more perfect, short of\na living mind, than in a work of art. There is a very fine Turner\nlandscape now [1] in the \u201cOld {56} Masters\u201d Exhibition at Burlington\nHouse--the picture of the two bridges at Walton-on-Thames. The picture\nis full of detail--figures, animals, trees, and a curving river-bed.\nBut I am told that if one attempts to cut out the smallest appreciable\nfragment of all this detail, one will find that it cannot be done\nwithout ruining the whole effect of the picture. That means that the\nindividual totality is so welded together by the master\u2019s selective\ncomposition, that, according to Aristotle\u2019s definition of a true\n\u201cwhole,\u201d if any part is modified or removed the total is entirely\naltered, \u201cfor that of which the presence or absence makes no difference\nis no true part of the whole.\u201d [2]\n\n[1] February 1892.   [2] _Poetics_, 8\n\nOf course, in saying that the part is thus essential to the whole, it\nis implied that the whole reacts upon and transfigures the part. It is\nin and by this transformation that its pervading identity makes itself\nfelt throughout all the elements by which it is constituted. As the\npicture would be ruined if a little patch of colour were removed, so\nthe little patch of colour might be such as to be devoid of all value\nif seen on a piece of paper by itself. I will give an extreme instance,\nalmost amounting to a _tour de force_, from the art of poetry, in\nillustration of this principle. We constantly hear and use in daily\nlife the phrase, \u201cIt all comes to the same thing in the end.\u201d Perhaps\nin the very commonest speech we use it less fully, omitting the word\n\u201cthing\u201d; but the sentence as written above is a perfectly familiar\nplatitude, with no special import, nor grace of sound or rhythm. Now,\nin one of the closing stanzas of Browning\u2019s poem _Any Wife to Any\nHusband_, this sentence, only modified {57} by the substitution of \u201cat\u201d\nfor \u201cin,\u201d forms an entire line. [1] And I think it will generally be\nfelt that there are few more stately and pathetic passages than this\nin modern poetry. Both the rhythm and sonorousness of the whole poem,\nand also its burden of ideal feeling, are communicated to the line\nin question by the context in which it is framed. Through the rhythm\nthus prescribed to it, and through the characteristic emotion which it\ncontributes to reveal, the \u201cwhole\u201d of the poem re-acts upon this part,\nand confers upon it a quality which, apart from such a setting, we\nshould never have dreamed that it was capable of possessing.\n\n[1] In order to remind the reader of the effect of this passage\nit is necessary to quote a few lines before and after--\n\n  \u201cRe-issue words and looks from the old mint,\n  Pass them afresh, no matter whose the print,\n    Image and superscription once they bore!\n  Re-coin thyself and give it them to spend,--\n  It all comes to the same thing at the end,\n    Since mine thou wast, mine art and mine shalt be,\n  Faithful or faithless, sealing up the sum\n  Or lavish of my treasure, thou must come\n    Back to the heart\u2019s place here I keep for thee!\u201d\n\nWe are not here concerned with the peculiar \u201caesthetic\u201d nature of\nworks of art, which makes them, although rational, nevertheless unique\nindividuals. I only adduced the above examples to show, in unmistakable\ncases, what is actually meant when we speak of \u201ca whole\u201d as constituted\nby a pervading identity which exhibits itself in the congruous or\nco-operating nature of all the constituent parts. In wholes of a higher\nkind than the whole of mere quantity the parts no longer repeat each\nother. They are not merely distinct, {58} but different. Yet the common\nor continuous nature shows itself within each of them.\n\nThe parts of a sum-total, taking them for convenience of summation\nas equal parts, may be called units; [1] the parts of an abstract\nsystem, such as a geometrical figure, may be called elements (I cannot\nanswer for mathematical usage), and the parts of a concrete system, an\naesthetic product, a mind, or a society, might be called members.\n\n[1] A unit of measurement implies in addition that it has been\nequated with some accepted standard. If I divide the length of\nmy room into thirty equal parts, each part is a \u201cunit\u201d in the\nsum-total; but I have not measured the room till I have equated\none such part with a known standard, and thus made it into a\nunit in the general system of length equations.\n\nBut every kind of whole is an identity, and its parts are always\ndifferences within it.\n\n_Nature of Knowledge_\n\n4. It will be well to sum up here what we have learnt of the nature\nof knowledge in general, before passing to the definition and\nclassification of Judgment.\n\nKnowledge is always Judgment. Judgment is constructive, for us, of\nthe real world. Constructing the real world means interpreting or\namplifying our present perception by what we are obliged to think,\nwhich we take as all belonging to a single system one with itself,\nand with what constrains us in sense-perception, and objective in the\nsense that its parts act on each other independently of our individual\napprehension, and that we are obliged to think them thus. The process\nof construction is always that of exhibiting a whole in its parts,\n_i.e._ an identity in its differences; that is to say, it is always\nboth analytic and synthetic. The objects of knowledge differ in the\nmode of relation between their {59} parts and the whole, and thus give\nrise to different types of judgment and inference; and this difference\nin the form of knowledge is a difference in the content of Logic, which\ndeals with the objects of experience only from the point of view of\ntheir properties as objects in an intellectual world.\n\n_Conclusion_\n\n5. I hope that these general lectures, which, as I am quite aware, have\nanticipated the treatment of many difficult questions which they have\nnot attempted to solve, have been successful in putting the problem of\nLogic before us with some degree of vividness. If this problem were\nthoroughly impressed upon our minds, I should say that we had already\ngained something definite from this course of study. The points which I\ndesire to emphasise are two.\n\n(1) I hope that we have learned to realise the world of our knowledge\nas a living growth, sustained by the energy of our intelligence; and to\nunderstand that we do not start with a ready-made world in common, but\ncan only enter upon the inheritance of science and civilisation as the\nresult of courage, labour, and reasonable perseverance; and further,\nthat we retain this inheritance just as long as our endurance and\ncapacity hold out, and no longer.\n\nAnd (2) I have attempted to make clear that this living growth, our\nknowledge, is like the vegetable or animal world in being composed\nof infinite minor systems, each and all of which are at bottom the\nsame function with corresponding parts or elements, modified by\nadaption to the environment. So that the task of analysing the form of\njudgment bears a certain resemblance to that of analysing the forms\nof plants. Just as from the single cell of the undifferentiated Alga,\nto {60} the most highly organised flower or tree, we have the same\nformation, with its characteristic functions and operations, so from\nthe undifferentiated judgment, which in linguistic form resembles\nan ejaculation or interjection, to the reasonable systems of exact\nor philosophical science, we find the same systematic function with\ncorresponding elements.\n\nBut the world of knowledge has a unity which the world of organic\nindividuals cannot claim; and this whole system of functions is itself,\nfor our intelligence, approximately a single function or system,\ncorresponding in structure to each of its individual parts, as though\nthe plant world or animal world were itself in turn a plant or animal.\nWe cannot hope to exhaust the shapes taken by the pervading fundamental\nfunction of intelligence. We shall only attempt to understand the\nanalogies and differences between some few of its leading types.\n\n\n\n\n{61}\n\nLECTURE IV   TYPES OF JUDGMENT AND THE GENERAL CONDITIONS\n             INVOLVED IN ASSERTION\n\n_Correspondence between types of Judgment and nature of objects as\nKnowledge_\n\n1. The question of correspondence between the types of Judgment and the\norders of Knowledge was really anticipated in discussing the relation\nbetween the content and the form of knowledge. We saw that the content\nor matter and nature known determines on the whole the form or method\nof knowledge by which it can be known.\n\nI give a few cases of this correspondence, not professing to complete\nthe list. We should accustom ourselves to think of these forms as\nconstituting a progression in the sense that each of them betrays a\nreference to an ideal of knowledge which in itself it is unable to\nfulfil, and therefore inevitably suggests some further or divergent\nform. And the defect by which the forms contradict the ideal, is felt\nby us as a defect in their grasp of reality, in their presentation of\nreal connections.\n\n_\u201cImpersonal\u201d Judgment_\n\n_a_. We think of the judgment as predicating an ideal content of a\nsubject indicated in present perception. But there are judgments\nwhich scarcely have an immediate subject at all, such as \u201cHow hot!\u201d\n\u201cBad!\u201d \u201cIt hurts!\u201d In the judgments thus represented the true subject\nis some {62} undefined aspect of the given complex presentation. Of\ncourse the words which we use are not an absolutely safe guide to the\njudgment--they may be merely an abbreviation. But there are typical\njudgments of this kind in which we merely mean to connect some namable\ncontent with that which can only be defined as the focus of attention\nat the moment. Such judgments might be called predications of mere\nquality. The only link by which they bind their parts into a whole is\na feeling referred to our momentary surroundings. A _mere_ quality, if\nnot defined or analysed, or a feeling of pleasure or pain, is the sort\nof object which can be expressed in such a judgment.\n\n_Perceptive Judgment_\n\n_b_. Then we have the very wide sphere of perceptive judgment, which\nwe may most conveniently confine to judgments which have in the\nsubject elements analogous to \u201cThis,\u201d \u201cHere,\u201d \u201cNow.\u201d Such particles as\nthese indicate an effort to distinguish elements within the complex\npresented. They have no content beyond the reference to presentation,\nand, in \u201chere\u201d and \u201cnow,\u201d an implication that the present is taken in\na particular kind of _continuum_. Otherwise they mean nothing more or\nother than is meant by pointing with the finger. We may or may not\nhelp out a \u201csubject\u201d of this kind by definite ideas attached to it as\nconditions of the judgment. If we do, we are already on the road to a\nnew form of knowledge, incompatible with the judgment of perception.\nFor so long as we keep a demonstrative, spatial or temporal, reference\nin the thought, the subject of judgment is not cut loose from our\npersonal focus of presentation. And as the existence of such a focus is\nundeniable, we are secure against criticism so far as the {63} content\nof the subject is concerned. But if we begin to specify it, we do so at\nour peril.\n\nSuch judgments as these have been called \u201cAnalytic judgments of\nsense.\u201d [1] The term is not generally accepted in this meaning, but\nis conveniently illustrative of the nature of these judgments. It\nis intended to imply that they are a breaking up and reconstruction\nof what, in our usual loose way of talking, is said to be given in\nsense-perception. They remain on the whole within the complex of \u201cthat\nwhich\u201d is presented.\n\n[1] Mr. F.H. Bradley, _Principles of Logic_, p. 48.\n\nFrom the point of view which we have taken, such judgments are not\nconfined to what we think it worth while to _say_, but are the essence\nof every orderly and objective perception of the world around us. In a\nwaking human consciousness nothing is unaffirmed.\n\nWe have no other term than perception to express the process which is\nemployed in scientific observation and experiment. But it is plain that\nso soon as the judgment that refers to \u201cThis\u201d is modified through the\ninevitable demand for qualification by exact ideas--\u201c_This_ hurts me,\u201d\n\u201c_What_ hurts you?\u201d \u201cThis old sprain, at the pace we are walking\u201d--a\nconflict of elements has arisen within the judgment. And as commonplace\nperception passes into scientific observation, the qualifying ideas, on\nwhich truth and relevancy depend, dwarf the importance of the \u201cthis,\u201d\nand ultimately oust it altogether. That is a simple case in which\nthe ideal of knowledge and the nature of reality operate within the\njudgment to split asunder its primitive form. The subject as expressed\nby a pure demonstrative refuses to {64} take account either of truth,\n_i.e._ consistency with knowledge as a whole, or of relevancy, _i.e._\nconsistency with the relation involved in the particular predication\nthat may be in question. Our commonplace perception halts between\nthese two extremes. It deals with the world of individual objects and\npersons, which, being already systematised according to our current\nobservations and interests, has, so long as we keep to its order, a\nsufficient degree of truth and relevancy for the needs of daily life.\nThus if I say, \u201cThis book will do as a desk to write upon,\u201d the truth\nof the qualification \u201cbook\u201d (_i.e._ the reality of the subject) is\nassumed on the ground of the facility of recognising a well-known\n\u201cthing,\u201d while the relevancy of the qualification \u201cbook\u201d is not\nquestioned, because we accept an individual thing as an object of\nhabitual interest _qua_ individual, and do not demand that whenever it\nis named those properties alone should be indicated which are relevant\nto the purpose for which it is named. The \u201cthing\u201d is a current coin of\npopular thought, and makes common perception workable without straining\nafter a special relevancy in the subject of every predication. Such\nspecial relevancy leads ultimately to the ideal of _definition_, in\nwhich subject and predicate are adequate to each other and necessarily\nconnected. A definitory judgment drops the demonstrative and relies\non qualifying ideas alone. It is therefore an abstract universal\nJudgment, while the Judgment of Perception, so long as it retains the\ndemonstrative, is a Singular Judgment.\n\n_Proper names in Judgment_\n\n_c_. But a very curious example of a divergence or half-way house in\nKnowledge is that form of the singular Judgment in which the subject is\na proper name. A proper name is {65} designative and not definitory.\nIt may be described as a generalised demonstrative pronoun--a\ndemonstrative pronoun which has the same particular reference in the\nmouth of every one who uses, it, and beyond the given present of time.\n\nSo the reference of a proper name is a good example of what we called\na universal or an identity. That which is referred to by such a name\nis a person or thing whose existence is extended in time and its parts\nbound together by some continuous quality--an _individual_ person or\nthing and the whole of this individuality is referred to in whatever\nis affirmed about it. Thus the reference of such a name is universal,\nnot as including more than one individual, but as including in the\nidentity of the individual numberless differences--the acts, events,\nand relations that make up its history and situation.\n\nWhat kinds of things are called by Proper Names, and why? This question\nis akin to the doctrine of Connotation and Denotation, which will be\ndiscussed in the next lecture. It is a very good problem to think over\nbeforehand, noting especially the limiting cases, in which either some\n_people_ give proper names to things to which other people do not give\nthem, or some _things_ are given proper names while other things of the\nsame general kind are not. These judgments, which are both Singular and\nUniversal, may perhaps be called for distinction\u2019s sake \u201cIndividual\u201d\nJudgments.\n\n_Abstract Judgment_\n\n_d_. The demonstrative perception may also be replaced by a more or\nless complete analysis or definition.\n\nWithin this province Definition of a concrete whole is one extreme,\n_e.g_. \u201cHuman Society is a system of wills\u201d; {66} that of an abstract\nwhole the other extreme, \u201c12 = 7 + 5.\u201d There are all degrees, between\nthese two, in the amount of modification which the parts undergo\nby belonging to the whole. There are also all sorts of incomplete\ndefinitions, expressing merely the effects of single conditions out of\nthose which go to make up a whole. These form the abstract universal\njudgments of the exact sciences, such as, \u201cIf water is heated to 212\u00b0\nFahr. under one atmosphere it boils.\u201d In all these cases some idea,\n\u201cabstract\u201d as being cut loose from the focus of present perception,\nwhether abstract or concrete in its content, replaces the demonstrative\nof the judgment which is a perception. These are the judgments which in\nthe ordinary logical classification rank as universal.\n\n_The general definition of Judgment_\n\n2. It was quite right of us to consider some types of judgment\nbefore trying to define it generally. It is hopeless to understand a\ndefinition unless the object to be defined is tolerably familiar. We\nhave said a great deal about knowledge and about judgment as the organ\nor medium of knowledge. Now we want to study particular judgments in\ntheir parts and working, and observe how they perform their function of\nconstructing reality.\n\nNow, for our purpose, we may take the clearest cases of judgment, viz.\nthe meanings of propositions.\n\nThe distinctive character of Judgment as contrasted with every other\nact of mind is that it claims to be true, _i.e._ pre-supposes the\ndistinction between truth and falsity.\n\nFirst, we have to consider what is implied in claiming truth.\n\nSecondly, by what means truth is claimed in Judgment.\n\n{67} Thirdly, the nature of the ideas for which alone truth can be\nclaimed.\n\n_What is implied in claiming truth_\n\n(i.) Claiming truth implies the distinction between truth and falsity.\nI do not say, \u201cbetween truth and falsehood,\u201d because falsehood\nincludes a lie, and a lie is not _prima facie_, an error or falsity of\nknowledge. It is, as may be said of a question, altogether addressed\nto another person, and has no existence as a distinct species within\nknowledge. Thus a lie is called by Plato \u201cfalsehood in words\u201d; the term\n\u201cfalsehood in the mind\u201d he reserves for ignorance or error, which he\ntreats as the worst of the two, which from an intellectual point of\nview it plainly is.\n\nNo distinction between truth and falsity can exist unless, in the act\nor state which claims truth, there is a reference to something outside\npsychical occurrence in the course of ideas. Falsity or error are\nrelations that imply existences which, having reality of one kind,\nclaim in addition to this another kind of reality which they have not.\nIn fact, all things that are called false, are called so because they\nclaim a place or property which they do not possess. They must exist,\nin order to be false. It is in the non-fulfilment, by their existence,\nof some claim or pretension which it suggests, that falsity consists.\nAnd so it is in the fulfilment of such a claim that truth has a\nmeaning. A false coin exists as a piece of metal; it is false because\nit pretends to a place in the monetary system which its properties or\nhistory [1] contradict.\n\n[1] For it is, I suppose, technically false, even if over value,\nif not coined by those who have the exclusive legal right to\ncoin.\n\nAs the claim to be true is made by every judgment in its {68} form,\nthere can be no judgment without some recognition of a difference\nbetween psychical occurrences and the system of reality. That is to\nsay, there is no judgment unless the judging mind is more or less aware\nthat it is possible to have an idea which is not in accordance with\nreality.\n\nThus, _if_ an animal has no real world distinct from his train of\nmental images, if, that is, and just because, these are his world\ndirectly, and without discord, he cannot judge. The question is, _e.g._\nwhen he seems disappointed, whether the pleasant image [1] simply\ndisappears and a less pleasant image takes its place, or whether the\nerroneous image was distinguished as an element in \u201ca mere idea,\u201d which\ncould be retained and compared with the systematised perceptions which\nforce it out, _as_ an idea with reality.\n\n[1] It will be observed that we are not treating the mental\nimages as being taken for such by the primitive mind. It is just\nin as far as they are _not_ yet _taken for such_ that they _are\nmerely such_. Mr. James says that the first sensation is for the\nchild the universe (_Psychology_ II. 7). But it is a universe\nin which all is equally mere fact, and there is no distinction\nof truth and falsehood, or reality and unreality. That can only\ncome when an existent is found to be a fraud.\n\nWe must all of us have seen a dog show signs of pleasure when he\nnotices preparations for a walk, and then express the extreme of\nunhappiness when the walk is not taken at all, or he is left at home.\nPeople interpret these phenomena very carelessly. They say \u201che thought\nthat he was going to be taken out.\u201d If he did \u201c_think that_, etc,\u201d then\nhe made a judgment. This would imply that he distinguishes between the\nimages suggested to his mind, and the reality of their content as the\nfuture event of going out, and knew that he might have the one without\nthe other following. But of {69} course it is quite possible that the\ndog has no distinct expectation of something different from his present\nimages, but merely derives pleasure from them, which he expresses, and\nsuffers and expresses pain when they are replaced by something else. It\nis here, no doubt, in the conflict of suggestion and perception, that\njudgment originates.\n\nOn the other hand, animals, especially domestic animals, do seem to use\nthe imperative, which perhaps implies that they know what they want,\nand have it definitely contrasted with their present ideas as something\nto be realised.\n\nHowever this may be, the claim of truth marks the minimum of Judgment.\nThere can be no judgment until we distinguish psychical fact from the\nreference to Reality. A mere mental fact as such is not true or false.\nIn other words, there is no judgment unless there is something that,\nformally speaking, is capable of being denied. When your dog sees\nyou go to the front door, he may have an image of hunting a rabbit\nsuggested to his mind, but so far there is nothing that can be denied.\nIf he has the image, of course he has. There is nothing that can be\ndenied until the meaning of this image is treated as a further fact\nbeyond the image itself, in a system independent of the momentary\nconsciousness in his mind. _Then_ it is possible to say, \u201cNo, the\nfact does not correspond to your idea,\u201d _i.e._ what we are ultimately\nobliged to think as a system is inconsistent with the idea as you\naffirmed it of the same system.\n\n_By what means the claim to truth is made_\n\n(ii.) The first thing then in Judgment is that we must have a world of\nreality distinguished from the course of our ideas. Thereupon the claim\nto truth is actually made by attaching the meaning of an idea to some\npoint in the real {70} world. This can only be done where an identity\nis recognised between reality and our meaning.