The original of tiiis book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924098139649 3 1924 098 139 649 In compliance with current copyright law, Cornell University Library produced this replacement volume on paper that meets the ANSI Standard Z39.48-1992 to replace the irreparably deteriorated original. 2003 BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF 1891 A: "^^ 7.^.N ;; ;: • /^/^ ? < THE THEORY OF Kl^OWLED&E THE THEORY OF KNOWLEDGE A CONTRIBUTION TO SOME PEOBLEMS OF LOGIC AND METAPHYSICS L. T. HOBHOUSE FELLOW AND AaSISTANT-TTJTOE, OF CORPUS CHRISTI COLLEGE OXFORD LONDON METHUEN & CO. NEW YORK: MACMILLAN & CO. 1896 B. % PREFACE The world of thought at the present day is in a somewhat anomalous condition. We have come to the point where science seems to stand in real danger of heing ruined by her own success. The mass of accumulated fact on which she justly prides herself has become too vast for any single mind to master. There could be no Aristotle ia the nineteenth century. Tear by year it becomes more difficult to take any sort of view of the whole field of fcaowledge which should be at once comprehensive and accurate. It results that positive knowledge can scarcely be said any longer to have a general purpose or tendency. Intellectually, it is an age of detail The unity which we miss in science we might hope to find in philosophy. And here, indeed, our century has done its best. In Germany, in France, and ia England it has produced great systems, containing elements of high permanent value. But these systems date from before the deluge of specialism. And they have all been, not so much refuted, — for a dialecticail refutation can, after aU, be lived down, — as imdermined by the subsequent movement of thought and discovery. Nor is this alL Not only is there no accepted scientific system, but in England, at least, the tendency of philosophic work is scarcely sympathetic to science. So far from seeing our way to a near or distant synthesis, we are more distracted than ever when we turn from science to philosophy. Instead of uniting the sciences, philosophy threatens to become a separate and even a hostile doctrine. The antagonism is doubtless veUed, and the philo- sopher, like the theologian, is careful to avoid direct conflict with a far stronger foe. But the veil is not difScult to pierce. viii PREFACE The reaction against the scientific spirit, so characteristic of our generation, has shown itself in the philosophic world in the decay of what has been called the English school. Along with many defects and limitations, that school, from Bacon and Locke to MiU and Spencer, has had the merit of dealing, or attempting to deal, in a sympathetic spirit with the problems and methods of the sciences. The shortcomings of empiricism have been pointed out adequately enough now by the brilliant series of critics who have drawn their inspira- tion from other sources, and the danger at present seems to be that the real services of the English school should be forgotten. On the other hand, the newer movement in our thought, now itself nearly thirty years old, has hardly fulfilled its promise of giving us on metaphysical groimds a better synthesis than could be hoped for from science. As time has gone on, the purely negative and critical side of the movement has tended to gain the upper hand ; and in the great metaphysical work of the keenest intellect which the school has produced, while everyone admits the force of the negative dialectics, such con- structive conceptions as remain seem scarcely at home. The net result is that in philosophy we tend towards negation. We get far enough to be sceptical about the foundations of science, and there we stop. In such a state of things the sinister interests in the commonwealth of know- ledge see their chance. The popular essayist tells us that there is really nothing to speak of that we can know with certainty. One behef is on the whole as untrue as another, and therefore why not keep to that which is recommended to us by authority as best suited to our needs? An elegant scepticism about science takes the place of the elegant scepticism of theology with which our forefathers were famUiar. If we dismiss scepticism as a mere symptom of temporary intellectual paralysis, the task before philosophy, if full of difificulty, seems equally full of hope. In many directions ideas have been struck out, principles suggested, old barriers to clear thinking removed, and detail work accompUshed in a thoroughgoing manner. The main difficidty is to blend the divergent currents of thought, and in particular the methods X PREFACE most powerful to be found. Mill and Mr. Bradley apart, perhaps I have learned most from Mr. Bosanquet's Logic and from the psychological work of Prof. James and Dr. Ward. My special thanks are due to Prof. Alexander for carefully reading the proofs, and for many most valuable criticisms and suggestions, which are incorporated as far as possible in the text and are not further acknowledged. One great difficulty in a work; like the present is to find illustrations of logical method. .Without special scientific training it is impossible to illustrate either adequately or accurately. I am conscious of great shortcomings on this head, but I have been greatly helped by Prof. Burdon Sanderson, who kindly read the chapters mainly concerned, and to whose suggestions I owe much. For the rest, I have collected illustrations as best I could from scientific text- books, elementary or advanced. It has not seemed necessary to make any more special acknowledgment of this debt. Lastly, I cannot close this list of obhgations without expressing some gratitude for aU that I learned from the private teaching of Prof. Case and Dr. Fowler, and from the lectures of Prof. Alexander and the late Mr. E. L. Nettleship. L. T. HOBHOUSE. OxpoED, Oct. 5, 1895. PREFACE IX of philosophy and science. For such a synthesis the first step needed is to break down the wall still maintained between the sphere of the systematised common sense which we call science and the world of ultimate reality. The contrast between the natural and supernatural, the shadow of which still lingers in the metaphysical contrast of phenomena and noumena, or appearance and reality, needs to be banished before we can even think of knowledge as a harmonious whole. But if science may claim to investigate the "really real," we need not suppose that its analytic method is the only process which can do so. The higher conceptions by which ideahsm has so firmly held are not to be " scientifically " treated in the sense of being explained away. What is genuinely highest, we have good reason to think, must also be truest, and we cannot permanently acquiesce in a way of thinking which would resolve it into what is lowest. The time would thus seem ripe for an unprejudiced attempt to fuse what is true and valuable in the older English tradition with the newer doctrines which have now become naturalised among us. In betaking ourselves to Lotze and Hegel, we need not forget what we have learnt from Mill and Spencer ; and if we can hold the old and new together we may perhaps find ourselves on the way to the synthesis which we seek. In trying to learn from sources so varied, I have incurred so many obHgations that it is difiBcult for me to make special acknowledgments. But in view of the discredit into which his work is supposed to have fallen, I should like to lay especial stress on my obligations to Mill. MiU was guilty of short- comings and inconsistencies, like other philosophers, but the head and front of his offending was that, unhke many other philosophers, he wrote inteUigibly enough to be found out. But Mill is not the only writer who has made mistakes, nor is he the only writer who remains great in spite of them. Of course, I also owe much to the many writers whose names appear on the following pages mainly where I have ventured to differ from them. In this connection I wish particularly to acknowledge my great debt to my friend Mr. F. H. Bradley, whom I have been compelled to single out for criticism simply because his statement of views which I wish to combat is the CONTENTS INTRODUCTION NATtniE OP THE Problem PAGE (1) Logic examines the content, grotmds, and validity of belief in general — (2) Its relation to psychology — (3) Its method is hypothetical (4) and, unavoidably, abstract — (5) It is the first stage of philosophy, rather than philosophy itself . , 1-11 PAET I.— DATA CHAPTEE I Simple Apprehension (1) Knowledge of the immediately present may be called appre- hension. It is a cognitive act— (2) Its content is of varying degrees of definiteness, (3) and wholly independent of thought- relations, (4) though not always the direct result of a sense- stimulus ; (5) it is fact even when it is Olnsion — (6) Eesult : Apprehension is the starting-point of knowledge . . . 15-37 CHAPTEE II The Content of Appeehension (1) May be complex within limits, and includes relations— (2) Exten- sion is matter of immediate apprehension — (3) So are size, shape, and even (4) position — (5) To suppose that time also can be present to apprehension seems self-contradictory, (6) but the term present is ambiguous. In fact, the apprehended content always has diu'ation, (7) the upper and lower limits of which can be roughly fixed — (8) The atomic sensation a figment . 38-59 xii CONTENTS CHAPTER III Obsoubb, Cleae, and Analysed Consciousness PAGE (1) The present may be obscure— (2) Relation of obscure and clear, (3) of clear and analysed contents. Analysis a movement of attention within the given ..... 60-67 CHAPTER IV Memokt (1) Not an image, but an assertion of the past, (2) and hence a refer- ence to something not now present ; (3) not to be explained by any persistence of the past. It is a distinct postulate of knowledge, but its accuracy may be tested, and (4) its exist- ence, very possibly, explained by psychological laws . , 68-80 CHAPTER V CONSTEITCTION (1) Brings wholes together, which have been given not as wholes but in all their elements, as in memory-synthesis or (2) in most oases of comparison ...... 81-84 CHAPTER VI Ideas (1) An idea is a content (2) referring to reality, and itself also an object of reference ; (3) otherwise it is a synonym for an image which logically is merely a present fact . . . 85-91 CHAPTER VII General Ideas (1) The general idea is a content existing many times in reality — (2) Apart from numerical plurality, a content must be either individual or indeterminate — (3) Transition from differences of context to differences of specific character — (4) Idea, image, and symbol — (5) Language, as symbolic, implies inference, and (6) a common but not necessarily a general reference . . 92-107 CONTENTS Xlll CHAPTER VIII Eesemblance aud Identity (1) Both are "ultimate " in sense of being given, and (2) either may serve as basis of a general idea — (3) Likeness rendered definite by the conception of degree — (4) Ideas may admit of definite specific differences— (5) " Sensible'' and "intelligible" re- semblance^(6) Distinction between exact resemblance and numerical identity ...... 108-121 CHAPTER IX The Qualitatitb Jtjdqment (1) Taken in full asserts the present to be a centre of resemblances — (2) This meaning not always explicit — (3) Further, it analyses and, more or less explicitly, distinguishes the present from other facts — (4) It may depend on inference, (5) but need not do so except as concerns its verbal expression — (6) When the other term of the resemblances is specified, it passes into the comparative judgment — (7) Relation of these and other allied functions ....... 122-138 CHAPTER X The Jtjdgments of Relation and Description ^ (1) The first deals with related elements of the given, (2) the second with the whole as consisting of elements — (3) The collective judgment — (4) The judgment as such deals with the order and resemblances of given facts 139-145 CHAPTER XI Geneeal Nattjee of Judgment (1) Judgment affirms the reference to reality contained in an idea; (2) in so doing it necessarily predicates something of something already otherwise known — (3) As distinct from a "mere" idea, it involves some degree of belief — (4) Negation rejects a sug- gested reference — (5) No definite boundary line between subject and predicate ....... 146-157 xiv CONTENTS CHAPTEE XII The Validity of Judgment PAGE (1) Subject and predicate are never identical— (2) The predication puzzle based on a confusion between the subject and the whole reality dealt with, (3) and on the double meaning of the copula (4) Judgment " combines " concepts, but not mechanically — (5) Qualities and relations imply one another, (6) but only as different aspects of the same reality — (7) A relation con- stituted hy its terms — (8) One whole constituted by many interrelated attributes — (9) Analysis does not involve unreal separation — (10) Space and time not proved unreal by infinite divisibility or infinite extent ..... 158-186 PART II.— INFERENCE , CHAPTEE I Imagination and its Factoks (1) Imagination forms "new" contents (2) working by construction and abstraction — (3) Abstraction depends on analysis, (4) but is limited by comparison, (5) apart from which it can only distinguish without separating — (6) Misuse of abstraction leads to dialectic, (7) which is vprongly regarded as of essence of thought. . 189-202 CHAPTER II Imaginatiok as Constructive (1) Unites ideas by a point of identity, (2) which involves the applica- tion of one to another — (3) Imperceptible and (4) "ideal" contents are special cases — (5) Conception . . . 203-214 CHAPTER III Infeebnce— General Characteeistics (1) Inference gives us "new " truth, but this not a sufficient criterion — (2) As a process it is more explicit than judgment, (3) and it rests on the conditional relation. Implicit inference, (4) distinct from "physiological inference" — (5) Conclusion not always "contained in" premisses — (6) Inference involves belief, (7) and implies validity of its process , . , 215-231 CONTENTS XV CHAPTER IV The Implications of Infbkenoe t . . PAGE (1) .Premisses either equivalent to conclusion or imply judgment which makes them so — (2) Argument from minor to conclusion implies major ....... 232-238 CHAPTER V Genekalisation (1) The universal judgment an indefinitely extended collective, (2) to be distinguished from the general idea — (3) It attributes con- nection both subjectively (4) and objectively ; (£) but is not hypothetical — (6) Its basis our main question . . . 239-249 CHAPTER VI Equivalent and Quasi-equivalent Inpeeenoes (1) Syllogism an equivalent inference (2) formed by construction and analysis — (3) Is it really inference? — (4) Yes, as explicitly recognising the conditional relation — (5) Inference from relations to their resultant distinct from syllogism — (6) ' ' Immediate " inferences involve no new principle — (7) Three types of inference ...... 250-261 CHAPTER VII The Basis op Generalisation (1) Generalisation rests on uniformity ; (2) may be supported by any parallel, and can only be opposed by a contrary case. Hence principle of generalisation, 'which implies (8) an assumption as to the connection of facts, and ultimately (4) the law of the ground ........ 262-272 CHAPTER VIII Development of the Pbinciples of Generalisation (1) Unity of effect — (2) Ground and cause. Continuity — (3) Logic of consistency ....... 273-279 CONTENTS CHAPTER IX Ceiticisms of the Theory op Genebalisation PAGE (1) Tte argument from particulars : what it means ; (2) what it does not mean— (3) Principle of identity useless . . . 280-288 CHAPTER X Peobable Reasoninq axd Analogy (1) Probability must have a definite ground, (2) namely, approximate conformity to fact— (3) "Weak probability derivable from partial resemblance ....••• 289-295 CHAPTER XI NUMEEIOAL PeOBABILITY (1 ) Gives approximation to truth (2) on assumption that most ' ' prob- able " event is actually most frequent — (3) What the casual is (4) Frequency proportionate to degree of connection — (5) This has a real meaning, (6) and is ultimately deducible from the law of the ground— (7) Difficulties in applying it— (8) It justifies analogical probability ..... 296-316 CHAPTER XII Possibility (1) A " mere " possibility (2) at first sight seems a pure impossibility, but (3) is sometimes only a worthless suggestion, (4) though at other times it should be categorically rejected . . , 317-326 CHAPTER XIII The Inductive METioDS Observed relation may be generalised with certainty if there is no ground for attributing it to a concomitant. Methods of generalisation : (1) Simple enumeration leaves us with four alternatives ; (2) with negative it proves some sort of connection — (3) Yariation of area generalises the connection, and (4) observation of definite coincidences make it more certain. Vagueness of these methods . . ... . 327-341 CONTENTS xvii CHAPTER XIV Scientific Induction (1) Continued identity or process prove relevance — (2) Method of difference (a) determines a factor in the cause, (6) assuming that it can adequately isolate its phenomena, of which there are (c) and (d) several sufficient tests .... 342-360 CHAPTER XV Scientific Indtjction {continued) (1) Concomitant variations may contribute to proof of connection — (2) Method of agreement incomplete by itself — (3) Joint method proves true universal — (a) Plurality of causes not a final objection — (5) Results practically limited by counteracting causes — (c) Argument from continuity may be substituted for method of difference — [d) Adequacy of test ultimately empirical ....... 361-384 CHAPTER XVI The Intekconneciion of Genebal Tbuths Inductions may be independent and yet support one another : (1) in case of causes differing from one another in definite quality or degree ; (2) by forming a single composite induction ; (3) by converging on same particular fact ; (4) by forming, construct- ively, an independently known total result ; (5) by mutually determining the action of concomitants. Result of conver- gence is certainty of science ..... 385-i07 CHAPTER XVII Induction and Htpothesis (1) We use hypothesis, but not the inverse method, which fails to explain validity of science — (2) Hypothesis distinguished from construction of conceptions — (3) Argument from effect to cause is net of inverse type, and may be certain or probable . 408-423 CHAPTER XVIII Constrtjctive Geneeahsation (1) Is based on experience, but implies certain axioms (2) which rest ultimately on a postulate of the judgment — (3) Mathematics CONTENTS rest on constructions generalised under these axioms — (4) Ordinary induction sometimes used to verify axioms — (5) Axioms formed by direct application of the postulate — (6) Construction is only inference if generalised . . . 424-441 CHAPTER XIX Explanation (1) That laws must be explicable, follows from principles of induction — (2) General character of explanation — (3) It assumes a starting-point, and certain elementary laws. But these last it interconnects, (4) (a) and (J) and aims at reducing them to a form in which they are intrinsically intelligible as depending on the general character of the causal nexus, (c) which is, further, such as to restrict the plurality of causes to narrow limits, but (5) forces us to admit an element of variability running through nature — (6) Explanation the ideal of science. The higher forms of classification subsidiary to it . . 442-474 CHAPTER XX SUMMAEY OP THE ThBOKY OF InFEKENOB In inference thought treats general relations as necessary. It works on many distinct but connected methods. Frimd fade a method is sound if used by thought and uncontradicted by experience. The validity of this assumption requires now to be examined ....... 475-480 PART III.— KNOWLEDGE CHAPTER I Validity (1) The conception of truth (2) involves power of correcting judg- ments. Corrected value of a judgment is its validity— (3) But what is the final test of validity ? — (4) Opinions on this point .......< 483-498 CHAPTER II The Validity of Knowledge (1) Validity depends on consilience — (2) Dissidenoe may be overcome by "explanation" — (3) Methods made valid by supporting CONTENTS one another. Result : knowledge valid as a system of judg- ments connected by valid methods — (4) Use of inductive principles in limited experience justified ultimately because they formulate methods successful in that experience — (5) The principle of validity itself guaranteed by the system which it forms ........ 499- ■516 CHAPTER III The Conception of External Reality (1) Logic should deal with our most generic conceptions of reality — (2) First, external reality — (3) This basec' on be laviour of certain objects (4) which cannot be explained as the "inward" effect of an " outer " order — (5) Objects are given to the mind, not constructed by it — (6) Perception not incorrect because "subjective "—(7) No contradiction in the view that appre- hension is of outer things ..... 517-539 CHAPTER IV Substance (1) The thing is an unity of many attributes in one space at one time — (2) This unity is given, but requires psycho-physical explana- tion — (3) The attributes, as qualifying one another, are what the thing is at any moment — (4) As determining its own persist- ence, a thing is substance ; and everything must be ultimately referable to a substance — (5) Interaction may affect a sub- stance in some of its attributes, but not in those which belong to it as such — (6) Conditionally self-determining wholes may be called empirical substances — (7) The thing is either the totality of its attributes or of its substantial character 540-557 CHAPTER V The Conception of Self (1) Self a conception obtained from experience. Not identical with subject — (2) Based on the stream of consciousness, (3) as referable to a "substantial " totality (4) which should contain soTne unchanging character— (5) Body and soul at least an " empirical " substance, but (6) the ultimate substance to which consciousness is referable remains doubtful — (7) The "self" means either the history of consciousness or the substantial whole to which consciousness belongs 558-576 XX CONTENTS CHAPTEE VI Reality as a System PAGE Reality an interconnected whole, (1) not explicable from without hut intelligible within ; (2) as such it must have a total resultant character to ■which every real fact contributes a necessary element, (3) and which cannot he mechanical or teleological, but might be organic . . ' . . . . 577-589 CHAPTEE VII Knowledge and Reality (1) All knowledge formed by activity of mind in relation to the given — (2) This activity constitutes knowledge, but not nature — (3) Hence knowledge is relative only in sense of being partial and inadequate to the whole — (4) Infinity isbeyond our conception, (5) and yet the whole is ultimately intelligible — (6) All we know is true of it, and our conception of it grows constantly less inadequate ....... 590-608 CHAPTER VIII Geotjnds op Knowledge and Belief (1) Logic a hypothetical reconstruction of knowledge. The methods which it recognises are real, but (2) are they exhaustive ? Beliefs are also based on the "concrete method" and on feeling. Their validity subject to the ordinary tests — (3) Conclusion : the function of philosophy is to interpret reality by a synthesis of knowledge in which the "truth of feeling" should be included ...... 609-623 Index . . . . . . . , . 625 THE THEORY OF KNOWLEDGE INTEODUCTION Philosophy is a subject which everyone in the end defines for himself, and in view mainly of the particular philosophy which he hiniself has formed. We labour as philosophers under the pecuhar and paradoxical difficulty, that we cannot properly state the questions which we are investigating until we are prepared with some kind of answer to them. Even if we could all agree on some abstract statement of the problem before us, and the methods available for solving it, the formulae used would probably mean very different things in the different mouths which should repeat them. Hence the Introduction to a work like the present must make no pretence to lay down the philosophical problem once for all as it must present itself to every inquirer. It describes the subject only as it has formed itself in the mind of the writer during the course of reflections explained in the foHowing chapters, and it pretends to no value except that of serving in some degree as a guide in following the line of thought in those chapters. It explains, in a word, the rules of the game which the reader is invited to play. Whether the game is or is not worth playing, and whether it is better or worse than any other game which might be played by other rules, can be determined only by the final result. My business, then, in the present Introduction is not to decide whether there can or cannot be a theory of knowledge, or what subjects must or must not be treated under this head, but merely to explain to the reader what he is to expect in the coming chapters, leaving those chapters to justify themselves. 1. With regard to any statement we like to take, there seem to be three questions possible. We may ask what is meant ; on what grounds is it stated ; is it true ? The first of 2 THE THEORY OF KNOWLEDGE these we may call technically the question of meaning or content. If you make a statement you must, of course, state something, and this something is what your assertion contains ■ — it is its content. The answer to the first question, then, con- sists in assigning the content of the statement, whether by mere repetition, or translation, or explanation, or in any other way. The second question might be said to assume too much. Perhaps some statements have no grounds at all ; and in a strict sense of the word this may be true. But every statement — even a lie — is motived in some way or another. It is uttered for a purpose, or is brought about by some psychological cause, just like any other human act. And if for the present we do not discriminate between these processes by which a statement may be brought forth, we may assume that every statement has some grounds or other. And, in fact, it is our constant employment to examine the grounds of this statement or that. This investigation is connected at once with the tliird question — whether the statement is true or false. Every state- ment falls into one or other of these two classes, while many appear, for our slqs, to fall into both at once. But to have some degree of truth or falsity is the common characteristic of all statements, differentiating them from other forms of ex- pression — prayers, commands, questions, aspirations, etc. Now these three questions, which are asked by special inquiries with regard to this or that statement, or this or that class of statements, are asked by our branch of study with regard to statements, judgments, assertions, or whatever we please to call them, in general. The conditions, the content, and the validity of our knowledge as a whole, are the questions with which we have to deal. Each of them demands a word of explanation. I begin with the conditions of knowledge. In ordinary life we are content with a very little in the way of proof. If I am told that there will be an eclipse of the moon to-morrow night, I take the statement as sufficiently " proved" by a reference to Whitaker's AlmavMck. If I am studying astronomy, I take the question a little further, and endeavour to understand the mass of observations and calculations by which the eclipse is determined. But here again, though no longer content with the ipse dixit of Whitaker, there are a good many steps in the train of proof which I should probably take for granted, but which would repay some examination. The demonstration will assume, for example, certain geometrical theorems ; and if we once begin to inquire into them and their grounds, we shall open up quite a new field of arguments, and perhaps of assumptions. It depends, once more, on the accuracy INTRODUCTION 3 and veracity of a number of observers, and perhaps on the make of their instruments ; and here again points are suggested which might plunge us into a lengthy discussion. We may cut this short by remarking that in any proof, scientific or otherwise, we ordinarily offer such grounds as satisfy ourselves, and into the truth of these grounds we do not further inquire. And this is the right practical attitude. But it is just here that the theory of knowledge, for reasons of its own, takes up the question. It cross-examines the witness whom everybody else leaves alone. It endeavours to give as complete an account as possible of all the factors involved in the ground of any statement, leaving no assumption unexpressed, nor, if possible, untested. Briefly, then, on this head the theory of knowledge aims at completing the inquiry which every science makes into the proof of any given assertion. Every partial demonstration, we may say, makes assumptions, some avowed, others implied. The theory of knowledge endeavours to analyse the first sort, expose the second, and test both. While, lastly, its operations are, of course, not confined to any class of judgments, but should apply, ideally, to all our knowledge and belief. That is, it aims at giving the broad, fundamental conditions on which our know- ledge and belief in general are founded; the application of these conditions belonging, of course, to special inquiries. With the content of knowledge we deal in a still more limited sense. To discuss everything hterally impHed by the words would be to write a treatise de omnibus rebus. But logic has to trace the question, " What do we know ? " so far as it is dependent on, or in turn illustrative of, the question. How we know ? To take an instance, the question of the knowledge of an external material world — a question of what we know — was no sooner propounded than it raised in its deepest form the question how we know anything at all. It is obvious that any satisfactory theory of the conditions of knowledge must explain the knowledge that we have, and it follows that the main types of this knowledge must be analysed and imderstood before we know what we have to explain. If, however, the main divisions of our knowledge are made clear, and if it is seen that the con- ditions which we have assumed are sufficient to account for them, it will not be presumptuous to suppose that the detail of each division is to be explained by the play of the same conditions on different material. If we can explain, say, our knowledge of cause and effect in the abstract, there will be Httle difficulty in admitting that the same conditions in varying circumstances will give us our detailed knowledge of concrete effects and their causes. The question of the content of knowledge, then. 4 THE THEORY OF KNOWLEDGE only enters into logic in a broad and general sense. We must endeavour to find the sMmma^rewcra of reality, and show that the conditions which we postulate explain our knowledge of them all. The detail of the various genera will not trouble us further. But at this point the question may be raised, whether all that claims to be knowledge is really such. It may be said that we are not bound to lay down such conditions as will explain every kind of "knowledge," for much that is called knowledge by the " ordinary " consciousness ceases to be such for the philosopher who analyses it. We have come, in fact, to our third question, which is logically anterior to that of the conditions of knowledge — the question, namely, of validity. Valid knowledge and illusion, however, have this much in common, that both of them consist of assertions, and the most illusory assertion is a fact to be explained just as much as the most scientific knowledge. Knowledge or correct assertion, moreover, is assertion made under certain differentiating conditions which it is the business of logic to discover; and hence we have, in fact, to deal with a wider genus of which "Imowledge" is a part only. The conditions of assertion in general, and of good or true assertion in particular, are the subject of our treatise, but the greatest of these is true asser- tion. And we shall deal with assertion at large only so far as it will aid us in determining the conditions of true assertion, or knowledge. Understanding knowledge, then, in its strict sense in which truth or validity are included, we may say that our purpose is to examine the conditions and contents of knowledge in their broadest aspect. 