\n\nThus (keeping to the Judgment of Perception) I say, \u201cThis table is\nmade of oak.\u201d This table is given in perception already qualified by\nnumberless judgments; it is a point in the continuous system or tissue\nwhich we take as reality. Among its qualities it has a certain grain\nand colour in the wood. I know the colour and grain of oak-wood, and if\nthey are the same as those of the table, then the meaning or content\n\u201cmade of oak\u201d coalesces with this point in reality, and instead of\nmerely saying, \u201cThis table is made of wood that has such and such a\ngrain and colour,\u201d I am able to say \u201cThis table is made of oak-wood.\u201d\n\nThis example shows the true distinction between the Logical Subject and\nPredicate. The fact is, that the ultimate subject in Judgment is always\nReality. Of course the logical subject may be quite different from\nthe grammatical subject. Some kinds of words cannot in strict grammar\nbe made subjects of a sentence, though they can represent a logical\nsubject quite well: _e.g._ \u201c_Now_ is the time.\u201d \u201c_Here_ is the right\nplace_.\u201d Adverbs, I suppose, cannot be grammatical subjects. But in\nthese sentences they stand for the logical subjects, certain points in\nthe perceptive series.\n\nThe true logical subject then is always reality, however much disguised\nby qualifications or conditions. The logical predicate is always\nthe meaning of an idea; and the claim to be true consists in the\naffirmation of the meaning as belonging to the tissue of reality at\nthe point indicated by the subject. The connection is always made by\nidentity of {71} content at the point where the idea joins the reality,\nso that _the judgment always appears as a revelation of something which\nis in reality_. It simply develops, accents, or gives accuracy to a\nrecognised quality of the real. This is easily seen in cases of simple\nquality--_e.g._ \u201cThis colour is sky-blue.\u201d The colour is given, and the\njudgment merely identifies it with sky-blue, and so reveals another\nelement belonging to its identity, the element of being seen in the sky\non a clear day.\n\nThe analysis is not quite so easy when there is a concrete subject like\na person; for how can there be an identity between a person and a fact?\n\u201cA.B. passed me in the street this afternoon.\u201d Between what elements is\nthe identity in this case? It is between him, as an individual whom I\nknow by sight in other places, and him as he appeared this afternoon in\nparticular surroundings. His identity already extends through a great\nmany different particulars of time and place, and this judgment merely\nrecognises one more particular as included in the same continuous\nhistory. \u201cHe in this context belongs to him in a former context.\u201d In\nthis simple case the operative identity is probably that of my friend\u2019s\npersonal appearance; but the judgment is not merely about that but\nabout his whole personality, of which his personal appearance is merely\ntaken as a sign.\n\nAny assertion which is incredible because the identical quality is\nwanting will illustrate the required structure. There is a story\ncommented on by Thackeray in one of his occasional papers, which\nimplied that the Duke of Wellington took home note-paper from a club to\nwhich he did not {72} belong. (Thackeray gives the true explanation of\nthe fact on which the suggestion was founded.) The identity concerned\nin this case would be that of character. Can we find an identity\nbetween the character involved in a piece of meanness like that\nsuggested and the character of the Duke of Wellington? No; and _prima\nfacie_ therefore the judgment is false. The identity which should bind\nit together breaks it in two. But yet, again: supposing the external\nevidence to be strong enough, we may have to accept a fact which\nconflicts with a man\u2019s character as we conceive it. That is so: in such\na case one kind of identity appears to contradict the other. I may\nthink that I saw a man with my own eyes, doing something which wholly\ncontradicts his character as I judge it. Then there is a conflict\nbetween identity in personal appearance and identity in character,\nand we have to criticise the two estimates of identity--_i.e._ to\nrefer them both to our general system of knowledge, and to accept the\nconnection which can be best adapted to that system.\n\nWe have got, then, as the active elements in Judgment a Subject in\nReality, the meaning of an idea, and an identity between them.\n\nIs this enough? Have we the peculiar act of affirmation wherever we\nhave these conditions?\n\nThis is not the question by what elements of language the judgment is\nrendered. We shall speak of that in the next lecture. The question is\nnow, simply, \u201cIs a significant idea, referred to reality, always an\nassertion?\u201d\n\nThe first answer seems to be that such an idea is always _in_ an\nassertion, but need not constitute the whole of an {73} assertion. If\nwe think of a subject in judgment which is represented by a relative\nsentence, it seems clear that any idea which can stand a predicate can\nalso form a part of a subject. \u201cThe exhibition which it is proposed\nto hold at Chicago in 1893\u201d--has in effect just the same elements of\nmeaning, and just the same reference to a point in our world of reality\nas if the sentence ran, \u201cIt is proposed to hold an exhibition at\nChicago in 1893.\u201d In common parlance we should say, that in the former\ncase we entertain an idea--or conceive or represent it--while in the\nlatter case we affirm it.\n\nBut if we go on to say that the former kind of sentence as truly\nrepresents the nature of thought as the latter, then it seems that we\nare mistaken. Even language does not admit such a clause to the rank of\nan independent sentence.\n\nIf we insist on considering it in its isolation, we probably eke it\nout in thought by an unarticulated affirmation such as that which\nconstitutes an impersonal judgment; in other words, we affirm it to\nbelong to reality under some condition which remains unspecified.\nThus the linguistic form of the relative clause, as also the separate\nexistence of the spoken or written word, produces an illusion which\nhas governed the greater part of logical theory so far as concerns the\nseparation between concept and judgment, _i.e._ between entertaining\nideas and affirming them in reality. In our waking life, all thought is\njudgment, every idea is referred to reality, and in being so referred,\nis ultimately affirmed of reality. The separation of elements in the\ntexture of Judgment into Subjects and Predicates which, as separated,\nare conceived as _possible_ Subjects and Predicates, is therefore\n{74} theoretical and ideal, an analysis of a living tissue, not an\nenumeration of loose bricks out of which something is about to be built\nup.\n\n_The kind of ideas which can claim truth_\n\n(iii.) \u201cIdea\u201d has two principal meanings.\n\n    (_a_) A psychical presentation and\n\n    (_b_) An identical reference.\n\nThis distinction is the same as that between our course of ideas and\nour world of knowledge. We must try now to define it more accurately.\n\n(_a_) An idea as a psychical presentation is strictly a particular.\nEvery moment of consciousness is full of a given complex of\npresentation which passes away and can never be repeated without some\ndifference. For this purpose a representation is just the same as a\npresentation; is, in fact, a presentation. Its detail at any given\nmoment is filled in by the influence of the moment, and it can never\noccur again with precisely the same elements of detail as before.\nIf we use the term \u201cidea\u201d in this sense, as a momentary particular\nmental state, it is nonsense to speak of having the same idea twice,\nor of referring it to a reality other than our mental life. The idea\nin this sense is a psychical image. We cannot illustrate this usage\nby any recognisable part of our mental furniture, for every such part\nwhich can be described and indicated by a general name, is something\nmore than a psychical image. We can only say that that which at any\nmoment we have in consciousness, when our waking perception encounters\nreality, is such an idea, and so too is the image supplied by memory,\nwhen considered simply as a datum, a fact, in our mental history.\n\n(_b_) To get at the other sense of \u201cidea\u201d we should think {75} of the\nmeaning of a word; a very simple case is that of a proper name. What\nis the meaning of \u201cSt. Paul\u2019s Cathedral in London\u201d? No two people who\nhave seen it have carried away precisely the same image of it in their\nminds, nor does memory, when it represents the Cathedral to each of\nthem, supply the same image in every detail and association twice over\nto the same person, nor do we for a moment think that such an image\n_is_ the Cathedral. [1] Yet we neither doubt that the name _means_\nsomething, and that the same to all those who employ it, nor that it\nmeans the same to each of them at one time that it did at every other\ntime. The psychical images which formed the first vision of it are dead\nand gone for ever, and so, after every occasion on which it has been\nremembered, are those in which that memory was evoked. The essence of\nthe idea does not lie in the peculiarities of any one of their varying\npresentations, but in the identical reference that runs through them\nall, and to which they all serve as material, and the content of this\nreference _is_ the object of our thought.\n\n[1] When we are actually looking at the Cathedral, we say,\n\u201c_That is_ the Cathedral.\u201d Does not this mean that we take our\nmomentary image, to which we point, to be the reality of the\nCathedral? Not precisely so. It is the \u201cthat,\u201d not our definite\npredication about it, which makes us so confident. The \u201cthat\u201d is\nidentified by our judgment, but goes beyond it.\n\nIn order to distinguish and employ this reference it is necessary that\nthere should be a symbol for it, and so long as it brings us to the\nobject which is the centre of the entire system, this symbol may vary\nwithin considerable limits.\n\nThe commonest and most secure means of reference is {76} the word or\nname. [1] So confident are we in the \u201cconventional\u201d or artificially\nadapted character of this mark or sign of reference, that we are\ninclined to treat it as absolutely unvarying on every occasion of\nutterance. But of course it is not unvarying. It differs in sound every\ntime it is spoken, and in context and appearance every time we see\nit in a written shape. Our reliance upon it as identical throughout\ndepends on the fact that it has a recognisable character to which\nits variations are irrelevant, and which practically crushes out\nthese variations from our attention. Unless we are on the look-out\nfor mispronunciations or misprints, they do not interfere at all\nwith our attention to the main reference of words. We know that it\nis almost impossible to detect misprints so long as one reads a book\nwith attention to its meaning. This then is a fair parallel to the\ndistinction which we are considering between two kinds of ideas. If the\nmomentary sound or look of a word is analogous to idea as psychical\npresentation, \u201cthe word\u201d as a permanent possession of our knowledge is\nanalogous to the idea as a reference to an object in our systematic\nworld, and is the normal instrument of such a reference.\n\n[1] \u201cA name is a sound which has significance according to\nconvention,\u201d _i.e._ according to rational agreement.--_Ar. de\nInterp_. 16a 19.\n\nBut either with the word or without it there may be a symbol of another\nkind. Any psychical image that falls within certain limits may appear\nas the momentary vehicle of the constant reference to an object. Just\nas in recognising the reference of a word we omit to notice the accent\nand loudness with which it is pronounced, or the quality of the paper\non which it is printed, just so in recognising the {77} reference of\na psychical image our attention fails to note its momentary context,\ncolouring, and detail. If it includes something that definitely belongs\nto a systematic object in our world of objects, that is enough, unless\ncounteracted by cross references, to effect the suggestion we require,\nand that, and nothing else, arrests our attention for the moment. When\nI think of St. Paul\u2019s Cathedral, it may be the west front, or the\ndome seen from the outside, or the gallery seen from the inside, that\nhappens to occur to my mind; and further, that which does occur to me\noccurs in a particular form or colouring, dictated by the condition\nof my memory and attention at the moment. But these peculiarities are\ndwarfed by the meaning, and unless I consider them for psychological\npurposes, I do not know that they are there. It is the typical\nelement only, the element which points to the common reference in\nwhich my interest centres, that forms the content of the idea in this\nsense, taken not as a transient feature of the mental complex, but\nas definitely suggesting a constant object in our constructed world.\nAnd it suggests this object because it, the typical element, is a\ncommon point that links together the various cases and the various\npresentations in which the object is given to us. In this sense it is a\nuniversal or an identity.\n\nHow can this conception of a logical idea be applied to a perfectly\nsimple presentation? It would be impossible so to apply it, but there\ndoes not seem to be such a thing as a simple presentation in the sense\nof a presentation that has no connection as a universal with anything\nelse. In the image of a particular blue colour, we cannot indeed\nseparate out what makes it blue from what makes it the particular {78}\nshade of blue that it is. But nevertheless its blueness makes it a\nsymbol to us of blue in general, and when so thought of, crushes out of\nsight all the visible peculiarities that attend every spatial surface.\nWe understand perfectly well that the colour is blue, and that in\nsaying this we have gone beyond the limits of the momentary image, and\nhave referred something in it as a universal quality to our world of\nobjects. An idea, in this sense, is both less and more than a psychical\nimage. It contains less, but stands for more. It includes only what is\ncentral and characteristic in the detail of each mental presentation,\nand therefore omits much. But it is not taken as a mental presentation\nat all, but as a content belonging to a systematic world of objects\nindependent of my thought, and therefore stands for something which is\nnot mere psychical image.\n\nIf therefore we are asked to display it as an image, as something\nfixed in a permanent outline, however pale or meagre, we cannot do\nso. It is not an abstract image, but a concrete habit or tendency. It\ncan only be displayed in the judgment, that is, in a concrete case\nof reference to reality. Apart from this, it is a mere abstraction\nof analysis, a tendency to operate in a certain way upon certain\npsychical presentations. Psychically speaking, it is when realised in\njudgment a process more or less systematic, extending through time, and\ndealing with momentary presentations as its material. In other words,\nwe may describe it as a selective rule, shown by its workings but not\nconsciously before the mind--for if it were, it would no longer be an\nidea, but an idea of an idea.\n\nEvery judgment, whether made with language or without, {79} is an\ninstance of such an idea, which may be called a symbolic idea as\ndistinct from a psychical image; \u201csymbolic\u201d because the mental units\nor images involved are not as such taken as the whole of the object\nfor which they stand, but are in a secondary sense, as the word in a\nprimary sense, symbols or vehicles only.\n\nSuch ideas can have truth claimed for them, because they have a\nreference beyond their mental existence. They point to an object in\na system of permanent objects, and that to which they point may or\nmay not suit the relation which they claim for it. Therefore the\njudgment can only be made by help of symbolic ideas. Mere mental\nfacts, occurrences in my mental history, taken as such, cannot enter\ninto judgment. When we judge about them, as in the last sentence,\nthey are not themselves subject or predicate, but are referred to,\nlike any other facts, by help of a selective process dealing with our\ncurrent mental images of them. We shall not be far wrong then, if in\nevery judgment, under whatever disguises it may assume, we look for\nelements analogous to those which are manifest in the simple perceptive\njudgment, \u201cThis is green,\u201d or \u201cThat is a horse.\u201d The relation between\nthese and more elaborate forms of affirmation, such as the abstract\njudgment of science, has partly been indicated in the earlier portion\nof this lecture. The general definition of judgment has therefore\nbeen sufficiently suggested on p. 72. Judgment is the reference of a\nsignificant idea to a subject in reality, by means of an identity of\ncontent between them.\n\n\n\n\n{80}\n\nLECTURE V   THE PROPOSITION AND THE NAME\n\n_Judgment translated into language._\n\n1. Judgment expressed in words is a Proposition. _Must_ Judgment be\nexpressed in words? We have assumed that this need not be so. Mill [1]\nsays of Inference that \u201cit is an operation which usually takes place\nby means of words, and in complicated cases can take place in no other\nway.\u201d The same is true of Judgment.\n\n[1] _Logic_ vol. I. c. i., init.\n\nWe may say in general that words are not needed, when thinking about\nobjects by help of pictorial images will do the work demanded of the\nmind, _i.e._ when perfectly individualised connections in space and\ntime are in question. Mr. Stout [1] gives chess-playing as an example.\nWith the board before him, even an ordinary player does not need words\nto describe to himself the move which he is about to make.\n\n[1] In _Mind_, no. 62.\n\nWords are needed when we have to attend to the general plan of any\nsystem, as in thinking about organisms with reference to their type,\nor about political relations--about anything, that is, which is not\nof such a nature that the members of the idea can be symbolised in\npictorial form. It would be difficult, for example, to comprehend the\nrespiration of plants under a symbolic picture-idea drawn {81} from the\nrespiration of the higher animals. The relations which constitute a\ncommon element between the two processes do not include the movements,\nfeelings, and visible changes in the circulatory fluid from which our\nimage of animal respiration is chiefly drawn; and we could hardly\nframe a pictorial idea that would duly insist on the chemical and\norganic conditions on which the common element of the process depends.\nIn a case of this kind the word is the symbol which enables us to\nhold together in a coherent system, though not in a single image, the\nrelations which make up the content of our thought.\n\n\u201cWords\u201d may be of many different kinds--spoken, written, indicated\nby deaf and dumb signs; all of these are derived from the word as\nit is in speech, although writing and printing become practically\nindependent of sound, and we read, like the deaf and dumb alphabet,\ndirectly by the eye. Then there may be any kind of conventional signals\neither for letters, words, or sentences, and any kind of cipher or\n_memoria technica_ either for private or for general use--in these the\n\u201cconventional\u201d nature of language reaches its climax, and the relation\nto a natural growth of speech has disappeared. And finally there are\nall forms of picture-writing, which need not, so far as its intrinsic\nnature goes, have any connection with speech at all, and which seems to\nform a direct transition between picture-thinking and thinking through\nthe written sign.\n\nAll these must be considered under the head of language, as a fixed\nsystem or signs for meanings, before we can ultimately pronounce that\nwe think without words.\n\nEvery Judgment, however, can be expressed in words, {82} though not\nevery Judgment need be so expressed or can readily be so.\n\n_Proposition and sentence._\n\n2. A Judgment expressed in words is a Proposition, which is one kind\nof sentence. A command question or wish is a sentence but not a\nproposition. A detached relative clause [1] is not even a complete\nsentence. The meaning of the imperative and the question seems to\ninclude some act of _will_; the meaning of a proposition is always\ngiven out simply for fact or truth. We need not consider any sentence\nthat has no meaning at all.\n\n[1] See above, Lect. IV.\n\n_Difference between Proposition and Judgment_\n\n3. Almost all English logicians speak of the Proposition and not of the\nJudgment. [1] This does not matter, so long as we are agreed about what\nthey mean. They must mean the proposition _as understood_, and this is\nwhat we call the judgment.\n\n[1] So Mill, Venn, Jevons, Bain (see his note, p. 80).\n\nIn order to make this distinction clear, let us consider the\nproposition as it reaches us from without, that is to say, either as\nspoken or as written. The words, the parts of such a proposition, as we\nhear or read them, are separate and successive either in time alone, or\nin time and space. Further, the mere sounds or signs can be mastered\napart from the meaning. You can repeat them or copy them without\nunderstanding them in the least, as _e.g._ in the case of a proposition\nin an unknown language. So far, the proposition has not become a\njudgment, and I do not suppose that any logician would admit that it\ndeserved the name even of a proposition. But if not, then we must not\nconfuse the attributes which it has before it becomes a proposition\nwith those which it has after.\n\n{83} Further, in understanding a proposition, or in construing a\nsentence into a proposition (if the sentence only becomes a proposition\nwhen understood), there are many degrees. I read upon a postcard,\n\u201cA meeting will be held on Saturday next by the Women\u2019s Liberal\nAssociation, to discuss the taxation of ground-rents.\u201d The meaning of\nsuch a sentence takes time to grasp, and if the words are read aloud\nto us, must of necessity be apprehended by degrees. We understand very\nquickly that a meeting is to be held next Saturday. This understanding\nis already a judgment. It is something quite different from merely\nrepeating the words which we read. It consists in realising them as\nmeanings, and bringing these meanings together into a connected idea,\nand affirming this idea to belong to our real world. The meanings are\nnot separate, outside one another, as the words are when we first\nhear or read them. They enter into each other, modify each other, and\nbecome parts of an ideal whole. This gradual apprehension of a sentence\nrecalls to one the boyish amusement of melting down bits of lead in a\nladle. At first the pieces all lie about, rigid and out of contact; but\nas they begin to be fused a fluid system is formed in which they give\nup their rigidity and independence, and enter into the closest possible\ncontact, so that their movements and position determine each other. But\nstill some parts, like words not yet grasped, remain hard and separate,\nand it is only when the melting is complete that this isolation is\ndestroyed, and there are no longer detached fragments, but a fluid body\nsuch that all its parts are in the closest connection with one another.\n\nThus then in understanding a sentence we have a judgment {84} from the\nfirst. The rest of the process of understanding consists in completing\nthe content of this judgment by fusing with it the meanings of the\nwords not yet apprehended; and in the completeness with which this\nis effected there will always be great differences of degree between\ndifferent minds, and also between the same mind at different times.\nSome of us attach a complete and distinct meaning to the words \u201cWomen\u2019s\nLiberal Association\u201d; some of us do not know, or have forgotten,\nexactly what it is, and what are its aims and history. All of us have\nsome conception of the purpose described as \u201ctaxation of ground rents,\u201d\nbut the phrase conveys a perfectly definite scheme hardly to one in\na thousand readers. Nevertheless, in so far as we have some symbolic\nidea which refers to this place or context in the world of objects,\nthe content of this idea enters into and modifies the total meaning\nwhich in apprehending the sentence before us we affirm of reality. The\nheard or written proposition (or sentence, if it is not a proposition\ntill understood) serves as an instrument by which we build up in our\nintellectual world a sort of plan or scheme of connected meanings, and\nalso, not subsequently but concurrently with this work of building,\naffirm the whole content thus being put together to be true of reality.\nThen we have what I call a Judgment. It is not that the words are\nnecessarily forgotten; they, or at least the principal significant\nterms, are probably still in the mind as guides and symbols; but yet a\nconstructive work has been done; a complex experience has been called\nup and analysed, and its parts fitted together in a certain definite\norder by the operation of universal ideas or meanings, each of which is\na system playing {85} into other systems; and the whole thus realised\nhas been added as an extension to the significance of the continuous\njudgment which forms our waking consciousness. The inconvenience of the\nterm \u201cproposition\u201d is that it tends to confuse the heard or written\nsentence in its separate words with the proposition as apprehended and\nintellectually affirmed. And these two things have quite different\ncharacteristics.\n\n_Parts of Speech_\n\n4. Thus we must be very careful how we apply the conception of\n\u201cparts of speech.\u201d The grammatical analysis which classifies words\nas substantives, adjectives, adverbs, verbs, and the like, is not to\nbe taken as telling us what words are by themselves, but just the\nopposite, viz. what they do when employed in a significant sentence.\nThey are studied separately for convenience in attending to them, as\nwe may study the wheels and pistons of an engine; but the work which\ngives them their names can only be done when they are together. This\ntruth is often expressed by saying that \u201cthe sentence is the unit\nof language,\u201d _i.e._ a word taken by itself cannot have a complete\nmeaning--unless it is a verb, or used with verbal force, for a verb\nis an unanalysed sentence. If any one uses a substantive or adverb by\nitself, we think that he has not finished his sentence, and no meaning\nis conveyed to our minds. We ask him, \u201cWell, what about it?\u201d The same\nis true, as we saw, of a relative clause. If we read in a newspaper\nsuch a clause as this, \u201cThe epidemic of influenza, which has appeared\nin England for three successive seasons,\u201d followed by a full stop, we\nshould infer, without hesitation, that some words had dropped out by\naccident. Of course such a {86} combination of words would make us\nthink something, but the meaning which we might ascribe to it would be\nconjectural; we should necessarily complete the thought for ourselves\nby some affirmation--some relation to reality--while recognising that\nno such relation was given in the clause as we read it. Nothing less\nthan a sentence, or, omitting the wish and the command, nothing less\nthan a proposition, conveys a meaning in which the mind can acquiesce\nas not requiring to be supplemented conjecturally. There are traces in\nlanguage that indicate the sentence to have been historically prior to\nthe word. I question whether the word could be certainly distinguished\nwithin the sentence in early languages that have not been reduced\nto writing. The tendency of reflective analysis, as in grammar and\ndictionaries, is to give it a more and more, artificial isolation. The\nGreeks did not separate their words in writing, and they wrote down\nthe change in a terminal consonant produced by the initial letter of\nthe next word, just as if it was within a compound word. Nor had they\nreally any current term co-extensive with our \u201cword.\u201d Where we should\nsay \u201cthe word \u2018horse\u2019\u201d they most commonly use the neuter article\n\u201cthe\u201d followed by the word in question as if in quotation-marks (\u201dthe\n\u2018horse\u2019\u201c). In defining noun and verb, Aristotle has no simple class\nname like \u201dword\u201c to employ as a common element of the definition, but\nuses the curious description \u201da portion of discourse, of which no part\nhas a meaning by itself.\u201c\n\nOf course, single words often stand as signs for propositions. It\nis interesting to note the pregnant meaning of a single word in the\nmouth of a child. Thus \u201cstool\u201d was {87} used to mean \u201c(1) Where is my\nstool? (2) My stool is broken; (3) Lift me on to the stool; (4) Here\nis a stool.\u201d [1] There is in this an interesting conflict of form and\nmeaning, owing to the child of European race having at command only\n\u201cparts of speech.\u201d In a less analytical language he might have at\ncommand a sound corresponding to a sentence rather than to a \u201cnoun\nsubstantive.\u201d\n\n[1] Preyer, quoted in _H\u00f6ffding, Psych_., 176.\n\nThe verb of inflected languages, [1] such as Greek or Latin, in which\nthe \u201cnominative case\u201d need not be supplied even by a pronoun, is the\ntype for us of a sentence not yet broken up.\n\n[1] In German and English, though the verb is inflected, custom\nforbids it to stand without the pronoun.\n\nThe bearing of this truth on Logic is to make us treat it in two parts\nand not in three. We do not treat of Name, Proposition, Syllogism, or\nof Concept, Judgment, Inference, but only of the two latter parts. The\nname or concept has no reality in living language or living thought,\nexcept when referred to its place in a proposition or judgment. We\nought not to think of propositions as built up by putting words or\nnames together, but of words or names as distinguished though not\nseparable elements in propositions. Aristotle takes the simple and\nstraightforward view. \u201cA term is the element into which a proposition\nis broken up, such as subject and predicate.\u201d [1] Of course different\nlanguages separate the parts of the proposition very differently,\n{88} and uneducated people hardly separate them at all. Formal Logic\nbreaks down the grammatical meaning of \u201cname,\u201d so far as to treat as a\n\u201clogical name\u201d any complex words that can stand as Subject or Predicate\nin a Proposition (_e.g._ a relative clause).\n\n[1] _Anal. prior_., 24b, 16. The opposite view seems to be\nexpressed in the beginning of the \u03c0\u03b5\u03c1\u1f76 \u1f19\u03c1\u03bc\u03b5\u03bd\u03b5\u03af\u03b1\u03c2 [= peri\nHermeneias, _de Interpretatione_], that the separate word\ncorresponds to the separate idea. I have attempted to explain\nthis as an illusion, p. 73, above.\n\n_Denotation and Connotation_\n\n5. The doctrine of the meaning of names has suffered from their\nrelation to propositions not being borne in mind. Mill\u2019s discussion [1]\nis very sensible, but, as always, very careless of strict system. More\nespecially it seems a pity to state the question as if it concerned\na division of names into Connotative and Non-connotative; because in\nthis way we from the first let go of the idea that the meaning of a\nname has necessarily two aspects, [2] and we almost bind ourselves to\nmake out that there are some non-connotative names. It is better to\nconsider this latter subject on its merits. Mill says that an ordinary\nsignificant name such as \u201cman\u201d \u201csignifies the subjects directly, the\nattributes indirectly; it _denotes_ the subjects, and implies or\ninvolves or indicates, or, as we shall say henceforth, _connotes_, the\nattributes.\u201d In short, the denotation of a name consists of the things\n_to which_ it _ap_plies, the connotation consists of the properties\nwhich it _im_plies. The denotation is made up of individuals and\nthe connotation of attributes. Denotation is also called Extension,\nespecially if we are speaking of Concepts rather than of names.\nConnotation is then called Intension. In the German writers it is\nmore usual to say that the Extension or Area (_Umfang_) consists not\nof the individuals, but of the species that are contained in {89}\nthe meaning of a general name. They oppose it to Content (_Inhalt_)\ncorresponding to our \u201cConnotation.\u201d Thus the \u201cArea\u201d of \u201crose\u201d would\nnot be the individual roses in the world, but rather all the species\nof rose in the world (_Rosa Canina, Rosa Rubiginosa_, etc.). This\nraises a difficulty as to the denotation of a specific name, but\nperhaps represents the actual process of thought, in the case of a\ngeneric name, better than that which Mill adopts. The difference is not\nimportant.\n\n[1] _Logic_, Bk. I. c. ii. \u00a7 5. Cf. Venn, 174 and 183, and Bain, 48.\n\n[2] See Bradley, p. 155.\n\nWell, then, according to Mill, when we say, \u201cThe Marshal Niel is a\nyellow rose,\u201d we refer directly to a group of real or possible objects,\nand we mean that all these individual objects are yellow roses. The\nattributes are only mentioned by the way, or implied. So Dr. Venn says\nthat the denotation is real, and the connotation is notional.\n\nBut there is another side to this question. The objects may be _what\nyou mean_ but the attributes seem to be _the meaning_, for how can you\n(especially on Mill\u2019s theory of the proposition) refer to any objects\nexcept through these attributes, unless indeed you can point to them\nwith your finger? And so again it seems, especially if we consider\nMill\u2019s account of predication, as if the Connotation were the primary\nmeaning and the Denotation the secondary meaning. The Connotation\ndetermines the Denotation; and if we \u201cdefine\u201d the meaning of the name\nit is the Connotation that we state. And so Mill tells us two or\nthree pages further on, that whenever the names given to objects have\nproperly any meaning, the meaning resides not in what they denote, but\nin what they connote. In short, {90} the denotation of a general name\nis simply the meaning of its plural, or of its singular, in that sense\nin which it implies a plural, while the connotation is the meaning _per\nse_, not considered in its instances.\n\nIt is clear then that every name has these two kinds of meaning--first,\na content, and then instances, whether possible or actual, of the\ncontent; and the two are obviously inseparable, although they are\ndistinguishable. Ultimately, indeed, the denotation itself is an\nattribute, and so part of the connotation. It is one of the attributes\nof man to be a unit in the plurality men, _i.e._ to be \u201ca man.\u201d It\nmay be said that some names have no plural. If so, these would be\nnon-denotative rather than non-connotative, but in fact this is not\ntrue. The content of a significant name can always, unless hindered\nby a special convention (see below on proper names), be _prima facie_\nregarded, in respect of its actual embodiment, as a unit against\nother possible units. Granting that there may be an object, which\naccording to our knowledge can only be real as an isolated case, the\nvery consideration of it as such a case is enough to distinguish its\nexistence, whether real or possible, from its content. Thus, as a real\nor possible existence, the object is _ipso facto_ considered in the\nlight of a particular, and as capable of entering into a plurality.\nBut its nature or content, the meaning of its name, cannot enter\ninto a plurality. Two _meanings_, two connotations, are alternative\nand irreconcilable. Denotation and connotation are thus simply the\nparticular, or particulars, which embody or are thought of as embodying\na content, and the single or universal content itself.\n\n{91} _Have Proper Names Connotation?_\n\n6. Therefore I think that Mill is wrong, when he goes on, \u201cThe only\nnames of objects which connote nothing are Proper Names, and these\nhave, strictly speaking, no signification.\u201d [1] If the name has no\nsignification, for what reason, or by what means, is it attached to a\nperson or a place? You may say that it is only a conventional mark. But\na mark which has power to select from all objects in the world, and\nbring to our minds, a particular absent object, is surely a significant\nmark. Granted that it is conventional, yet by what mechanism, and for\nwhat purpose, does the convention operate?\n\n[1] Cf. Venn, 183 ff, and Bradley, 156.\n\nMill\u2019s point, however, is quite clear. To be told the name of a person\nor object does not inform us of his or its attributes. Directly,\nit only warns us by what sign the same person or object will be\nrecognisable in language again. [1] If a name is changed, the new name\ntells us nothing different from the old, [2] whereas if an object that\nwas called vegetable is now called animal, our conception of it is\nradically transformed. A name expresses the continued identity of an\nobject, and this implies only a historical continuity of attributes and\nrelations, and no constant attribute whatever.\n\n[1] We cannot make it a distinctive mark of proper names that\nthey recur in different and quite disconnected meanings, because\nthe words which are used as general names have this same\nproperty. Nor can we say that a proper name is not used in the\nsame sense of more than one object. Family names and national\nnames make this plainly untrue. Through these, and names\ntypically employed, there is a clear gradation from proper to\ngeneral names.\n\n[2] The case of marriage may be urged. But a lady\u2019s change of\nname does not by itself indicate marriage. It is a mere fact,\nwhich may have various explanations. The change of title (from\n\u201cMiss\u201d to \u201cMrs.\u201d) is more significant, but it is not a change of\nname.\n\n{92} Thus a _proper_ name is a contradiction in terms. [1] A name\nshould have a meaning. But a meaning cannot be proper--that is,\nparticular. The name-word is therefore like a demonstrative pronoun,\nif this were attached, by a special convention, to one identifiable\nobject only. It acquires meaning, but its meaning is an ever-growing\ncontradiction with its usage. The meaning is necessarily general, the\nusage is _ex hypothesi_ particular.\n\n[1] So, from the complementary point of view, is a _general_\nname. A name, it may be urged, _is_ meant to designate a\nparticular thing or things. And this a name with a true\n\u201cmeaning\u201d cannot do.\n\nThis convention of usage, which prevents a proper name from becoming\ngeneral, _i.e._ from being cut loose and used simply for its meaning,\nis always on the point of breaking down. [1] Christian names usually\nindicate sex; family names, though now with little certainty, descent\nand relationship. There are germs of a general meaning within the\nseveral usages of names; while a Solon, a Croesus, a Christian, a\nMahometan, have become purely general names cut loose from all unique\nreference. Still in a proper name, as such, we have no right to build\non any general meaning. Recognition is its only purpose; and the law\npermits, it has been said, that a man should have one name for Mondays,\nWednesdays, and Fridays, and another for Tuesdays, Thursdays, and\nSaturdays. The essence of a name is a reference to unique identity; it\nemploys meaning only to establish identity.\n\n[1] See note on last page.\n\nWhat kinds of things have proper names given, then? Always things\n_individually_ known to the people who give {93} the name, and\ninteresting to them for some reason beyond generic or specific\nqualities. Pet animals have names, when other animals of the same kind\nhave not. The peasants throughout England use names, it is said, for\nall the fields, although strangers are not usually acquainted with them.\n\nA Proper Name, then, has a connotation, but not a fixed general\nconnotation. It is attached to a unique individual, and connotes\nwhatever may be involved in his identity, or is instrumental in\nbringing it before the mind.\n\nWhen we think of history, the importance of proper names becomes\nvery great. This is the characteristic logical difference between\nhistory and science. \u201cEngland\u201d and \u201cFrance\u201d are proper names, names\nof individual existences in contact with our world of perception, not\nscientific abstractions. Even the words, \u201c1892 A.D.,\u201d are partly of the\nnature of a proper name. They say nothing merely general or abstract\nabout this year; they assign the year a name by counting forwards from\na unique point in the series of years, itself designated by the name\nof a historical personage. Everything that is simply distinguished by\nits place in the series of events in space and time is in some degree a\nproper name. Thus we could not identify the French Revolution by mere\nscientific definition. It is known by its proper name, as a unique\nevent, in a particular place and time. When thus identified it may have\nall kinds of general ideas attached to it. It would be hard to show\nthat \u201cOur earth,\u201d \u201cOur solar system\u201d are not proper names, in virtue of\ntheir uniqueness.\n\n{94} _Inverse ratio of Connotation and Denotation_\n\n7. It has sometimes been said that Connotation is in inverse ratio [1]\nto Denotation. Mill explains the fact upon which any such idea\nrests. [2] If we arrange things in classes, such that the one class\nincludes the other--_e.g. Species_ \u201cButtercup,\u201d _Genus_ \u201cRanunculus,\u201d\n_Order_ \u201cRanunculaceae,\u201d--of course the genus will contain many species\nbesides the one mentioned, and the order many genera besides the one\nmentioned. The object of the arrangement is that they should do so, and\nthus bring out the graduated natural affinities which prevail in the\nworld. Thus the denotation of the genus-name is larger than that [3] of\nthe species, and the denotation of the order-name is larger than that\nof the genus-name.\n\n[1] See Venn, p. 174, for reference to Hamilton. Venn points out\nthe fallacy.\n\n[2] _Logic_, Bk. I. ch. vii. \u00a7 5.\n\n[3] Or \u201cthan the species,\u201d if we take the denotation as made up\nof species.\n\nBut further, in such an arrangement the genus can contain only the\nattributes which are common to all the species, and the order can\ncontain only the attributes which are common to all the genera; so the\ngenus-name implies fewer attributes (less connotation) than any one\nspecies-name under it, and the order-name implies fewer attributes\n(less connotation) than any one genus-name under it.\n\nThat is the fact which suggests the conception of Denotation and\nConnotation as varying inversely.\n\nBut in any case it would not be right to speak thus mathematically of\nan inverse ratio, because there is no meaning in a numerical comparison\nof attributes and {95} individuals, and the addition of one attribute\nwill exclude sometimes more and sometimes fewer individuals. [1]\n\n[1] See Jevons, p. 40.\n\nAnd there are more important objections to the whole idea of a\ncorresponding gradation in these two kinds of meaning. The idea\nof abstraction thus implied is altogether wrong. The meaning of a\ngenus-name does not _omit_ the properties in which the species differ.\nIf it did, it would omit nearly all properties. What happens is that\nthe genus-idea represents the general plan on which the species are\nbuilt, but provides for each of the parts that constitute the whole,\nvarying in the specific cases within certain limits. Thus in the\nRanunculaceae some species have no petals. But we do not omit the\ncharacter \u201cpetals\u201d from the genus-idea. We state the general plan\nso far as this element is concerned as \u201cPetals five or more; rarely\nnone.\u201d This is read by a botanist to mean that in some groups the\npetals tend to be aborted, and sometimes are actually missing. In a\nsymbolic representation of the genus-idea such a property may stand as\nA, and its various specific forms as A1, A2, A3, etc. There is nothing\nto prevent these specific phases approaching and sometimes reaching\nzero. No doubt if the classification is pursued in the direction of\n\u201cuniversals\u201d containing fewer and fewer properties, it is possible\nto arrive at concepts which appear to have a larger denotation and\na smaller connotation than those \u201cbelow\u201d them. \u201cRanunculaceae,\u201d\n\u201cDicotyledons,\u201d \u201cPlants,\u201d \u201cOrganisms.\u201d\n\nBut this is only because we choose to form our system by that\nprocess of abstraction which consists in leaving out properties.\n_E.g._ comparing Frenchmen with men in general, {96} we assume that\n\u201cFrenchman\u201d indicates (_a_) all the qualities of humanity as such,\nand (_b_) the qualities of French humanity in addition to these. But\nis this so in fact? Humanity, considered as a wider, and therefore\nas a deeper, idea, may have more content, as well as more area, than\nFrenchmanity. We do not really, in thinking of humanity, omit from our\nschematic thought all references to qualities of Greek, Jew, English,\nand German, and their bearing and interaction upon one another. It is\nonly that we have been drilled to assume a certain neatness in the\npyramidal arrangement by which we vainly try to reduce the meaning of\na great idea to something that has no system and no inter-relation of\nparts, but approaches as near as possible in fixity to the character\nof a definite image, though far removed from such a character in the\nimpossibility of bringing it before the mind.\n\nSo we can only say, \u201cthe greater the denotation the less the\nconnotation,\u201d and \u201c_vice vers\u00e2_\u201d, in as far as we arrange ideas by\nprogressive abstraction in the sense of progressive omission. But\nit is not the only way of regarding them. Things may develop new\ninter-relations as their number increases. Has the community, as Mr.\nBradley asks, less meaning than the individual person? But we must not\nconsider the community, would be the answer; we must simply consider\nthe relation of an idea of one individual to any idea that applies\nto many individuals. This is simply to rule out those relations that\narise within progressively larger wholes. We can do so, if we think the\nexclusion necessary in the interests of logical purity, but it is only\nby doing so that we can maintain the traditional view of connotation\nand denotation. It is worth while to think out the {97} matter for\nourselves in relation to such familiar ideas as those of man and\nanimal. It is plain that the idea of \u201canimal\u201d cannot omit all reference\nto intelligence, but must in some way allow for the different phases\nof this property which run throughout the animal kingdom, and only\nfind a climax in man. And it is plain also, that even if intelligence\nwere wholly omitted, this would not leave behind, as in a simple\nstratification, properties in which the whole animal kingdom was the\nsame. Man\u2019s animality is modified throughout in a way corresponding\nto his rationality, so that no general idea could be framed including\nhim and other animals, simply by collecting properties which are\nthe same and omitting those which are different. The idea of \u201cman\u201d\nreally becomes richer when considered in the light of a comparison\n[1] with the rest of the animal world. Our great systems of natural\nclassification, representing affinities graduated by descent, are what\ngive the view which we have criticised a certain objective importance.