2. The emphasis laid on validity is a characteristic which tends to distinguish the logical from the psychological treat- ment of the intellect. To psychology every mental state is of interest simply as a mental state ; and if as psychologists we are investigating a belief, our main point would be to deter- mine, not whether it is right or wrong, but how it came about, or of what mental stufl' (so to say) it is made ; whether it is allied to the volitional or emotional side of our nature, whether it is accompanied by a constriction of the small arteries or a tension of the muscles of the scalp, or a rise of blood pressure, how many thousandths of a second it takes to form, to what associations it will give rise, or any other question which the wit of man, or of an experimental psychologist, may suggest. But if we are logicians these questions are of value only if they suggest answers to the fm-ther questions — is this behef true or false ; does it correspond to fact or not ? In short, we have to deal with knowledge, that is, the relation of belief to fact : we INTRODUCTION 5 consider the mind "non tantum in facultate propria sed quatenus copulatur cum rebus." I do not wish to draw an academic distinction between logic and psychology. I mean for my own part to draw on psychological results whenever convenient. Distinctions between the sciences should, to quote Bacon again, be taken for lines and veins rather than for sections and separations. And the real meaning of the strong line of separation within which Metaphysics has so often tried to entrench herself is simply, it is to be feared, that she did not wish to be embarrassed by any awkward psychological or physical fact. Seriously, it is nonsense to speak of a thing being true for psychology but false for metaphysics. If truth is anything it is one and the same for every method of investiga- tion, and the phrase can at best be but a manner of speaking. All I remark, then, is that logic and psychology have different centres of interest, and that I shall make no further excuse for faihng at several points to follow up questions of great psycho- logical importance. I make no attempt to draw a line of demarcation between the two sciences, nor should I expect much result from any attempt to do so. 3. The data of logic we have seen to be the mass of thoughts, judgments, or, as we shall call them generically, assertions, which we actually find made or entertained by men. To explain these is to exhibit the conditions under which they arise ; and though logic, as we have seen, is mainly concerned with the conditions under which their truth is assured, the two sets of conditions must (if there is such a thing as truth at all) tend often to coincide, and in one respect the method of deter- mining them is the same. For in any case, the most hopeful way of trying to explain a mass of data, is to proceed by the hypothetical method. Start at any point you like and consider the conditions which seem to be involved in the assertion con- sidered. Then take these conditions and apply them in other cases. In this way you first test the alleged conditions, and see whether they are fundamental factors in knowledge or mere results of a particular collocation of circumstances. And then, supposing them genuine, you see how far they will go. If you find some assertion which they will not explain there must be some residual condition which you must determine. If, on the other hand, you arrive at any point at a set of con- ditions, one or other or all of which appear to afford, in such general terms as you could reasonably expect, an explanation of any class of judgment which can be specified, then yon would seem to have arrived at a true and even a complete account of the conditions of knowledge. I will give a simple and rough 6 THE THEORY OF KNOWLEDGE example. Take the judgment, " I saw him when I was in London three years ago " ; ask its ground, and you are told it is memory. Now about memory two questions may be asked. Is it, first, an ultimate fact or factor in our mental economy, or can it be in turn resolved into simpler elements, or explained on a psychological basis ? And, secondly, taking memory for whatever it may be worth, how far will it carry us ? This must be tested by a second judgment, such as, " I think you will find him a very objectionable person." Now, if we tried to explain this by memory too, the judgment would fall back into the less pretending one — " he certainly was so three years ago." But he may have changed, and so between these two judgments there is a gulf fixed which memory alone cannot bridge, and which forces us to a further postulate. Our method then will be hypothetical, and, for the rest, we shall try to justify the use we make of it in our concluding chapters, when, weU or ill, its work is done. 4 The method iu question labours under one peculiar danger or difficulty of which notice should be given at the outset. In using it we are bound to deal with abstractions, with the anatomy of thought rather than with the living whole. We have to take thought to pieces and exhibit it in fragments, each of which by itself is never a true living thought, but only some side or aspect or function of mental activity. In doing this we are only carrying the work of thought itself a step further. For the whole process of the mind in dealing with reality involves abstractions and separations which constantly tend to emasculate the truth. The mind, with all its powers, is incap- able of grasping the whole even of the " flower in the crannied wall." It deals with it first under this aspect, and then under that — as a thing of beauty, as suggestive of a Wordsworthian sonnet, as injurious to the structure of the wall, as a Composita, as consisting mainly of carbon, oxygen, hydrogen, and nitrogen in certain proportions, as decomposing so many cubic feet of carbonic acid per diem under the influence of sunlight. And whichever aspect we like to take we are pretty sure to leave out the rest. The sonnet would be deranged by a thought of the carbonic acid. And yet somehow all these aspects belong to the flower. The whole, which is the real, contains or pre- sents them all and many more. And so we learn our first lesson about thought, that to grasp anything at all we must leave out the greater part of it. We need not agree with Father Ogniben, that no man ever yet proclaimed a truth but he uttered twenty falsehoods to back it ; but we must admit that the mind never yet sifted out a grain of truth without INTRODUCTION 7 letting twenty other grains slip past unnoticed. And here is the danger of all thought — that it takes the fraction of reality which it has secured for itself as the whole, or as significant of the whole. The first of these assumptions is a downright mistake ; the second is dangerous, and justified only by special conditions. All the onesidedness, the narrowness, and, above all, the intolerance of the world comes from this inevitable abstraction of thought. And so the mind, though it must abstract, limit, ignore, is bound always to supplement its partial dealings ; it must " strive always towards the whole," and if it cannot become the whole, it must try at least to understand its own limits. Now, just as thought is abstract in its dealings with reality, so logic is abstract in its deahngs with ordinary thought. Poor as thought is in comparison with the real, it is warm and living by the side of the bloodless (but necessary) formulas of the logician. The reason is just the same as before. Thought tries to grasp what of reahty it can, but cannot grasp much. So it takes hold of a part, a fragment, and grips it tight, and fixes it before the mind, and names it, and consigns it to its pigeon-hole. It does that over and over again, and by this piecemeal process, in which much is always omitted at each stage, but the defects at one point are supplemented or corrected by what is done at another, the mind painfully carries on its reconstruction of reahty in a form in which it becomes intel- ligible at length as a whole. Now logic does just the same thing with thought. It takes it in bits and it misses out much at each step, but it puts in corrections as it goes on, and so in piecemeal fashion it tries to reconstruct the world of thought for itself. Thus logic uses words, clauses, sentences as symbols of thought. But any one of these taken in the isolated manner which logic can scarcely avoid is an abstraction, if not even a fiction. The word which is often thought of as representing an idea, clearly by itself represents nothing which can stand alone, unless it can be so much sound or so much ink. "We shall have to notice this later, but I will point out here that even the sentence which is ordinarily supposed to stand for a complete thought is really an abstraction. You do not know what it really means unless you take it in its context. Every- body knows the use which can be made of quotations without their context ; but if the question be pressed how much context ought to be given, it would be difiicult often to draw the line short of the whole book, and even of the circumstances in which it is written. In many cases at least you can neither comprehend 8 THE THEORY OF KNOWLEDGE nor do justice to a man's utterance on a single point without knowing a good deal of general history in addition to that of the man himself. Take this sentence : " It is death to souls to become water." Taken by itself this is mere talk, meaning nothing at aU. Nor is it fully intelligible without a fairly exhaustive study of the fragments of Heraclitus in relation to all that we know of thought and science in the fifth and sixth centuries B.C. The doctrine then appears as the natural con- sequence of certain physical theories drawn with much acute- ness and imagination from the somewhat scanty data at the disposal of an early Greek philosopher.^ The single sentence is always more or less unintelligible when taken alone, i.e. apart not only from previous conversation but from the circumstances in which we are placed, the interest which we are understood to have in common, or the landscape which lies before us both. It is only an eccentric who, like " Mr. F's Aunt," plumps down remarks which bear no apparent relation to anything at all. As with the sentence or the judgment, so with inference and all other processes of thought. We never assign the whole of the grounds on which we rest a result. What is more, we could not assign them if we tried. There are subtle indications, shreds and fibres of thought, complexities of relation in which each of our beliefs stands, which are all felt, which all have their effect, and which the most powerful and subtle mind could not unravel. No doubt one part of the advance of knowledge consists in becoming more explicit, so that we come to under- stand that which before we only knew ; but this advance is very gradual, and perhaps its maia effect hitherto has been to create some distrust of explicit reasoning as tending to half truths. We feel that there is more in our own reasonings than we our- selves know. Our results, then, will at first be abstract in two ways. We shall have to take judgments and inferences more or less in isolation, that is, ia abstraction from the other judgments and inferences with which they really stand in connection. And we shall have to deal with many functions or aspects of thought which may turn out, not to be real acts of thought at all, but rather to be involved as elements along with other elements in the structure of some real, concrete activity. In both cases we shaU try to guard against errors which might arise from these limitations. It must be understood throughout that we are ' See Bumett's Early Greek Philosophy (chap. iii. ). The whole book affords repeated and admirable illustrations of the method of piecing together seemingly meaningless fragments into intelligible -wholes. INTRODUCTION 9 dealing piecemeal with a single structure. Each fragment that we take implies other fragments, and ultimately, we may say, the whole, just as the human hand impKes the arm, and ultimately the whole structure of the body. But just as for certain purposes the hand may be studied alone so for certain purposes, and with good results up to a certain point, we may take any fragment of thought's work by itself, though ultimately to understand it all we shall be forced on to other fragments, and so little by httle to some account of the whole. 5. Supposing our difficulties overcome, the results to be arrived at in the present work could not in any case figure as a system of philosophy. It is of some importance, with a view to understanding the real aim and scope of the theory of know- ledge, to make as clear as possible the part which it plays in philosophy as a whole. We must first, therefore, get some notion of what we, for our part, mean by philosophy. Philo- sophy, lilie any special science, is, or aims at becoming, a body of connected, systematic, reasoned truth. Now every science has its own appropriate subject-matter marked out more or less clearly from other things. Quantity, space, the general attributes of matter, the specific characters of different sub- stances form the basis of mathematics, physics, and chemistry. But every science must, as we have seen, deal with abstractions, and limit its view to one side of reality. The aim of philo- sophy is ultimately to make good the deficiency by taking some view over reahty at large. Eeahty as a whole is the subject of philosophy, and no fact is too poor or too remote to come withia its range. This view is caricatured when the philosopher is taken to be a kind of Professor of Things-in- General. In reality, as Comte pointed out, he is as much a specialist as anybody else. No one claims for the philosopher that he can know physics like a physicist, and geometry like a mathematician. His speciality consists of the principles and results of other speciahties, and it is enough for him — and difficulty enough too — if he can master these sufficiently for his purpose. The true philosophy, then, would be the synthesis of all that is known and, perhaps we should add, of much also that is only felt or hoped. Confining ourselves for the present to " what is known," it is clear that we should range ourselves with those who look on philosophy as essentially a synthesis of the sciences. Now, to this synthesis the theory of knowledge contributes only one element. It is not, that is to say, a theory of reality or a theory of all that is known. It is a theory only of the conditions of genuine knowledge and of certaia broad aspects of the results or tendencies of knowledge which seem 10 THE THEORY OF KNOWLEDGE to be bound up with any just conception of its conditions. Of course this is, in a way, a theory of reality ; ^ and of course, in a way, any theory that professed to be a theory of anything, must claim to deal with reality. But by a theory of reality I should understand an attempt to deal with the real world as a whole, not merely with those elementary presuppositions as to its nature which seem to be involved in our knowing it at all. Briefly, then, we have to do, not with the results of knowledge, but with the outHne plan upon which these results may ultimately be pieced together. I may explain this by an analogy. Suppose we wished to construct a philosophy of everything that is visible — the material world, with its many-sided visible char- acters of colour, form, movement, and the like. Our complete account would include the results of many sciences ; for we should have to take geometry and physics, and even biology into account, as dealing, all of them, with things seen. And our complete philosophy would set forth the systematised results of all these investigations. But among the sciences which would be pressed into the service is one not mentioned in the above list — that of physiological optics, the study of the structure and functions of the eye itself. And one thing which we should discover from this science is that the eye is far from being a perfectly correct optical instrument. Its deliverances, which we ordinarily trust with the most impKcit confidence, are not always correct, as tested by consistency with one another, and the facts of touch. Now this might, if it went far enough, introduce an element of error into our whole theory of the visible. Through coloured glass everything looks red or blue, as the case may be ; and so, if there is anything wrong with the organ of vision, who can tell where mistakes will end ? Now what physiological optics do for the eye the theory of knowledge attempts for the mind. Our common knowledge and the special sciences, all, as we know, have a certain vaUdity of their own. They claim our confidence as practical guides. If we govern our conduct by them we succeed in our purpose, and that in itself is a sufficient claim on our respect. To each science then suus constet Iwnos. But when we come to judge of the world-whole by these fragments, the whole ' And accordingly I feel the less disturbed when I find the very possibility of a science of cognition denied by so high an authority as Mr. Bradley (Appear- ance and Reality, p. 76). I feel sure that the difference is rather in the method of stating or handling the question than in anything more vital. And accordingly I find that the problems treated by Mr. Bradley are very much those with which I myself have to deal. INTRODUCTION 11 question of their ultimate validity and significance revives in quite a new form. Do they give us ultimate reahty, or do we live in a world of appearances ? If our world is appearance, can we get ever at the real ? If it is itself the real, is it all the real, or do we know enough of it to judge of the broad outlines of the real whole ? These are the kind of questions we encounter, and these must be solved before the true synthesis of the sciences can begin. We must know the direction in which we are going, and something of the conditions of the journey, before we can travel with success. Or to vary the metaphor, the human equation must be determined before the results of science can be allowed finality. It is then this first stage of philosophy with which we shall be concerned in the following chapters. We shall deal first with the postulates of knowledge, and go on to consider its content and validity. PART I DATA CHAPTER I Simple Apprehension " All knowledge," says Kant, " begins with experience " ; and " all knowledge," says Locke, " comes from experience." Our first inquiry, then, must be, What is the simplest and most primitive form of experience ? Where, if at all, is the ultimate datum to be found from which knowledge starts ? Is there any fact or any state of mind which we can take as ultimate, which will help us to explain or justify other thoughts, but which needs for itself neither justification nor explanation ? Locke, we may remember, found such an unit of knowledge in his Simple Ideas. And these simple ideas were of two classes, those of Sensation and those of Eeflection. If we inquire into the common character, uniting " ideas " of both kinds, we shall find it, not in their dependence on any sense organ, or on any special kind of physiological stimulus, but in their imme- diate presence to consciousness. The phenomena of what Kant afterwards distinguished as the " inner " and the " outer " sense agree in this point. The headache which I feel, the blue outline which I see, the sweetmeat that I taste, are all, in some sense, facts immedi- ately present to my consciousness, and the " plain man " would probably agree with Locke that no further proof could be given, or even reasonably demanded, for the existence of these facts, beyond this, that I feel, or see, or taste them. Frimd facie, then, we are, as Locke held, from time to time aware of the present reahty, and this " awareness " is a " primitive " act of knowledge. It depends on nothing but itself. Is Locke's account true ? or, abstracting from peculiarities of the theory of simple ideas, is there an act of knowledge concerned with present reality, and with that alone ? If so, what logically and psychologically is its character ? Is it " primitive," i.e. a self-evident foundation from which further knowledge starts, or is it in turn derivative ? It will be the object of this chapter to answer these questions. Taking those 16 DATA states of consciousness in wMch we have been supposed to apprehend present reality, we have to inquire into their character as mental states, and their value as elements of knowledge. On the words " mental state " we must briefly repeat the caution given in the introductory chapter. The true mental state of the adult man is complex to the point of indefiniteness. We do not find apprehension succeeded by judgment, judgment by feehng, feeling by an act of will, and so on. If we did, our problem would be immensely simplified. But, in fact, every one of these terms represents an abstraction from the normal state of consciousness. Take what seems a purely intellectual state — a process of reasoning such as that by which we follow a geometrical demonstration. The actual consciousness of the reasoner is more or less absorbed in this subject, as the case may be. If he is an unwilling schoolboy, his wandering atten- tion mingles ideas of escape and recreation with his geometrical constructions and syllogisms ; and even the half of his atten- tion which is devoted to the argument is coloured and qualified by the sense of effort with which he follows it. If he is a budding mathematician, his whole soul is concentrated on the work before him; but in this very concentration there is an effort and an interest involved which bring elements from the emotional and volitional side of his nature into play. Pure thought, pure will, pure feeling are not names of concrete mental states. This or that state may approximate more or less closely to the one type or the other; but how far this approximation may go, and whether it ever reaches complete- ness, it would be hard to say. The question is one for psychologists. All that we have to remark is, that when, for the purposes of our logical analysis, we speak of describing a mental state, such as a feeling or a judgment, we mean to describe, not any given state in its full individuality, but merely so far as it is a feeling or a judgment. That being understood, we may proceed to our first task — that of assign- ing the general characteristics of the mental state in which we apprehend present reality. I. GENERAL CHAEACTEPJSTICS OF APPREHENSION 1. The act which we have to discuss is perhaps more easily illustrated than described. It is, at anyrate, more easily described by negative than by positive attributes. To begin with, it is not a judgment. If, looking on the ground, I say, " this is grass," this assertion, simple and obvious to the point SIMPLE APPREHENSION 17 of superfluity as it probably is, still takes me far beyond the region of present consciousness. It implies a comparison of the present with past sensations, without which this which I see would be an irregular surface of a particular shade of green, but would not be to me grass. To make use of the conception " grass " is to apply the result of many judgments and infer- ences. For "grass" undoubtedly means something which is not only coloured green, but has a certain " feel " and taste, and, moreover, exhibits certain uniform characteristics of life and growth. To all these there is an implicit if not an avowed reference in the apparently simple judgment of perception, " this is grass " ; and, what is especially to be noticed, the judgment in question would fail to be true if the object before my eyes turned out, on investigation, to fail in any of the char- acteristics contained in the conception of grass. If, on my approach, it recedes or vanishes, it turns out not to be grass at aU, but a mirage ; and a quite different predicate is assigned to it. Summing up, the simple judgment, " this is X," is not the , mere consciousness of what is present ; it asserts characteristics or relations which are not present ; and it may be true or false. If we reduce the judgment of perception or Qualitative Judgment — to call it provisionally by that name — to the barest possible assertion that can still be called a judgment, the same truths hold of it. If its subject " this " refers only to the present, its predicate " that or the other '' refers to something beyond. Accordingly it is susceptible, though in a diminishing degree, of truth and falsity. If for " this is grass " I substitute the more modest assertion, " this is green," I escape the risk of confutation by a mirage. Mirage or no mirage, I had a vision of green. " That's the four o'clock express " is more liable to be wrong than "that's a train"; and the poorer judgment, " that's a loud rushing noise," is safer still. But clip your predicate as you will, as long as you predicate something of the present, you make an assertion which goes beyond the present, and you are accordingly hable to error. This liabihty diminishes, as I say, rapidly ; and practically, no doubt, m the simple judgments quoted above it disappears. Theoretically, it remains as long as the assertion goes beyond the present. This will be clearer when we have analysed the quahtative judgment. For the present, it may be enough to point out that it depends on the correct apphcation of an idea to the present reality, — an operation which common experience shows may be often enough performed incorrectly, though to err in a simple case might be held to argue imbecility. 18 DATA I conclude, then, that if we wish to arrive at the mental condition in which we are entirely occupied with the immediately present, and with nothing else, we must go further back than the simplest form of judgment, if by judgment we are to mean an act of thought expressible in words. The simple judgment, whether in the set form, " here is X," or in the loose interjectional form, " Pire ! " " Freezing ! " is a further reaction of the mind supervening on the consciousness of what is present, and usirig the content of that consciousness as part of the material for its own assertion. The actual consciousness of the present goes before the judgment. But now it will be asked— If we go behind the judgment, what do we come to ? To the apprehension of the present.^ But is not this merely feeling or sensation under another name ? And is it not written that f eehng and knowledge are for ever distinct ? For example, to take one statement out of an infinity, in Prof. A. Seth's admirable Scottish Philosophy, p. 87, we read : " The philosophical point is the complete or generic distinction between Perception and Sensation, — between Knowledge and Feeling, — which for ever precludes any deriva- tion of the one from the other. On this distinction Eeid is prepared to stake the whole question between himself and the ideal scepticism. It is the same issue by which Kant also chooses to abide." As against this we would maintain, that if by feeling Prof. Seth means our consciousness of the present, this consciousness is itself an act of knowledge. It possesses the two essential features of such an act — if at this early stage we may speak provisionally of essentials. It is the act of a conscious sub- ject, and it has an object or content. The first position can only be denied by questioning the existence of the subject ; and that question, if raised at all, must apply all along the line, to the highest judgment as to the simplest sensation. The second poiat can hardly be denied without altering the meaning of the terms used. The object or content of a thought or judgment is that with which in that thought or judgment the mind deals, or is occupied, which it has before 1 I use the term Apprehension for the state or act of mind known sometimes as sensation, sometimes as perception, sometimes as immediate consciousness. If I owe the reader an apology for introducing a new usage, my excuse must be that each of the terms in use conveys a meaning which I am anxious to avoid. Apprehension has certainly a wider meaning than the technical one which I wish to give it, but this wider meaning is so general that no confusion can result from it. I may say that I shall frequently use perception, sensation, and consciousness as variants for apprehension when no confusion can result from so doing, and when the use of either term seems specially appropriate. SIMPLE APPREHENSION 19 it. None of these phrases are explanations ; they are simply- different ways of putting the matter. Of the fact itself, that in any act of knowledge the mind has some content before it, there is neither explanation nor proof. Now, as in judgment, so in apprehension, the miad has an object or a content ; only whereas in a judgment the object may be anything from the building of Aladdiu's palace to the prospects of the next general election, in apprehension it is always the immediately present, the warmth of the fire, or the blue of the sky. Now this, I shall be told, is obvious in a sense ; but the whole question is (a) whether in these cases it is the present merely that is before me, and (&) whether some activity other than that of mere passive apprehension is not involved in the matter. These questions I shall deal with presently. For the moment I wish merely to recognise, or rather to insist, that if the present is to be known to us as such at all, the appre- hension of it must be regarded as an act of knowledge; in short, as an assertion. ^ 2. Assuming for the moment that we do apprehend the present, we must admit that apprehension to be a kind of assertion.2 Now, of this kind of assertion, we are able to say generically several things, two of which should be noted here. Thus (a) every apprehension involves a measure of attention, varying from zero to a maximum. (6) Broadly, the clearness of the content present varies with the attention, increasing as we concentrate attention on it, diminishing as our minds are attracted to something else. (a) The psychological facts here are well known, and are verifiable by anyone for himself. We all know the difference between a concentrated and a distracted attention, and we also know (6) that if we wish to see or hear clearly, we must con- centrate attention as far as possible. We are not in apprehension left to the mercy of the physical stimulus applied. Other things equal, the same stimulus produces a content of the same clearness ; but then ' As a matter of words, "feeling'' may mean, not the "act" of consciousness, but its object. We have then to insist that it is an object of knowledge. See on the same point Dr. Ward (Ency. Brit. art. " Psychology," 9th ed. p. 41), who shows the error of arguing from the "subjectivity" of sensation as a state of mind to the denial that sensation is an object presented to mind. ^ Objection may be taken to the use of the term Assertion in this connection. I may explain that I use it here and elsewhere as a general expression for every act of knowledge (whatever its nature or source, whether it be sensation or thought), and for every act of lelief, whether it be true or untrue. All these acts have a certain character in common, and to express this character we want some single word. I employ the word assertion as more free than any other from special associations from which I wish to be clear. 