\nBut they do not establish it as an exclusive logical doctrine.\n\n[1] If we insist on throwing the whole of this comparison, in\nexplicit shape, into the complete idea of man, then the progress\nto the idea \u201canimal\u201d can add nothing; even so, however, it loses\nnothing, but simply becomes the same set of relations, looked\nat, so to speak, from the other end.\n\n\n\n\n{98}\n\nLECTURE VI   PARTS OF THE JUDGMENT, AND ITS UNITY\n\n_Parts of the Judgment_\n\n1. The result of taking the Judgment as one with the Proposition\nhas been to assume that its parts were the same as those of the\nProposition; [1] and moreover the same as those of the Proposition in a\nvery artificial form, viz. as analysed into three separable elements,\n\u201cSubject,\u201d \u201cPredicate,\u201d \u201cCopula,\u201d commonly represented in the examples\nof the text-books by Substantive, Adjective or Substantive, and the\nVerb \u201cis.\u201d\n\n[1] This assumption involves (see Lecture V.) a confusion\nbetween the Proposition as thoroughly understood, and the\nProposition as a series of partially significant sounds or\nsigns. For obvious reasons, this confusion is very readily made.\n\nFor the operation of Formal Logic it is almost necessary to have\nthese parts, because it is requisite to transpose the terms (as in\nConversion) without changing their meaning, [1] and to get rid of\n_tenses_, which do not belong to Scientific Judgment, and are very\ntroublesome in Formal Inference.\n\n[1] If the \u201cpredicate\u201d is a Substantive, this presents no\ndifficulty; and if it is an Adjective, it can be done by a\nlittle straining of grammar, or the insertion of \u201cthing\u201d or\n\u201cthings.\u201d With a verb it is more clumsy.\n\nThus in Formal Logic we prefer the shape of sentence \u201cGold is lustrous\u201d\nto \u201cGold glitters,\u201d and \u201cThe bridge is {99} cracked\u201d to \u201cThere is\na crack in the bridge.\u201d And practically all propositions can be\nthrown into this shape, which is convenient for comparing them. The\neducational value of elementary formal logic consists chiefly, I am\nconvinced, in the exercise of paraphrasing poetical or rhetorical\nassertions into this typical shape, with the least possible sacrifice\nof meaning. The commonest mistakes in the work of beginners, within my\nexperience as a teacher, consist in failures to interpret rightly the\nsentence given for analysis.\n\nBut this type is not really ultimate. The judgment can be conveyed\nwithout a grammatical subject, and without the verb \u201cis\u201d--indeed\nwithout any grammatical verb at all. On the whole this agrees with\nMill\u2019s view in the chapter \u201cOf Propositions.\u201d [1] He points out (\u00a7 1)\nthat we really need nothing but the Subject and Predicate, and that the\ncopula is a mere sign of their connection _as_ Subject and Predicate.\nHe does not, however, discuss the case in which the grammatical Subject\nis absent.\n\n[1] Mill\u2019s _Logic_, Bk. I. ch. iv.\n\n_Copula_\n\n2. In analysing the Judgment as an act of thought we may begin by\ndismissing the separate Copula. It has no separate existence in thought\ncorresponding to its separate place in the typical proposition of\nFormal Logic. It has come to be considered separately, because the\nabstract verb \u201cis\u201d is used in our languages as a sign of the complete\nenunciation. But there is not in the Judgment any separate significant\nidea--any third idea--coming in between the Subject and Predicate of\nJudgment. We should try to think of the Copula not as a link, separable\nand always {100} intrinsically the same, [1] connecting two distinct\nthings. We should think of it rather as the grip with which the parts\nof a single complex whole cohere with one another, differing according\nto the nature of the whole and the inter-dependence of its parts. Benno\nErdmann [2] has strikingly expressed this point of view by saying,\nthat in the Judgment, \u201cThe dead ride fast,\u201d the Subject is \u201cthe dead,\u201d\nthe Predicate \u201cfast riding,\u201d _and the Copula \u201cthe fast riding of the\ndead_.\u201d In other words, the Copula is simply the Judgment considered\nexclusively as a cohesion between parts of a complex idea, the\nindividual connection between which can only be indicated by supplying\nthe idea of those parts themselves.\n\n[1] In a comic Logic, with pictures, meant to stimulate dull\nminds at a University, I have seen the Copula represented as\nthe coupling-link between two railway carriages. This is an\nexcellent type of the way in which we should _not_ think of it.\n\n[2] _Logik_, p. 189.\n\n_Are Subject and Predicate necessary?_\n\n3. The explicit Predicate is more necessary than the explicit Subject.\n\nWe have spoken of Judgments expressed by one word, \u201cFire!\u201d \u201cThieves!\u201d\netc., and also of impersonal Propositions, \u201cIt is raining,\u201d \u201cIt\nis thawing.\u201d These two classes of Judgments show hardly any\nexplicit Subject at all. But we could not assert anything without\na Predicate--that would be to assert without asserting anything in\nparticular.\n\nAs these Judgments have, roughly speaking, a Predicate and no\nSubject, I do not think it convenient to call them, with Dr. Venn,\nexistential judgments. It is true that they refer to reality, but their\n_peculiarity_ is in not referring to a distinct subject. And when used\nfor definite and complex assertions they become very artificial, _e.g._\n\u201cThere is a {101} British Constitution by which our liberties are\nguaranteed.\u201d Instead of organising the content of the Judgment, such a\nform of assertion simply tosses the whole of it into the Predicate in a\nsingle mass.\n\nThe question is only one of words; but it appears to me more convenient\nto reserve the term Existential judgments for those highly artificial\nassertions which actually employ the Predicate \u201cexist\u201d or \u201cexistence,\u201d\n_e.g._ \u201cMatter exists.\u201d These are at the opposite end of the scale\nfrom those last-mentioned, and are the nearest approach to Judgment\nwith Subject and no Predicate. That is to say, their Predicate is\nthe generalised abstract form of predication [1] without any special\ncontent--the kind and degree of existence asserted being understood\nfrom the context.\n\n[1] Expressed in Greek by the word corresponding to \u201cis,\u201d used\nwith an accent, which does not belong to it in its ordinary use.\nHe is good = \u1f04\u03b3\u03b1\u03b8\u03cc\u03c2 \u1f10\u03c3\u03c4\u03b9 [= agathos esti]; He exists = \u1f14\u03c3\u03c4\u03b9 [=\nesti Tr.].\n\nExcept, however, in the case of these peculiarly abstract and\nreflective assertions, it must be laid down that a predicated content\nis necessary to judgment, while an _explicit_ subject of predication is\nunnecessary.\n\n_Two Ideas of Things_\n\n4. If it is possible, in some cases, to throw the whole content of\njudgment into the predicate, this rather disposes us to criticise the\nnotion that there must be two distinct matters, objects, ideas, or\ncontents, in every judgment. The notion in question has two forms.\n\nIt is thought that the Judgment consists in putting two _ideas_\ntogether, [1] or,\n{102} That the Judgment consists in comparing two or\nmore things. [2]\n\n[1] For this conception, see Hamilton\u2019s _Lectures on Logic_, i.\n227, and for a criticism on it. Mill\u2019s _Logic_, Bk. I. ch. v.,\n_init_, Dr. Venn seems to incline to Hamilton\u2019s view, but I do\nnot feel sure that he intends to discuss the question in the\nform in which it is referred to in the text. See his _Empirical\nLogic_, pp. 210 and 211.\n\n[2] See Jevons, pp. 61-2; and Mill, Bk. I. ch. iii., _init_.;\nand ch. iv., _init_.\n\n_Two Ideas_\n\n(_a_) The notion of \u201ctwo ideas\u201d has two principal difficulties.\n\n_Notion of mental transition pure and simple_\n\n(i.) In its simplest shape the notion of \u201ctwo ideas\u201d involves the\ngreat blunder which I explained in Lecture IV. It suggests that the\nparts of Judgment are separate and successive psychical states, and\nthat the Judgment consists in a change from the one to the other.\nHerbert Spencer, as I understand him, considers every relation to be\napprehended as a mental change or passage from one idea to another.\nThis view would degrade logical connection into mere psychical\ntransition. I do not say that there is no psychical transition in\nJudgment. I do say that psychical transition is not enough to make a\nJudgment. The parts of Judgment, as we saw in the last lecture, do\nnot succeed one another separately like the parts of a sentence. The\nrelation between Subject and Predicate is not a relation between mental\nstates, but is itself the content of a single though continuous mental\nstate. Mill has rightly touched on this point. \u201cWhen I say that fire\ncauses heat, do I mean that my idea of fire causes my idea of heat?\u201d\n[1] and so on. The fact is that \u201cFire-causing-heat\u201d is itself the\nsingle content or meaning represented in my symbolic idea; it is not a\nsuccession of psychical states in my mind, or a passage from the idea\nof fire to the idea of causing heat.\n\n[1] _Logic_, Bk. I. ch. V. \u00a7 I.\n\n{103} _Absence of assertion_\n\n(ii.) But further, understanding now that the Judgment is composed of\na single ideal content, and is not a transition from one mental state\nto another, there is still a difficulty in the conception that its\ncomponent elements are nothing but ideas. If the Subject in Judgment is\nno more than an ideal content, how, by what means, does the Judgment\nclaim to be true of Reality? \u201cThe Subject cannot belong to the content\nor fall within it, for in that case it would be the idea attributed to\nitself.\u201d [1] If the Subject were only a part of an ideal content it\nwould not claim to be true of Reality, and where it _appears_ to be\nonly an ideal content there is much dispute in what sense the Judgment\ndoes claim to be true of Reality. \u201cViolations of a law of nature are\nimpossible.\u201d \u201cThe three angles of a triangle are equal to two right\nangles.\u201d \u201cAll trespassers will be prosecuted.\u201d In these Judgments we\nshould find it hard to make out that the Subjects are real things\ncorresponding to our ideas. And yet, if they are not, how can the\nJudgment attach itself to Reality? This is the difficult question of\nthe distinction between the categorical and the hypothetical Judgment,\nand we shall have to return to it. In the meantime, we must adhere to\nour judgment of perception as the true underlying type. The Subject\nis here not an idea, but is the given reality, _this_ or _that_, and\nthe Judgment is not a conjunction of two ideas, but is present reality\nqualified by an idea. We say, \u201cIt is very hot,\u201d meaning that heat, the\ngeneral quality embodied for us in an ideal content, is true of--forms\none tissue with--the surroundings which here and now press upon our\nattention. Or again, \u201cThis is red,\u201d {104} _i.e._ the content of the\nidea red is what my attention selects and emphasises within the mass\nof detail presented to it in its own unique focus which the pronoun\n\u201cthis\u201d simply points out as though with the finger. We shall find such\na structure underlying all the more artificial forms of Judgment.\n\n[1] _Bradley\u2019s Principles of Logic_, p. 14.\n\n_Two Things_\n\n(_b_) Thus it would seem that Jevons and Mill are much nearer the real\npoint when they say that the proposition has to do with two Things,\nor with a Thing and a group of Things. But we must notice in passing\nthat Mill, [1] after fighting hard against calling them Ideas, takes\nour breath away by saying that they are states of consciousness. There\nis, of course, a difficulty, which I will not try to deal with now, in\nthe fact that however much we _refer_ to things, we have nothing to\n_work with intellectually_ but our ideas of them, and in some types\nof Judgment the reference to real things is difficult to trace. Mill\nfurther emphasises this by showing, that what we assert in ordinary\n_general_ Judgment is co-existence of attributes. [2] \u201cNow when we\nsay, Man is mortal, we mean that wherever these various mental and\nphysical phenomena (the attributes of man) are all found, then we have\nassurance that the other physical and mental phenomenon called death,\nwill not fail to take place.\u201d That is, no doubt, a very indirect way of\nreferring to the real things which we call men. Moreover, he treats all\nconclusions in geometry and mechanics as hypothetical. [3] All this we\nshall have to return to, in order to reconcile it with our doctrine;\nwhich is apparently coincident with {105} Mill\u2019s view in the place\nfirst alluded to, that the subject in Judgment is always reality.\n\n[1] _Logic_, Bk. I. ch. V. \u00a7 5.    [2] _Ibid_., \u00a7 4.\n\n[3] _Ibid_., Bk. II. ch. vi. \u00a7\u00a7 3, 4.\n\nBut our point at present is only the duality ascribed to the Judgment\nby saying that it essentially deals with _two_ things or groups of\nthings. Jevons even says [1] that every Judgment is a comparison of\ntwo things--though these \u201cthings\u201d are really, it would seem, groups\nof things. [2] We thus have it impressed upon our minds that there\nis one \u201cthing\u201d corresponding to the Subject-word (or clause) of the\nPropositional sentence, and another \u201cthing\u201d corresponding to the\nPredicate-word (or clause), and that these are somehow separate, like\ntwo railway carriages, till we bring them together by the coupling-link\nof the copula. This is a very inconvenient way of looking at the\nmatter. It is not true that all Judgment is comparison, in the proper\nand usual sense of the word. It is not true that Judgment involves two\nthings; two or more things may be mentioned in a Judgment, but they\ncannot correspond respectively to the Subject and Predicate. It is a\nreal Comparison if you say, \u201cA.B. is taller than C.D.,\u201d but C.D. is\nhere not a term in the Judgment. The one person, A.B., is qualified by\nthe ideal content \u201ctaller than C.D.,\u201d and the idea of A.B. so qualified\nis referred to, or discriminated within, perceptive reality. Comparison\nis a rather complex process, and consists in a cross-reference by which\neach of two objects is judged according to a standard furnished by the\nother; but this complex process is not necessary to all Judgment, and\ncannot be expressed with complete convenience in a single Judgment. And\nin {106} any case the two objects that enter into the comparison do not\ncorrespond to two essential parts of Judgment.\n\n[1] _Elementary Lessons in Logic_, p. 61.   [2] _Ibid_. p. 62.\n\nIt is far more simple and true to say that Judgment is always the\nanalysis _and_ synthesis of elements in some one thing or ideal\ncontent. \u201cGold is yellow\u201d has not within it, as Jevons says it has, [1]\nany direct comparison of gold with other yellow substances. It simply\ndrags to light the property \u201cyellow\u201d as distinct within the complex of\nattributes belonging to gold, while at the same time insisting that\nthis property--this meaning of an idea--belongs to, is of one piece\nwith, perceived reality in so far as gold is given in such reality.\nThe Judgment exhibits the content in its parts. It breaks it up, and\npronounces it to be all of one tissue, by one and the same indivisible\nact. We should practically have a much fairer chance of seeing clearly\nwhat Judgment is if we began by considering it as not two things or\ntwo terms \u2014 but as one thing or one term drawn out into elements by\ndiscriminating selection. Even if the paradox that every \u201cThing\u201d is\na Judgment neglects some necessary distinctions, I am convinced that\nwe shall understand Judgment much more clearly if we do our best to\napproach it from this point of view. Whenever we look or listen, and\n_notice_ features and qualities in the perceptions that arrest the\neye and ear, we are rapidly and continuously judging. \u201cThe fire is\ncrackling,\u201d \u201cThe daylight is waning,\u201d \u201cThat bookshelf is not full,\u201d\n\u201cThe window-curtain is twisted.\u201d In none of these cases is there\nany separation other than an intellectual distinction between the\npredicated content and the perceived reality. The Judgment is simply\na distinct {107} insistence on a quality within a certain focus of\nreality as belonging to that reality. This is the fundamental nature of\nJudgment.\n\n[1] _Loc. cit_.\n\nTherefore, to draw our conclusion as to the Unity of the Judgment, it\nis not a transition from one mental state to another; the relation of\nwhich it consists is not between ideas in it, but is the content of the\nidea which forms it. Judgment is not primarily comparison between two\nthings; it is a thing or content displayed as possessing some definite\nrelation or quality within its identity. Every Judgment is the content\nof one idea, but you may of course distinguish relations between ideal\nelements within this idea. \u201cFire causes heat\u201d is a single content or\nidea, the nature of fire, expanded into one of its properties.\n\n_Distinction between Subject and Predicate_\n\n5. But then, if the whole Judgment is a single content, what is the\ndifference between Subject and Predicate, and is it necessary to\ndistinguish Subject from Predicate at all? If _some_ Judgments can be\nmade without explicit Subjects, cannot _all_ be made in that way?\n\nThis suggestion is very useful as carrying on the simplest type of\nJudgment throughout the whole theory of Judgment. By a little torture\nof expression any Judgment can be thrown into a form in which undefined\nReality is the general subject, and the whole mass of the Judgment\nis the Predicate. \u201cWilliam Pitt was a great statesman\u201d = \u201cThere was\na great statesman named William Pitt\u201d; \u201cThe three angles of every\ntriangle are equal to two right angles\u201d = \u201cThere are figures known as\ntriangles with their three angles equal to two right angles\u201d; \u201cAll\ncitizens are members of a moral order\u201d = \u201cThere is a moral order,\nincluding the {108} relations of citizenship\u201d; \u201cAll trespassers will\nbe prosecuted\u201d = \u201cHere are conditions which ensure the prosecution of\npossible trespassers.\u201d Or you might always put a subject, \u201cReality is\nsuch that\u201d--\u201cReality is characterised by.\u201d\n\nThus we see that, as we have said before, in every Judgment the\nultimate subject is Reality, the world in contact with us as we have\nalready qualified it by previous Judgment. It is a less mistake to\nreject the Subject and Predicate in the Judgment altogether, than to\nthink that they are separate things or ideas, and that in judging you\npass or change from one to the other. Always bear in mind that it is\npossible to mass the whole Judgment as a single Predicate directly or\nindirectly true of Reality.\n\nHaving said this much, to make the Unity of the Judgment unmistakable,\nwe may now safely distinguish between the Subject and Predicate\nin the Judgment. And we shall find the safest clue to be that the\nexplicit Subject, when there is one, marks the place at which, or the\nconditions under which, Reality accepts the Predicate. The natural\nSubject is concrete, and the Predicate abstract; the Subject real, and\nthe Predicate ideal, but pronounced to be real. The reason of this is\nthat every Judgment is the connection of parts in a whole, and to be\na whole is the characteristic of reality. In other words, the natural\ncourse of thought is to define further what is already in great part\ndefined, and our real world is that which we have so far defined. The\nisolated judgments of the text-books make it very hard to grasp this,\nbecause you seem to begin anywhere for no connected reason at all. But\nif we reflect on actual thought, {109} we find that, as Mr. Stout very\ncleverly says, we are always developing a \u201csubject\u201d which is in our\nminds (in the ordinary sense of a \u201csubject of conversation\u201d), and this\nsubject is some region or province of the world of reality.\n\nNow the explicit Subject in Judgment or the grammatical Subject in\nProposition does not always set out the full nature of this, but\nmerely some mark or point in it which we wish to insist upon. So\nthat we may find in Judgment almost anything serving as explicit\nSubject. Thus, as Aristotle said quite plainly and sensibly, it is\nnatural to say \u201cThe horse is white,\u201d but we _may_ have occasion to say\n\u201cThis white is a horse\u201d; it depends on the way in which the Subject\ncomes into our minds. [1] Usually the Subject will be what Dr. Venn\ncalls the heavier term, _i.e._ the term with more connotation. When\nthere is no difference of concreteness between parts and whole, the\nJudgment becomes reversible as in the equation 7 + 5 = 12. There is no\ndistinction here between Subject and Predicate. The real underlying\nunity or Subject is the numerical system.\n\n[1] See Prof. Bain, p. 56, upon the Universe, and Universe of\nDiscourse, _i.e._ the general subject which you have in your\nmind.\n\nTherefore by recognising Subject and Predicate we represent the\norganisation of knowledge, and the connection of inherence or\nconsequence within the content of our knowledge. If we do not\nrecognise this distinction we throw the whole of Judgment into an\nundifferentiated mass of fact, running all assertion into the same\nmould, \u201cIt is the case that,\u201d etc. One difficulty still remains. If\nthe relation between Subject and Predicate is within an idea, and\nnot between ideas--that is, if the whole explicit content, Subject\nand {110} Predicate together, can be regarded as predicated of\nreality,--why is the act of predication expressed by a verb, _i.e._\na sign of activity within this content? Why is a verb often if not\nalways the form of predication which connotes Subject and Predicate?\nNot because it is a time-word. On the contrary, we want to get rid\nof the tense in Logic. The time of a Judgment ought to be determined\nonly by the special connection between Subject and Predicate, not by\ntense, because tense is always subjective, merely relative to the time\nof speaking, and is accidental to the content of Judgment. Action\nseems nearer to what we want; the _verb_ expresses both action and\npredicate. But the _idea_ of action again does not make a predication,\nand the verb \u201cis\u201d does not _really indicate_ action. Perhaps it is the\ndemonstrative element in a finite verb that makes it the vehicle of\npredication, _i.e._ in a finite verb you have a meaning referred by a\ndemonstrative element to something else. Originally the meaning was\nalways an action; \u201cis\u201d of course meant \u201cbreathes.\u201d But now the verb has\nlost vitality by wear and tear, and only refers something to something\nelse. The puzzle is that the Judgment is not referred to us who make\nit, but is expressed as if it was accomplished by something outside us.\nThat puzzle points to the essential feature which we insisted on, viz.\nits objectivity; in predication we refer what is mentally our act to a\nsubject that represents the real world, not to ourselves at all. When\nI say \u201cGladstone comes to London this week,\u201d the verb which expresses\nGladstone\u2019s action also expresses that my real world in his person\naccepts the qualification \u201ccoming to London this week.\u201d Because of this\nobjectivity of thought, I attribute to {111} the real world and not to\nmyself the connection which is presented to my mind, and so it takes\nits place as an act of the real world. But I might throw the whole\ncontent into the Predicate by saying, \u201cThe ideal content \u2018Gladstone\ncoming to London this week\u2019 is a predication true of Reality.\u201d Thus\nthough the distinction between Subject and Predicate best exhibits the\nliving structure of knowledge, we must beware of the notion that two\nideas or two things are needed for Judgment.\n\n\n\n\n{112}\n\nLECTURE VII   THE CATEGORICAL AND HYPOTHETICAL CHARACTERS IN\n              JUDGMENT\n\n_Some criticism on the ordinary scheme_ [1]\n\n1. We will first consider why we want to examine the types of Judgment,\nand then what arrangement of them best fulfils our want.\n\n[1] Read Mill, ch. iv. (Bk. I.), on Propositions; Venn,\n_Empirical Logic_, ch. ix., x. Cf. _Knowledge and Reality_ pp.\n57-8; and Venn, p. 264. Ordinary statement, Jevons, p. 60, ff.;\ncf. p. 163.\n\n_Why we need an arrangement_\n\n(_a_) If we attended purely to the propositions in common use, we\nshould get an unmanageable variety of forms, though the reality of\nthought would be fairly represented. We cannot quite do this; we must\ntry to select the forms which for some reason are the most fundamental\nand constant.\n\nOn the other hand, it is possible to think simply of what is convenient\nin logical combination; and then for working with syllogistic Logic we\nget the well-known scheme of four propositions, each with Subject and\nPredicate; and for working with symbolic Logic we get the existential\nscheme in which Subject and Predicate disappear, and \u201cAll S. are P.\u201d\nturns into \u201cThere exists no S. which is not P.\u201d; or we get Jevons\u2019\nEquational Logic, in which \u201cAll A is B\u201d stands as A = AB. Now every\nJudgment has a great many aspects, {113} being really a very complex\nsystematic act of mind, and a logical method can be founded on any of\nthese aspects which is sufficiently constant to stand for the Judgment.\nYou can take \u201cAll men are mortal\u201d to mean \u201cThere are no not-mortal\nmen,\u201d or \u201cMen = some mortals,\u201d or two or three more meanings. The two\nformer are artificial or formal corollaries from the natural Judgment,\nrepresenting it for some purposes but omitting a great part of its\nnatural meaning. They tell you nothing about a relation of causality\nbetween the content of man and the property mortal, and they destroy\nall implication of existence in the Subject man.\n\nWhat we want is neither to follow _mere_ everyday language, nor be\nguided by mere convenience of logical combination. We want to look at\nthe Judgment on its merits with reference to its power of expressing\nthe principal kinds of our experience, which in fact are constructed in\nthe medium of Judgment. The great kingdoms of intellectual experience\nare Perception, History, and Science, and of these three, Science,\nincluding Philosophy, is the form towards which all knowledge presses\non, and its judgment must therefore be considered as the most complete\ntype.\n\n_The common scheme_\n\n(_b_) With this purpose in mind, let us look at the traditional scheme,\nomitting the negative Judgments of which we have not yet spoken. We may\ndismiss the Indefinite Judgment \u201cMen are mortal\u201d as imperfect by not\nbeing \u201cquantified,\u201d and we have left, as Categorical Judgments, the\nParticular Affirmative \u201cSome men are mortal,\u201d the Universal Affirmative\n\u201cAll men are mortal,\u201d and the Singular Affirmative \u201cSocrates is\nmortal.\u201d The Singular Affirmative, however, is not treated of any\nfurther under the old scheme, {114} because in it the Subject is taken\nin its full extent, and therefore the Singular Affirmative Judgment is\nranked with the Universal Affirmative. So as Categorical Judgments we\nhave left the Particular Affirmative and the Universal Affirmative.\n\nOutside the account of the Categorical Judgment we find the\nHypothetical and Disjunctive Judgments touched on as a sort of\nAppendix, standing as \u201cConditional.\u201d The historical reason of this\nis, that they were not recognised by Aristotle, and have never been\nincorporated in the diagram of judgments employed in traditional Logic.\nThen on the ordinary scheme we have--\n\n         Categorical.                 Conditional.\n\nParticular     Universal       Hypothetical Disjunctive\nJudgments.     Judgments,             Judgments.\n               including\n               Singular\n               Judgments.\n\nThe defects of this scheme from our point of view are\u2014\n\n(i.) Our Impersonal and Demonstrative Judgments are omitted. They\n_might_ be classed under the particular, which also has an undefined\nelement in the subject.\n\n(ii.) The Singular Judgment (of which the chief instance is the\njudgment with proper name) is rightly classed as Universal, but yet is\nwrongly absorbed in the abstract universal, from which it ought to be\ndistinguished.\n\n(iii.) In the treatment of the Universal Judgment there are two\ndefects\u2014\n\n  (1) The Collective Judgment, resulting from enumeration, {115} direct\nor indirect, is not distinguished from the Generic Judgment, resting\non a connection of content or presumption of causality. \u201cAll the [1]\npapers have been looked over\u201d should be distinguished from \u201cAll\ntriangles have their three angles equal to two right angles.\u201d\n\n[1] \u201cThe\u201d as here used indeed practically = \u201cthese,\u201d so\nthat, by our analysis, such a judgment has no claim to rank\nas a universal judgment It is difficult to find a plainly\ncollective judgment which has not some affinity to judgment with\ndemonstrative pronoun or proper name. A judgment in which \u201cAll\nM.P.\u2019s\u201d stands as subject, has affinity with the latter.\n\n  (2) The nature of the Universal Judgment is not examined with a view\nto the distinction between Categorical and Hypothetical. The common\nLogic does not go behind the grammatical form, which on this point is\nnot decisive.\n\n(iv.) The Hypothetical Judgment [1] is said to consist of two\ncategorical propositions, or to be \u201c_complex_\u201d But of course it is a\nsimple judgment, _prima facie_ expressing a relation of reason and\nconsequent. Its parts are not Judgments, for they are not such as to\nstand alone.\n\n[1] Bain, p. 85; Jevons, p. 160.\n\n(v.) The Disjunctive Judgment is often (_e.g._ by Mill and Bain) said\nto be equivalent to two Hypothetical Judgments. The strange thing\nis that both of these writers take the wrong two. [1] If we allow\nconversion of a Hypothetical Judgment two are enough, but of course\nthey must be the two which cannot be got from each other by conversion,\nviz. the two beginning, \u201cIf A is B ...\u201d and \u201cIf A is not B ...\u201d\nrespectively. If we do not admit conversion we must have all four.\nLet the disjunction be, \u201cThis signal light is either red or green.\u201d\nIn order to know this we must know not {116} only that, \u201cIf it is\nred it is not green\u201d (with its equivalent, \u201cIf it is green it is not\nred\u201d), but that, \u201cIf it is not red it is green\u201d (with its equivalent,\n\u201cIf it is not green it is red\u201d). The former by itself leaves open the\npossibility that it may be not red or green, but blue or yellow; the\nlatter by itself the possibility that when it is red it may also at\nthe same time be green. The former secures that the two terms exclude\neach other; the latter, that, taken together, they exclude all other\npredicates.\n\n[1] Mill, ch. iv.; Bain, p. 86.\n\nIn any case, the disjunctive is more than any combination of\nHypotheticals, and really tends to be Categorical, and ought not to be\nclaimed as Conditional.\n\n_Which are Categorical?_\n\n2. We will now look at these Judgments in order, consider their real\nmeaning, and also ascertain the limits of the Categorical Judgment,\nviz. that which affirms the existence of its Subject, or in other\nwords, asserts a fact.\n\n_The Particular Judgment_\n\n(i) The Particular Judgment of common Logic, \u201cSome S. is P.,\u201d has\ndifferent meanings according as it is understood naturally, or tied\ndown to be a result of enumeration.\n\nIn any case it is an imperfect, unscientific Judgment, in which the\nmind cannot rest, because it has an undefined limitation imposed upon\nthe Subject.\n\n_Its natural meaning_\n\n(_a_) For the natural meaning, take the example, \u201cSome engines can\ndrag a train at a mile a minute for a long distance.\u201d [1] This does\nnot _mean_ a certain number of engines, though of course they _are_ a\ncertain number. It {117} means certain engines of a particular make,\nnot specified in the Judgment. The Judgment is Categorical, because\nthe undefined reservation implies a reference to something unanalysed,\nbut merely touched or presented in experience. If it was a mere idea\nit would have to be clear; and if the full description or definition\nwere inserted, the Judgment would cease to affirm the existence of\nthe engines in question. _And the Judgment itself challenges this\ncompletion._\n\n[1] To be accurate, the Judgment would demand the insertion of\nprecise details about train, distance, and other matters. But\nthis illustrates the point of the text, because the assignment\nof such details would naturally extend to the Subject, and then\nthe \u201cSome\u201d would be displaced.\n\n_A narrower meaning_\n\n(_b_) A more artificial meaning is to take the Judgment as not formed\nby imperfect description, but by imperfect enumeration (understanding\nit almost wholly in denotation). \u201cSome Conservatives are in favour\nof women\u2019s suffrage.\u201d This means or may mean that we have counted a\ncertain number, large or small, who are so, and we may or may not know\nabout the others. _Thus understood, the Judgment challenges complete\nenumeration_; it contains of course the elements of a fraction--half,\nmost, nine-tenths of, and so on.\n\nThis again is Categorical; not merely because it implies counting, but\nbecause it implies counting units separately given to experience.\n\nThe Particular Judgment does not include our Impersonal and\nDemonstrative Judgments; they are not classed in the common text-books.\nBut as referring to perception they too are categorical and assert\nfacts, whether they have ideas to help out the perceptive reference or\nnot. And there is no reason against including them under the Particular\nJudgment. The assertion, \u201cThis engine can drag a train a mile a\nminute,\u201d is much the same kind of Judgment as, \u201cSome engines can, etc.\u201d\nEither of these would be false {118} if no such engines existed. _These\nJudgments are of the essence of perception_. They have the connection\nof content and the undefined complex of presentation struggling\ntogether in them. They assert fact.\n\n_Singular Judgment_\n\n(2) The Singular Judgment of the common Logic is pretty much our\nJudgment with a proper name, which I call Individual, and which, as we\nsaw, is in part rightly called universal--because the Subject extends\nbeyond perception, and the Predicate follows the Subject. But it is\na concrete or individual Universal, not an abstract Universal, and\ntherefore asserts the existence of its Subject. The reason why it is\ntaken to assert the reality of its Subject must be, I suppose, that\nit _can_ assert this, its Subject being a name for an existence that\nhas limited reality within the temporal series, and _cannot_ assert\nanything else, not having any general fixed content or connotation\nwhich could imply a _general_ connection of Subject and Predicate. The\ngeneral connection of content which is so fatal to the asserting of\nfact does not exist in this case. We see this in Mill\u2019s instance. \u201cThe\nsummit of Chimborazo is white,\u201d When the Subject is a unique name with\nprecise connotation, \u201cThe centre of gravity of the material universe\nis variable,\u201d then we are passing into the abstract Universal, and I\nthink we may take such a Judgment perhaps as one of the best examples\nof a conjunction of categorical and hypothetical meaning, _i.e._ of\na connection of content ascribed to a Subject affirmed to exist. But\nusually one meaning or the other is uppermost.\n\nThese Judgments, called Singular or Individual, correspond to the\nregion of history or narrative. The realities {119} with which they\ndeal have their definite position in a single system of time and space,\nand this is often made emphatic by the use of tenses. But these change\nwith the date relative to the speaker, so that a Judgment with real\ntense must once have been false, or must become false by lapse of\ntime. Thus the Judgment of fact may be not absolutely true. Nothing is\ngenuinely true which a change of date can make false. The permanently\ntrue time-relations between Subject and Predicate are determined by\ntheir content, and the copula is not a tense, but a mere sign of\naffirmation. The Singular as Categorical is sharply distinguished from\nthe Abstract Universal, with which common Logic classes it.\n\n_Universal Judgment_\n\n(3) Down to this point the judgment states a _fact_. When we come to\nthe ordinary universal affirmative, we see at once that it may express\nvery different meanings. In its natural meaning it strongly _implies_\nthat its Subject has a particular existence within the series of time\nand space, but hardly asserts it.\n\n_Import of Propositions_\n\nMill, for example, says \u201cthe objects are no longer individually\ndesignated, they are pointed out only by their attributes;\u201d \u201cmost of\nthem not known individually at all.\u201d That means that the explicit\nSubject is not made of individuals. The natural meaning is disputed; I\nincline to think with Venn, that the Subject is naturally taken _more_\nin Denotation (not solely, which is unmeaning), and the Predicate\n_more_ in connotation. But clearly in literal form the Subject is\nsimply a significant idea, and its existence in things or events is\nnot affirmed though it may be strongly implied. Hamilton [1] {120}\nsays quite calmly--\u201c\u2018Rainy weather is wet weather\u2019 is a Categorical\nProposition; \u2018If it rains it will be wet\u2019 is Hypothetical.\u201d Between\nthe two I can see no distinction of meaning at all. [2] If indeed we\ntake the Universal Affirmative in the pure sense of aggregate formed\nby enumeration, and therefore finite, it _may_ be said that we assert\nthe existence of the individuals composing it; but this is a very\nunreal view of the meaning of the Judgment (though suggested by its\ncustomary form), and even then it would be hard to prove that we\ncontinue to think of the Subject as individuals. This reference to\na finite aggregate makes the _Collective Judgment_ or _Judgment of\nAllness_. It cannot really exist in the case of a class like man, of\nunknown extension, and is confined, at its widest, to such cases as\n\u201cAll present Members of Parliament have to take a line on the Irish\nquestion.\u201d This _might_ be Categorical, but need not be so.\n\n[1] _Lectures_, vol, iii. p. 327.\n\n[2] Contrast Jevons, _Elementary Logic_, p. 163.\n\nOtherwise, the Universal Affirmative of common Logic is literally\nHypothetical, though in some cases it may strongly imply the assertion\nof reality. Dr. Venn has discussed this question. [1] He says the\nimplication of existence is much stronger with a single-word Subject\nthan with a many-worded Subject; _i.e._ perhaps with a natural than\nwith an artificial conception. But in any case, the expressed bond with\nperception is lost, and in pure form the Subject is a mere abstract\nidea, so that the relations of content entirely predominate over the\nimplication of existence.\n\n[1] _Empirical Logic_, pp. 258-9.\n\nThus the Universal Affirmative in its full meaning fairly {121}\nrepresents the sciences of classification, combining a subordinate\nmeaning of Allness or numerical totality with a primary meaning of\nconnotation of attributes or presumed causality. When we say \u201cAll the\nButtercup family have an inferior corolla,\u201d of course we mean that\nthere is a reason for this. Often we omit the term all, as in \u201cHeat\nis a mode of motion.\u201d In doing this we wipe out the last trace of a\nreference to individual objects, and we pass to the pure hypothetical\nform which absolutely neglects the existence of objects.\n\n_\u201cHypothetical\u201d Judgment_\n\n(4) The simplest type of this Judgment is, if A is B it is C. This\nJudgment corresponds to abstract science, but it is only making\nexplicit what was implied in the Universal Affirmative. That\nexpressed a presumption of causality, this expresses a clear Reason\nand Consequent or scientific necessity. The point of this form is\n(i.) that it drops all reference to individual objects, (ii.) that\nit challenges you to explain how the Subject-content is tied to the\nPredicate-content. \u201cWater boils at 212\u00b0,\u201d is a statement we should\ngenerally pass in so-called Categorical form, because it does not\nchallenge any great accuracy of connection. But \u201cIf water boils, it\nis at a temperature of 212\u00b0,\u201d puts us upon asking, \u201cIs the condition\nadequate?\u201d and we see at once that we must at least say, \u201cIf water\nboils _under pressure of one atmosphere_, it is at a temperature of\n212\u00b0,\u201d or else the judgment is untrue. Of course we may apply the form\nrightly or wrongly, as you may fill up your census paper rightly or\nwrongly. We can only say that it calls upon you to put in an adequate\ncondition. Therefore I rather object to the form \u201cIf A is, B is,\u201d\nbecause it adds very little to the so-called Categorical shape.\n\n{122} We have now to ask how the Hypothetical Judgment connects its\ncontent with reality, _i.e._ how it is a Judgment at all? And the same\nexplanation must apply to so-called Categorical Judgments, which can be\nthrown into this form without change of meaning.\n\nThe point from which the explanation starts is taking hypothesis as\nsupposition. This is much more true, I think, than connecting it with\n_doubt_. In Dr. Venn\u2019s _Empirical Logic_ the connection of Hypothetical\nJudgment and doubt to my mind disfigures the whole treatment of the\nScientific Judgment. Supposition is distinct from affirmation--that\nis true--but just because it is distinct from affirmation, it cannot\nindicate doubt. It probably arose out of doubt, but as a method of\nscience it does not imply doubt, but only the accurate limitation of\nattention. What doubt is there when we judge \u201cIf equals be added to\nequals, the wholes are equal\u201d? We are attending to one particular\nthread of the nexus.\n\nHypothetical Judgment, then, is Judgment that starts from a\nsupposition. Every supposition is made upon a certain basis of\nReality. Take as an extreme case, \u201cIf you ask permission of A.B., he\nwill refuse it.\u201d This is a supposition and its result, on the basis\nof the known character of A.B. And the full judgment is \u201cA.B. is of\nsuch a character, that, supposing you ask him for permission, etc.\u201d\nThe Hypothetical Judgment may be true, as an assertion about A.B.\u2019s\ncharacter, though you may never ask.\n\nHere, then, is the clue to the analysis of _all Abstract Judgments_,\nLike Perceptive Judgment, they affirm something of Reality, but they\ndo this indirectly and not directly. {123} Underlying them there is\nthe implied Categorical Judgment, \u201cReality has a character, such\nthat, supposing so and so, the consequence will be so and so.\u201d And\nif this implied assertion is true, then the Hypothetical Judgment is\ntrue, although its terms may be not only unreal, but impossible. \u201cIf\na microscopic object-lens with a focal length of 1/100 in. were used,\nits magnifying power with an A eye-piece would be so many diameters.\u201d\nThis is a mere matter of calculation, and is unquestionably true,\ndepending upon the effects of refraction upon the optical image. But I\ndo not suppose that such an object-lens could be made, or used. Does\nsuch a Judgment, although true, express a _fact_? No, I should say not,\nalthough common usage varies. I remember a _Pall Mall_ leading article\nwhich said, \u201cIt is an absolute fact, that, if Mr. Gladstone had not\ndone something--the Government would have committed--some iniquity\nor other.\u201d Is this what we call a fact? We observe that the content\nactually mentioned was never real at all. The implied connection\nwith reality is \u201cThere existed in reality a condition of things\n(unspecified) in which _if_ Mr. Gladstone, etc., etc.\u201d Are mathematical\ntruths facts, and in what sense? Abstract truth need not, and perhaps\ncannot express fact, but implies fact indirectly.\n\n_Disjunctive Judgment_\n\n(5) The Disjunctive Judgment \u201cA is either B or C,\u201d is again not\na judgment of doubt but a mode of Knowledge, It may be taken as\nnumerical; then it gives rise to the statement of Chances. But in its\nperfect form it is appropriate to the exposition of a content as a\nsystem, and it may be taken as returning to the Categorical Judgment,\nand combining it with the Hypothetical, because its {124} content is\nnaturally taken as an individual, being necessarily concrete.\n\nThe peculiar point of the Disjunctive is that it makes negation\npositively significant.\n\n\u201cThis signal light shows either red or green.\u201d Here we have the\ncategorical element, \u201cThis signal light shows some colour,\u201d and on the\ntop of this the two Hypothetical Judgments, \u201cIf it shows red it does\nnot show green,\u201d \u201cIf it does not show red it does show green.\u201d You\ncannot make it up out of the two Hypothetical Judgments alone; they do\nnot give you the assertion that \u201cit shows some colour.\u201d [1]\n\n[1] The example in the text, chosen for its simplicity, may\nbe objected to as involving perceptive concreteness by the\npronoun \u201cthis.\u201d You can have a disjunction, it may be said,\ndealing with \u201cthe triangle\u201d as such; and why should this be\nmore \u201cCategorical\u201d than the assertion that the triangle has\nits angles = three right angles? Still, it might be replied,\nthe development of a single nature into a number of precise\nand necessary alternatives, always gives it an implication of\nself-completeness.\n\nDoes this state a fact? I think it implies a fact much more distinctly\nthan the hypothetical does, but of course it is a question whether an\nalternative can be called a fact. It seems a precise expression of\nsome kinds of reality, but it is not a solid single momentary fact.\nIt is very appropriate to the objects of philosophy as the higher\nconcrete science, which are conceived as systems of facts bearing\ndefinite relations to each other; _e.g._ \u201cSociety is a structure of\nindividual characters, having positions which are not interchangeable.\u201d\nTaken all as a mass, they are conjunctively connected, but taken in\ndistinguishable relations they are disjunctively related. A human\nbeing as such has some position and no other, and this is ultimately\ndetermined by {125} the nature of the social whole to which he\nbelongs. He is if this, nothing else, and if nothing else, then this.\nA more artificial example, which illustrates the degree in which\nactual abstract knowledge and purpose can be embodied by man in\nmachinery, is the interlocking system of points and signals at a great\nrailway station. I suppose that the essence of such a system lies in\narrangements for necessarily closing every track to all but one at a\ntime of any tracks which cross it or converge into it. The track X\nreceives trains from A, B, C, D; if the entrance for those from A is\nopen, B, C, and D are _ipso facto_ closed; if A, B, and C are closed,\nD is open, and so on. This is a disjunction consciously and purposely\nincorporated in material fact, and differs from a Disjunctive Judgment\nonly in so far as existence necessarily differs from discursive thought.