20 DATA other things are not always equal. A strong stimulus — it does not matter here whether we are speaking of the physiological change or of the mental state on its first appearance — will, on an average of instances, produce clearer contents for apprehen- sion than a weak stimulus. But if the weak stimulus is "interesting," it drives the strong one out of the field by arousing the activity above named. The loud, even roar of the torrent down in the valley passes almost unnoticed as I write, while the first sound of a cock-crow at once arrests attention, because that particular noise happens to exasperate me. In general— possibly in the last analysis in all cases — the power of arresting attention depends, not on the inherent character of an object, but on its connections; on the ideas, hopes and fears, anger or gratitude, that it raises. But this is a psycho- logical question. All we have to notice is that attention once roused disturbs the balance of clearness and dimness. Alert and swift, it seizes on one of the many details present, drags it forward into clear light, and examines it to the bottom. It promotes and degrades, without reference to the original strength of stimulus. It brings a dim, far-off voice or the distant colour of a well-known dress into the very focus of apprehension, and all else is relegated to the dim, indefinite backgroimd of consciousness, from which the object of interest stands out.^ A very small degree of introspection carries us a step further. Actual consciousness never is wholly definite. Con- centrate as you will on the point before you, you are always vaguely conscious of its surroundings. According to Wundt's famous simile,^ the apprehending consciousness is like the eye. Whether we see, hear, or feel, there is a point of clear consciousness, a point rather of clearly-defined content on which consciousness is concentrated, whUe around and about this point are dimmer, vaguer forms, which shade away gradually into the dark. Indefiniteness is not an accident of consciousness ; it is a constant element in its character. Now, looking to the logical natm-e of the act, we must 1 It is usual to say that attention makes the object "clear"; bnt on this point we must follow Mr. Shand's distinction between the clearness attaching to the object as its own character, and the clearness which is really synonymous with the fact of being attended to. You may attend to a dim light and note that it is dim, or to a confused medley of sights or sounds and remark that it is a confused medley. So far what is obscure before attention remains obscure to attention. But it is also clear, as being now definitely Ijefore the mind (see " An Analysis of Attention," by A. F. Shand, Mind, N. S. No. 12; and cf. infra, chap. iii. p. 64.). The connection of attention and clearness is there'- fore a degree more complex than would appear from the text. 2 GriivdzTige der FhysiologiscJien Psychologie, vol. ii. p. 235 (3rd ed. 1887). SIMPLE APPREHENSION 21 regard apprehension as aware, not of the definite only, but of the indefinite as well. The whole that is present to me at any moment is the content of my apprehension for that moment. As I write, the words before me and the movements of my pen occupy the forefront (in Wundt's simile, the Blickpunkt) of consciousness ; but along with them goes the plashing of the fountain below my window, and farther off the rattling of a waggon on the road, while the mass of organic sensations and bodUy pressures form a dim, uncertain background, which is there and yet not there, affecting consciousness and yet hardly apprehended as such. With some of the logical difficulties which suggest themselves here we will deal later. At present we point out only that we are in someway aware of the whole that is present, and that, therefore, apprehension cannot be identified with any particular degree of attention. To deny this would be to introduce a feeling which is neither an act of knowledge nor a content for knowledge. If (which, of course, we have yet to prove) the present is anything at all for us, we must have knowledge of it, and that knowledge we have called apprehension. But the same reasoning must apply to every element of the present. Whatever is such an element must be so for our apprehension. It follows that theories of the nature of attention as a psychic activity do not afi"ect our present position. We may as psychologists hold, with Wundt, that a special form of mental activity, acting in accordance with laws of its own, picks out tliis or that object that comes within the field of consciousness and brings it into clear light. Or we may retort, with Miinsterberg, that the whole process of attention ^ can be explained by the same psycho-physical laws as are postulated by every change in the content presented. We are not, fortunately for us, called upon to enter this contest. The logical result alone affects us. There is a definite content recognised when attention is concentrated, and an indefinite when or in so far as it is distracted. The mechanism by which attention is concentrated or distracted, whether it be psychic or physiological, special or general, does not touch this result. This point is worth noting, in view of a possible mis- interpretation. In describing present consciousness as an assertion, I might be understood as inventing an unreal ' It is better, I think, to translate "Apperception" by this term than to import the ■word into English, more especially as Apperception itself, not to speak of its meaning in Leibnitz and Kant, is used by the Herliartian's in a different sense. 22 DATA separation, between the act of consciousness and its content. This is far from my intention. I do not mean that we have first the content rising before consciousness on its own account, and then a reaction on the part of the mind recognising that content. This would really be the precise opposite of the position I am maintaining. It would involve us once more in an unapprehended, im perceived, and therefore unknown state of mind. We Tiiay (if Wundt's theory be correct) have an object first apprehended, and then by a separate act attended to. We cannot have a content first in consciousness and then apprehended. To be in consciousness and to be apprehended are the same things. We do not, in short, attempt at this stage to define the relation of consciousness to its object. All we say is, that whatever our immediate consciousness may be, it is not merely an affection of the mind in this way or that, but an assertion of this or that, a cognitive act. That is one of its characters, whatever the rest may be. .On our first question, then, of the general nature and characteristics of immediate consciousness, I conclude that such consciousness has the general character, shared by all knowledge, of being an assertion ; that it is an assertion of the present ; and that it is to be distinguished from any judgment naming or describing the present, since such a judgment includes in its content something that is not present. II. THE PEIMITIVB CHARACTEE OF APPREHENSION 3. I have now to show that the apprehension of the present is, in the world of knowledge, a primitive act and an ultimate fact. Of course it has conditions of its own ; but if we were asked to name them in the present state of our knowledge, we could only suggest some physical or physiological antecedents of a somewhat hazy character. With these conditions we have nothing to do in the present chapter. But there are quite other conditions alleged, without which, it is said, our apprehension of the present could not be ; either it could not exist at all, or at least it could not be genuine knowledge. The apprehended content is " made what it is," " determined," " constituted," by the synthetic or correlative activity of thought. This view, as is well known, appears in sundry forms and in divers writers. To give an instance, here is one among a multitude of Professor Green's accounts of the matter — " The so-called ' immediate intuition ' only has any content just so far as it is not merely presentative. Just as when, in SIMPLE APPREHENSION 23 view of Locke's doctrine, that that only is ' real existence ' which can be known in ' actual present sensation,' we ask how much of any supposed real object is reducible to 'actual present sensation,' we find that the object disappears, so is it when we ask how much of an object of intuition remains after abstraction of all that belongs to it as representative. ' This book ' is an object of intuition, but all qualities in virtue of which I recognise the object as a book depend on its relations to objects not now presented in intuition at all, of which relations, therefore, the knowledge is representative, not presentative. In the absence of these, nothing remaius as merely presented but the ' here ' and ' there,' ' now ' and ' then,' ' this ' or ' that ' ; and can even the ' this ' and ' that ' be said to be merely presented ? " ^ Briefly, if we " exclude from what we have considered real all qualities constituted by relation, we find that none are left." ^ Abstract from the presented book all its quahties, and nothing remains. That is clear enough. These qualities depend on, or are constituted by, relations to non-presented qualities or objects. Here we must distinguish. The existence of the given qualities depends causally on something past, no doubt. But that is not what we are told. We are told that the present qualities are constituted hy relations, and that the knowledge of them depends on these relations. Take the first statement. How does a relation constitute a quality ? " The book has a brown cover," i.e. the cover is related by way of resemblance to other brown surfaces, and by way of difference to any other colour we hke to take. But does the relation con- stitute the brown, or do the browns and other colours constitute the relations ? It is quite certain that if this book had not the colour which resembles other brown surfaces, it would not itself be brown. It is equally certaiu that if it were not that which I apprehend, it would not resemble other brown surfaces. The colour present to me resembles other colours ; but this does not prove that to apprehend it is to apprehend that resemblance, and therefore a relation. On the contrary, the fact here present is not a relation, and never becomes a relation. In the development of knowledge it may become a correlate of countless other terms, the meeting -point of innumerable relations; it is never itself a relation.^ Is it, ' Works, vol. ii. p. 168. ^ FroUgmntna to Ethics, p. 23. ^ This Green Iiimself admits. "No feeling, as such or as felt, is a relation " (Proleg. p. 39). This is -well enough. But when we read a few lines lower down of the idealism which interprets facts as relations, we ask in despair. Is feeling a fact or not ? Do we never really feel at all ? 24 DATA then, a correlate ? Certainly ; but it is not given as such to simple apprehension, in the case before us. "What I apprehend is the colour, and not the relation of the colour to something else. No relation to anything outside an apprehended content can be an element in that apprehended content. What, then, is the given ? I am asked. A quahty. What quality ? The colour brown. Why, then, I shall be told, you have admitted oiir whole point. You say you apprehend the content apart from its relations, and when you are asked to say ^vliat you have apprehended, the very first term you use is the name of a general quality which instantly expresses hosts of relations in which the object stands. Undoubtedly, in using the general term " brown " I have described the fact through its relations, but I have come to mention its relations precisely because I am now describing and not apprehending. I am no longer apprehending the fact present to me, but describing to you what I have apprehended. Description undoubtedly is by general attributes, and therefore by relations. But as undoubtedly description is of the already apprehended fact. To apprehend the fact is one thing, to describe it another, and therefore there is no reason to assign to apprehension that assertion of general attributes without which description cannot begin. Apprehension, in fact, is of contents which turn out to resemble other contents, i.e. present general qualities, or stand in relation to other facts, — put it as you please. To describe what you have apprehended is to state in words these general qualities or relations. The descriptive judgment, that is to say, is a further mental act of which apprehension is the basis. It is precisely the act which judges some quality of the apprehended fact to be general, i.e. to resemble qualities of other facts. Now name such a quality, call it X, and say, if that content which I apprehended just now had not possessed the quality X, it would have been simply nothing at all. All that is perfectly plain ; but it is quite another thing to argue that, therefore, I apprehended the content as X, i.e. as a general quahty, and therefore I did not really appre- hend it at all, but made a judgment in which the non-presented instances of X were involved or implied. That judgment I did make when I described my apprehension. It was what I added by my description to the datum of apprehension which went before.^ It was not the apprehension itself. ^ It is, no doubt, involved in this view that (apart from the case of com- mand or request, which do not here concern us) speech is tlie expression only of a judgment or the results of a judgment. So far Green might seem justified in the remark (Introduction to Hume, p. 36) that "a consistent sensationalism SIMPLE APPREHENSION 25 The statement that the content apprehended is constituted by relation to other contents, might mean one of two things. It might mean, first, that the content, actually asserted by the mind is always in the cases considered some relation between the present fact and some non-present fact ; i.e. that to be aware of my present feeling, is to judge its relations. In that case I would ask how we know what the " it " is whose relations we judge. A relation involves terms related. How do I know those terms ? How can I judge the relation of a feeling to something else, unless I have knowledge of the feeling itself ? How can I tell that the rose in your hand is sweet, unless I can see the rose and smell the scent? Once more, though the exclamation " toothache again ! " is very closely bound up with a given feeling, yet the feehng is not the judgment of the relation between this toothache and yesterday's. The feeling is not the judgment, the judgment is about the feeling. But, secondly, if a relation is not actually asserted when- ever we apprehend a fact, it may be urged that the theory we are combating does not intend this, but merely holds that the fact apprehended is meaningless except as the term of a relation. But this is ambiguous. If it means that a fact except as related is indescribable, it is true ; but it is a truth that concerns description, not apprehension. If it means that any given content must, in fact, stand in relation to others, that the given A must be at least comparable to some B or C, this is again true. But it does not follow that in apprehending A, I apprehend its relation to B or C. There is no unrelated particular. Every fact is a centre of relations, but I do not know that by merely apprehending the fact itself. If, lastly, you mean that as an unrelated content — a content whose relations are unknown — a fact could be nothing for me, you say that which your own qualitative judgment contradicts when it says, this is hot, meaning the fact apprehended. Por if the apprehended were nothing for me, how could I logically must be speechless.'' But this would hold only if knowledge consisted entirely of sensation, not if knowledge while based on sensation includes judgment about sensation. Such a judgment is the act of naming. The naming is a judgment (or, if you prefer it, the verbal expression of a judgment) ; that which you name is (in the cases considered) the content of a sensation, or, as I should call it, an apprehension. Green's remark {op. cit. p. 16), that the individual sensation is "unnameable, because while we name it, it has become another," involves a confusion. In naming the sensation's content our total mental state has passed from one of pure sensation (if, for the sake of argument, we grant the possibility of such a condition) to a state in which sensation and judgment are blended. But the sensation itself is either as a mental event over, or it remains a pure sensation. It does not pass into judgment. Wc pass from apprehending it into judgment about it. 26 DATA assign it a predi jate ? You may urge that the apprehension cannot logically or psychologically go before the simple judgment because the " manifold must collapse into unity " before it can be matter of knowledge. Then how, in that case, did you know that it was a manifold ? ^ If you did not often enough apprehend the manifold as a manifold and pigeon-hole it by a distinct act, you would be quite sure that knowledge began in pigeon-holes and not in chaos. As it is, you talk of the chaos in one breath, and in the next deny yourself any possibility of knowing it. No doubt in ordinary adult life we do not go through a psychological process beginning with apprehension and passing on to a qualitative judgment. The two acts are merged in one concrete, mental state. But even this can hardly be proved in all cases. Whenever we are placed in unusual circum- stances necessitating close attention to strange things, the qualitative judgment becomes consciously a reflective attempt to analyse what is given. If I try to follow, for instance, the changing shapes of an amceba, I concentrate all my efforts on the object seen on the sHde, and then with another conscious effort grope about for qualities or relations which will describe its successive figures and vague, clumsy motions. Still more clearly the "stunning" effect of a crash and a flash delays the process of attention, arrests judgment, stops one's power of "taking in," i.e. judging, what has happened. In such cases the act of apprehension stands out clear and defined, separated from the other activities which normally accompany it, or rather are so fused with it as to form one mental state.^ And whether or not there is this de facto separateness, the qualitative judgment implies the independent validity of the act of apprehension. Without it the subject of the judg- ment would be an unknown thing. This might have seemed clear enough from the form of the judgment, "this is X." But Green detects a relation involved even in the word " this " ; for instance, in lines following the passage I have ^ Green expressly tells us (Hume, loc. cit.) that the sensation is " unknow- able, the very negation of knowability. " Then how could he possibly be in »• position to tell us two lines above that it is "fleeting, momentary, unnameable" ? Surely we have learnt from Green's own masterly criticism of the Thing-in-itself doctrine that the unknowable is also the meaningless, and that even to postulate it (as, for example, Professor Seth speaks of postulating sensation, Scot. Phil. p. 89) is to involve ourselves in a purely gratuitous contradiction. '^ I.e. we get something like a "pure" state of apprehension. But, as above stated, it is difficult to say whether we ever have it completely pure. Probably ideas begin to rise on the outskirts of consciousness while the present content occupies the centre. But we have it pure enough to mark the distinction of the two acts. SIMPLE APPREHENSION 27 quoted above, p. 23. "Does not 'this' always indicate a relation of something to, and distinction of it from, a subject conscious of itself as not beginning or ceasing with the presentation of ' this,' through the medium of which again the present something is related to, and distinguished from, other ' somethings ' ? But neither the identity of the ego nor the past somethings to which, through common relation to the ego, the present is related, can properly be said to be presented." ^ It is significant that the relation alleged to be involved is here changed. It is no longer a relation directly to other things, but a relation of the presented fact to self, and to other things through self, which we are told the word " this " implies. Observe ; my contention is that the qualitative judgment represents in words the attempt to bring the present into relation with other things. The predicate then (including the copula) should give the relation, the subject should state the reference to the present. Now we find that Green himself does not contend for a direct reference to other things in the subject. Directly there is only a reference to self; so far as direct reference to other things is concerned, the qualitative judgment on Green's showing bears the required witness on my side. But the reference to self is open to the same criticism as the alleged reference to other things was before. In saying "this" I do not consciously assert a distinction between myself and what is present to me. Such a distinction becomes obvious later on, when other activities are brought into play ; but we want to isolate a particular activity and find out what it gives us taken by itself, and the way to get at this is not by confusing its report with that of a crowd of further acts of the mind.^ It would be better, in the interest of Green's contention, to do away with this last subtlety and urge simply and straightforwardly that the " this " of the judgment implies a distinction (and hence a relation) between the given content and others. This distinction is sometimes the explicit purport of the demonstrative (e.g. ' this book, not that, is the one which I want '), and might be taken as ordinarily implied. But then, again, it must be remembered that the use of the general term ^ WorJcs, loc. cit. ^ On the doctrine ' ' that a thought, in order to know a thing at all, must expressly distinguish between the thing and its own self," Professor James remarks : "This is a perfectly wanton assumption, and not the faintest shadow of reason exists for supposing it true. As well might I contend that I cannot dream without dreaming that I dream, swear without swearing that I swear, deny without denying that I deny, as maintain that I cannot know without knowing that I know. " 28 DATA " this " to designate the subject belongs to the proposition, and accordiagly represents a part of the act of judgment ; that act which, according to our contention, exists in order to bring the immediately known present into relations (whether of dis- tinction or connection) with other facts. And granting that the " this " expresses a correlation, what does it correlate ? What meaning has it if not a reference to the present fact, distinguished, if you please, from other facts. But if the fact is not there, what can there be to distinguish ? ^ Its mere distinctness from B does not constitute A. Nor in appre- hending A itself do I apprehend its distinctness from B. A is distinct from B as I find out when I consider them both together, and I then know that if it were not so I could not have apprehended A alone. But apprehending A alone is not in itself the same thing as apprehending A-l-B.^ The judgment dealing with the present " this " is absurd and seLE-contradictory, if there is no " this " present to me. I must be aware of the present in order to make judgments about it. This awareness must be either an element in the judgment itself, or a state of consciousness antecedent to the judgment. And here we may make a concession. If all that is iatended by Green's criticism is that, psychologically considered, appre- hension is an element in judgment (or some more complex mental state) and not a state of mind complete in itself, we can afford to leave the question open for logic. Psychologically, we believe that there is evidence (as urged above) that appre- hension of the present sometimes exhausts the whole field of consciousness. But we are only concerned with logical factors in knowledge and logical distinctions, and on that ground we maintain that apprehension is a distinct factor, postulated as a condition by judgments of perception, and that its content is a distinct part within the more complex whole which judgment asserts. ' "The idea of this would te falsely used, unless what it marks were actually presented " (Bradley, Logic, p. 68). '^ " It cannot be said that we have the idea of red as red only when we distinguish it from blue or sweet, and only by so distinguishing it. . . . There could be no conceivable occasion for attempting such a distinction, nor any possibility of succeeding in the attempt, unless there were first a clear conscious- ness of what each of the two opposites is in itself" (Lotze, Logic, Eng. trans, bk. i. chap. i. see. 11). In the following sentence the same doctrine is implicitly applied to sensations or impressions. On the significance and implications of words like "this'' or "here," we shall have more to say when we come to the judgment. They vary, of course, according to the context. Our only contention at present is that the main purpose of the words in the simplest qualitative judgment is to indicate the present as such. The distinction they involve is a mere means to this reference. SIMPLE APPREHENSION 29 4 Then, is the apprehension of the present entirely undeter- mined by antecedent experience and by thought of such experience ? Not certainly in all cases. When, after staring at a bright red object, I turn my eyes upon a white sheet of paper and watch the dim green after-image rise, the content now before me is determined by the antecedent experience. So in all the manifold cases falling under what is loosely termed Weber's law ; so in all cases of colour contrast, and no doubt in many other instances. In all these cases the past experi- ence actually contributes to modify or even create the present by acting on the condition of the sense-organ or the brain. Here experience determines the present sensation, but not the thought of past experience. However, thought also may be said to contribute to determining the content of sensation, for instance, whenever practical interests determine the direction of attention, or when knowledge of the real character of an object enables me to see in it what I could not distinguish before I knew what to look for. The latter case will be familiar to anyone who has used a microscope imder the guid- ance of another person, or who has looked at a distant object in the company of someone more familiar with it than him- self.i But it is only by a confusion that instances of this kind can be imported into the present discussion. Consider the issue. We have been contending that the content of appre- hension is a primary datum for knowledge ; that is, that we may take it as fact without implying an assertion of any other fact, or postulating the existence of any activity except that of apprehension itself. Against both these contentions it was urged that either a whole or a part of the content claimed for apprehension was, in fact, the work of thought. This argument we have met on general grounds and dismissed. Now certain cases are alleged in which an undoubted thought modifies the content given. But nothing is alleged to show that any element in the content given could only exist for thought or only be known by thought — that it is, in short, a thought- product and not a sensible fact. Thought is shown in these cases to be one among the antecedent conditions determining sensation; but neither thought nor any thought-product is proved to be an element constituting the whole present to sense. A factor in the cause is mixed up with an element in the effect, an antecedent condition with a constituent element. 1 See Mr. Bosanqnet's interesting paper on "An Essential Distinction in the Theories of Experience " in the forthcoming "Proceedings of the Aristotelian Society " (1895). I refer, by kind pennission, to a proof in my possession. 30 DATA Apprehension as an occurrence in consciousness always has its conditions, and these broadly may be divided into two sets, the physical stimuli acting upon the sense-organ, and the condition of the organ, or rather of the whole organism, at the moment. Any alteration in either of these factors may modify the resulting state of consciousness. But none of these con- ditions enters into the sensation which results from them. To perceive a flash of Kght is not to be conscious of a wave of molecular change in the optic nerve; the antecedent condi- tion of the sensation is not an element in the sensation itself. Now among the conditions of sensation one of the most im- portant is the state of attention at the time — a state which has, no doubt, its mental and its physiological side. Preparation helps out the stimulus, fills up gaps which would be left in the sensation if the same stimidus acted on an unprepared mind ; or defines what, without it, would be given as a vague blur. And thought acts by putting attention on the stretch — i.e. by preparation. Whenever it does this, thought is a part cause of apprehension. But the fact apprehended under these conditions is no whit the less given to apprehension than any other. It is for apprehension its own present self, and not its relation to other things ; and in apprehending it we are directly aware of it as fact. Thought, then, never constitutes the apprehended content as such ; ^ but it is sometimes an antecedent condition of apprehension, without which the apprehension would hot be precisely what it is. It acts indirectly by modifying attention, and the nature, extent, and frequency of its action is purely a question for psychology. There seem to be abnormal cases (as in hysteria), where it may be the main or even the sole deter- minant of the sensible change. But that it is an universally necessary condition of our apprehending anything there is no evidence whatever. Normally its result is to modify the effects of the physical stimulus, chiefly in point of clearness or intensity. And all our reasonings on the subject presuppose ' It is often urged that some perception is constituted by thought because the actual data are not adequate to the reality which we claim to perceive. Take an extreme ease. "I observe" the structure of a protococcus under the microscope by means, in effect, of a complex series of inferences. And this inferential process can be traced in all perception. But here there is simply another confusion between apprehension and judgment. What I see is really such and such an outline, colour, change of size, shape, or what not. By comparison with one another, helped by what 1 know of the stnicture of the microscope, I interpret these as meaning much more than I actually see. But I am loosely said to see what I only infer. In this case what is ordinarily called perception is a judgment involving true inference from the given, and it must be distinguished from the case in the text where preparation actually modifies the perceived datum. SIMPLE APPREHENSION 31 the independence of sensation ; since, first, the effects of atten- tion can only be proved by a deflection of the conscious state from that effect of the stimulus which we take to be due to the stimulus as such ; and, secondly, we can only allege the inter- ference of thought when past experience can be assigned to supply thought with its material, and this supposes that the thought acting on this sensation is itself based on past sensa- tion. Apprehension, therefore, does not postulate any activity of thought as its necessary condition, nor does thought contri- bute any element to its content. The contrary view, in fact, is but one of the many forms of confusion between sensation and stimulus. The stimulus is taken as being the sensation. Then it is shown that we apprehend more than the stimulus itself, or perhaps something quite different to the stimulus itself. And this difference is set down to the account of thought. The simple fact is that we do not necessarily apprehend the stimulus at all. The stimulus is the cause of apprehension, and need by no means be the fact apprehended. And the same holds of the circumstances, mental or physio- logical, which modify the effects of the stimuli. They are causes antecedent to apprehension, not themselves apprehended, nor yet activities of thought operating on what is apprehended.