\n\nThe disjunction seems to complete the system of judgments, including\nall the others in itself, and it is wrong in principle to distinguish,\n_e.g._ between a hypothetical and categorical disjunction, or to\nconsider how a disjunction can be denied. For disjunction in itself\nimplies a kind of individuality which is beyond mere fact and mere\nabstract truth, though allied to both; and all intelligible negation\nis under, not of, a disjunction. Negation of a disjunction would\nmean throwing aside the whole of some definite group of thoughts as\nfallacious, and going back to begin again with a judgment of the\nsimplest kind. It amounts to saying, \u201cNone of your distinctions touch\nthe point; you must begin afresh.\u201d\n\n\n\n\n{126}\n\nLECTURE VIII   NEGATION, AND OPPOSITION OF JUDGMENTS\n\n_Distinction between Contrary and Contradictory opposition_ [1]\n\n1. The only important point in the traditional diagram of opposition\nof Judgments is the distinction between contrary and contradictory\nopposition, the opposition, that is, between A and E, and the\nopposition between A and O, or E and I.\n\n[1] Read Bain, pp. 55-6, on \u201cNegative Names and the Universe\nof the Proposition,\u201d also on \u201cNegative Propositions,\u201d p. 83\nff.; Venn, _Empirical Logic_, pp. 214--217; Jevons, _Elementary\nLogic_, ix., on \u201cOpposition of Propositions\u201d; Mill, ch. iv. \u00a7 2.\n\nIn _Contrary_ Opposition the one Judgment not only denies the other,\nbut goes on to deny or assert something more besides. The mere\ngrammatical shape \u201cNo man is mortal\u201d conceals this, but we easily see\nthat it says more than is necessary to deny the other, \u201cAll men are\nmortal.\u201d\n\nIn _Contradictory_ Opposition, the one Judgment does absolutely nothing\nmore than is involved in destroying the other.\n\nThe _Contrary_ Negation has the advantage in positive, or at least in\ndefinite import.\n\nThe _Contradictory_ or pure Negation has the advantage in the\nexhaustive disjunction which it involves.\n\nThis is plain if we reflect that Contrary Negation only {127} rests on\nthe Law of Contradiction, \u201cX is not both A and not A.\u201d\n\n_Ordinary Diagram of Opposition of Judgments_.\n\n[The diagram has diagonal lines, not represented here, from corner A to\ncorner O, and from corner E to corner I, each labelled \u201cContradictory\nOpposition\u201d. Tr.]\n\n\n  A                                         E\n             Contrary Opposition.\n\n\n\n\n\n            Sub-contrary Opposition.\n  I                                         O\n\n  A = Universal Affirmative.    All men are mortal.\n  E = Universal Negative.       No men are mortal.\n  I = Particular Affirmative.   Some men are mortal.\n  O = Particular Negative.      Some men are not mortal.\n\nSub-contrary Opposition has no real meaning; the judgments so opposed\nare compatible.\n\nIt is not _true_ both that \u201cAll M.P.\u2019s are wise,\u201d _and_ that \u201cNo\nM.P.\u2019s are wise,\u201d but both may be false; while Contradictory Negation\nimplies the Law of Excluded Third or excluded Middle, \u201cX is either\nA or not A,\u201d the principle of disjunction, or rather, the simplest\ncase of it. It is not {128} _false_ both that \u201cAll M.P.\u2019s are wise\u201d\nand that \u201cSome M.P.\u2019s are not wise.\u201d The point is, then, on the one\nhand, that in Contradiction you can go from falsehood to truth, [1]\nwhile in Contrariety you can only go from truth to falsehood; but also\nthat in Contradiction the Affirmative and Negative are not at all on\na level in meaning, while in Contrariety they are much more nearly\nso. Then if we leave out the relations of mere plurality, of All and\nSome, which enable you to get contrary negation in pure negative form\nin the common Logic, we may say generally that in contrary negation\nsomething is asserted, and in contradictory negation taken quite\nliterally nothing is asserted, but we have a \u201cbare denial,\u201d a predicate\nis merely removed. In actual thought this cannot be quite realised,\nbecause a bare denial is really meaningless, and we always have in our\nmind some subject or universe of discourse within which the denial is\nconstrued definitely. But this definite construing is not justified by\nthe bare form of contradiction, which consists simply in destroying a\npredication and not replacing it by another. In as far as you replace\nit by another, defined or undefined, you are going forward towards\ncontrary negation.\n\n[1] _I.e._ Contradictory alternatives are exhaustive.\n\n_Contrary Negation_\n\n2. Thus, Contrary Negation in its essence is affirmation with a\nnegative intention, and we may take as a type of it in this wider\nsense the affirmation of a positive character with the intention of\ndenying another positive character. _E.g._ when you deny \u201cThis is a\nright-angled triangle\u201d by asserting \u201cThis is an equilateral triangle,\u201d\nyou have typical contrary negation. It is not really safe to speak of\ncontraries except with reference to _judgments_, intended to deny each\n{129} other; but it is common to speak of species of the same genus as\ncontraries or opposites, because the same thing cannot be both. [1]\n\n[1] Bain, p. 55 ff.\n\nWe must therefore distinguish _contrary_ from _different_. Of course\nthe same thing or content has many different qualities, and even\ncombines qualities that we are apt to call contrary or opposite. But\nas Plato was fond of pointing out, a thing cannot have different or\nopposing qualities in the same relation, that is to say, belonging to\nthe same subject under the same condition. The same thing may be blue\nin one part of it and green in another, and the same part of it may be\nblue by daylight and green by candlelight. But the same surface cannot\nbe blue and green at once by the same light to the same eye looking in\nthe same direction. _Different_ qualities become _contrary_ when they\nclaim to stand in the same relation to the same subject. Right-angled\ntriangles and equilateral triangles do not deny each other if we leave\nthem in peace side by side. They are then merely different species of\nthe same genus, or different combinations of the same angular space.\nBut if you say, \u201cThis triangle is right-angled,\u201d and I say \u201cIt is\nequilateral,\u201d then they deny each other, and become true contraries.\n\nThen the _meaning_ of denial is always of the nature of _contrary_\ndenial. As we always speak and think within a general subject or\nuniverse of discourse, it follows that every denial substitutes some\naffirmation for the judgment which it denies. The only judgments in\nwhich this is not the case are those called by an unmeaning tradition\nInfinite Judgments, _i.e._ judgments in which the negative predicate\n{130} includes every determination which has applicability to the\nSubject. This is because the attribute denied has no applicability\nto the Subject, and therefore all that has applicability is\nundiscriminatingly affirmed, in other words, the judgment has no\nmeaning. \u201cVirtue is not-square.\u201d This suggests no definite positive\nquality applicable to virtue, and therefore is idle. You may safely\nanalyse a significant negative judgment, \u201cA is not B\u201d as = \u201cA is not B\nbut C,\u201d or as = \u201cA is X, which excludes B.\u201d For X may be undetermined,\n\u201ca colour not red.\u201d But then if the meaning is always affirmative or\npositive, why do we ever use the negative form?\n\n_Why use Negation?_\n\n3. In the first place, we use it because it indicates exclusion,\nand without it we cannot distinguish between mere differents on the\none hand and contraries on the other. If you ask me, \u201cAre you going\nto Victoria, London Chatham and Dover station?\u201d and I answer, \u201cI am\ngoing to Victoria, London Brighton and South Coast,\u201d that will not be\nsatisfactory to you, unless you happen to know beforehand that these\nstations are so arranged that if you are at one you are not at the\nother. They might be a single station used by different companies, and\ncalled indifferently by the name of either. To make it clear that the\nsuggestion and the answer are incompatible, I must say, \u201cI am _not_\ngoing to Victoria, London Chatham and Dover,\u201d and I may add or not add,\n\u201cI _am_ going to Victoria, London Brighton and South Coast.\u201d That tells\nyou that the one predicate excludes the other, and that is the first\nreason why we use the generalised form of exclusion, _i.e._ negation.\n\nBut in the second place, it can give us more, and something absolutely\nnecessary to our knowledge, and that is not {131} merely exclusion, but\nexhaustion. In literal form negation is absolutely exhaustive, that is\nto say, contradictory. The Judgment \u201cA is not B\u201d forms an exhaustive\nalternative to the Judgment \u201cA is B,\u201d so that no third case beyond\nthese two is possible, and therefore you can argue from the falsehood\nof either to the truth of the other. Now this form is potentially of\nimmense value for knowledge, and all disjunction consists in applying\nit; but as it stands in the abstract it is worthless, because it is\nan empty form. \u201cA is red or not-red.\u201d If either of these is false the\nother is true. But what do you gain by this? You are not entitled to\nput any positive meaning upon not-red; if you do so you slide into mere\ncontrary negation, and the inference from falsehood becomes a fallacy.\nMake an argument, \u201cThe soul is red or not-red.\u201d \u201cIt is not-red \u2234 it is\nsome other colour than red.\u201d The argument is futile. We have construed\n\u201cnot-red\u201d as a positive contrary, and that being so, the disjunction is\nno longer exhaustive. We had no right to say that the soul is either\nred or some other colour; the law of Excluded Middle does not warrant\nthat.\n\nI pause to say that the proof of the exhaustiveness of negation, _i.e._\nthat two negatives make an affirmative--that if A is not not-B, it\nfollows that A is B--is a disputed problem, the problem known as double\nnegation. How do you know that what is not not-red must be red? I take\nthe law of Excluded Middle simply as a definition of the bare form\nof denial, or the distinction between this and not-this; \u201cnot-this\u201d\nbeing the bare abstraction of the other than this. Others say that\nevery negation presupposes an affirmation; so \u201cA is not-B\u201d presupposes\nthe affirmation \u201cA is B,\u201d and {132} if you knock down the negative,\nthe original affirmative is left standing. Sigwart and B. Erdmann say\nthis. I think it monstrous. I do not believe that you must find an\naffirmative standing before you can deny.\n\n_Stage of Significant Negation. Combination of Contrary and\nContradictory_\n\n4. Well, then, the point we have reached is this. What we mean in\ndenial is always the contrary, something positive. What we say\nin denial--in other words, the literal form which we use--always\napproaches the contradictory, _i.e._ is pure exclusion. The Contrary\nof the diagram denies more than it need, but still its form is that\nof exclusion. Now we have seen that in denial, as used in common\nspeech, we get the benefit of _both affirmation and exclusion_, but in\naccurate thought we want to do much more than this; we want to get the\nwhole benefit of the negative form--that is, to get a positive meaning\ntogether with not only exclusion, but exhaustion.\n\nI will put the three cases in one example, beginning with mere\naffirmations of different facts.\n\n_Different Affirmations_\n\n(1) \u201cHe goes by this train to-day.\u201d \u201cHe goes by that train to-morrow.\u201d\nThis conjunction, as simply stated, gives no inference from the truth\nor falsehood of either statement to the truth or falsehood of the other.\n\n_Contrary Opposition, exclusive_\n\n(2) \u201cHe goes by this train,\u201d and \u201cHe goes by that train,\u201d with a\nmeaning equivalent to \u201cNo, he goes by that.\u201d If it is true that in\nthe sense suggested by the context he goes by this train, then it is\nnot true that he goes by the other, and if it is true, in the sense\nexplained, that he goes by the other, then he does not go by this. Each\nexcludes the other, but both may be excluded by a third alternative.\nIf it is _not_ true that he goes by this {133} train--nothing follows.\nThere may be any number of trains he might go by, or he might give up\ngoing; _i.e._ your Universe of discourse, your implicit meaning is\nnot expressly limited. If it is _not_ true to say, \u201cNo, he goes by\nthat\u201d--taking the whole meaning together, and not separating its parts,\nfor this combination is essential to the \u201ccontrary\u201d--nothing follows as\nto the truth of the other statement. He may not be going at all, or may\nbe going by some third train, or by road.\n\n_Combined Contrary and Contradictory Negation_\n\nBut if you limit your Universe, or general subject, then you can\ncombine the value of contrary and contradictory negation. Then you say,\n\n(3) \u201cHe goes either by this train or by that.\u201d Then you can infer not\nonly from \u201cHe goes by this train,\u201d that \u201cHe does not go by that,\u201d but\nfrom \u201cHe does not go by this train\u201d to \u201cHe does go by that.\u201d\n\nThe alternative between \u201cA is B\u201d and \u201cA is not-B\u201d remains exhaustive,\nbut not-B has been given a positive value, _because we have limited\nthe possibilities by definite knowledge_. The processes of accurate\nthinking and observation aim almost entirely at giving a positive value\nC to not-B, and a positive value B to not-C, under a disjunction,\nbecause it is then that you define exactly where and within what\nconditions C which is not B passes into B which is not C. Take the\ndisjunction, \u201cSound is either musical or noise.\u201d If the successive\nvibrations are of a uniform period it is musical sound; if they are of\nirregular periods it is noise. This is a disjunction which assumes the\nform,\n\nA is either B or C. That is to say, If it is B it is not C. If it is\nnot B it is C.\n\n{134} Therefore I think that all \u201cdetermination is negation\u201d--of\ncourse, however, not bare negation, but significant negation; the\nessence of it consists in correcting and confirming our judgment of\nthe nature of a positive phenomenon by showing that _just when_ its\ncondition ceases, _just then_ something else begins, and when you have\nexhausted the whole operation of the system of conditions in question,\nso that from any one phase of their effects you can read off what _it_\nis not but the _others_ are, then you have almost all the knowledge\nwe can get. The \u201c_Just-not_\u201d is the important point, and this is only\ngiven by a positive negation within a definite system. You want to\nexplain or define the case in which A becomes B. You want observation\nof not-B; but almost the whole world is formally or barely not-B, so\nthat you are lost in chaos. What you must do is to find the point\nwithin A, where A1 which is B passes into A2 which is C, and that will\ngive you the _just-not-B_ which is the valuable negative instance.\n\n_Negative judgment expressing fact_\n\n5. You will find it said that a Negative Judgment cannot express fact;\n_e.g._ that a Judgment of Perception cannot be negative. This is worth\nreflecting upon; I hope that what has been said makes clear how far it\nis true. The bare form of Negation is not adequate to fact; it contains\nmere emptiness or ignorance; we nowhere in our perception come upon a\nmere \u201cnot-something.\u201d No doubt negation is in this way more subjective\nthan affirmation. But then as it fills up in meaning, the denial\nbecomes more and more on a level with the affirmation, till at last\nin systematic knowledge both become double-edged--every affirmative\ndenies, and every negative affirms. When a man who is both a {135}\nmusician and a physicist says, \u201cthis compound tone A is a discord Y,\u201d\nhe knows exactly how much of a discord, what ratio of vibration makes\nit so much of a discord, how much it would have to change to become a\nconcord (X which is not Y), and what change in the vibration ratio from\na1 to a2 would be needed to make it a concord. To such knowledge as\nthis, the accurate negation is just as expressive as the affirmation,\nand it does not matter whether he says \u201cA is Y,\u201d or \u201cA is by so much\nnot X.\u201d It becomes, as Venn says, all but impossible to distinguish the\naffirmation from the negation. No doubt affirmative terms come in at\nthis stage, though the meaning is negative. Observe in this connection\nhow we sometimes use the nearest word we can think of, knowing that the\nnegative gives the positive indirectly--\u201cHe was, I won\u2019t say insolent,\u201d\nmeaning _just not_ or \u201c_all but_\u201d insolent; or again, \u201cThat was not\nright,\u201d rather than saying bluntly \u201cwrong.\u201d\n\n_Operation of the denied idea_\n\n6. Every significant negation \u201cA is not B\u201d can be analysed as \u201cA is X\nwhich excludes B.\u201d Of course X may not be a distinct C; _e.g._ we may\nbe able to see that A is not red, but we may not be able to make out\nfor certain what colour it is; then the colour X is \u201can unknown colour\nwhich excludes red.\u201d\n\nHow does the rejected idea operate in Judgment? I suppose it operates\nby suggesting a Judgment which as you make it destroys some of its\nown characteristics. It is really an expression of the confirmatory\nnegative instance or \u201cjust-not.\u201d _Just_ when two parallel straight\nlines swing so that they can meet, _just_ then the two interior angles\nbegin to be less than two right angles, which tells us that the {136}\nstraight lines are ceasing to be parallel. Just in as much as two\nstraight lines begin to enclose a space we become aware that one or\nother of them is not straight, so that A in turning from Y to X turns\n_pari passu_ from A1 to A2, and we are therefore justified in saying\nthat A, when it is Y, cannot be X.\n\nThis lecture may pave the way for Induction, by giving some idea of the\nimportance of the negative instance which Bacon preached so assiduously.\n\nIn a real system of science the conceptions are negative towards each\nother merely as defining each other. One of them is not in itself\nmore negative than another. Such a conception, _e.g._, is that of a\ntriangle compared with two parallel straight lines which are cut by\na third line. If the parallels are swung so as to meet, they become\na triangle which gains in its third angle what the parallels lose on\nthe two interior angles, and the total of two right angles remains\nthe same. Thus in saying that parallels cut by a third straight line\ncannot form a triangle, and that the three angles of a triangle are\nequal to two right angles, we are expressing the frontier which is at\nonce the demarcation between two sets of geometrical relations, and the\npositive grasp or connection of the one with the other. The negation is\nno bar to a positive continuity in the organism of the science, but is\nessential to defining its nature and constituent elements. This is the\nbearing of significant negation when fully developed.\n\n\n\n\n{137}\n\nLECTURE IX   INFERENCE AND THE SYLLOGISTIC FORMS\n\n_Inference in general_ [1]\n\n1. The Problem of Inference is something of a paradox. Inference\nconsists in asserting as fact or truth, on the ground of certain given\nfacts or truths, something which is not included in those data. We\nhave not got inference unless the conclusion, (i.) is necessary from\nthe premisses, and (ii.) goes beyond the premisses. To put the paradox\nquite roughly--we have not got inference unless the conclusion is (i.)\nin the premisses, and (ii.) outside the premisses. This is the problem\nwhich exercises Mill so much in the chapter, \u201cFunction and Value of the\nSyllogism.\u201d We should notice especially his \u00a7 7, \u201cthe universal type\nof the reasoning process.\u201d The point of it is to make the justice of\ninference depend upon relations of content, which are judged of by what\nhe calls induction. That is quite right, but the question still returns\nupon us, \u201cWhat kind of relations of content must we have, in order to\nrealise the paradox of Inference?\u201d This the \u201ctype of inference\u201d rather\nshirks. See Mill\u2019s remarks when he is brought face to face with {138}\nInduction, Bk. III. ch. f. \u00a7 2. An Inference, as he there recognises,\neither does not hold at all, or it holds \u201cin all cases of a certain\ndescription,\u201d _i.e._, it depends on universals.\n\n[1] Read for Lectures IX. and X., Mill, Bk. II ch. i., ii.,\niii.; Bk. III. ch. i. and ii. at least; Venn, ch. xiv., xv.;\nJevons, _Lessons_ xv. and xxiv.; De Morgan\u2019s _Budget of\nParadoxes_.\n\nI ought to warn you at once that though we may have novelty in the\nconclusion of Inference (as in multiplication of large numbers),\nthe necessity is more essential than the novelty. In fact, much of\nInference consists in demonstrating the _connection_ of matters that\nas _facts_ are pretty familiar. Of course, however, they are always\nmodified in the process, and in that sense there is always novelty. You\nobtain the most vital idea of Inference by starting from the conclusion\nas a suggestion, or even as an observation, and asking yourself how it\nis proved, or explained, and treating the whole process as a single\nmediate judgment, _i.e._ a reasoned affirmation. Take the observation,\n\u201cThe tide at new and full moon is exceptionally high.\u201d In scientific\ninference this is filled out by a middle term. We may profitably think\nof the \u201cmiddle term,\u201d as the copula or grip which holds the conclusion\ntogether, made explicit and definitely stated. Thus the judgment pulls\nout like a telescope, exhibiting fresh parts within it, as it passes\ninto inference. \u201cThe tide at new and full moon, _being at these times\nthe lunar tide plus the solar tide_, is exceptionally high.\u201d This is\nthe sort of inference which is really commonest in science. Such an\ninference would no doubt give us the conclusion if we did not know it\nby observation, but it happens in many cases that we do know it by\nobservation, and what the inference gives us is the connection, which\nof course may enable us to correct the observation.\n\n{139} _Conditions of the possibility of Inference_\n\n2. In the strictest formal sense there can be no inference from\nparticulars to particulars. When there seems to be such inference, it\nis merely that the ground of inference is not mentioned, sometimes\nbecause it is obvious, sometimes because it is not clearly specified\nin the mind. Suppose we say, \u201cMorley and Harcourt will go for\nDisestablishment, and I think, therefore, that Gladstone will.\u201d I do\nnot _express_ any connecting link, merely because every one sees at\nonce that I am inferring from the intentions of some Liberal leaders to\nthose of another. If the terms are really particulars, \u201cX is A, Y is B,\nZ is C,\u201d one is helpless; they do not point to anything further at all;\nthere is no bridge from one to the other.\n\nInference cannot possibly take place except through the medium of an\nidentity or universal which acts as a bridge from one case or relation\nto another. If each particular was shut up within itself as in the\nletters taken as an instance just now, you could never get from one\nwhich is given to another which is not given, or to a connection not\ngiven between two which are given.\n\nTake the simplest conceivable case, which hardly amounts to Inference,\nthat of producing a given straight line. How is it that this is\npossible? Because the direction of the straight line is universal and\nself-identical as against possible directions in space, and it acts as\na rule which carries you beyond the given portion of it. This might\nfairly be called an \u201cimmediate inference.\u201d So I presume that any curve\ncan be constructed out of a sufficient portion of the curve, although,\nexcept with a circle, this is more than repeating the same line over\nagain. The content has a nature which {140} is capable of prescribing\nits own continuation. A curve is not a direction; a truth which is a\npuzzle to the non-mathematician--it is a law of continuous change of\ndirection.\n\n_System the ultimate condition of Inference_\n\n3. _Ultimately_ the condition of inference is always a system. And\nit will help us in getting a vital notion of inference if we think,\nto begin with, of the interdependence of relations in space--in\ngeometrical figures, or, to take a commonplace example, in the\nadjustment of a Chinese puzzle or a dissected map. Or any of the\npropositions about the properties of triangles are a good example.\nHow can one property or attribute determine another, so that you can\nsay, \u201cGiven this, there must be that\u201d? This can only be answered by\npointing to the nature of a whole with parts, or a system, which just\nmeans this, a group of relations or properties or things so held\ntogether by a common nature that you can judge from some of them what\nthe others must be. Not all systems admit of precise calculation and\ndemonstration, but wherever there is inference at all there is at\nleast an identity of content which may be more or less developed into\na precise relation between parts. For example, we cannot construct\ngeometrically the life and character of an individual man; we can argue\nfrom his character to some extent, but the connection of facts in his\npersonal identity is all that we can infer for certain; and even this\ninvolves a certain context of facts, as in circumstantial evidence.\nYet this simplest linking together of occurrences by personal identity\nis enough to give very startling inferences. Thackeray\u2019s story of the\npriest is a good instance of inference from mere identity. \u201cAn old\nabb\u00e9, talking among a party of intimate friends, happened {141} to say,\n\u2018A priest has strange experiences; why, ladies, my first penitent was\na murderer.\u2019 Upon this, the principal nobleman of the neighbourhood\nenters the room. \u2018Ah, Abb\u00e9, here you are; do you know, ladies, I was\nthe Abb\u00e9\u2019s first penitent, and I promise you my confession astonished\nhim!\u2019\u201d Here the inference depends solely on individual identity, which\nis, as we saw, a kind of universal.\n\nBut in this case was there really an inference? Does not the conclusion\nfall inside the premisses? It must in one sense fall inside the\npremisses, or it is not true. But it does not fall inside them until we\nhave brought them into contact by their point of identity and melted\nthem down into the same judgment. I admit that these inferences from\nindividual identity, assuming the terms not to be ambiguous, are only\njust within the line of rational inference, but, as we see in this\ncase, they bring together the parts of a very extended universal. What\n_is_ the lower limit of inference?\n\n_Immediate Inference_\n\n4. In the doctrine of _immediate Inference_ common Logic treats of\nConversion and the Opposition of judgments.\n\nIs a mere transposition of Subject and Predicate, where the truth\nof the new judgment follows from that of the old, an inference? It\nis a matter of degree. [1] Does it give anything new? \u201cThe Queen\nis a woman.\u201d \u201cA woman is the Queen.\u201d If we make a real difference\nbetween the implications of a Subject and a Predicate, we seem to get\nsomething new; but it is a point of little interest. {142} Comparison\nor Recognition are more like immediate inferences. Comparison means\nthat we do not let ourselves perceive freely, but take a particular\ncontent as the means of apperception of another content, _i.e._ as\nthe medium through which we look at it. I do not merely look at the\nsecond, but I look at it with the first in my mind. And so far I may\nbe said to infer, without the form of proof, from data of perception\nto a relation between them. \u201cYou are taller than me,\u201d is a result\nobtained by considering your height from the point of view of mine, or\n_vice vers\u00e2_. Recognition is somewhat similar. It is more than a mere\nperception, because it implies reproduction of elements not given,\nand an identification with them. I recognise this man _as_ so-and-so,\n_i.e._ I see he is identical with the person who did so-and-so. It is\na judgment, but it goes beyond the primary judgment, \u201cHe is such and\nsuch,\u201d and is really inferred from it. It is a matter of degree. Almost\nevery Judgment can be broken up into elements, and recognition fades\ngradually into cognition--we \u201crecognise\u201d an example of a law, a right,\na duty, an authority; not that we knew _it_, the special case, before,\nbut that in analysing it we find a principle which commands our assent,\nand with which we identify the particular instance before us.\n\n[1] The collective or general judgment, as commonly explained,\ncannot be converted \u201csimply,\u201d because the predicate is \u201cwider\u201d\nthan the subject, and the same rule is accepted for the relation\nof consequent to antecedent. The aim of science, it might almost\nbe said, is to get beyond the kind of judgment to which this\nrule applies.\n\n_Number of Instances_\n\n5. The difference between guess-work and demonstration rests on the\ndifference between a detached quality or relation striking enough to\nsuggest something to us, and a system thoroughly known in its parts as\ndepending on one another. This is so even in recognising an individual\nperson; it is necessary to know that the quality by which you recognise\nhim is one that no one else possesses, or else {143} it is guess-work.\nStill more is this the case in attempting a scientific connection.\nAll scientific connection is really by system as between the parts\nof the content. A quality is often forced on our attention by being\nrepeated a great many times in some particular kind of occurrence, but\nas long as we do not know its _causal_ connection with the properties\nand relations involved in the occurrence it is only guess-work to\ntreat them as essentially connected. This is a matter very easy to\nconfuse, and very important. It is easy to confuse, because a number\nof instances does help us really in inference, as it always insensibly\ngives us an immense command of content; that is to say, without knowing\nit we correct and enlarge our idea of the probable connection a little\nwith every instance. So the connection between the properties that\nstrike us becomes much larger and also more correct than it is to\npeople who have only seen a few instances. But this is because the\ninstances are all a little different, and so correct each other, and\nshow transitions from more obvious forms to less obvious forms of the\nproperties in question which lead us up to a true understanding of\nthem. If the instances were all exactly the same they would not help\nus in this way, but our guess would still be a guess, however many\ninstances might have suggested it.\n\nI remember that a great many years ago I hardly believed in the\nstone-age tools being really tools made by men. I had only seen a few\nbad specimens, one or two of which I still think were just accidentally\nbroken flints which an old country clergyman took for stone-age tools.\nThis was to me then a mere guess, viz. that the cutting shape proved\n{144} the flints to have been made by men. And obviously, if I had seen\nhundreds of specimens no better than these, I should have treated it as\na mere guess all the same. But I happened to go to Salisbury, and there\nI saw the famous Blackmore Museum, where there are not only hundreds\nof specimens, but specimens arranged in series from the most beautiful\nknives and arrow-heads to the rudest. There one\u2019s eye caught the common\nlook of them at once, the better specimens helping one to interpret the\nworse, and the guess was almost turned into a demonstration, because\none\u2019s eyes were opened to the sort of handwork which these things\nexhibit, and to the way in which they are chipped and flaked.\n\nNow this very important operation of number of examples, in helping the\nmind to an explanation, is always being confused with the effect of\nmere repetition of examples, which does not help you to an explanation,\n_i.e._ a repetition in which one tells you no more than another.\nBut these mere repetitions operate _prima facie_ in a different\nway, viz. by making you think there is an _unknown_ cause in favour\nof the combination of properties which recurs, and lead up to the\nold-fashioned perfect Induction and the doctrine of chances, and not to\ndemonstration. [1]\n\n[1] Ultimately the calculus of chances may be said to rest on\nthe same principle as Induction, in so far as the repetition of\nexamples derives its force from the (unspecified) variety of\ncontexts through which this repetition shows a certain result\nto be persistent. But in such a calculus the presumption from\nrecurrence in such a variety of contexts is only estimated, and\nnot analysed.\n\nOn the road from guess-work to demonstration, and generally assisted\nby great experience, we have _skilful_ {145} guess-work, the first\nstage of discovery. This depends on the capacity for hitting upon\nqualities which _are_ connected by causation, though the connection\nremains to be proved. So a countryman or a sailor gets to judge of\nthe weather; it is not merely that he has seen so many instances, but\nhe has been taught by a great variety of instances to recognise the\nessential points, and has formed probably a much more complex judgment\nthan he can put into words. So again a doctor or a nurse can see how\nill a patient is, though it does not follow that they could always say\nwhy this appearance goes with this degree of illness. In proportion\nas you merely _presume_ a causal connection, it is guess-work or pure\ndiscovery. In as far as you can _analyse_ a causal connection it is\ndemonstration or proof; and for Logic, discovery cannot be treated\napart from proof, except as skilful guess-work. _In as far as_ there\nis ground for the guess, so far it approaches to proof; _in as far as_\nthere is no ground, it gives nothing for Logic to get hold of--is mere\ncaprice. A good scientific guess really depends on a shrewd eye for the\nessential points. I am not mathematician enough to give the history\nof the discovery of Neptune by Leverrier and Adams, \u201ccalculating a\nplanet into existence by enormous heaps of algebra,\u201d [1] but it must\nhave begun as a guess, I should suppose it was suggested before Adams\nand Leverrier took it up, on the ground of the anomalous movements of\nUranus indicating an attraction unaccounted for by the known solar\nsystem. And I suppose that this guess would gradually grow into\ndemonstration as it became clear that nothing but a new planet would\nexplain the anomalies of {146} the orbit of Uranus. And at last the\ncalculators were able to tell the telescopist almost exactly where\nto look for the unknown planet. The proof in this case preceded the\nobservation or discovery by perception, and this makes it a very\ndramatic example; but if the observation had come earlier, it would not\nI suppose have dispensed with the precise proof of Neptune\u2019s effect on\nUranus, though it might have made it easier.\n\n[1] De Morgan, _Budget of Paradoxes_, p. 53.\n\n_Figures of Syllogism_\n\n6. In illustration of this progress from guess-work to science, [1]\nI will give an example of the three Aristotelian figures of the\nSyllogism. I omit the fourth. I assume that the heavier term, or the\nterm most like a \u201cthing,\u201d is fitted to be the Subject, and the term\nmore like an attribute to be the Predicate. The syllogistic rules\ndepend practically on the fact that common Logic, following common\nspeech and thought, treats the Predicate as wider than the Subject,\nwhich corresponds to Mill\u2019s view (also the common scientific view),\nthat the same effect may have several alternative causes (not a\ncompound cause, but different possible causes), and that consequent\nis wider than antecedent. [2] It is this assumption that prevents\naffirmative propositions from being simply convertible, _i.e._ prevents\n\u201cAll men are mortal\u201d from being identical with \u201cAll mortals are men,\u201d\nand but for it there would be no difference of figure at all, as there\nis not for inference by equation.\n\n[1] Cf. Plato\u2019s _Republic_, Bk. VI., end.   [2] See p. 141, note.\n\nThis progression is here merely meant to illustrate the universal or\nsystematic connection of particulars in process of disengaging itself.\nBut I do _not_ say that the first {147} figure with a major premise is\na natural form for all arguments.\n\nI take the scheme of the first three figures from Jevons, and suggest\ntheir meaning as follows:--\n\n  X denotes the major term.\n  Y denotes the middle term.\n  Z denotes the minor term.\n\n                  1st Fig. 2nd Fig. 3rd Fig.\n  Major Premise   YX       XY       YX\n  Minor Premise   ZY       ZY       YZ\n  Conclusion      ZX       ZX       ZX\n\nFig. 3. _An observation and a guess._\n\n  Yesterday it rained in the evening.\n  All yesterday the smoke tended to sink.\n  \u2234 The smoke sinking ( may be       ) a sign of rain.\n                      ( is sometimes )\n\nThe conclusion cannot be general in this figure, because nothing\ngeneral has been said in the premisses about the subject of the\nconclusion. So it is very suitable for a mere suggested connection\ngiven in a single content--that of the time \u201cyesterday,\u201d implying\nmoreover that both the points in question have something to do with the\nstate of the atmosphere on that single day.\n\nFig. 2. _A tentative justification_.\n\n  Smoke that goes downwards is heavier than air\n  Particles of moisture are heavier than air.\n  \u2234 Particles of moisture may be in the descending smoke.\n\nA universal conclusion in this figure would be formally bad. But we\ndo not care for that, because we only mean it to be tentative, and we\ndo not draw a universal affirmative {148} conclusion. We express its\nbadness by querying it, or by saying \u201cmay be.\u201d The reason why it is\nformally bad is that nothing general has been said in the premisses\nabout the middle term or reason, so that it is possible that the two\nSubjects do not touch each other within it, _i.e._ that the suggested\nspecial cause, moisture, is not connected with the special effect, the\nsinking of the smoke. The general reason \u201cheavier than air\u201d may include\nboth special suggested cause and special suggested effect without their\ntouching. Smoke and moisture may both sink in air, but for different\nand unconnected reasons. Still, when a special cause is suggested which\nis probably present in part, and which would act in the way required\nby the general character of the effect, there is a certain probability\nthat it _is_ the operative cause, subject to further analysis; and\nthe argument has substantive value, though bad in form. The only good\narguments in this figure have negative conclusions, _e.g._--\n\n  Smoke that is heavier than air goes downwards.\n  Smoke on dry days does not go downwards.\n  \u2234 Smoke on dry days is not heavier than air.\n\nThis conclusion _is_ formal, because the negative throws the second\nSubject altogether outside the Predicate, and so outside the first\nSubject. The one content always has a characteristic which can never\nattach to the other, and consequently it is clear that some genuine\nunderlying difference keeps them apart. Such an inference would\ncorroborate the suggestion previously obtained that the presence of\nmoisture was the active cause of the descending smoke on days when rain\nwas coming.\n\nFig. 1. _A completely reasoned judgment_.\n{149}\n  All particles that sink in the air in damp weather more\n  than in dry, are loaded with moisture when they sink.\n\n  Smoke that descends before rain is an example of particles\n  that sink in the air in damp weather more than in dry.\n\n  \u2234 Smoke that descends before rain is loaded with moisture\n  when it descends (and therefore its sinking is not\n  accidentally a sign of rain, but is really connected with\n  the cause of rain).\n\nThe major premise belongs only to this figure. In the other it is mere\ntradition to call it so, and their two premisses are the same in kind,\nand contribute equally to the conclusion, and for that reason the\naffirmative conclusion was not general or not formal. If your general\nconclusion is to follow by mere form, you must show your principle\nas explicitly covering your conclusion. But if you do this, then of\ncourse you are charged with begging the question. And, in a sense,\nthat is what you mean to do, when you set out to make your argument\ncomplete by its mere form. If you have _bon\u00e2 fide_ to construct a\ncombination of your data, you cannot predict whether the conclusion\nwill take this form or that form. Using a major premise meant, \u201cWe\nhave got a principle that covers the conclusion, and so explains the\ncase before us.\u201d Granting that the major premise involves the minor\npremise and conclusion, that is just the reason why it is imperative\nto express them. The meaning of the Syllogism is that it analyses the\nwhole actual thought; the fault is to suppose that novelty is the\npoint of inference. The Syllogism shows you how you must understand\neither premise in order that it may cover {150} the conclusion. Or,\nstarting from the conclusion as a current popular belief, or as an\nisolated observation or suggestion by an individual observer (and this\nis practically the way in which our science on any subject as a rule\ntakes its rise), the characteristic process through the three stages\ndescribed above consists in first noting the given circumstances under\nwhich, according to the _prima facie_ belief or observation, the\nconjunction in question takes place (\u201cyesterday,\u201d _i.e._ \u201cin the state\nof the atmosphere yesterday\u201d); secondly in analysing or considering\nthose given circumstances, to find within them something which looks\nlike a general property, a law, or causal operation, which may attach\nthe conjunction in question to the systematic whole of our experience\n(the presence of something heavier than air in the atmosphere); and\nthirdly, in the exhibition of this ground or reason as a principle, in\nthe light of which the primary belief or observation (probably a good\ndeal modified) becomes a part of our systematic intelligible world.\n\n\n\n\n{151}\n\nLECTURE X   INDUCTION, DEDUCTION, AND CAUSATION\n\n_Induction_ [1]\n\n1. Induction has always meant some process that starts from instances;\nthe Greek word for it is used by Aristotle both in his own Logic and\nin describing the method of Socrates. It meant either \u201cbringing up\ninstance after instance,\u201d or \u201ccarrying the hearer on by instances.\u201d And\nstill in speaking of Induction we think of some process that consists\nin doing something with a number of instances. But we find that this\nnotion really breaks down, and the contradiction between Mill and other\nwriters (Jevons, ch. i.) shows exactly how it breaks down. The question\nis whether one experiment will establish an inductive truth. We will\nreview the meanings of the term, and show how they change.\n\n[1] Read N. Lockyer\u2019s _Elements of Astronomy_; Abney\u2019s _Colour\nMeasurement_; Introduction to _Bain on Induction_; Jevons\u2019s\n_Elementary Lessons on \u201cObservation and Experiment\u201d_ p. 228, and\non _Induction_, p. 214 (about Mill).\n\n_Induction by simple Enumeration_\n\n(_a_) Induction by simple enumeration was what Bacon was always\nattacking, and saying, quite rightly, that it was not scientific. It is\nthe method which I stated in the Third Figure of the syllogism, almost\na conversational method; the mere beginning of observation. \u201cI am sure\nthe influenza is a serious illness; all my friends who have had it have\nbeen dreadfully pulled down.\u201d\n{152}\n\n  A B C have been seriously ill.\n  ABC have had influenza.\n  \u2234 Influenza is a serious illness.\n\nNow this popular kind of inference, as Bacon says, \u201cPrecarie concludit,\net periculo exponitur ab instantia contradictoria.\u201d Suppose you come\nacross one slight case of influenza, the conclusion is upset. This\ntype of reasoning really appeals to two quite opposite principles;\none the principle of counting, which leads up to statistics and the\nold-fashioned perfect Induction or the theory of chance, the other the\nprinciple of scientific system.\n\n_Enumeration always has a ground_\n\n(_b_) In counting, we do not think of the reason why we count, but\nthere always is a reason, which is given in the nature of the whole\nwhose parts we are counting. If I count the members of this audience,\nit is because I want to know how many units the whole audience consists\nof. I do not ask why each unit is there; counting is different from\nscientific analysis; but yet the connection between whole and part is\npresent in _my reason for counting_. So really, though I only say,\n\u201cOne, two, three, four, etc.,\u201d each unit demands a judgment, \u201cThis is\none member--that makes two members, that makes three members,\u201d etc.\nCounting is the construction of a total of units sharing a common\nnature; measurement is a form of counting in which the units are also\nreferred to some other standard besides the whole in question, _e.g._\nthe standard pound or inch.\n\n_Perfect Induction_\n\n(_c_) _Mere_ counting or \u201cenumeration\u201d only helps you in induction by\ncomparison with some other numerical result, and, if imperfect, only to\nthe extent of suggesting that there {153} is a common cause or there is\nnot a common cause. _E.g._ if you throw a six with one die fifty times\nrunning, you infer that the die is probably loaded. This is because\nyou compare the result with that which you expect if the die is fair,\nviz. a six once in every six throws. You infer that there is a special\ncause favouring one side. The principle is that ignorance is impartial.\nIf you know no reason for one case more than another, you take them\nas equal fractions of reality; if results are not equal fractions\nof reality, you infer a special reason favouring one case. [1] Pure\ncounting cannot help you in Induction in any way but this. _Perfect\nInduction_ simply means that the total is limited and the limit is\nreached; you have counted 100 per cent, of the possible cases, and the\nchance becomes certainty. The result is a mere collective judgment.\n\n[1] See Lecture IX, p. 144, note.\n\n_System_\n\n(_d_) The principle of scientific system is quite a different thing.\nEssentially, it has nothing to do with number or with a generalised\nconclusion. It is merely this, \u201cWhat is once true is always true, and\nwhat is not true never was true.\u201d The aim of scientific induction is\nto find out \u201cWhat _is_ true,\u201d _i.e._ what is consistent with the given\nsystem. We never doubt this principle; if we did we could have no\nscience. If observation contradicts our best-established scientific\nlaws, and we cannot suppose an error in the observation, we must\ninfer that the law was wrongly, _i.e._ untruly stated. Therefore, as\nMill says, one case is enough, _if_ you can find the truth about it.