^ To sum up. Thought relations never constitute a content of immediate apprehension. Such contents do stand in manifold relations which are unfolded by judgments about them ; but the apprehension of them is not the thought of their relations, nor does it depend for its existence in consciousness upon these relations. The judgments themselves would have no meaning if they did not refer to the data as apprehended. Apprehension, therefore, does not depend on any hitherto assigned mental activities.^ ^ On the actual determination of one sense datum by another, a sort of secondary doctrine of relativism has been founded by certain writers, such as Mill, Spencer, Hoffding, Wundt, and Professor Bain. This theory has been sufficiently refuted by Dr. Ward {op. cit. p. 49) and Professor James (Principles, chap, xvii.). It is enough to remark here that the facts of colour contrast, etc., do not begin to disprove the validity of apprehension. The white of this paper is to my sense -perception white, though if I lay it on snow it becomes dirty yellow. All this proves is as before, that the stimuli received by my retina from the rays coming from this paper do not wholly determine the resultant sensation. Other simultaneous or antecedent stimuli contribute to the result. But in either case the sensation is what it is, and is known for what it is, and all we learn is, as Professor James says, " that the same real thing may give us quite different sensations when the conditions alter, and that we must therefore be careful which one to select as the thing's truest representative." But the consideration of this question belongs to quite another department of logic. * It depends, of course, on a capacity for apprehension, just as eating depends on a capacity for deglutition ; but we are not much advanced by con- siderations of this kind. 32 DATA III. THE CONTENT OF APPREHENSION IS FACT. 5. If this has not akeady been admited on all hands, it is rather because thinkers have doubted the existence of appre- hension than that they have recognised it and denied its validity. By almost universal consent we are in closest contact with reality in sensation, or in other forms of im- mediate consciousness, all of which I include under the term Apprehension. Those who deny any other knowledge of reality have taken our judgments to refer to what we did or shall, or under certain circumstances should, perceive. And if we do not allow, with Berkeley, that of all the objects of perception the esse is percipi, we may convert the phrase and say, that for all matters of immediate apprehension the percipi is esse. And thus far, perhaps, we may go with Berkeley, that whatever else we may mean when we say that this or that exists, we at least mean that we did or shall, or under appropriate circumstances should, apprehend it; while, con- versely, the content, being once apprehended, is eo ipso fact without further question.^ To be finally convinced of this it is only necessary, I imagine, to remove certain confusions and misconceptions. ^ Hegel {Phdnomenologie dcs Geistes A. i. pp. 73 ff.) has tried to show that immediate consciousness or apprehension contradicts itself. It takes its object as simple and immediate, i.e. it is the "this," and that means again the "now" and the "here." But what is the "now"? It is, e.g., night. But then again it is day: it contradicts itself. "We might answer, the "now" which is day and the "now" which is night are different "nows." It is not " the now " (das Jctzt), but "now " of which we say that it is night ; and one "now" is not another "now." Hegel would reply that he provides for this by saying that the truth is that the " now " is universal, including all sorts of "nows." This is, of course, true enough; but, by tlie same reasoning, its universality consists merely in "now-ness,"i.e. presence, and this is compatible with any amount of difference in the content of each several "now." The validity of the particular momentary content is therefore unaffected. Lower down, after remarking that the " contradiction" in the content of the " here " and "now" as ohie.aX, [Gegcmtand) drives us back into our subjective appre- hension of them, and that this also is general (since the "I" is so), Hegel finds the reality in the totality of the consciousness and its objects, the whole sense-certainty itself. But of this sense-certainty we must become aware and while we do so it ceases to be present. It no longer has existence {seyn), it is past (ein Gewcscnes, p. 78). This shows, of course, what we have already admitted, that you cannot describe or know aiout the present fact without a judgment, and for argument's sake we may suppose the judgment necessarily to follow apprehension in time. If my mind were confined to the present, it could never know that it was so, still less communicate it. But because 1 can know more than the present, it does not follow that I know less. I know the present by one act, and know that I know it by another. The second act may not be immediate, and its object may be past, but if so that object is just this — that a moment ago I was conscious of the then present object. I cannot therefore think that Hegel has shaken the validity of immediate consciousness, or shown that its object is other than the individual present fact as such. SIMPLE APPREHENSION 33 Take the case, which occurs at once, of an illusion. " That's a man in the corner of the room — no, it is a shadow." Clearly this is an error, as above explained, of comparison and inference. But it may be objected, the figure of a man was actually before my consciousness. Or take a clearer instance : "We cannot help seeing the new moon bigger than the old one "in its arms," though we know that the outlines are segments of the same circumference. Surely this is an error of vision, not of judgment ? Of vision, yes. Of apprehension, no. The error is due to retinal " irradiation," not primarily to any intellectual process ; therefore it is quite correct to call it an error of vision. But if we make strict enquiry, and ask where error begins, the answer is, not till you form some such judgment as, " that irregular outline is the present shape of the moon." This judgment is false : the apprehension, on the contrary, is merely an assertion of what is present to you, and the irregular light and dark shape is present to you. The assertion that it is the moon says a great deal more about it than you see. It says that the content with which attention is now occupied is a part of the surface of a distant body, etc. It is in the predicates thus assigned to the content that error consists. And this, I venture to say, will be found to be universally the case. Confine yourself to the assertion of a fact before you, and there is no error. Make comparisons and draw inferences, explicitly or implicitly, and error comes in. But the very act of attention itself sometimes brings about an illusion, for example, an imaginary pain. Is such a pain real ? Undoubtedly, if we mean by pain strictly the mental condition of the moment. The rheumatism of an amputated leg is as much pain to the sufferer as the burn on his sound arm. When we say it is not real, we mean it is not really rheumatism, i.e. a bodily affection existing in the place where it is supposed to exist. Similarly a hysterical pain exists " nowhere " as a bodily affection, or if we ask for its seat as a physical derangement, we shall look for it in the centre rather than the periphery of the nervous system. But it again is every whit as much paia to the subject. Once for all, if by pain is meant a mental feeling, a " malade imaginaire " may really suffer as much as his heart could wish, and the hypnotic patient who is not aware of any pain when his teeth are drawn really has none. It will further illustrate my meaning if I point out that this doctrine in no way conflicts with the difficulty, widely recognised in psychology, of accurately observing one's pre- sent condition. Prof. James, following Mill and Wundt, has at 34 DATA once insisted on this difficulty, and explained it.^ It is often very difficult to observe one's present mental state. How can that be i£ the present content is always fact, and nothing but fact ? Easily enough, considering that observation for scientific purposes means fixing, retention, naming, classifying. All that passes through the swift mind is for the moment somewhat ; but what ? — i.c. what name has it, in what class does it fall, in what precise order did it come ? Before these questions are well asked, still more before the ideas requisite for the com- parisons are ahve in the memory, the present facts have hurried past, jostled and crowded away from the focus of con- sciousness. They are already past, and the question is not for apprehension, what they are, but for memory, what they were. Even supposing the naming or comparing to be done for the object whUe present, the comparison itseK involves memory, and is not therefore infallible. Apprehension is for ever giving us fact, and taking it away again, and hence it is that for steady and certain knowledge we want so much more than apprehen- sion. Thus the familiar question, " Is this real ? " does not ask whether that which I apprehend is fact, but whether it is something else besides itself — whether something further is true of it than that which I apprehend. " Is this a dagger which I see before me ? " means not, is there really the appear- ance in question, but, will that which I see stab ? If I clutch at it, will it resist my touch, be hard, sharp, smooth, heavy, stab my guest ? That which appears is as it appears real, but are these judgments which I am at once inclined to make about it true or false ? Does it stand in relations which I suppose for it as soon as ever I apprehend it ? The error comes in in the assertion of these relations. And this assertion is no part of the content of apprehension. But according to the relations in which it stands, one and the same given content has in- definitely different meanings, belongs, as we ordinarily say, to totally different " orders of reality." In which of two sets of relations a fact stands, what are its concomitants, its conditions, its results, what, in short, are the other facts with which its ^ See especially his Psychology, ii. pp. 189 ff. As I understand Professor James, the above account is substantially his ; the judgment, "this is cold," is cei'tainly a different state from the feeling cold. I only do not understand him when he says broadly : ' ' No subjective state, whilst present, is its own object ; its object is always something else." Surely a feeling is its own object, what other object has it f Professor James could, I think, only object to this if he adopted Wundt's theory of apperception, which I do not understand him to do. Then, indeed, every act of attention would have " something else" for its object. But I imagine that Professor James really is thinking of the judgment, which must always have some other content as its object, a fact which is sufficient to prove his general position. SIMPLE APPREHENSION 35 existence is bound up, are questions which we must answer if we are to understand the fact ; and how we answer them makes all the difference in the world to its significance. But the answer comes not from apprehension, but from judgment ; and though by the answer it gives the kind of reality to which the fact is attributed may be altered, the fact itself as appreheTided, if we confine ourselves strictly to what is apprehended, is never altered and never unreal^ A further comparison will illustrate the necessary correct- ness of apprehension. In an ordinary judgment — one of memory, for instance — the content asserted gives its quality to the assertion. Now the assertion, " I met you here last spring," may be true or false, but if we put it, " Well, I certainly have the distract remembrance of meeting you," then — apart, of course, from the case where from " intent to deceive " the words do not correspond to our actual mental condition — the truth of the judgment cannot be contested. And the explanation we usually give is, " My memory no doubt has deceived me, but I certainly have the recollection," etc. This is precisely parallel to the optical illusion, "My eyes perhaps deceive me, but I certainly see that man pass two soHd iron hoops into one another." Quite so. I do see it ; I do remember it. If for the memory-judgment I substitute the assertion of what is at present in my consciousness, viz. the idea of a certain content in a certain position in past time, then there is no getting rid of the reality of that idea. If, that is, I substitute for the memory-judgment proper, which is an assertion of something absent, the apprehension of the content of the memory judgment as an idea or belief at present in my mind, then my judgment is infallibly true. I am asserting that which is, in fact, qualifying my present consciousness. So with all apprehension. Its content is true, because what is present to consciousness exists as a quality of, or element in, that con- sciousness, if in no other relation ; and apprehension as such does not decide in which kind of relation the fact exists. As soon as we do decide we are judging, and at the same moment we become liable to error. 6. I conclude, then, that the consciousness in which we are directly or immediately aware of the content present to us, a state which I venture to call apprehension, is a primitive or underived act of knowledge. Apprehension has the general characteristics of awareness, or assertion, shared by aU the ^ The interpretation of the question, "Is this real?" as="In what rela- tions does it stand ? " has never been better expressed or defined than by Green, Frolegomena, bk. i. chap. i. 36 DATA intellectual actions which constitute knowledge; there is, however, no logical ^ reason to analyse it into an act of atten- tion or apperception on the one side, and of sensation or feeling on the other. It is further " primitive " in the sense that with it knowledge begins, that its existence postulates no further knowledge, or mental activity of any kind, as its antecedent condition. The content of apprehension is Fact, and the basis of our use of the term fact, and on this account we shall find that apprehension is the primitive datum of knowledge in a more ultimate sense, for to it we have to refer questions of vahdity, and — whatever may be the antecedent conditions of an act of apprehension — its deliverance is always an ultimate and final court of appeal which no consideration of anterior conditions can upset. The fact apprehended, then, is not only the beginniug of knowledge, but is also the ultimate — or at least, let me say, one ultimate — source from which our judgments of vaUd truths are derived. Lastly, to remind ourselves here of a remark already made, we do not contend that apprehension is ordinarily found bare by itself, stripped of all other kinds of mental activity. Hence in speaking of it as the primitive mental act, we are not intending to give an adequate description of concrete acts of the mind in its early stages. What precisely may be the character of the mind in infancy must be discovered, if it is at all discoverable, from the observation of infants, and not from the analysis of adult knowledge. For our purpose it is in- different whether an act of apprehension ever exists by itself in the sense of forming the whole state of consciousness for the time being. We are contending merely that such an activity is to be found on analysis iu many of our mental states ; that- it is a condition of knowledge ; and that by itself it takes us a certain distance and no further. It is useful for our purpose to find cases where this activity is actually in the concrete isolated from others, such as the qualitative judgment, with whose operation it is easily confused. But its separaten'ess as a condition of knowledge from other conditions depends, not on distinction of time, but on distiuction of function. We are fuUy prepared to admit, therefore, that the apprehension of the present is not normally a separate activity of the mind in the sense of exhausting all that the mind is at a given moment. Possibly it is never so. Our actual state of consciousness at any moment is, as a rule, very complex, involviag the apprehen- sion of many different objects by more than one sense, together with judgments, inferences, and the Hke. Nor would it ba ^ I mean as distinct from a psychological reason. SIMPLE APPREHENSION 37 true to say that the apprehension of any one fact A always, as a psychological event, goes before the judgment that asserts that it is A. All we contend is that analysing that section of our mental state for the moment which is concerned with the judgment, this is A, one subsection will be found to consist of the apprehension of the given, and another of the assertion of its character or relations. In carrying out this analysis we do what every science does. By analysing concrete phenomena, we endeavour to isolate certain conditions — which may never exist in isolation — and obtain their results taken by them- selves. Gravity does not exist apart from other quaUties of body, but we can disentangle it as a condition of motion, and accurately measure its effects taken by themselves. Siooilarly the problem of logic is to disentangle the conditions of asser- tions, — conditions rarely found operating in isolation, — and to determine what portion of the asserted content it is for which each condition is severally responsible. CHAPTEE II The Content of Apprehension 1. Foe examples of sensation, our thoughts turn naturally to the simple qualities of things — cold, sweet, blue, loud, and so on. When questions of its function in knowledge have arisen, the tendency has been to identify sensation with these qualities. And this done, the further question at once followed — how about the relations in which these qualities stand ? what of their coexistence and succession, their resemblance and difference, their order in space, and so forth ? And keeping to the idea of sensation as giving these simple sense-qualities and nothing else, two courses became open, one adopted by thoroughgoing sensationalists of "explaining" relations as due to some composition of sense-qualities, the other re- sorted to by Eeid, and with a more penetrating analysis by Kant, of attributing the relational element, so to call it, to another activity of the mind different from its mere power of receiving impressions, to " spontaneity " instead of " recep- tivity." The Kantian view is a rigorous deduction from its premises. If sense gives us qualities in which no element of relation is present, it is quite certain that no mental chemistry can build up relations out of qualities. If we immediately perceive colours that have no extension and no order in space, sounds that have no duration and no order in time, then it is clear that no combination of such colours will begin to give us space, and no cluster of such sounds would bring about the perception of time. It would remain to separate the " given " quality and the " order " which the mind constructs for itself. If, therefore, there is an answer to Kant, it must be found in a revised con- ception of the " given " element in knowledge. Now here we find the greater part of the work already done for us, and that in large measure by Kant's descendants. It has been pointed out now often enough by successive writers that the simple quality supposed to be the primitive datum 38 THE CONTENT OF APPREHENSION 39 for consciousness is, in fact, an abstraction. Who ever saw a colour that was not spread over a certain space, or heard a sound that did not last an appreciable time, or even felt a pain that he did not vaguely locate somewhere ? There may or may not be more primitive elements to be discovered by analysis in these data of sensation ; but if so, they are not themselves data of sensation as they stand. There is no sensation but has extent in time or in space, or in both ; and if this be questioned in the interests of sensationalism, we can only retort upon the objector the famous demand of his philosophical father, " I desire it be produced." To deal, first, with such relations as resemblance and differ- ence, I have shown above that apprehension has nothing to do with the assertion of relations between the present and the absent. But there are relations of this kind between the ele- ments of the present itself. Looking at two peas or two oranges, their resemblance is a matter of immediate apprehension. Looking at the lines on the page before me, their distance apart, their directions, their parallelism are similarly present to my consciousness. Two cautions are needed here. First, we do not mean that the act of apprehension is equivalent to the judgment, " These peas are ahke," " these lines are parallel." This judgment, expressing itself in general language, involves the subsumption of the given under a general idea, and this subsumption is not the work of apprehension. But the judg- ment, as we have seen above, aims at expressing that which I apprehend; the present hkeness, the present parallelism, being apprehended form the basis of the judgment. Secondly, the likeness and the parallelism are abstract terms ; but we do not apprehend the likeness or the parallelism as abstract facts, that is to say, in separation from their context. We apprehend the whole fact — two peas, two straight lines. The resemblance of the peas is a characteristic, an abstract characteristic, if we regard it by itself, of the two peas con- sidered together. But in apprehending, we do not regard it by itself. We apprehend the whole content with all its characteristics, of which the resemblance in question is one. The knowledge of this resemblance, then, does not as such in- volve any addition to what is given in apprehension, nor a knowledge of anything apart from the case in which it is given ; it involves simply the consciousness of this among the rest of the manifold characteristics of the given. To deny this, it must be first argued that we cannot appre- hend two peas or two straight liaes together, and that if we wish to know their resemblance, we must first attend to one 40 DATA pea, then to the second, and then " construct," or in some other way arrive at, the relation between them. But why stop at one pea ? If you deny that we can in one and the same moment of time be aware of two small round coloured objects, why should you find it easy to be aware of one such object ? Each pea consists of parts in space, and has very many different characteristics. How is it that we can apprehend such a complex object aU in one moment ? Clearly the argument once seriously faced reduces our knowledge hterally to atoms. There must be some original dot of colour or what not that forms the primitive sensation. Of the theorist who contends for this, we can only say with Herodotus, that he escapes confutation by carrying his tale to the region of the invisible. A sensation of this kind is not verifiable by con- sciousness. If it exists, we are not aware of it, and we do not for our part desire to go beyond what we can observe. But if we are guided by observation, we shall admit that two peas are as readily apprehended as one — nay, we shall have to allow that if they lie close together, it is impossible to observe and difficult to attend to one of them alone. In fact, the contents from time to time present to us are normally com- plex, not simple. It may be asked, if you admit complexity, where do you put the limit ? If you apprehend two peas, why not twenty ; and if twenty, why not a million ? My reply is, that I do not find that I can apprehend a million objects of any kind at once. I do find that I can apprehend two peas at once. Then how many can I apprehend at once ? This I cannot tell pre- cisely by simple introspection. I am quite sure that I can apprehend two, and equally sure that I cannot apprehend a thousand as distinct objects. But between the two there is a point at which my attempt to analyse and class my mental state becomes confused, memory beginning to help out apprehension. But is not this fatal to the whole theory ? Apprehension must have definite limits, and surely it must know what its own limits are. Not at all. Apprehension is a form of assertion which I come to know by attending to and analysing my own consciousness in relation to its objects. The apprehension of A B is not itself the consciousness that I apprehend A B. This consciousness is a new mental state, having the former state as its object, and may be a much more difficult state to arrive at. In point of fact, apprehension of a series of objects, A B C D, passes continuously into memory. At any given point it either is apprehension or memory, and when it is the one it is not the other. But which it is at any THE CONTENT OF APPREHENSION 41 point is a question to be answered, not merely by having the mental state, but by analysing, naming, and classifying it — a very different matter. We have aU sorts of mental states •without always being able to analyse them aright. The difficulty is not peculiar to apprehension. And experience has shown that introspection in such cases must be helped out by experiment. By simple self-observation we can only get such crude results as I have already mentioned. We can be quite sure that two peas can be presented simultaneously as distinct objects, and that a hundred cannot be. But if we wish to get a more definite conception of the matter, we must use ex- periment, i.e. observe our perceptions under special and artificially determined conditions. Thus Mr. Cattell found that he could distinguish from four to five disconnected objects (such as letters, figures, or lines) under conditions which eliminated the possibihty of successive acts of apprehension. If, however, the elements were so connected as to form together some known content, he could apprehend about three times that number.^ Less exact experiments tending to the same result are quoted from Hamilton and Jevons by Prof. James,^ who also mentions M. Paulhan's observations on the power of attending to distinct mental operations such as the recitation of verses carried on simultaneously with a process of multipHcation. The time-results here indicate that the atten- tion can be successfully distributed between the two objects at once. In all these cases it must be remembered that the separate objects are clearly distinguished, and therefore occupy the focus of attention. The whole field of consciousness must be, as Wundt argues, considerably larger. But confining our- selves to clear consciousness, we find that we can apprehend four or five disconnected objects simultaneously, and from twelve to fifteen if they form part of a whole.^ But even this is not all. The simple objects, the single lines, and a fortiori the single letters of Cattell's experiments, are themselves already complex facts in which an upper and lower, a curve or a straight Hne, can be distinguished. Hence, unless we are prepared to produce the sensational atom out of which these objects which we know are constructed, we must allow these complex contents to be the ultimate data of knowledge. The ^ "Wundt, Grundzuge, chap. xv. § 3. ^ Op. cit. i. pp. 406, 407. ' Prof. James says that within any one ' ' system " (by which he means what I have called a whole), "the parts may be numberless" ; but then, as he rightly adds, we attend to them "collectively." For me the question is. How many connected parts can be known distinctly as parts ? and the best answer here available is Cattell's — from twelve to fifteen. On the fmi;her extension of apprehension, we shall speak presently in connection with duration. 42 DATA simplest sensations verifiable by experience allow themselves on analysis to be resolved into related elements.^ There is no reason whatever to suppose that the elements and the relations are given by different processes. If we apprehend the one, we apprehend the other ; if, e.g., apprehension distinguishes an A from a B, an M from a W, it must distinguish the relations of the lines composing these letters. The contents of appre- hension are therefore wholes consisting of related elements, and the elementary relations of things are given, just as much as the elementary qualities of things. The whole difficulty on the point has arisen from the dogma that the original data of knowledge are simple in character. This dogma appears to have rested on a confusion. It was held, and I shall presently argue, correctly held, that the mind could not invent or construct any simple characteristic of things, or, to put it better, could only form fresh contents of thought out of elements already given it. The simple characteristic thus became an ultimate datum for knowledge. Then it was, I think, unconsciously argued, knowledge must begin with these simplest elements; they must be given in their simplicity. Not at aU. All the first position proves is that the simple elements must all have been given or presented to the mind. Hov) presented it does not say. Now our argument admits of their being given, but points out that they are given, not in isolation, but always, to use a well-known expression, " in some context which is individual and peculiar." From the alleged simplicity of the data of knowledge arose half the difficulties of sensationalism. By it also was occasioned Kant's answer to the sensationalists. The philosophic descend- ants of Kant have occupied a curious position in the matter. They have apparently seen, what Kant did not see, that the original premiss is false. They have pointed out that the sensation, as interpreted by Hume and his followers, is an abstraction. They have gone much further than I can follow them in dwelling on the relations necessarily present in every datum of sense. Now this cuts the ground from beneath Kant's feet ; it destroys every argument for a spontaneous action of the mind, constituting the relations in which sense-data stand. Yet the very thinkers who annihilated Kant's premises have pushed his conclusions to their extremest point, and have taken the whole of the data of apprehension as constituted by the activity of thought. The case stands, roughly speaking, ^ I speak throughout as though this were true of all such contents ; and so I helieve it is, for reasons to be given lower down. But I may remark that it is ciuite enough for our purpose that some sense-contents should be complex. THE CONTENT OF APPREHENSION 43 thus. Hume,^ developing the atomic view of sensation, spoke loosely of a knowledge of the order of impressions or ideas without appearing to see that this postulated a very different kLad of knowledge from that of the "atoms" themselves. Hume's followers explained this knowledge as arising out of the sensations themselves by a psychological process. Kant, seeing that this was impossible, explained the element of order and relation as arisiug from the mind, as " spontaneity." Kant's followers, arguing that the separation between sense-data and their relations was a figment, extended Kant's idea in such wise as to make the activity of thought constitute the whole of experience, subject to more or less doubtful reservations in the interests of the " given " element. But their argument, instead of developing Kant's idea, extinguishes it. Just because there is no sensation given without relation, it follows that there is no need to postulate any mental activity to make us aware of relations except the capacity to apprehend them. 2. But it will at once be asked, What of space and time ? The distinctions and relations we have examined involve a spatial or temporal order. We cannot perceive our two peas unless they are separate either in space or time. Then are space and time also apprehended? Not perhaps space and time as two great individual wholes, but the spaces and times in which qualities and relations are presented to us. These are just as truly given as the quahties which occupy them. If I lie on my back on the grass and gaze up at a cloudless summer sky, what do I see ? Not a congeries of blue poiats which I combine into an extended surface, but from the begiuning a blue extent.^ I see extension just as I see colour. There is no more reason to say that I see the colour and con- struct the extension, than to suggest that I am given the extension and lay on the colour. The two characteristics of the whole are distinguished only by an act of abstraction. As given, they are indivisible. Nor is this all. What I actually see is not a blue surface merely, but a deep vault at a distance from myself, and into which I seem to see. In short, it is not surface only, but volume. If, lastly, as I gaze a cloud comes up, I see it in a particular part of the blue expanse ; and if there ^ " The idea of time is not derived fi-om a particular impression mixed up with others and plainly distinguishable frpm them ; but arises altogether from the manner in which impressions appear to the mind, without making one of the number " (Hume, Treatise, part ii. § 3. Green & Grose's edition, p. 343). Cf. Locke, Essay, bk. ii. chap. xiv. § 3. Space, indeed, is still for Locke a simple idea (bk. ii. chaps, iv. and xiii. ). To Hume it is the ' ' manner of appear- ance" of coloured or tangible points (Treatise, loc. cit. p. 341). ^ Contrast Hume, loc. cit. 44 DATA are many clouds, I see their shapes and sizes, and the inter- spaces of blue that part them. That is, I see position, magnitude, and distance. Yes, it will be replied, you see all this because you have learnt to see it. It is no primitive perception, but acquired ; formed by the clustering of many sense elements originally distinct, but now so grown together that you take them for one. Or another objector in the interests of a different school may urge, your present object may be a primitive, original kind of representation, but you must not talk of it as being apprehended or given. What is given you is the mere sensation, the mere isolated feeling or multitude of feelings. Your own mind reactiag on these forms the extended surface. Beginning with the first objection, let us mark our position, which, be it remembered, is dictated by the requirements, not of psychology, but of logic. We may admit at once that our present space-perceptions are in a great degree the result of education. I should not see so accurately as I do if I had not been seeing all my life ; while you, who have specially trained your sight for this purpose or that, can see many things to which I am blind. Attention and discrimination can be cultivated, no one doubts, and attention and discrimination must have their effect on our perceptions of space. But this much can be said of every conceivable perception. To go no further than the eye, the artist's sense of colour is very different from yours or mine. He sees shades to which we should be blind ; and if he can teach us in turn to see them, it proves all the more how much the training of the faculties can do. I do not, then, contend that my space-perceptions as I now have them are the same as they were the first day I saw the light. Beyond a doubt they are products of development. But so, I add, are hundreds of other perceptions enjoyed by the adult man. But if we give up " originality " in this sense, what do we maintain? Two things: (a) that however much our space- perceptions have developed, there is no evidence that they are evolved from non-spatial perceptions; (6) that our present space-perceptions are simple acts of apprehending what is given, not resolvable into a composite activity consisting of a sensation, plus something further. Of these contentions the first is matter primarily for psychologists, since it concerns development. But, in fact, it depends mainly on the second contention, which is of immediate concern for us. Let us turn, then, to this contention. Our opponents, we have said, are of two classes, which the reader will, no doubt, have already recognised and named THE CONTENT OF APPREHENSION 45 Empiricists and Kantians. Differing widely in general result, they agree in one supposition, and further than that supposition we shall not need to follow them. They both postulate that what is given is really a spaceless sensation ; and that being assumed, they try to show in different ways how this sensation is formed into an extended object. This postulate we deny. So far from being necessary or plausible, all experience is against it. We never see an unextended object, we never touch one. From the beginning, so far as self -observation or memory can inform us, we are given objects extended in space. Some psychologists would go a step further, and say that we are never aware of any sensation whatever that is not extended or voluminous. Sound, smell, and taste are all, however vaguely, extensive and locahsed. Aches and pains have their seats ; nay, emotions and thoughts, when I observe them in myself attentively, seem to take their place in my head — my thoughts, for example, seem located just behind my forehead. But we need not generahse so hastily. It is enough for our argument that 710 sense-content definitely known to us as exteTided is also known, or can be remembered, as heing given in an unextended form. That is, the unextended datum /rom which space is to he formed is a figment. It is an invention, not a discovery. Equally fabulous is the act of the mind, which imposes the form of space on this non-spatial content, and equally unverified the association which calls up other unextended sensations to amalgamate with the present. It results that the apprehension of things in space is not a composite act in which one element only is given, but a simple act the whole content of which is given. Space, then, is given in apprehension ; and the apprehen- sion of space is an apprehension of the present, not an act which introduces to it relations that are not presented. 3. So far we have dealt with extension as such. With regard to the special question of visual perception of distance, there are, no doubt, difficulties psychological and stiU more physio- logical.^ But here again the primary fact, the best known fact, is the analysis of what we adult men actually see. That much of what our sight means is due to experience, no one could deny. But this does not prove that we do not see what we do see. As I sit in the garden and look through the misty September air at the house, I see the interval as well as I see the house. This interval means to me {inter alia) so many paces, such and such an effort, such and such a time, if I want ^ I say nothing further of these, since it would be absurd for me to attempt to add anything to Professor James' masterly discussion (Principles, chap. xx. p. 212 ff.). 46 DATA to go into the house. This meaning is tacitly a correlation of my present perception with many memories of touch, and of the sensations, whatever they are, involved in walking. With- out these memories the interval would mean much less. Like a baby, I should stretch out my hand to pluck the clematis on the wall. This is all verifiable, for (at least on the smaller scale) I observe it. If I compare the distance as it looks to-day with my recollection of it a week ago when the air was clear, I am aware that in appearance it has increased ; and it is only an experience some steps, at least, of which I can recall which has taught me to aUow for the difference made by a mist ; has taught me, namely, that what is for my walking or my touch one and the same distance, is to my sight greater or less according to the nature of the mediimi that intervenes. But in all this there is nothing to show, nothing to suggest, that the visual perception of distance is itself acquired. The relation of this perception to others depends, doubtless, on those others ; but it depends also on the given quality of the perception itself. You cannot eliminate either term and leave the equation standing.^ Lastly, extension as such is only the most abstract characteristic of extended things. What is extended contains also size, shape, and position ; if it is given in the first character, it is given m these three as well. I no more add these quali- fications to the objects I see, than I add their extension. This will become clearer if we deal with two objections. First, it may be urged that if anything is relative it is size and position. Take size. What do I mean by saying that this table is 3 feet long? Simply that its extremities will tally precisely with those of a yard measure, that it is half a fathom line, and so on. That is, I mean by the alleged size one or more equations, one or more relations between this object and others. This is true in its way. The total meaning of a size includes relations to other sizes. But that these relations should subsist there must be something to be related. What is it now that is equal to a yard measure ? This surface ; and how do I judge it equal ? by apprehending its size as given.^ ^ In any case the difficulty concerns vision only, and not the perception of depth, as such. This seems often to be overlooked in discussions of the problem. You need only dip your lingers into water to convince yourself that touch gives extension as three-dimensional. And there seems no evidence v?hatever that the perception in this case is in anyway derivative. ^ Of course, this judgment may be based on superposition and then collapses into a perception of coincidence between the boundaries of the contiguous objects. But we form approximate judgments of size without employing measurement, and they are based on the size as given. It is to these that the text refers. THE CONTENT OF APPREHENSION 47 Quantities are given, and when given they are related. If they were not given there would be nothing to relate. If we grant to the full that a given size is definable only by relation to others, this only puts size on the same footing as any other given content, and does not begin to destroy it as an apprehended characteristic of the present. 4. With regard to position the ease is different. We may doubt whether any meaning can be attached to this word unless it expresses the relation of one object to another.^ How, then, can such a relation be given? Eeadily enough, if the apprehension of relations be admitted, whenever an extended surface presents us with two or more points. But that is as much as to say that every definite perception of an extent is the perception also of positions. The direction of the lines, the position of the words on this page, are as much parts of my present apprehension as the extent of the page itself. It is impossible to regard the one as given and the other as recognised by any other process. There is, indeed, one difference which brings us to the second objection. Above, in arguing that space is appre- hended, we were able to characterise the non-spatial colour or touch as mythical. But can we now stigmatise the sizeless, figureless, positionless extension in the same way ? Professor James teUs us that we cannot.^ There are indefinite space- perceptions without form or order — such, for instance, is my headache ; or, to take a more interesting example, the " murmur of innumerable bees " that is all round me and everywhere this morning, a vaguely extended sound, shapeless, and without special position. Can we regard a vague extension like this as the source of our definite ideas of shape, position, and size ? In a certain degree, I suppose, we not only can, but must. It is in accordance with all analogy to suppose that our knowledge of space progresses from the vague to the definite, and how vague its beginning may be we cannot well say. But granting this, there are two ways. in which the progress may take place. One is by analysis (of which, in general, we shall treat presently), the other by synthesis. If the process is analysis we may be said to find parts, quantities, positions, etc., in the given whole ; if synthesis, we must be regarded as constructing the whole from given elements. I will briefly state my reasons for supposing analysis to be the process here concerned. ^ I do not say that this is the whole meaning of the word. I merely wish to take the question in the fonn presenting most difficulty to my own theory. ^ Loc. cit. p. 145. 48 DATA In the developed visual perception of space its parts appear to us as given elements in the whole. The position of each point either is its relation to some other point determined by some interest attaching to it, or is its relation to the whole. In this case the position of the point appears as given, just as the extension of the whole is given. The only new element required is an analytic movement of attention (of which we shall speak presently), which singles out this point as some- thing to be regarded on its own account. Now here, as it appears to me, we have the ultimate account of the matter. It is no explanation of space ; it is a mere analysis of the facts. But, it is objected, it is an insufficient analysis not taking account of all the facts. For to make our account possible any point A must be known in some way in itself : it must at least affect us differently from B. Otherwise, in the given surface we should not see A and B as two points, but as one. But how can A and B by themselves affect us differently ? We cannot, the argument goes on, know A's position as long as we only know A; for how can we attribute position to a point except in relation to some other ? We are involved, then, in a paradox. Two points qualitatively alike differ in position and are known to differ. But if you take either point singly it is just like the other, for it differs only in position, and its position, while you take it alone, is non-existent. From this paradox the theory delivers us through the conception of local signs. A and B have each a peculiar mark (other than their colour, etc.), felt by us, which, while not itself the fact of their position, indicates their position to us. By an associative synthesis of such points, each with its own local sign, we get the relations of the points in space. This theory appears to me to make its own difficulty. You may take two views of position. Either it is a quale attaching to A and B as such and separately ; or it is an expression for A's relation to B, and for B's to A (supposing no other points to be taken into account). If, first, it is a quale, there is no difficulty in regarding it, the position itself, as immediately given in the apprehension of A and B separately. If it is not a quale, then nothing of the kind is given when we perceive A and B separately ; but when we attend to the two together they are together given as connected by the line A B. This would be only one of a multitude of cases where two things together constitute something more than the sum of the two regarded as a matter of pure addition. But it will be answered, A and B must affect us differently, or we should not see them to differ. Doubtless, if you regard them as physical objects they must act on different points of the retina: a different physiological THE CONTENT OF APPREHENSION 49 process must be assigned to each, and the sum. of these processes produces in consciousness the apprehension of the whole A B. And on the hypothesis that position can only be known through relation, we must assume that the point A, regarded as a physical object, sets up a physiological process a, issuing in the apprehension of A sole and therefore position- less : that similarly B sets up b, physiologically different from a, but not different enough to issue in a consciousness different from that of A ; while A B together set up a b, a total process which results in the perception of A and B in their relation to each other. The point in which a and b differ may then be called the Local Sign. Whence, on this hypothesis, the local sign is an element in the physiological process incapable of mental expression unless in combination with another local sign. In such a combination it gives rise to the apprehension of position: otherwise it remains a purely physiological process. To the Local Sign theory then I propose a dilemma. Either your sign means, in fact, the position of the point regarded as belong- ing to the point as such ; or it is a characteristic to be postulated in a physiological process. In neither case is it a content present to the mind distinct from but indicating position.^ If, indeed, I could for my own part verify the existence of such a content in my consciousness, I should accept the existence of local signs, though I should still have great difficulty in understanding how they help me to form my space-perceptions. But when I am told of the difference between a prick on my hand and a similar prick on my foot, between a toothache in my left upper and the same in my right lower jaw, I can only feel that the difference is one of position. I can think of this position as attaching to the pain itself, but only as the very same characteristic which brings it into relation with other feelings. I conclude that either the position of the feeling is itself an element in the total content making up that feeling, in which case it is given in and with the feeling ; or that it is the relation of the feeling to some other, in which case it is given when the two feehngs are given together. Since we cannot apprehend any point by itself, we cannot strictly decide between these alternatives; but in no case is there evidence for any further felt characteristic attach- ing to a sense-content other than its position, which is yet the detenninant of its position.^ The simplest account then, on 1 The dilemma is not quite parallel to that propounded by Mr. E. Ford {MiTid, N. S. No. 6, p. 218). But the argument is essentially the same, and so is the conclusion, viz. that position cannot be explained as derivative. " For the opposite view, see James, loc. cit. pp. 153 ff. I am greatly indebted to Dr. Ward's account of "Local Signs," which is nearly identical with the above (op. cit. p. 54), but I do not see why he should retain Lotze's 50 DATA my view,' starts from the given wholes of space : it recognises that these may be comparatively definite or indefinite as they are presented to us : it holds that by attention and analysis we can detect in these data parts or elements, that is to say, figures of definite size and position ; it recognises that differences of physiological process in nerve and brain must accompany the apprehension of different positions, but it can verify no felt element in consciousness corresponding to such processes excepting the apprehension of the positions themselves. 5. It remains to ask whether time and contents, like change and continuity, involving time, are also matter of apprehension. The analogy of space would suggest that they are — that we apprehend extended processes just as extended objects. But contents involving time present a logical difficulty. The fact apprehended, we have seen, is present to, and so qualifies, the apprehending consciousness. That which is past, therefore, it would seem, cannot be matter of apprehension. Now change, for example, occupies time, nay, the very conception of it involves time. The first phase in a changing object is over before the second one is present. Hence it would appear that the two stages cannot be present together ; and if not, how can they be apprehended as change ? If we apprehend A, and then again B, we have two successive apprehensions of two different contents, but not the apprehension of change. We can say, " There was A and there is B," but what do we mean by saying A has changed into B ? By successive apprehension of different facts we do not approach the idea of change. It may be urged that the statement that A must be over before B is present is false ; in fact, the definitely marked stages A and B are the results of an alistraction. There is no gap in time. There is continuity. Quite so, but how do you apprehend continuity? That, it will be admitted, involves time ; it must have beginning and end, or at least earlier and later. A continuous process in which there was not earlier and later would be like a line in which there was no distance separating its termini ; it would, in fact, be a point in time. But if there be an earlier and a later, can they both be present at once to consciousness, so as to be apprehended as one process ? If not, how do we apprehend continuity ? Once more, the apprehension of A, succeeded by another apprehension of A, is not the apprehension of a contiauous A — A. The same consideration destroys in advance a theory that might otherwise account for the idea of change. It might be terminology. For Lotze's view see Metaph. bk. iii. chap. iv. and cf. Ziehen Phys. Psych, pp. 76 £f and 122 (Eng. trans.). ' THE CONTENT OF APPREHENSION 51 said — in the change from A to B, if you analyse it a little further, you will find an identical element, such as X, persist- ing amid differences such as a and b ; so that really we have, not A and then B, but aX and then bX; and this identity in dijfference is what we mean by change. But clearly we should not (at least by means of apprehension) be given the identity of X — X unless we were aware of them as forming a continuity. Neither continuity nor change, motion nor rest, duration nor succession, can be given to successive acts of apprehension, imless given to each act singly. We are then in a dilemma. Either these contents — all contents, in short, involving time — must be constructed out of data of apprehension by some different process ; or, if we are to regard them as apprehended, we muat admit that successive facts are present to one and the same act of apprehension. Paradoxical as it seems, I believe the second alternative to be the right one. The immediate past remains actually present to the apprehending consciousness. When I am aware of a change from A to B, the stage A is present to my mind along with B, and the whole present to me is to be expressed as " A. followed by B," or "A passing into B." At first sight this appears a direct contradiction in terms. A is past ; how can it be present ? I admit that it requires a little explanation. 6. To begin with, apprehension itself, regarded as a psychical event, occupies time — how much time is a very difficult thing to determine experimentally, but some time. Even the simplest fact requires time to take it in. Here, then, it seems, is an explanation ready at hand. An act of apprehension occupies, say, a second.^ All that goes on in that second, change, rest, motion, persistence, the abstract character of the dm-ation of the second itself, is all contemporaneous with that act of apprehension, is therefore present to it. This, if put forward as an explanation, however, ignores the whole difficulty. Duration (and all facts involving it), to be known at all, must be known as a whole including parts, as having an earlier and a later. Now, if we keep to the idea of the "present" as something of which the parts are simultaneous and concurrent, we shall see that our act of apprehension, extending over a second, will be aware of everything that happens in that second, but that there will be no point in it at which it wiU be aware of the whole. Eepeating the argument for any fraction of a second, you get the same result. Duration is something com- posed of earlier and later. The two are never physically present together. The earlier is present to an earlier part of ^ For the actual experimental determination of its duration, see below, p. 68. 52 DATA the act of apprehension, the later to a later part, but never both to one and the same part. Conceive apprehension or its object as two processes going on in time (whether at rest or in change), and take a section through them both at any moment ; you will find always a point in the one watching a point in the other. Here a possible explanation suggests itself. There is some irreducible atom of apprehension of exceedingly small duration ; to this is given the simultaneous stage of the observed process. Now, after a certain time, these atoms accumulate, and compel attention, which thereupon fuses them into a whole, and turns out a perception of change. The last fractional part of the change is still matter of immediate consciousness, but all the earher parts are really memories, and the apprehension of time is a fusion of present apprehension with primary memory images. But there are two objections to this. In the first place, it is not so. We cannot " produce " the atom of appre- hension, the momentary awareness of a tiny bit of fact. Every apprehension of a fact, or (equally) every fact as appre- hended by consciousness, lasts an appreciable time, whether at rest or in process. Our datum, as introspection gives it us, is an apprehended content, with appreciable duration. And, further, though the facts are not so, if they were so they would not help us. For the atom of sensation must still occupy time, and the same difficulties recur on the smaller scale. Does it, or does it not, apprehend, as a whole, all that passes before it ? We must therefore substitute a different conception for that of atoms of apprehension. Every act of apprehension lasts an appreciable time, say a second, and yet forms in a sense a single whole. All that comes before consciousness during that time remains present during the whole of the time. At the end of the second all the process that has been presented from the beginning is present to the mind, along with the final stage of the process. The mind views the process as one whole. This does not, of course, mean that that which is past is at the same time present in the same sense in which it is past. It means that the act of apprehension is of the immediately past as well as of the present.^ That which has been presented remains in the mind, stUl qualifying it, still going to form the content present to it, along with that which is now being presented for the first time. The completion of an act of apprehension involves the apprehension of all that has been presented to that act.^ 1 Or, in other words, "past" has two meanings: (a) = " earlier than any en point of time ; (Ji) gone from consciousness ; and if the given point be the low," what is past in sense (a) need not be so in sense (/3). ' Cf. Ward (pp. cit. p. 64), and James, Principles, chap. xv. THE CONTENT OF APPREHENSION 53 To further illustrate and explain, let us divide our second into quarters, apprehending the process abed. Now, whether as an event independent of consciousness, or as an occurrence in consciousness, a is certainly not contemporaneous with d. But a is presented to the mind in the beginning of the second, and as a content apprehended by the mind continues to exist through the successive presentations of b c d, i.e. its occurrence at the beginning of the second continues to be an element of apprehension until the end of that time. Thus, at last, the whole a b c d as facts succeeding one another are all simultane- ously presented. The apprehension is of what has just arisen together with that which is just now arising. Both together form the actual present content of consciousness. Again, we must not, because a b c remain present after they are given, infer that at the stage d they are apprehended otherwise than as they have been given. On the contrary, the retention of the earlier elements is merely that which enables us to apprehend the whole as it is given. But what is given is not a + b + c + d, but a b c d, a continuum in which a passes into b, b into c, and so on without a break. This continuxim, therefore, is the true datum of apprehension, and so, when we speak of a as remaining present along with b c d, we must remember that it is present in a different way at each stage. At the stage a it is the incomer, at b it is passing, at c it is removed further, at d it is vanishing. What is presented is a passing process of which we see always a segment. And each point in this segment is continuously altering its relation to our consciousness as it approaches, occupies, or recedes from the focus of attention. None of the words we use can explain this perception. They can only express it ; and our business, be it remembered, is not to explain, but merely (a) to formulate what is given, (h) to explain away any apparent contradiction in our statement. In this case the given (in our view) is a segment of a temporal process, and the apparent contradiction the difficulty of understanding how a segment of time could be present in one moment. Our " explanation " consists merely in pointing out (a) that the earlier time or phase is present in a sense that does not contradict its pastness, i.e. it is " past " as preceding the " focus," and present as remaining in apprehen- sion ; and (V) that though remaining, it is apprehended as pre- ceding the newer phase. We do not therefore pretend to explain the perception of time or continuity. We only say that, in fact, we do perceive time, and that the two postulates which this perception involves offer no real difficulty, but are verified by our actual consciousness when we examine it. 54 DATA We may compare and contrast our present suggestion with a well-known physiological law. A momentary stimulus may or may not give rise to a sensation, but if it does so the sensation outlasts the stimulus. In accordance with the law of the persistence of sensation, an electric spark, lasting ^^^^ of a second, gives rise to a seen spark enduring for an appreci- able time. Hence, if two sparks be passed in rapid succession before the eye, though, as physical occurrences, one is demon- strably over before the other begins, they are actually seen simultaneously, they appear to be two simiiltaneous sparks. Now in this ease it is a physical process outside the body which passes and leaves behind it an effect upon the nerves, and a sensation which we call the perception of the outer process. The perception, then, though present to the mind, is the perception of something that is physically past. So far we have a parallel to our case. But in the perception of duration it is not merely the physical stimulus, but the earlier part of the perceived process, which is past and yet present, which is apprehended as having just occurred, and as passing into the next phase. Thus in the spark-experiment duration is per- ceived, not because the perception of the spark does, in fact, last longer than the stimulus, but because the mind appre- hends the rise, persistence, and extiuction of the spark as present to it in one final moment of apprehension. In per- sistence of sensations, then, the effect of the physical stimulus lasts on iu consciousness after the stimulus is over; in the perception of duration, the first apprehended fact remains present to the consciousness during the apprehension of the next. Nor is the mere persistence of a content equivalent to the perception of continuity or change. The same sensation might continue for hours, but its persistence would not be the knowledge that it persists. Once for all, knowledge of con- tinuity means, not the persistence of consciousness in an identical condition, but a persistence which involves change, which presents, indeed, the content of one moment to the apprehension of the next, but presents it as earlier.