\nPeople object that you cannot make a whole science out of one case,\nand therefore you must have a number of instances. That is a {154}\n_practical_ point to be borne in mind, but it has no real scientific\nmeaning. \u201cInstance\u201d cannot be defined except as one observation, which\nis a purely accidental limitation. The point is, that you use your\ninstances not by counting cases of given terms, but by ascertaining\nwhat the terms really are (_i.e._ modifying them), and what is their\nreal connection. This is the simple secret of Mill\u2019s struggle to base\nscientific Induction, on Induction by simple Enumeration; the latter is\nnot the evidence, but the beginning of eliciting the evidence--so that\nthe Scientific Induction is far more certain than that on which Mill\nbases it. Aristotle\u2019s statement is the clearest and profoundest that\nhas ever been made. [1]\n\n\u201cNor is it possible to obtain scientific knowledge by way\nsense-perception. For even if sense-perception reveals a certain\ncharacter in its object, yet we necessarily perceive _this_, _here_,\nand _now_. The universal, which is throughout all, it is impossible to\nperceive; for it is not a this-now; if it had been it would not have\nbeen universal, for what is always and everywhere we call universal.\nSince then demonstration (science) is universal, and such elements it\nis impossible to perceive by sense, it is plain that we cannot obtain\nscientific knowledge by way of sense. But it is clear that even if we\nhad been able to perceive by sense [_e.g._ by measurement] that the\nthree angles of a triangle are equal to two right angles, we should\nstill have had to search for a demonstration, and should not, as some\nsay, have known it scientifically (without one); for we necessarily\nperceive in particular cases only, but science comes by knowing the\nuniversal. Wherefore if we could have been on the moon, and seen the\nearth coming between it and the {155} sun, we should not (by that mere\nperception) have _known_ the cause of the eclipse. Not but what by\nseeing this frequently happen we should have grasped the universal,\nand obtained a demonstration; for the universal becomes evident out\nof a plurality of particulars, and the universal is valuable because\nit reveals the cause;\u201d and again, [2] \u201cAnd that the search of science\nis for the middle term is made plain in those cases in which the\nmiddle term is perceptible to sense. For we search where we have had\nno perception,--as for the reason (or middle term) of an eclipse,--to\nknow if there is a reason or not. But if we had been upon the moon, we\nshould not have had to inquire if the process (of an eclipse as such,\nand not some other kind of darkness) takes place, or for what reason,\nbut both would have been plain at once. The perception would have been,\n\u2018The earth is now coming between,\u2019 carrying with it the obvious fact,\n\u2018The moon is now suffering an eclipse,\u2019 and _out of this_ the universal\n(connection) would have arisen.\u201d\n\n[1] Aristotle, _An. Post._ 87, b. 28.   [2] _Ibid._ 90, a. 24.\n\n_Analogy_\n\n(_e_) I showed you a method on the way to this in the shape of\nAristotle\u2019s second figure, which we may call _analogy_. The plain sign\nof it is, that you give up counting the instances and begin to weigh\nthem, so that the attributes which are predicates fall into the middle\nterm or reason. In the former inference about influenza we did not\nsuppose that you had any idea _why_ influenza was a serious illness;\nbut in analogy there is some suggestion of this kind, so that the\nconnection is examined into. Here at once you begin to get suggested\nexplanations and confirmation from the {156} system of knowledge. You\ncannot have analogy by merely counting attributes.\n\nI begin from _Enumerative Suggestion_ drawn from observation of\nButterflies.\n\n1. Three species of genus _x_ closely resemble three species of _y_.\n\n2. The species of _x_ would be protected by resembling _y_ (because _y_\nis distasteful to birds).\n\n\u2234 The resemblance may be a \u201cprotective resemblance,\u201d _i.e._ a\nresemblance brought about by survival of those thus protected.\n\nOn this there naturally follows _Analogy_.\n\n1. Protective resemblances naturally increase through series of species\nfrom slighter to closer resemblances.\n\n2. The resemblances in question increase in genus _x_ through series of\nspecies from slighter to closer resemblance to _y_.\n\n\u2234 The resemblances in question show important signs of being protective\nresemblances.\n\nWhen we get thus far, a single syllogism will not really represent\nthe argument. It can only analyse with convenience a single step in\ninference. But now we have connected the reason of the resemblances\nwith the whole doctrine of natural selection, the gradual approximation\nof the species is most striking, and we could set up a corroborative\nanalogy on the basis of every feature and detail of these resemblances,\nthe tendency of which would be to show that no cause or combination of\ncauses other than that suggested is likely to account for the observed\nresemblances.\n\n{157} I give a confirmatory negative analogy.\n\n1. No protective resemblance can grow up where there is no initial\ntendency to resemblance.\n\n2. The non-resembling species in the genus _x_ show no initial tendency\ntowards _y_.\n\n\u2234 The non-resemblances observed are such as could not produce\nprotective resemblances. This is a formally bad argument from two\nnegative premisses justified by its positive meaning, which implies\nthat _just where_ the alleged effect ceases, the alleged cause ceases\ntoo.\n\nIf you look at the case in the Natural History Museum [1] you see the\nnormal Pierinae down one side, not approaching Euploinae. They are the\npositive examples, negatively confirming the explanation of those which\ndo approach Euploinae. These latter all start from some form which\nvaried slightly, by accident we presume, towards Euploinae, and then\nthis partially resembling series splits into three sets, each leading\nup to a different and complete protective resemblance.\n\n[1] These cases in the entrance-hall of the Natural History\nMuseum at South Kensington afford excellent practical\nillustrations of Inductive Method. I strongly urge the London\nstudent to try his hand at formulating them.\n\nI said _mere_ number was no help in scientific Induction. But do not\nthese three sets of resemblances make a stronger proof than any one\nwould? Yes, because we need a presumption against accident. You would\nnot want this if you could unveil what really happens in one case,\nbut as infinite conditions are operative in such matters, and it is\nimpossible to experiment accurately, [1] this cannot be done; {158}\nand it might be said that _one_ such resemblance was an accident,\n_i.e._ that it was owing to causes independent of the protection. But\nas the cases become more numerous it becomes more improbable that\ndifferent circumstances produce the same effect, which would then be\na mere coincidence, in so many different cases. If, however, we knew\nby positive and negative analysis what circumstance did produce the\neffect, this confirmation would be useless.\n\n[1] Ultimately, no experiments are absolutely accurate. There is\nalways an unexhausted background in which unsuspected causes of\nerror may be latent.\n\n_Negative Instance_\n\n(_f_) In order to show _exactly_ what circumstance produces a given\neffect, a system must be brought to bear on the phenomenon through\nnegation. The only test of truth is that it is that which enables you\nto organise your thought and perception.\n\nThe first means of doing this is Observation, then Experiment, then\nClassification and Hypothesis, which takes us into Deduction.\n\nObservation is inaccurate, until you begin to distinguish what is\nconnected from what is not connected. When you do this, you are very\nnear experiment, the use of which is to introduce perfectly definite\nand measurable changes into what you are observing. [1] There is no\nabsolute distinction between observation and experiment. Looking at a\ntissue through a microscope is observation; putting on a polariscope,\nthough it changes the _image_ altogether, is observation; if you\nwarm the stage, or put an acid on the object, that, I suppose, is\nexperiment, because you interfere with the object {159} itself. What\nshould we say, for example, as to spectroscopic analysis of the Sun\u2019s\ncorona?\n\n[1] Jevons, _loc. cit_., esp. quot. from Herschel (p. 234).\n\nThe moment you begin accurate observation you get a negative with\npositive value, which is really the converse by negation of your\npositive observation, a1 is b1; b2 (which is _just_ not-b1) is a2\n(which is _just_ not-a1). Thus the two may be represented as the same\njudgment in positive and negative forms, which confirm one another.\n\u201cYellow is a compound of red and green\u201d--in Experiment, \u201cif, and as far\nas you take away the red or the green you destroy the yellow.\u201d That\ndescribes an experiment with the colour-box. I have inverted the order\nin the conversions in compliance with the rule of common Logic, that\nPredicate is wider than Subject; but in accurate matter it is a false\nrule, and very inconvenient. The common rule means that a man who is\ndrowned is dead, but a man who is dead need not have been drowned; but\nof course if he has the signs of death by drowning then he has been\ndrowned.\n\n_Classification and Generalisation_\n\n(_g_) _Classification_ is a consequence of all systematic theory; it\nis not a separate method of science. It is merely the arrangement\nof positive contents negatively related. No doubt where we have a\nkind of family relations between individuals classification is more\nprominent, and in the theory of continuous matter or operation, where\nindividualities are not remarkable--_e.g._ in geometry--it is less\nprominent. But both are always there--classification and theory.\nClassification which expresses no theory is worthless, except that\nintended for convenient reference, such as alphabetical classification.\n\nUnder classification I may say a word on generalisation. {160} The\ncommon idea of inference from many cases, because they are many, to\nall cases of the same kind, is quite without justification. The only\ngenuine and fundamental law of generalisation is \u201cOnce true always\ntrue.\u201d But this might fail to suffice for our practical purposes,\nbecause it might save its truth by abstraction. Let us take the\nexample, \u201cWater is made of oxygen and hydrogen.\u201d If that is true once,\nit is always true _in the same sense_. If you find some fluid of a\ndifferent composition which you are inclined to call water, then you\nmust identify or distinguish the two, and this is a mere question of\nclassification. _Practically_, however, we could not get on unless our\nknowledge had some degree of _exhaustiveness_, _i.e._ unless we knew\nroughly that most of _what we take for water_ will have the alleged\nproperties. But no Induction or analysis, however accurate, can assure\nus against confusion and error, viz. assure us that everything we take\nto be water will be made of oxygen and hydrogen, nor that water will\nalways be found on the earth. I call this accurate analysis, which\n_may_ be made in a single instance only, and is the only perfectly\nscientific generalisation, generalisation by mere determination. Its\nclassification is hypothetical, _i.e._ in it the individuals are merely\npossible individuals.\n\nBut this passes into another kind of generalisation, which may be\ncalled generalisation by concrete system, as when we attach scientific\nanalysis to some extensive individual reality, _e.g._ to the solar\nsystem or the race of man. Then our judgments have a place in the\nreal world, and our classification is categorical classification. The\ngeneralisation in this case does not follow from the judgment being\nextended {161} over a great plurality of possible similar subjects, but\nfrom the subject to which it applies having as an organised totality\na large place in the world; _e.g._ \u201cThe human race alone gives moral\ninterest to the history of bur planet.\u201d These judgments come by making\nexplicit the reality which underlies such hypothetical judgments as\n\u201call men are capable of morality.\u201d It means that we actually venture to\nassign a place in the universe to the system we are speaking of. Then,\nthough it is an individual, and unique, its name has a meaning, and is\nnot a mere proper name. The solar system is good instance. Judgments\nabout it or parts of it are universal but not purely hypothetical,\nand as our knowledge of this kind increases it becomes even a little\nexhaustive.\n\n_Generalisation by mere likeness or analogy_, on the other hand, is\nprecarious. It is what popular theory has in its mind in speaking of\nInduction, viz. a conclusion from a truth to judgments concerning all\nsimilar cases, _e.g._ from \u201cWater is made of Oxygen and Hydrogen\u201d to\n\u201cAll liquids which we choose to take for water are made of Oxygen and\nHydrogen.\u201d No scientific method can possibly give us this result. In as\nfar as it has value it depends upon our guessing rightly by analogy.\nIt may be replied, \u201cthat the signs of recognition are set down in\nthe law or truth.\u201d Well, if they are certain, generalisation by mere\ndetermination is enough; if they are doubtful, no induction can warrant\nyour judgment of them in particular cases. Practically, of course, we\nget them right pretty often, although wrong very often.\n\n_Hypothesis_\n\n(_h_) Hypothesis is merely supposition; it consists in suggesting a\nfact as if it were real, when it is the only way of {162} completing\ngiven facts into a consistent system. If the hypothesis is proved that\nis a demonstration. It has been said that \u201cFacts are only familiar\ntheories.\u201d If a bell rings in the house, I say unhesitatingly, \u201cSome\none rang that bell.\u201d Once in ten years it may be rung, not by a person,\nbut by some mechanical accident, in which case the \u201csome one\u201d is a\nhypothesis, but one always treats it as a fact. The only proof of a\nhypothesis is its being the only one that will fit the facts, _i.e._\nmake our system of reality relatively self-consistent. We believe many\nthings we can never verify by perception, _e.g._ the existence of the\ncentre of the earth, or that you have an idea in your minds; and if we\ngo to ultimate analysis, perception itself involves hypothesis, and\n_a fortiori_ all experiment involves hypothesis. Every experimental\ninterference with nature involves some supposition as to a possible\nconnection which it is intended to confirm or disprove.\n\n_Deduction_\n\n2. Classification and hypothesis bring us into Deduction, which is not\nreally a separate kind of inference from Induction, but is a name given\nto science when it becomes systematic, so that it goes from the whole\nto the parts, and not from the parts to the whole. In Induction you are\nfinding out the system piecemeal, in Deduction you already have the\nclue; but the system, and the system only, is the ground of inference\nin both. Induction is tentative because we do not know the system\ncompletely. Their relation may be fairly represented by the relation\nof the first figure of the Syllogism to the second and third. The\ndifference is merely that in deduction we are sure of having knowledge\nwhich covers the whole system. If a man observed, \u201cThe difference\n{163} between the dark blood in the veins and the bright blood in the\narteries calls for explanation,\u201d that is the beginning of Induction. If\na man states the circulation of the blood as an explanation, that is\nDeduction. Really Induction is only a popular name for such Inference\nas deals with numbers of instances. Mill\u2019s experimental methods do\nnot depend upon number of instances, but only upon content; they\npresuppose the instances already broken up into conditions A, B, C, and\nconsequents a, b, c.\n\nI must distinguish subsumption and construction as two forms of\ndeduction. Only the former _properly_ employs Syllogism in the first\nfigure.\n\n_Subsumption_\n\n(_a_) Subsumption is argument by subject and attribute; _i.e._ when\nwe do not know the system so as to construct the detail,--_e.g._ a\nman\u2019s character,--and can only state _in_ what individual system the\ndetails occur. Then we _really want_ the major premise to lay down the\nproperties of the system, and all deduction _can_ therefore be employed\nwith a major premise, _e.g._ a mathematical argument might ultimately\ntake the form, \u201c_space is such that_ two parallels cannot meet.\u201d\n\n_Construction_\n\nBut (_b_) when the nature of the subject is very obvious, and\nthe combinations in it very definite, then the major premise is\nsuperfluous, and adds nothing to the elements of the combination.\n\n  \u201cA to right of B, B to right of C.\n  \u2234 A to right of C.\u201d\n\nThis is clear, but it is not formal; as a syllogism it has four terms.\nIt is simply a construction in a series of which the nature is obvious.\nAnd if you insert a major premise it would be, \u201cWhat is to the right\nof anything is to the right {164} of that which the former is to the\nright of,\u201d and that is simply the nature of the series implied in the\ninference stated in an abstract form. \u201cInference is a construction\nfollowed by an intuition.\u201d [1] The construction, I think, however,\nmust be a stage of the intuition. I am therefore inclined to suggest\nthat a factor of general insight into principle is neglected in this\ndefinition, from which much may undoubtedly be learned.\n\n[1] Bradley, _Principles of Logic_, p. 235.\n\n_Causation_\n\n3. I have said very little about causation. The fact is, that in\nLogic the cause necessarily fades away into the reason, that is, the\nexplanation. If we follow Mill\u2019s account, we see how this takes place.\nI will put the stages very briefly.\n\n_Cause_\n\n(_a_) We start, no doubt, by thinking of a cause as a real event in\ntime, the priority of which is the condition of another event, the\neffect. Pull the trigger--cause--and the gun goes off--effect.\n\n_Complete conditions_\n\n(_b_) The moment we look closer at it, we see that this will not\ndo, and we begin to say with Mill, that the cause is the antecedent\nwhich includes _all_ the conditions of the effect. The plurality of\nalternative causes breaks down, through the conditions defining the\neffect. Pull the trigger?--yes, but the cartridge must be in its place,\nthe striker must be straight, the cap must be in order, the powder must\nbe dry and chemically fit, and so on, and so on, till it becomes pretty\nclear that the cause is a system of circumstances which include the\neffect.\n\n_Law_\n\n(_c_) But then our troubles are not ended. Only the essential and\ninvariable conditions enter into the cause, if the {165} cause is\ninvariable. This begins to cut away the particular circumstances of\nthe case. You need not use the trigger, nor even the cap; you may\nignite powder in many ways. You may have many kinds of explosives. All\nthat is essential is to have an explosion of a certain force and not\ntoo great rapidity. Then you will get this paradox. What is merely\nessential to the effect, is always something less than any combination\nof real \u201cthings\u201d which will produce the effect, because every real\nthing has many properties irrelevant to this particular effect. So,\n_if the cause means something real_, as a material object is real, it\ncannot be invariable and essential. If it is not something real, and\nis essential, it fines down into a reason or law--the antecedent in a\nhypothetical judgment.\n\n_Ground, or real system with known laws_\n\n(_d_) We can only escape this by identifying both cause and reason\nwith the complete ground; that is, the nature of a system of reality\nwithin which the cause and effect both lie. But even then, though the\nground is _real_, it is not antecedent in time. We see, indeed, that\nthe conditions of an effect must be continuous through the effect. If\nthe process were taken as cut in two at any point, its connection would\nbe destroyed. If _a_ cause and _b_ effect were really detached events,\nwhat difference could it make if, instead of _a_, _c_ preceded _b_?\n\n_Postulate of Knowledge_\n\n4. The postulate of Knowledge, then, is very badly stated as\nUniformity of Nature. That was due to the vulgar notion of Inductive\n\u201cgeneralisation.\u201d It must be stated in two parts: first, \u201cOnce true\nalways true;\u201d and secondly, \u201cOur truth is enough for us,\u201d that is, it\ncovers enough of the universe for our practical and theoretical needs.\nThe {166} two parts may be put together by saying, \u201cThe universe is a\nrational system,\u201d taking rational to mean not only of such a nature\nthat it can be known by intelligence, but further of such a nature that\nit can be known and handled by our intelligence.\n\n_Conclusion_\n\n5. These lectures have been unavoidably descriptive rather than\nthorough, and yet, as I warned you, descriptive of properties which\nare in a sense not at all new, but quite familiar, and even trite. You\nwill not feel, at first, that the full interest which I claimed for\nthe science of knowledge, really attaches to these dry relations of\nabstract thought. You will get no permanent good unless you carry the\nstudy forward for yourselves, and use these ideas as a clue to find\nyour bearings in the great world of knowledge.\n\nAnd I would give you one hint about this. _I_ do not suggest that you\nshould neglect philosophy but yet you should remember that philosophy\ncan tell you no new facts, and can make no discoveries. All that it\ncan tell you is the significant connection of what you already know.\nAnd if you know little or nothing, philosophy has little or nothing to\ntell you. Plato says, \u201cThe synoptical man, the man who has a conspectus\nof knowledge, is the philosopher; and the man who is not synoptical,\nwho cannot see two subjects in their relation, is no philosopher.\u201d\nBy all means read good logical books; but also and more especially\nread good and thorough systematic books on science, or history, or\npolitics, or fine art--I do not mean on all of these subjects, but on\nsome, wherever your interest leads you. You cannot learn the nature of\ninference, of systematic necessity, of the construction of reality,\nby reading logic exclusively; you must {167} feel it and possess it\nby working in the world of concrete knowledge. I give one example in\npassing. If you study social questions, test for yourselves the value\nof statistics--_i.e._ sets of enumerative judgments. Consider what the\ncausal analysis of any problem demands; remember that all enumeration\nimplies a ground or whole, on which its value depends; and contrast\nthe exhaustive examination of an instance thoroughly known, with the\nenumeration of thousands of cases lumped under a general predicate.\nDetermine always to know the truth; welcome all information and all\nsuggestion, but remember that truth is always systematic, and that\nevery judgment, when you scrutinise it, demands a fuller and fuller\nconnection with the structure of life. It is not cleverness or learning\nthat makes the philosopher; it is a certain spirit; openness of mind,\nthoroughness of work, and hatred of superficiality. Each of us,\nwhatever his opportunities, can become in a true sense, if he has the\nreal philosophic spirit, in Plato\u2019s magnificent words, \u201cThe spectator\nof all time and of all existence.\u201d\n\nTHE END","title":"The Essentials of Logic, Being Ten Lectures on Judgment and Inference","tradition":"philosophy-ethics","translated_text":null,"word_count":48667}