^ 1 Another physiological law has a more direct bearing. Any given stimulus a {e.g. a ray of light) may be insufficient to produce a sensation, but may aid another to do so ; so we may have two stimuli a, b, each severally inadeq uate to move my attention, but together capable of causing a sensation. In this case of summation of stimuli each stimulus has its physiological efifect, and each effect contributes to the result in consciousness ; yet neither would have any effect on consciousness without the other. Thus the lowest sound I can hear, the dimmest light I can see, have already a certain intensity. Stimuli failing to produce sensations of such intensity produce no sensation at all, but nave some physiological effect all the same. They produce a subminimal excitation. Now, if a b c are simultaneous and similar in kind, they simply THE CONTENT OF APPREHENSION 55 Lastly, our division of apprehension into parts, with definite contents abed must not mislead us. We shall see presently what value such divisions may have. But we must note here that a is not given as a stationary content to which, with a leap, b succeeds. The full concrete account of the matter is that the transition a - b is the given fact. We can mark out stages a b c d as those at which the several features in this transition are in the first stage of their presentation, but the progress from one to another is continuous. And it is precisely this continuity which is always present. When a has passed con- tinuously through b into c, this passage is all present to apprehension at once ; and the same is true mutatis mutandis at every point in every stage. Thus, if we now consider a moment in the process, if we take a section as we did before, we find a different result. If we figure a division between the stream of apprehension as a subjective act on the one hand, and the stream of its object on the other, each section of apprehension will exhibit, not merely the corresponding section of a given process, but the preceding ones in addition as pass- ing into the present. Or, trying to avoid a somewhat imreal separation, taking the stream of consciousness as a whole, and hitting upon any temporal point in it, this point has for its content, not a timeless or " atomic " content, but a segment of definite duration, the several elements in which are appre- hended as in different temporal relations to the atomic fuse, and in fusing add to one another's intensity, thus producing a sensation where there was none, or intensifying the sensataon already present. But if they are not simultaneous but successive, and not similar but changing, another event is possible. They may produce the perception of a process, a percep- tion vrhich (if a and b are subminimal) may begin with the action of c, but which may include the whole process a b o. This seems to happen when a process goes on some time without awaking attention. When attention is roused we apprehend more than exists in the moment of waking. Thus you can pick up the striking of a clock at the third or fourth stroke and count it successfully. We are generally said to effect this by primary memory images, but in some cases I think these images are really the first belated apprehension of the fact. Here, then, is summation of stimuli, so acting that the earlier object, together with the later, are present to consciousness. This, then, is simply a special case of apprehending duration. In the ordinary case abed are each apprehended successively : the apprehension of each is formed before we apprehend the whole, and if some disturbing cause interfere, the process of our apprehension might break off at a or b or o without prejudice to its clear- ness. In this case the already apprehended contents persist in their order in consciousness and continue to qualify it along with d, so that we finally appre- hend the whole process a b c d at once. In the second case, a b c are not adequate physiologically to give rise to consciousness until d is added to them. Here the act of apprehension is not in itself complete until all the elements are present. Until we apprehend a b c d as a whole we have no apprehension at all. This will happen when abed together form in time or intensity the minimum apprehensible. And both formed apprehension and preparatory pro- cess exhibit a closely analogous law of persistence. 56 DATA moment taken. Finally, the act of apprehension has a certain minimum time as a psychological event, and cannot have less than a certain minimum of duration presented to it. A series of stimuli inadequate to the presentation of a content of the required minimum will present no content at all, but will remain a merely physiological process. 7, What, then, is the actual capacity of apprehension in the way of duration? What is the greatest duration that can be presented to it, and what the least ? How much of duration can we feel at one moment, and how small a duration can we distinguish ? Both depend a good deal on the nature of the sense organ affected, and of the stimuli affecting it, and on the state of attention. Thus, listening to the sound of successive strokes, and attempting to apprehend a number simultaneously, Wundt and Dietze found that the highest results were obtained when the strokes followed one another at intervals of 0-2" to 0-3". If the intervals were more or less than this, attention became confused. If the intervals exceeded 4 seconds or fell below 0-18 to Oil, it was no longer possible to grasp the strokes as members of a group at all. Again, much depended on the grouping of the strokes. It was found impossible not to group them mentally at least in pairs, and so arranged 16 single (or 8 double) strokes could be grasped simultaneously; while grouping them by 8's, no less than 40 sounds could be successfully apprehended, involving a duration of from 8 to 12 seconds.^ This may be taken as marking the maximal extent of the "present." For the minimum the figures 0-18 to O'll 1 Wundt, PJiys. Psych, vol. ii. chap. xv. § 3, pp. 248-252 (3rd ed. 1887), 288- 292 (4th ed. 1893). See also James, vol. i. chap. xv. pp. 612, 613, and notes. I give Wundt's figures as they stand, hut must confess to some scepticism. All they seem to me actually to prove is that five groups of eight sounds each can make a distinct impression on the mind as a whole and without counting. But that the whole of this long series of sounds are actually contained in sensation at once, does not seem to me proved. The line between apprehension and primary memory is not easily drawn, and I do not see that Wundt took pains to draw it. We may therefore ask whether the first group of strokes has not really become matter of memory before the last is in consciousness, or to take a further possibility, whether the apparent perception of the five groups may not be rather a felt total impression resulting from the forty separate sense-impulses, but not equivalent to a perception of them, and hence capable of persisting after some or all of them have disappeared. I do not see how either of these possi- bilities admits of disproof except by introspection, which would be very difficult in such a case. The only real evidence adduced by Wundt for his interpreta- tion of the results is the remark lower down (ibid. p. 251), that the limit beyond which the impulses cannot be grasped together is very sharply marked by a sudden increase of errors to 50 per cent, of all the cases — i.e. to their practical maximum. This point is interesting, but again (to press the sceptical point) might mark the limit of primary memory rather than of apprehension. On the difficulties of drawing a line between memory and direct perception, we shall have a few words to say in the following chapter. THE CONTENT OF APPREHENSION 57 give us some idea. The increasing difficulty of distinguishing more rapid sounds, suggests that here we have the normal Hmit of clear and easy attention — i.e. it suggests OH as the time during which a content must ordinarily occupy apprehension, if it occupies it at aU. But very much lower figures have been given for the absolute limit. Thus Exner appears to have distinguished the "snaps" of two electric sparks at an interval of 0-00205".i These results throw light on another point — what is in- tended by an act of apprehension ? Since I first used the word the reader has probably been objecting that it is a vicious abstraction. Apprehension is, in fact, a continuous stream, and to break it up into so many acts is, it will be said, to make artificial and unreal separations. Well, we may note paren- thetically that this would not interfere with our account of time-perception. All we should have to say would be that without limiting ourselves by separate " acts," any point of the stream of apprehension has, as its object, a certain extent of the continuum of presented objects. But admitting the continuity of apprehension, we must also insist that it falls naturally, not into separate parts, but into distinct divisions. We may form these divisions from the point of view of the act of appre- ' Quoted by James, loc. cit. p. 614. These results should, I think, be received with some caution. It is, we should remember, the interval between the stimuli which is accurately known ; and because two stimuli at an interval of -jj^ of a second cause distinct impressions, it does not follow that we can appre- hend -sot"- If so, we ought to be able to apprehend 500 sensations as distinct in a second. Now Griinhagen (quoted by James, ibid.) speaks of feeling 10,000 electric shocks in a second as interrupted. But could he have discriminated them from 5000 or 1000, or even 100 ? Did not his sensation really amount to a very rapid repetition of, nevertheless, discrete shocks. Such a feeling, if one IcTiew the actual number of the shocks to be 10,000, could be easily taken for a separate feeling for each shock. But unless you could differentiate the feeling of 10,000 from that of 10,001, the inference would be illegitimate. We must further distinguish, at least in thought, between three quantities, aU requiring experimental determination. They are — (a) the minimum time during which a content must occupy consciousness ; \h) the minimum interval requisite between the apprehension of two contents, in order that they may be perceived as successive ; (c) the accuracy with which intervals may be judged. The second and third points are distinguished by James {loc. cit.). I know of no direct experiments on the first. But the determination of the second throws light upon it, because it would seem that if the contents remain distinct there must have been time to apprehend the first, and if not, not. But the second clause here is more accurate than the first. For content a, though distinct from b, may continue in consciousness together with b — i.e. it will last lon-ger than the interval between them. This interval, then, gives an outside lower limit to the duration of contents. They must last, at least, for the interval, and may have to last longer. Hence we should take the highest figures, such as "Wimdt's, to determine question (a) ; and the lowest, such as Exner's, for question (6). Question (o) is the main subject of Miinsterberg's essay on the "Time Sense " (Beitrdge, Heft 2), but does not here concern us. 58 DATA hension, or from that of the limits of the content presented. Thus we may speak of a fresh movement of attention (a) when- ever there is a change in the object to which we are attending, or (b) whenever attention, though fixed on the same object, renews itself. Under these last circumstances there is ordinarily a fluctuation of attention at periods (according to K Lange ^) of from 2*5 to 4-0 seconds, the time varying slightly according to the sense organ employed. By a move- ment or act of apprehension, then, we may mean any redistribu- tion of attention, whether involving a change in the object or not, and we learn that such redistribution is constantly pro- ceeding at a speed which varies within limits, not normally exceeding 4" nor giving any distinguishable results in less than •002" as a minimum. The actual change in consciousness is of, course, continuous; these times mark the upper and lower limits of its distinguishable phases. So much for the act of apprehension. The fact of apprehension or the present content must similarly fall within at most (according to Dietze's experiments) 8"-12"; it may thus (taldng Lange's figures) occupy at least a double act of apprehension. Then we may distinguish as separate facts of apprehension, or separately- apprehended contents, all such as, whether continuous or not, together occupy more than 8-12 seconds. "Where we break up, such a fact may be arbitrary, since it may be given continuously. But even if it exceeds the limit by a small fraction, its ex- tremes cannot be present simultaneously, and it therefore must include, at least, two given contents wherever we draw the line. Thus, if, as is perhaps most natural, we reckon from the end, the beginning of the fact must be a separately given content, and the knowledge of the beginning must rest on a- different principle to that of apprehension pure and simple. We have then a double continuity and, normally, a double discreteness in apprehension. On the one hand, apprehension forms a continuous stream through time, while the things of time form also a continuous stream of content for apprehension. ^ Wundt, loc. cit. pp. 254-257. Miinsterberg oontesta Lange's results and Wundt's interpretations of them (Beitrdge, Heft 2, Schwanhwngen d&r Aufmerk- soumkeU). But the controversy turns mainly, not on the fact of fluctuation, but on its cause, the ApperceptionslhMiglceU being, as usual, the stone of stumbling, and Miinsterberg contending for the " peripheral " origin of the phenomena. Some of Mlinsterberg's figures, however, differ from Lange's, and he denies that the Schwankungen are universal. (See, e.g., the brief account of his contentions, p. 123. ) The question of peripheral or central origin need not concern us, our only object being to get some definite notion of an "act" of apprehension — a notion which experiment alone can adequately limit and fill up. In Wundt'si 4th edition (pp. 295-301) the results of Pace and other observers are given. The- main divergence of interest concerns the regularity of the phenomenon. THE CONTENT OF APPREHENSION 59 On the other hand, but a limited portion of this stream is viewed by apprehension at any one moment : this portion is in constant movement along the time stream; its movement is never stopped and never broken by a leap as long as we are conscious ; so at no two moments will it be the same. Only those lesser segments which fall within one such portion can be said to belong to the same fact of apprehension, and hence arises the discreteness or multiplicity of apprehended facts. Lastly, the stream of apprehension itself is marked into acts or movements by the changes in direction, or the periodical rise and fall in concentration, of attention. 8. We conclude that apprehension, rightly understood, can give us relations as well as qualities, and time relations as well as others. And, briefly to indicate the general results of our dis- cussion so far, we have foxmd that the contents of apprehension are concrete and continuous ; that an apprehended content is apprehended as fact: and that to be aware of it does not involve reference to any further fact ; but that within such a single content time and space, quahties and relations, may be found. False views of apprehension we have found to consist in a confusion of it with the judgment on the one side and the physiological stimulus (or, again, the physical object supposed to cause that stimulus) on the other. And these different confusions, we may add, have tended to play into one another's hands. The " atomic " character of such a physical stimulus as the impact of a ray of light on a single rod or cone of the retina, suggests at once the unrelated sense-datum, and the unrelated datum must be pieced together by some synthetic activity before it can do duty as true sensation. In this and similar ways a whoUy arbitrary conception grew up of what " pure sensation " would be if you ever got at it, and it was easy to show that such an abstraction could subserve httle or no function in the growth of knowledge. The straw man was easily enough knocked over by the critic who set him up.^ ^ The confusion of sensation with stimulus is at its lieight in Schopenhauer {Four/old Hoot, § 21. Cf. World as Will and Idea, bk. i. supplement, chaps, ii. and iii.). He goes so far that if by " sensation " we understand stimulus, and by "understanding " sensation, we should almost bring him back to some- thing like our own account. The confusions in Green are more various, and it would scarcely be possible to extract from him any consistent idea of the fono- tiou of sensation except that it is a contemptible one. The true character of sensation is grasped in its essentials and presented with force by Mr. Shad worth Hodgson {Philosophy of Reflection, bk. ii. chap. iv. par. 3, and bk. iii. chaj). viL par. 1), and is admirably developed in Professor James' chapters on Time {Prin- ciples, chap. XV.), Space (chap, xx.), and Sensation (chap. xvii.). Eiehl's criti- cism of Schopenhauer and Helmholtz is also valuable {Der Philosopliische Kriticismus, Bd. iL Th. ii. o. iii.). CHAPTER III Obscure, Cleae, and Analysed Consciousness 1. We have argued that apprehension, rightly understood, makes us aware of concrete wholes in which quahties are given to us in relation to one another. So far, however, we have shown only that these relations are given in the concrete contents apprehended ; and this is not a peculiarity of relation. What- ever characteristics of reality are given in apprehension, appear always as characters of some concrete content. An effort of abstraction is required to separate them in thought from their "context." Has this effort any connection with the act of apprehension, or is it carried on entirely by thought working on the basis of the given ? We are here confronted with the rise of general knowledge, and our question is. What basis can we find for such knowledge in apprehension ? or, perhaps better, what medium can we find through which the momentary apprehension of the particular concrete now present passes into those general judgments which compose the system of permanent knowledge ? Of the connecting links one at least can be observed and described ia close connection with the act of apprehension, and the discussion of it wiR also serve to illustrate some important characteristics of that function to which we have not yet aUuded. We have argued at some length in Chapter I. that the con- tent of apprehension is fact, and always fact, and nothing but fact. There is no error possible ia apprehension. We dealt with various cases of illusion, and urged that they offered no real exceptions to our rule. Let us now take a rather different case of difficulty which will serve to introduce our present subject. We are asked, " Which is the louder of these sounds, the brighter of these colours, the taller of those two men ? How many fingers do I hold up ? Is that milk sour ? Is this nice ? Is that seat comfortable ? Are you enjoying yourself ? Does that book bore you ? " Common experience tells us that it is not always easy to answer these questions, yes or no. " I OBSCURE AND CLEAR CONSCIOUSNESS 61 really cannot say what I feel." Yet I am asked about my actual present feeling. Is not this a direct contradiction of our view that apprehension gives us fact ? A possible answer has been already supphed. The question is put in general terms, and requires a general answer. Yes, this is sour. Soui" is a general term, taking us beyond the presented fact in a way which we shall further analyse when we deal with the qualita- tive judgment. Now it is quite possible that the doubt or error may be on the side of the idea. That is to say, in the case of error we may apply the wrong idea, in the case of doubt we may not know what idea to apply to the given content. This is, in truth, always the case in an error of description, but at the same time it would be incorrect always to impute the failure to want of lucidity in our ideas. I may be uncertain whether Mansfield Park is dull or not, but I am quite sure that Pride and Prejudice is amusing. This shows that the want of clearness rests, not in my idea ^ of what is dull or amusing, — for give me the appropriate sensations, and I have no doubt about the ideas corresponding to them, — but in the sensations with regard to which the question is asked. Now there is no real paradox in tliis. Mansfield Park as I read it gives me a series of sensations, feelings, ideas, and what not ; but the attributes of dulness or amusement simply are not sufiBciently prominent among them to characterise them in a definite way. Or — as it may be objected that Mansfield Park is not a simple given fact, but a name for a long string of presentations — take a simple sense quality. Had Mr. Pickwick's punch orange-peel in it or not ? The punch gave Mr. Pickwick certain definite sensations apparently of a gratifying character ; but had it the flavour of orange-peel or not? It will be remembered that a special experiment had to be made to settle this question in the negative ; but that once settled, Mr. Pick- wick was so confident of it that he was able to make several confirmatory experiments without fear of harm — from the orange-peel. Now, here we observe two things. First, the original sensation of taste had a perfectly definite character of which no one expressed any doubt. Secondly, Mr. Pickwick's idea of orange-flavour was definite enough. What was in- definite or uncertain was the presence of the flavour in the first crlass of the punch. As a matter of fact, in the punch, regarded as a physical liquor, there was no orange-peel ; but in Mr. Pick- wick's sensation in tasting it there was, it is to be supposed, " a suggestion " of the taste of that substance. So again, if an 1 My idea, in the sense of my taste, may, of course, be very lad, but that does not affect its clearness. 62 DATA experimenter asks me to determine which of two colours is the brighter, regarding the colours as etherial vibrations or as stimuli of the optic nerve, there is no doubt that one is, as a matter of fact, stronger than the other. Again, the two colours have each, as I apprehend them, certain quite definite characteristics. But taking them as contents of my appre- hension, and asking about this particular characteristic, — their relative intensity, — what do I find ? Eeally I cannot tell. 2. We are now in a position to give an account of these facts in harmony with our general theory. The simplest case arises when the content about which I am asked simply does not occur in my apprehension. You ask me which is the brighter. Eeally I do not see. There is (as the experimenter knows) a difference in the intensity of the stimulus. But this difference does not produce a corresponding difi'erence to the mind of the " subject " experimented on. He sees two colours ; he does not see the required relation. In all such cases, then, the content about which inquiry is made, and about which we are left in doubt, is one which is usually or possibly present as the result of certain physical stimuli, but is not present in this case. But there are not only cases where we simply and definitely do not know. There are all gradations of certainty, from blank doubt to positive assurance. These depend, then, on the definiteness or clearness with which the content is given, which may range from to 1. The content may be thoroughly definite in certain of its characteristics, as explained above, while very indefinite in others ; or it may have a very low degree of definiteness altogether. As far as it is indefinite or dim, whether in whole or part, just so far is it difficult for the mind to catch the relation in which it stands to its ideas. Now, what do we mean by this " clearness " or " definiteness " of a content? How can clearness have degrees, or a content be other than that which it definitely is ? Two suggestions may be negatived. First, clearness is not the same thing as intensity, though there is a loose general relation between them. A presentation must be given with some degree of intensity to be given at all; above this limit intensity and clearness increase together up to a certain maximum, beyond which, as intensity increases, clearness rapidly declines until the effect becomes stunning. Thus many pains which have distinct and well-marked characteristics in their moderate degrees become merged as they increase in a simple, un- distinguishable, overpowering agony. Second, the distinction between clear and obscure does not depend on two ways of having a content presented. It is often loosely said that the OBSCURE AND CLEAR CONSCIOUSNESS 63 sensation X was present all along, though we did not observe it, or was confusedly present though we did not distinguish it, or was really felt by us though we did not attend to it. Thus the overtones of a note are really present to me, — or I should not appreciate its timbre, — but my ear must be educated if I am to distinguish them as separate tones. Or, again, half the effectiveness of the true Doric column arises from its slight convexity, though not one per cent, of its admirers suspect it of deviating from perfect straightness.^ The curvature, the overtone, must then be present to consciousness, though not present as such. But this as it stands is a flat contradiction. Either X is present to consciousness or not. But if present, it is present as X, not as anything else. That it should be present and yet not be present as itself is an impossibility. Then, is it present unconsciously ? This would be another contradiction, for the present is simply that of which we are conscious. Then what is its relation to the mind ? There are two possibilities — first, that explained above : X is the result of a stimulus x. Under one set of circumstances m, however, X does not produce any sensation ; change the circumstances to n, and free play is given to it to produce X Then we say X was present all along, meaning really the objective stimulus X. This is the case with Hehnholtz's^ instance of musccc volitantes, which as a rule are altogether unnoticed. What is always present here is simply the flecks of opaque matter in the vitreous humour. There is no seen spot presented to the normal consciousness. So with the blind spot and countless instances. But, secondly, there is a more subtle case in which the stimulus x, working along with m, really produces a certain modiflcation of the resultant consciousness. The curvature of the Doric column is not seen to be curvature ; but if it were not there much of the seen or felt grace of the column would be gone. So with numberless artistic effects and impressions of every sort and kind. When we cry out triumphantly, " That's what I have been feeling all along," we feel the clearing up, the crystallising of elements of conscious- ness that were already there in a sense. But in what sense ? Not the new content now perceived, but some other content, corresponding to it, was really present. Not the curvature, but the proportions attaching to it, not the overtones, but the sound constituted thereby, was the real element in the unanalysed consciousness. Not the metre or the cadence, but the feeling produced by them, is first perceived, then comes ^ Fergus3on, History of Architecture, vol. L p. 249 if. ' See James, op. cit. ii. pp. 516-522. 64 DATA analysis of metre or cadence, and perception of the feeling as interwoven with them. Now, if we may f ormidate the case as a whole, the stimulus x operates on the mind all along, at first introducing a modification into the consciousness M such that it becomes M', and then when attention is aroused, producing in it the distinct element X, upon which the previous modification of M is seen to depend. To give a rather simpler instance than we have yet suggested, when I peer through a fog and gradually make out a number of dim outlines to be a man, a horse, a tree, and so on, each one of these " objects " regarded as physical things existed all along ; and each one was represented in my first perception, that is to say, the clear contents of my second and clearer perception are judged to correspond, each for each, with the dim shapes of my first. The outer object is represented in consciousness throughout ; it is represented by elements which differ, but yet are felt or judged to correspond. If, now, in this easier case, we ask in what the correspondence consists, we shall see that it is the persistent presence of some attribute to which, in the " clearer " consciousness, more attributes are attached.^ The dark object before me turns gradually into a man. It never ceases to have a separate and continuous outline, to be marked out by contrasts of colour and so on, though to these bare attributes many more are added in the clearer apprehension. They form a kind of outline which the later consciousness fills in. The clearer consciousness contains what was present to the more obscure, only further determined by fresh character- istics. There must be an element of identity between the two or we have no relation at all, and there must be an element added or we have no change. Speaking generally, then, any content either is present in consciousness or it is not. Its being given, or present, our being conscious of it, are simply different expressions of the same fact; it can never be given clearly or obscurely, for it is simply itself, and can be given only as itself and only in one way. But it may be looked on as presenting clearly what another content pre- sents obscurely, when it contains attributes which further characterise and differentiate those already given in the " obscure " content.^ Of this further definition or differentia- ^ The fm-ther attributes, that is, characterise the very object to which the present attribute already belongs. That is what we mean by such expressions as "interwoven," used above. Other expressions, such as "dependent on" "constituted by," are appropriate to special relations of the attributes, which will become clearer when we deal with analysis. But the common point in all cases is the persistence of an attribute and the accretion of others round it. 2 Hence it happens that, as Mr. Shand has shown (in the article q^uoted OBSCURE AND CLEAR CONSCIOUSNESS 65 tion there will be two cases. It may consist merely in an added emphasis or intensity — e.g. a vague, dim colour may brighten and define itself into an mimistakable green or brown. Here the clear content is as simple as the obscure, and it is known as clear merely because it is more distinct than others. Or the differentiation may involve some fresh determinant, making the whole more complex. What was before a mere modification of the feeling M, so far operative as to make it M', but indistinguishable and inseparable from the feeling as a whole, stands out now as a distinct attribute X. Our content is still as a whole M', but it consists of parts M and X. 3. Now this complexity is not peculiar to objects of clear apprehension ; all presented contents consist of elements or distinguishable aspects. Further, these elements may be such that attention may be concentrated on them separately. If M is extended in space, and consist of m + ^, we may narrow attention so as to turn it from M as a whole and confine it to m or /A. In this case we pass merely from one simple apprehension to another, just as we might pass from M to a wholly different P. But m and /i may also be what we know by comparison as abstract or general attributes of M, — for example, m may be a colour and ^ its figure, — and then we cannot attend to the one without being conscious of the other as well. We may, however, call them elements of M, because though inseparable they are yet distinguishable.^ Similarly, when m or /i were separate spaces, they could still be called parts of the whole M, if I attend to that whole, while distinguishing m from /i, as its parts. In fact, we may at any time recognise, not the whole only that is given, but any part or element as a part or element of that whole, distinct — though not necessarily separate in existence — from other parts. We have then an analysis of the given, not yet, as we shall see, an analytic judgment, but an act of analytic attention. This term may be apphed to any state in which we become aware of any element in the given as a part of a whole above), we may be clearly aware of an obscure object, viz. if we concentrate attention on that object in such a way as not to intensify the physical stimulus. To put the paradox in another way, the indefinite has its own definite character of indefiniteness, and this, too, we may recognise. As far as this character is concerned, the content might even be said to lose something in gaining those further characteristics which make it clear. All we have to note is that the " obscure" is like the "clear," a bond fide content of apprehension, not a self- contradictory appearance that at once is and is not. ' Whether psychologically we should be capable of distinguishing them if we did not compare them with similar elements differently combined, is a question which we need not here discuss. It is enough for our purpose that they are distinguishable, whatever psychical mechanism this may postulate. 66 DATA distinct from other parts. Now, this singling out of the attribute does not destroy nor obscure the apprehension of the whole, but the movement of attention makes us distinctly aware of the attribute attended to as one character of a wider or richer content. Looking at that billiard ball, the fringe of consciousness is occupied by the table and the walls beyond, but I clearly and definitely apprehend the ball (or, more strictly, its coloured surface), and upon the ball — within, that is, the content of definite apprehension — I notice the spot of light where the rays from the window are reflected. Now, dropping the fringe of consciousness out of sight, we have still a complex fact before us. "We have the apprehension of the ball as a whole, and the analytic movement of attention which singles out one or more attributes as characterising, as con- tributing to form that whole.^ Thus the ideal form of such analysis can exhibit a whole M as constituted by elements p q r ; but any act in which we become aware of p as an element iu M, while q and r remain an unanalysed residuum, is pro tanto analysis. It is the beginning of it, not the completion. Up to a certain point and in certaia contents the operations of clearing up and of analysing the given coincide. Thus, to break up a confused medley of colours into a distinct pattern of so many reds, blues, etc., is at once to make each elementary colour clear, and to distinguish it as a part of the whole. In short, so far as clearing up consists in unravelling a complexity, it is the same thing as analysis. On the other hand, the clear content may be relatively simple. It may even be a product of analysis (as an element in some whole), not itself admitting of analysis. A clear content, then, is not necessarily an analysed content. Nor, again, is an analysed content always fully clear. Qud analysed, it is merely known as constituted by such and such elements, features, or characters. Clearness in. this special point is the peculiar work of analysis. In carrying out this work, analytic attention — and this is why we treat of it at this early stage — does not advance beyond the present. It is not essential to the process of analysing A = F (a+mb+etc.) that these different contents, should receive general names, that is, should be classified and described. If we would, as before, isolate this activity, it- ' It may be asked what we mean by " cbaraoterising," " contributing,*' etc.. I can only answer that the words express the relation of an element of a content to a whole. Neither this relation nor the terms " element," " whole," etc. , can be defined. They can only be pointed out, and terms such as I have-, used are merely variants for describing them OBSCURE AND CLEAR CONSCIOUSNESS 67 consists in a movement of attention within the sphere of the given, not in an assertion of aught that lies beyond. It may be said that we should never thus concentrate and analyse if we had not general ideas to direct and stimulate us. True, we should not go far without such aid. But it may be that we have here a case of the cumulative action of causes in which analytic attention logically takes the lead. Analysis, as we shall see, is the source of general ideas, and general ideas in turn facilitate and improve analysis, which again brings to light better and more accurate ideas, and so on indefinitely. But the mere act of analysis itself is not either the formation of a general idea nor the subsumption of the present content under one. It is an activity in which the mind operates upon the given content, but does not yet make an assertion of anything beyond the present. There are further conditions on which such an assertion in its simplest form depends, and into these we have now to inquire. Meanwhile our results have gone to show that what is given to our apprehension contains the elements of a very great part, if not the whole of subsequent knowledge. The relations, the order, of facts are given no less than their sensible quahties. Nor is there any difficulty, if the nature of apprehension is understood, in regarding duration and any contents involving it as " present "" to our apprehension. Apprehended contents have more or less definiteness of character in accordance with which their resemblances and differences are more or less marked, and they are more or less easy to describe. A concentration of apprehension known as attention acting in response to stimuli of a special kind rearranges the contents of consciousness as regards their clearness, and further con- centration on any point or aspect of a content may go along with a perfectly clear apprehension of the content as a whole. We then become aware of the part as an element in the whole, that is, we have begun to analyse the whole. The completion of this process gives us the totality as constituted by all its parts, features, or characteristics. This state of knowledge must be held to involve an operation on the apprehended content which we may call analytic attention, but does not involve the thought of any reality beyond the present. CHAPTEE IV Memory A FACT, we have seen, can be present to us for but a brief moment. But the fact that it has existed and been present to us may be matter of permanent knowledge. This persistence or retention of knowledge we have now to investigate. 1. We have already seen a form of retention at work in analysing the apprehension of duration. Here the conception of time as a continuum to which we are forced, compels us to admit that the first elements of a sensible process are presented to the mind earUer than those which follow, notwithstanding which the mind has both earUer and later simultaneously before it. For this purpose it must, as we saw, retain the earlier for a while as matter of consciousness. Again, all phenomena of habit depend on what we may call physiological retention. Higher and lower nerve-centres, and not only nerve-centres, but sense-organs, muscles, bone, and skin, all retain their experiences in the sense that they are often permanently affected by what they do or suffer — affected in such wise that their subsequent reactions are modified. But retention would never be known by us for what it is, it would never be known as an effect of past experience on the present moment, if it did not from time to time give rise to assertions of the past as past, that is, to memory. I can only explain this or that present reaction of my limbs or my mind as due to some past experi- ence, if I can remember that past experience, that is, believe in it as something which has happened.^ It is this result of retention which we who are studying the conditions of assertion, and assertion only, have to consider. What, then, precisely is memory ? To begin with, it is not a mere image or fainter repetition of something which is de facto past.^ If such an image were all I had by way of remem- ' It might be urged that I may know the past experience by inference ; but we shall see later that inference in its turn involves memoi-y, both to set it going and to coniirm it. ^ Contrast Volkmann, Lchrbuch der Fsychologie, vol. i. pp. 403 and 474 68 MEMORY 69 brance, it would be difficult to see how I could know or even suppose that it was an image of the past ; for where woxild my knowledge of the past be ? The image as an image is always present fact, which vanishes in its turn and requires memory to recall it from the limbo of departed thoughts. No doubt an image is a normal part of vivid memory, and sometimes becomes a kind of mechanism through which memory endeavours to refresh and strengthen itself. When " I remember the house where I was born," a very distinct and vivid image doubtless rises of the " little window " with its picturesque adjuncts ; but that image is something now present to me, something which I apprehend. To have this image before my miud is to apprehend a present fact, not to remember my old home. It may be urged that, image or not, in any case a memory is a present content. What I remember occurred twenty years ago, but I have the memory of it now ; and what is more, my present remembrance is or can be matter of apprehension, the content present to my apprehending consciousness. That is true ; but the content in question is not a mere image, but an assertion of some past event. If I am aware of remembering X, I am aware of believing X to have happened, to have been present at some time in the past. " X happened " — that is the minimum content of memory. " X," i.e. the image of X, is less than the minimum. We remember sometimes what we can but imperfectly image, and we image very perfectly that of which the remembrance is inaccurate. Thus, to cite a wide and well- known class of cases, it is very difficult to image a feeling or an emotion, but quite easy to remember one. I can quite well remember how sleepy I was last night, but I cannot in this morning's freshness repeat the faint echo of sleepiness which we call an image. Again, " I have perfectly distinct vision of it in my mind, but whether it really happened I cannot telL" Here is the image without the memory judgment.^ In short, memory - judgments and memory-pictures are not the same thing, though they tend to coincide, since both are due to the same fundamental facts — the permanence of modifications effected in the organism by experience. Memory, then, is an assertion — or, if you prefer to employ the word as a name for a permanent capacity of the mind, unknown to us except by its results — it is a faculty of making assertions. Now, what sort ' It must be admitted that this case is not so common as the converse. It would be unfair to quote the much commoner oases when one's vivid image is proved inaccurate by other evidence, for here there is a iovA fide memory- judgment, though it happens to be false. 70 DATA of thing does memory assert? We have said above that it asserts that X or Y happened, i.e. its assertions are of facts that have been in the past. But this definition might be objected to as too wide and too narrow. On the one hand, we are said to " remember " permanent truths, Uke the multiphca- tion table ; and, on the other, it is clear that not all assertions about the past are memories. The life of Julius Csesar is not re- membered, but (for us and our historians) inferred from records. Only that can be remembered which has been given. And in this sense I may be said to remember the date of Julius Caesar's assassination, that is, I remember to have learnt it. But here another difficulty may be raised. What exactly in this case do I remember ? I learned the date in question some time in childhood; I have forgotten the learning, but I remember the date. This does not affect our definition, but suggests a distinction within it. I do not remember the date beiag taught me, but it must have been taught me. If I were reading about it for the first time I could not be said to remember it. Memory, therefore, is only of that which has been given. But — and this is the distinction — it may either affirm its content to have been given, or simply affirm it to be true, without specifying that it has been given. Thus, if I say that the opening of the second JEneid describes the treachery of Sinon, etc., this is a memory-judgment in the second sense. I know the fact, because I have read the second uEneid, though when or where I read it I may have forgotten. On the other hand, when I remember the great snowstorm of 1881, my assertion is of the first class ; I recollect that I was out in it. Memory, then, has a broader sense, in which it is the power of asserting anything that has once become known, and a narrower, in which it is the power of asserting that something has been presented to self. In the broader usage some characteristics of the remembered content — all that is implied in its relation to myself — are dropped. We treat then of the narrower sense as the most typical, and as including all that would have to be said of the other.^ The most typical memory-assertion, then, is not only that X happened, but that X has been given to me. It is included in this that X is past and was present. It is also implied that X may be a single, individual, given fact, and may be known as such. What is given is individual in that, though it may contain many parts, it forms a continuous whole in time and space. ' Cf. "Wundt's distinction (FTiys. Psych, chap. xvii. § 4) between Erinncrung and Smeuerung. I do not find, however, that he marks off the renewal of an image Irom the reassertion of a content. MEMORY 71 Memory as a reassertion of what has been given reasserts such individual facts. It can discriminate similar individuals from one another, and judge their number. It asserts not merely " X," but " that X " which it distinguishes from " the other X." I remember, not merely that I have had a headache, but I remember the headache which I had last week, and distinguish it from that which I had yesterday. It is irrelevant here to ask how this distinction is effected, to question whether it is possible to distinguish similar contents otherwise than by diversity of context. This question will come up in its own place. It is enough at present to point out that, by whatever means, memory does distinguish individual cases of given facts, and that it is concerned with such facts, not merely as regards their character, but as regards their occurrence, their existence in the past as facts that have been given. The fuU assertion of memory, then, is of the form " that X was given." 2. Now these assertions of the past are continually made, and enter into the very structure of knowledge. Apart from apprehension of the immediate present, knowledge could hardly exist without them. Memory, then, is a postulate of knowledge, like apprehension. That is to say, if we believe our knowledge to be sound, we must admit that we can from time to time assert the past, and know that we assert it with truth. But now as asserting a past fact, memory is sharply con- trasted with the conditions of knowledge which we have hitherto discussed. Apprehension is the assertion of the present, and analytic attention operates within the present. The content of each of them is fact, because it is present. In memory the assertion is of the past. The content which it asserts is there- fore separate from the act which asserts it. This assertion is now for me present, if I think of it. It is present fact. But it is an assertion of an event which is past. In short, the content is one event, the assertion of it another. Hence, at once the assertion may be either true or false. The past event may or may not correspond to the present memory of it. The series of apprehended contents may or may not contain the one which at present I assert. Hence arise two questions about memory — how do we explain it, and how do we justify it ? First, however, let us be quite clear about the distinction. Memory, we say, is a beUef about the past, essentially distinct in character from an apprehension of the present. But apprehension, we ourselves insisted, stretches back into the past, and the apprehended fact passes continuously into the memory-image. Where, then, does true memory begin ? Can we use the time-distinction as drawing an absolute line ? 72 DATA We might say that the remembered content is separated by an interval, and is recognised as separated by an interval from the consciousness which remembers it. The memory -judgment asserts that "that was then" contrasting the then with the now. But an interval is already present, and recognised as present within apprehension itself. Any point at the back of the perceived segment must be presented as separated by an interval from the point in which attention is focussed. The mere conception of an interval is not therefore a sufficient criterion. To make it adequate, we must further specify that it is an interval separating, and recognised as separating, the remembered content from the whole present fact. In other words, the " pastness " afBrmed by memory involves, not merely a time-interval, but a contrast with the presented as presented.! What is remembered has been, and is not, a content present to apprehension. In connection with this contrast we may add that the state of consciousness judging, believing, or (broadly) thinking about a content is generically different from the state of consciousness which apprehends a content. Thought and sensation are different states of mind. I can think about what I feel, but qud thinking about it I am not feeling it, and qud feeling it I am not thinking about it. I do not know that we can reduce this difference to simpler terms, but we can easily be aware of it by attending to our own consciousness. Now memory is a form of thought ; it is a belief about something absent, not a consciousness of some- thing present. As soon, then, as our apprehension of a fact passes into the form of thought and recognises an interval separating the fact from all that is present in the form of apprehension, so soon it has become memory. We may illustrate our point by reverting to the subject of images, and especially " after-images." If " Music when, soft voices die Vibrates in the memory," this is strictly not a memory-judgment, but the persistence of an " auditory image," echoing down the corridors of imagina- tion long after the sensation which gave rise to it has ceased. The " vibration " is as much present apprehended fact as the original music. But when we call it an image, its character has become ambiguous. A reference to the original is introduced. ' The "present," we saw, had two meanings — [a.) the "atomic now," and (A) the presented or apprehended. Similarly, the past is {«.) that which is before the atomic now, and (/3) that which is no longer presented. A content must be past in the second sense to be matter of memory (cf. p. 52, note). MEMORY 73 And this reference tacitly postulates true memory to compare it with the original, and judge that it is an image. Hence an easy confusion between image and memory-judgment. The contrast between the two is more immediately clear when the after-image is negative. Here the image could not possibly be identified with memory, or we should be compelled to say that my remembrance of a red spot is a vision of green, and my recollection of the sun a dark circle dancing before my eyes. Finally, the case of Primary Memory, though more difficult, seems exphcable as a combination of the after image with the memory-jiidgment. It is, in short, the case where, whether by accident or by a voluntary effort of attention, I get a good after image, and use it as a basis or a help for memory. In the total consciousness here image and memory -judgment are fused, or the consciousness which forms the one acts at the same time as spectator to the other. The vivid impression which I retain of a striking scene is thus at once perception and remem- brance. It is sensation on one side and thought on the other. And if we want memory to remain at its best, we invoke the image from the moment of apprehension onwards, and con- centrate attention long and lovingly upon it: if we let the moment go, we have lost the chance — "Many a face I so let flee, A"h , is faded utterly. Ere the parting hour go by, Quick, thy tablets, Memory." 3. Eeturning now to the problem of explanation, note, first, that it is really a matter for psychology. The problem is to show how a mind can come to be which knows to-day what it experienced yesterday. It is a question, that is, not of the truth or value of memory, but of the conditions under which it exists. We need not treat this as a " final inexphcability." There are final inexphcabihties enough anyhow, and we need not multiply them, as the old adage goes, prceter necessitatem. Very likely the progress of physiology and psychology will throw a good deal of light upon the subject. But we must remark that nothing is gained by straining to assimilate memory to other mental operations. To see in memory an identity of past and present, or a continued presence of the actual past fact, is a sheer mistake. The remembered fact is not present to the mind like the apprehended fact. It is asserted ; but if we bring our memory into relation with our apprehen- sion, it is at once asserted as past, as having been presented, but as being presented no longer. It is " in the mind " as a 74 DATA part of the mind's thought, and in no other sense. It is a mere misuse of language to interpret this " in " more literally.^ If the present moment is not distinct and separate from the past, if the past fact is not absent and gone, then these words cease to have meaning, the most typical instances from which they are derived fail us, and there can be no such things as distinctness or absence. Nor, again, does memory give us the sHghtest warrant for supposing an actual persistence of the remembered content. The mere persistence of such a content, supposing it possible, would explain our possession of a memory-picture, but would not give us a memory- judgment.^ Nor is there in memory any assertion of the present as the persistent past. There is an assertion of the past as distinct from what is now, and the only condition which such an assertion postulates is that the past should have such an effect on us, whether on brain or mind, that we are able at a subsequent time to assert it. What mechanism this involves can be determined only by observation, not by assumption. We shall return to this question presently. Meanwhile observe that our second question — how memory is to be justi- fied — ^is more important for logic. To understand it, suppose a recollection for a moment, isolated — uncorroborated by any- ^ Some furtter ambiguities whicli might give trouble here are discussed below, Pt. III. Chap. III. ^ It may be said that the memory-image has a "noteof pastness," a temporal sign locating it in the past, just as those moors have a sign in their colouring that makes me locate them five miles away. This, if I understand Dr. Ward, seems to be at bottom his explanation of memory, and the knowledge of succession {op. cit. pp. 57-66). But to know the sign I must first know the thing signified. If the past is once known by memory, I may study it, and so learn the signs of nearness and remoteness ; but if the past is never known directly, how does any character of the present come to be a sign of it ? How do our temporal signs get their value ? A similar criticism applies to Mr. Shadworth Hodgson's account {Philosophy of Reflection, pp. 274 S.): "The present representation of cold appears in iico surroundings, those called tww, and those called half an hour ago. How can this amount to the judgment, ' ' I was cold half an hour ago, " unless by calling a representation ' ' half an hour ago " I mean that it represents something that then was and now is not — in short, unless we postulate the memory -judgment in a more reflective stage ? Merely to attend to a present representation is not to be aware that it is a representation, nor is it to think of what it represents— unless by a representation of X we mean a thought of X, and that thought (if X is a past experience) is the memory-judgment. Mr. Hodgson's "two present representations," one in past the other in present surroundings, seem really to mean respectively the past fact remembered, and the present memory of it. Mr. Bradley remarks {PrincipUs of Logic, p. 74, quoted with approval by Mr. Bosanquet, Knowledge cmd Reality, p. 18, note): " Events past and future . . . exist /or ms only as ideal constructions connected, by an inference through identity of quality, with the real that appears in present perception." The MEMORY 75 thing else. " I remember walking up here last year." Here is a belief. Can we take it as true ; and if so, how can we justify our procedure ? If our walk was known by an inference, there would be something to appeal to, something to justify that inference. For example, I might prove to you that I had been there before by correctly naming points in our view. An inferred belief then rests on something else, some fact or admission from which it foUows. But on what does the uncorroborated memory rest ? On nothing but itself. A felt behef is in the case of memory its own guarantee.^ Be. facto this guarantee is ordinarily taken as sufficient. No one questions memory without a reason. But for logic the de, jure value of such a guarantee is a matter of question, and the question is of fundamental importance. But it is a problem that can only be discussed in relation to the validity of knowledge in general. Here we need only define our position provisionally by remarking that — (a) Felt personal conviction is not a final guarantee of truth, inasmuch as the strongest convictions sometimes play us false, and that in the region of memory as in other cases. Thus the guarantee offered by memory cannot be absolute and final. This, however, does not hinder it from being a reasonable ground of behef in the absence of stronger reasons to the contrary. first part of this statement appears to me to hover between a truism and a fallacy. My knowledge of the past is, of course, not the bodUy existence of the past in my mind. It is not the past's self, but an idea of the past. This is a truism. But to say that that idea is what I know when I exert memory, is a fallacy. The idea or "ideal construction " is another name for the knowledge. We have not (a) the past, (J) an idea, or ideal construction now present, and (c) the knowledge of this idea, which knowledge is memory. Either (J) and (c) are one and the same fact differently expressed, or (c) is not memory at all, but a name for the state of the psychologist examining the phenomena. Much the same criticism applies to Mr. Bradley's declaration immediately above : " If a fact or event is what is felt or perceived, then a fact that is past is simple nonsense." If the premiss here means "a fact is something felt now" it is a petiiio principii, for the whole question is whether the reality known to us must be confined to present feeling. If it means, " A fact = something felt," the conclusion does not follow, for then to remember a fact is simply to Judge that something was felt. The argument as it stands does not distinguish between "is" = "is now," and "is" = "is whenever or wherever the subject exists." ^ Mr. Bradley in the passage above quoted, and more explicitly on pp. 72 and 73 of his Logic, argues that the past to be known must he connected with the present through some identity of content. A remembered content must undoubtedly be related to the present in time, and is so far akin to the present that it also was present, and present to me. But none of these points sufSce to differentiate it from an imaginary content — whether ihe imagination be wilful or involuntary. If, then, there is some mark in the content of a memory by which the truth of the memory can be inferred, that mark is stiU to seek (cf. Bosanquet, op. cit. p, 118). How far its content affects the value of a memory we shall consider in a later chapter. 76 DATA This we shall assume memory to be, pending our fuller dis- cussion of validity. (6) Memory is doubtless much more trustworthy under some conditions than under others. Freshness and felt clear- ness, for example, are important points. But these vary in degree, and it is impossible, speaking in the abstract, to draw a line above which the trustworthiness of memory is to be taken as absolute. Our position will simply be that as felt certainty is to be taken as a reasonable ground of belief, its strength as a ground is ceteris paribics proportionate to the clearness and intensity of the feeling. (c) In point of fact our remembrances do not stand in isolation. Normally, they corroborate one another, and can be supported by inference. The value of such corroboration will be considered later. We have then to take memory and its normal correctness as a fresh postulate of knowledge, not to be resolved into anything simpler or more immediate ; and the content of memory we take to be the assertion that some fact has been apprehended in the past. That is to say, our knowledge and our beliefs as they stand imply, inter alia, the general trust- worthiness of our beliefs about our past experience ; and this trustworthiness in turn cannot be based on any more ultimate mental process, or any more evident truth, which does not tacitly assume it. To that extent the credibility of memory is for logic a postulate. As far as postulates or presuppositions can themselves be subjected to test, so far the credibility of memory can be tested ; and how far this can be done we shall inquire later. We only deny that a memory-judgment can be resolved into any sort of inference from premisses not them- selves involving memory. Memory is in logic one of our postulates, and not one that can be resolved into any simpler postulate. It is a direct or immediate belief about the past, not a belief based on some other truth ; and it claims to be trusted for its own sake, and not on the ground of any premise or any other process.^ 4. It does not follow that memory is to be explained as the work of a distinct faculty. Strictly speaking, indeed, " explanation " on such lines is out of the question, inasmuch as the faculty of memory is nothing more than a general ^ In view of this directness and immediacy, Mr. W. G. Ward was in some degree justified in producing memory as an instance of an "Intuition." But if so, it is a very fatal instance to intuitionism, since it is admitted that memory may be fallacious, and an intuition is nothing if its certainty is not absolute. There are, I think, other objections to the use of the term, as tending (if rightly understood) to identify memory -with perception. MEMORY 77 expression for the fact that we remember things, or can do so under appropriate circumstances. If we drop the notion of explainiag, there can, of course, be no priind facie objection to the view that memory is a distinct and unanalysable faculty. This would only be another way of saying that it is inexplicable. But it is important to make clear that our view of memory by no means necessitates this conclusion. Memory may or may not be capable of psychological explanation. All we contend is that, explained or not explained, its primd facie trustworthiness is a postulate of knowledge. If it can be explained psychologically, physiologically, or psychophysically, we shall be all the better pleased. Our main contention being thus made clear, it may repay us to return to the psychological question and consider for a moment the possibilities of explanation. Taking, first, the Association view, we would remark that it belongs to this division of the subject, and not to any other — to the psycho- logical explanation of memory, not to the analysis of its content, nor to its logical justification. Assume for the sake of argument that I am reminded of A by its association with B, this association is neither the content of the remembrance of A, nor is it a logical ground for the behef that A happened. Punch's traveller remembers Eome as the place where he bought his hat or his gloves, but the sight of his hat is not the memory of Eome, nor is the fact that Ms hat is on that peg a premiss from which he can logically infer that he was in Eome last April The only way in which the hat can serve as a premiss is by entering in turn into a memory -judgment — " I certainly bought that hat in the Piazza di Spagna last April ; therefore I was in Eome at that time." An associated idea — unless itself a memory — cannot be a ground of memory. It may, however, be a cause of our remembering ; and association is, in fact, the only cause definitely established at the present time. Whether it is the whole cause of memory is quite another question. Three considerations seem to make against its claim to be so. (a) Granting that association may produce behef, this power would be regarded on all sides as proportionate to the strength or vividness of the association itself. But the associations leading up to memory are often so weak as to be untraceable. And even if the associated ideas are clear, we may feel that the connection is so slight as to be whimsical. A look, a sound, and, above all, a scent " put us in mind " of a far off event, but surely have nothing in the world to do with our belief that that event took place. (5) Clearly when 7 8 DATA association or, still better, logical connection is present, memory works most easily. Thus, if I forget a line ia a poem, I may hark back to the beginning of the verse; and having got a start, may say the whole correctly. But this instance tells the other way. For ia the middle of an other- wise correct piece of repetition, a word may suddenly drop out for no apparent reason, leaving a kind of gap in the otherwise connected " run " of remembrance.^ Now, if associa- tion were the sole cause of remembrance, this dropping out would be almost inconceivable, (c) Association is not verifiable as a condition in all cases, and there are countless instances which do not look at all like its work. Memory is almost as capricious as imagination. A recollection " pops up," you cannot tell why. It " comes into your head " in no apparent connection with anything present or past. You think of the distant and remote just as you dream of them, and an un- pleasant recollection will in morbid states dominate the mind for days, resisting all attempts to dislodge it, and forcing itself, an irrelevant and unwelcome intruder, into all your real and immediate interests. It is as though certain memories were waiting on the edge of consciousness ready to rush in as soon as a door is opened to them,^ whde others again have gone wandering far afield, and require a hue and cry to hunt them down. Passing for a moment to a different hypothesis, the crudest form of psychophysical theory accounts for remembrance (of course) by the re-excitation of the cerebral centres. Let a centre C be excited in a given way. This is a sensation. Now excite it again in a similar way, only rather less. This is a remembrance of the first excitement. Professor James * has justly pointed out that this is an impossible explanation. If the centre is the same and the excitation similar, we could only get a repetition of a similar sensation, or, at most, an image corresponding to that sensation, not, in any case, a memory of the sensation. Such a memory being a different mode of consciousness, with a different content, involves a difference in its physiological concomitant. Professor James accordingly suggests as an alternative that, while the " nerve ^ Thus I once heard tlie following from a distinguislied and deeply regretted lecturer : "As Shakespeare says — ' The native hue of resolution Is — in some way affected — hy the pale oast of thought.' " ^ Hence, as Volkmann has shown (op. cit. i. 410 ff.), the removal of inhibitions is as potent >» factor as direct association. The mythological expression of this truth should not blind us to its importance. ■ ^ Op. cit. chap, xvi, MEMORY 79 centres active in the thought " of the remembered fact and its " setting " (i.e. date concomitants, etc.) are excited, there is excited along, and in connection with them, a centre which is active in present sensation or the thought of some present fact. It would perhaps seem simplest, for purposes of pure hypothesis, to suggest a difference between centres of thought and centres of feeling. We might suppose a centre of feeling F normally discharging into a centre of thought T, so that the excitement r in T, due to the disturbance S in F, corresponded always to the primary memory . | of the sensation S. Now T will ^-^ f"^^ /'~\ be connected with many other ( j ( T ) ( F j centres besides F, and any mole- — ^ ^s«|.^^ cular disturbance coming along a I fibre such as T will produce excitements in T. These excitements would be of aU sorts and kinds. Suppose one of them to have the same form as r. That should correspond to a primary memory. But it will differ in point of its origin, and so wiU be contrasted with the excitement q at present being propagated in the centre from F, and corresponding to the primary memory of the moment. Thus the thought accompanying r, wMle a memory, will be contrasted with the primary memories, and its contents will be recognised merely as past. The exacter determination of its date will then depend on the associative awakening of v-^, rj, rj, etc., in connection with r. Now, without attaching the least importance to the detail of this or any similar hypothesis, what I wish to point out is that the physiological aspect of the subject goes to show that the causes of a remembrance, whatever they are, must be much more varied and subtle than any psychological association. For as soon as we conceive the remembrance as going along with a physiological excitement, we have to admit any cause of such excitement as a possible cause of memory. Now we do not know much of the causes or the nature of molecular changes in the cortex (or elsewhere). But what we do know is decidedly against the association theory. If a centre like T in our diagram stands in multifarious connections with other centres (as, e.g., any pyramidal cell of the cortex is connected by perhaps four fibres or more with other cells, and those cells again are interconnected in endless ramifications) ; and if, as is probable, a molecular disturbance, beginning at any point of a brain area, will tend, unless inhibited, to propagate itself in all directions indiscriminately, it follows that the state of any one cell is subject to modification by the action of innumerable 80 DATA others. Then let the excitement r be produced by a molecular force P. Now, whatever systems of forces concentrated on T have a resultant equal to P, will produce the same excitement. And any number of systems, the circumstances being what they are, might have the same resultant. We have no business to limi t the reproduction of r to excitement by some associated disturbance r^. The waves of excitement which result in r may vary each time r is produced. Causes altogether remote from association, alterations of blood pressure, of nutrition, altered excitability of the tissues, extent to which important paths are occupied by other waves, attitude of attention, and so on, may all of them play their part.^ In fact, here as else- where we are coming to the point where the full complexity of the problem is dawning on us. We have not yet got the answers to many problems of psychology, but we are at least beginning to understand the questions. And it is at this point that we must leave the problem of the psychological explanation of memory. The results on which we would insist may be summarised in a very few sentences. Memory is an assertion of a past experience, which may be true or false. Whatever its psycho- logical explanation, its validity is one of the ultimate postulates of our knowledge, and must be examined in connection with the validity of our knowledge as a whole. It is not to be explained or justified by "resolving it" into that which it is not. ^ One factor is worth noticing as quasi-associative. It often happens that, not having thought of last night's dream all day long, it comes back to you as you lie down in bed again. Here the physical and physiological circumstances are very nearly repeated, and that seems to set the old process going, although your thoughts may be far from the present. You do not follow up a train of thought such as " Bed again — sleep— dream — last night — very uncomfortable — wild bull after me — stopped and said good-morning to him — bull quite polite after all " ; but skipping all intermediate thought links, you find yourself suddenly picturing a wild bull offering to shake hands, and then remember that you dreamt that last night. The links, therefore, are of physiological character only, and the process is a mimicry of association. CHAPTEE V CONSTEUCTION 1. Confining ourselves strictly to memory as we have defined it, we find only reassertion of that which already has been asserted. But it is easy to see that this does not limit our view of the past. Our actual memory is not of a series of isolated facts, but its content tends to acquire a certain con- tinuity, — a continuity which, regarded as a whole, has never been given ia apprehension. For example, " it has taken me a long time to write this page," is a memory-judgment in which I review a process of many minutes' duration, and assert it now as forming a whole. "We have already seen that in the appre- hension of change or continuity the immediately past remains present, and continues to form the content of the apprehending consciousness along with that which succeeds it. But this is not the fuU explanation of the present phenomenon. What- ever the precise psychological limits of the act of apprehension may be, no one pretends that one and the same fact continues to form the present content of the mind for more than a few seconds from the time of its presentation. Even if the content of apprehension remains qualitatively alike, its early stages become distinguishable from the present as matter of memory. It is clear, then, that we do not apprehend as a whole any fact of many minutes' duration, and therefore in asserting such a whole we are asserting what has not been given, in the form in which it is now asserted, to apprehension. On the other hand, every part of the process so remembered has formed matter of apprehension, though at difi'erent times. I do not, I imagine, apprehend a clock striking twelve, i.e. the twelve successive sounds are not simultaneously present to a single act of appre- hension. I apprehend each single stroke, however, and the assertion that the clock has struck twelve combines all the apprehended contents into one. StiU we have not got an exhaustive accoimt of the matter. If each stroke is a separate isolated datum, how do the twelve get put together ? We 6 82 DATA want a connecting lipk, which is supplied by the apprehended succession of the strokes, moment by moment. If the clock strikes with moderate speed, the first stroke is still present to consciousness when the second falls — the actual content of my apprehension should be represented, not as " ting," but as " ting — pause — ting." For stroke three the same thing holds, so that I have the actual succession of the twelve given me bit by bit. Consider a more continuous process, say the passage of a cart along the road. Here as the process attended to is less broken, so also is the apprehension. But, as before, consider the apprehending consciousness at any moment subsequent to the first. To that moment of consciousness is present, not a mere point of the process, but an appreciable though short part of it. Take a fresh moment very near the first, its content overlaps the first. "We may represent it graphically. Apprehension Process To the apprehension at the point A, a is just dying away, and a is in the centre of consciousness ; at B the process a, b is fully clear ; to C, b c is equally clear, but a is gone : thus the whole a b c is present to the apprehension in its course from A to C, though it is not present to any stage of it as a whole at any one moment. We have already seen in Chapter II. that at each point in the process of apprehension we are aware of a certain section of the process apprehended. We now see that taking two neighbouring stages, their sections, without being identical, will overlap. Hence, if we consider the whole section of apprehension in which the stages are taken, we find that its object will be a continuum reaching from the beginning of the section first present to the end of that presented last. At no single point wiU this be apprehended as a, whole. Yet, when the process is complete, the whole will have been given. It will have been given, not all at once to any single moment of apprehension, but by degrees to successive stages of the appre- hending process. Thus in watching a long process we are continuously aware of every part in its continuity with the adjoining parts. We are never aware of the whole as a present fact, but we can assert the whole by a retrospective act ^hich thus brings all the contents given into the compass of a CONSTRUCTION 83 single assertion. This bringing together we may call memory- sjnithesis. Notice carefully the extent of its operation. It does not find relations for elements given as unrelated. It does not make a chain out of separate links. Each element is given in its relation to its neighbours, and all that the memory- synthesis does is to take a comprehensive view of the whole which has been thus given bit by bit. Clearly, though, this power of taking comprehensive views is important, since to it memory owes aU its " sweep " ; by it we know all processes on a large scale, and linking together everythiag in which we can find any continuity form the idea of the whole series of our past experience, the whole reality that has been actually given to US.1 2. This memory - synthesis is simply an application to memory of an activity which appears in many difi^erent forms, but which always performs the same logical operation. That is to say, it asserts a content never apprehended as a whole, but composed of elements every one of which has been apprehended or otherwise arrived at before its work begins. We must recognise in it a factor of knowledge not reducible to either of the three we have already mentioned ; and looking to the relation between its result and its data, we may call it Con- struction. We shall have to deal with several of its applica- tions in the following chapters. Let us begin with one of the simplest. We have seen that a resemblance or difference between two facts may be matter of apprehension, that is, supposing the two facts to be given simultaneously. This apprehension of re- semblance no more argues any special " comparative " activity of the mind than does the apprehension of any other kind of relation. The resemblance is given like other relations, and there is no ground for the view which some writers ^ have put ' Even our memory of individual facts takes part of its character from au implied memory-synthesis. A fact to be remembered at all must be re- membered as past ; but its location in the past can only be the vaguest possible as long as it remains isolated. It gets its date by correlation with other contents of memory, i.e. by position in the whole given by niemory-sjTithesis. If the whole is definite and full, its date is precise. If otherwise, it is vague ; but even the distinction between "a long time ago" and "recently" implies some knowledge, not merely of the particular event remembered, but of the interval that separates it from the now ; and the knowledge of this interval is a summation of particular experiences. Apart from such synthesis all remembered facts would be known simply as "before" the present, not as forming an order or occupying different stages in the "before." Memory-synthesis, then, is a condition of "dated" memory, and precision in dating goes along with com- pleteness of synthesis. * E.g. Mr. Herbert Spencer, Principles of Psychology, part vi. chap, xxvii. ; cf. Professor Bain in Mind, No. Iv. p. 372. 84 DATA forward that likeness and unlikeness are the real forms of the mind, — in fact, it is impossible to hold this view without regard- ing all relations as of simOar origin. But comparison is possible, not only between given facts, but also between the present and the past, or between two remembered facts. In either of these cases we have a simple construction. A and a. being given together, present a certain resemblance. This resemblance is not a separate content different from A and a; it is not A and it is not a. Nor even is it the whole A + a, for in this whole, peculiarities dis- tinguishing A and oi, will be apparent ; but it is a part or an aspect, of the whole given content A and a. As such it is given in the apprehension of A -f a, and it can be distinguished as a character or element of this whole by the analysis of attention. This is what happens when we are aware of the present A and a as resembling one another. Now, if A is past and a present, they are not apprehended together ; but, when I remember A, I assert it as somethiag I have apprehended, while at the same time I assert a, as present. The contents of these two assertions put together construct the whole content A and a, in which a resemblance is a part, related to the whole as before, and detected as before by analysis. What we call comparison, then, that is, a relation of likeness or difference, is known, in the simplest case, by an analysis of the given. In the slightly more complex cases now considered, it is arrived at by analysis of the contents of memory and construction. The result of analysis as applied to these contents is just what it would be if the contents were given instead of being re- membered or constructed. This will serve to illustrate an important principle. The factors of knowledge which we have treated in isolation are not normally isolated in their actual working. Analysis, memory, and construction work together on the given. We analyse what we construct, and construct the elements known by analysis ; and from such constructions we get the concrete acts of thought with which we are familiar. In short, by this means, so far as memory holds good, we command intellectually the whole of our past experience as though it were now present to us. The forms of thought and knowledge which results from this power will form the subject of the following chapters. CHAPTEE VI Ideas 1. In the first place, what is an idea ? The simplest and most natural answer was given by Hume, when he defined it as the " faint copy " or image of an impression. As I watch the snow falKng outside, the idea of summer arises by contrast ; that is, the impression of sunny skies and singing birds repeats itself faiatly for me. It is in quahty the same, but fainter ; and if I proceed to the thought that summer after aU will come again, this lelief is only a growing strength of the image. Thus the idea is explained as an image, and behef as a kind of idea. Nothing further remains except to deny the possibihty of any kind of behef not explicable by this means, i.e. not capable of being represented as a \dvid image. Of course the existence of " images " is a fact ; it is also a fact that such images are ordinarily called ideas. To repudiate this usage would be to raise a needless and unwarrantable verbal difficulty. But that an idea is always or as such an image, is a view that need scarcely now be combated. The same instances and the same arguments which we used in the case of memory will apply for the most part here. I have a perfectly clear idea of indigestion, though when weU I can image the pain but feebly. Moreover, — and it is on this that I wish to lay most stress, — our ideas are ideas of something ; they have a meaning or reference ; their interest does not, to adapt Bishop Butler's phrase, " determine upon themselves " ; you can ask about an idea, not perhaps whether it is true or false, but certainly whether it is correct or incorrect. In a word, like assertion, it deals with some further reality with which it may or may not correspond. My idea of a balloon, or a sea fight, or a revolution, is something more or less adequate and exact. It is capable of being tested by comparison with reahty, and acknqwledges the test. No doubt some of these ideas present themselves to me in the garb of images ; but even 60 the mind is aware that they are images, good or bad, of the 86 DATA reality, and in using them as ideas does not take the images as final; in short, it does not, in employing the idea, mean the image, but the reality. I have in my mind a certain idea or image of a compound engine. This particular engine conforms to that idea, and I judge accordingly, "This is a compound engine." But if I am corrected by someone who knows, I should never dream of defending my statement on the ground that the machine before us corresponded to my idea as I had it. I should admit my statement to be wrong, and wrong because the idea was incorrect. The idea, then, is concerned with a real engine or engines ; it does not refer to the image of an engine in my head. We have compared ideas with assertions ; it is perhaps equally legitimate, and certainly more usual, to contrast them. The very point, it is generally held, which marks off an idea from a judgment is that it is not an assertion. " Ghosts do not exist," "There is such a thing as multiple personality"; these are "judgments," assertions, or denials of existence. " Ghosts," " multiple personality "; these are ideas, and anyone may have what ideas he likes, ideas enjoying a liberty not granted to judgment. Similarly, to "have an idea," and to " make an assertion," are distinct states of mind. How, then, can we compare them ? Two points will help us. First of all, if it is only a question of having an idea, my state of mind may vary within wide limits. I entertain the idea of a thing equally whether I assert, doubt, or deny, question, wish, or command it. The idea of a fairy, or a genie, or a dragon, is as clear in my mind when I deny their reality, as it is to the child as he reads of Aladdin, or the Princess Peri Banou. You cannot, like the March hare, deny a thing, without knowing what you deny. When you order a mutton chop, you have the idea of it in your mind just as clearly as when you are told it is ready. You cannot even doubt whether V - 1 has any meaning, without in some degree knowing what V - 1 means. That I entertain an idea, then, is true of me in many different mental states ; that they deal with the same idea is a common character in states otherwise divergent, or even opposed. Secondly, and conversely, the term idea is not strictly a name for a complete, self-sufficient mental state. I can pro- nounce single names usually taken to represent " mere " ideas without making them part of a sentence. But if I do so one of three alternatives seems to follow, either (a) the name pro hac vice is taken in defiance of grammar to represent a judgment, question, command, or what not. Instances are, "raining," " caught," " beaten," " London." Here the word gives the idea, IDEAS 87 and the intonation, or some gesture, or the existing circum- stances do the rest, i.e. make of the idea a judgment, wish, or command, as the case may be. Or (6) I am taken, and rightly taken, to be uttering words without tneaning, i.e. mere sounds which on other occasions mean something, but for me and my hearers at this moment mean nothing. Or (c) the word is treated as an incomplete expression of a state of mind, and leaves the hearer dissatisfied and expectant.^ " The right of combination " does not, as it stands, express any actual state of my mind. I may judge it to be a benefit to workmen, wish that it existed in Russia, question whether it can be said to exist in Germany, deny that it existed in England between 1800 and 1824, and so on. All these are or may be actual states of mind. But the idea represented by the words, " right of workmen to combine," while it may enter into all of these states, cannot be a state of mind by itself. The utterance of the words does not imply the existence of such a state, but of one of the others, leaving it uncertain which. Nor does it caU such a state into the hearer's mind, but one of the others, though it is again uncertain which. If this reasoning is correct, " idea," unless it simply means image, is a name, not for any particular kind of mental state, but for the content of mental states of many kinds, as distinguished from the way in which the content is entertained. My idea of a fact is what I assert about it ; my idea of a possibihty is what I ask ; my idea of a desideratum, what I desire or command. Regarded as a mental fact, the idea is an abstraction ; it is a part of a psychic whole, which does not exist independently ; and from this the important corollary follows that we must deter- mine the nature and meaning of the ideas which we possess from that of our behefs, wishes, etc., and not vice versd. The idea , may be the unit of knowledge ; but units, it is well to remember, j — are generally artificial preparations, not data ready to hand. 2. But still two questions remain which may be urged upon us. To begin with, is there not an actual, verifiable state of mind which we call that of merely having an idea, entertaining an idea, or by some such name, the intention of which is to signify that the state in question is neither assertion, nor denial, nor suggestion, nor anything so definite, but merely that of ideation ? In this case, then, is not the idea as such an actual state of consciousness ? Or if we are able to main- tain our first position, and treat the idea as a content, must we not (the second question urges) define this term a little more closely ? We will deal with these points side by side. Let us ^ Cf. Bosanquet's Logic, p. 13. My obligations to his whole exposition (Introduction, §§ 2-7) wiU be obvious throughout. 88 DATA take an ordinary categorical affirmation about which we have no manner of doubt, and consider the position of the idea con- tained, " There was a majority of 40 for Home Eule at the G-eiieral Election of 1892." According to the view here main- tained, two elements may be distinguished in my state of mind when I form this judgment. These are (a) the idea employed, (b) the fact that I assert it. We have called the idea the content of the assertion, meaning that without it the assertion is nothing, though we distinguish it from the assertiveness of the assertion, because all manner of different contents can equally well be asserted ; and, on the other hand, this very same content can equally well enter into a question, doubt, or denial, according to the state of our knowledge. But, now, can we say anything more definite ; can we define the content of an assertion ? With regard to the affirmation as a whole, it is clearly a refer- ence to a reality, to a reality which is past and distinct from the asserting consciousness. Can we now go a step further, and include this reference in the content ? Can we say that the content is itself a reference to reality which we may affirm, doubt, or deny, as the case may be ? So long as we confine ourselves to affirmation we get on very well, for the object of reference (in our example, the Home Eule majority of 40) is taken as real. There seems accordingly no difficulty in saying, here is a fact known once for all. At any subsequent time we may refer to this fact. This reference is an idea, and making the reference we call " having " or " entertaining " the idea, thinking about the fact. There is no difficulty in speaking of a reference, for there is something which refers, and something which is referred to. And we may proceed to distinguish the mere reference from the assertion of the fact, which we may say simply adds to the reference the element of intellectual accept- ance.^ The idea, one may put it, is maintained (as against a doubt or a question) by an act of assertion or judgment. The reference to reality is common to both, and there is nothing between them psychologically regarded but this element of assertiveness. This solution is not so simple when we turn to question or denial. For in these cases it is precisely the existence of the object referred to which is doubted or denied ; and how can there be an act of reference, unless there is something to which the act refers ? If I say, " The Manchester school no longer exists," or, " there are no Freisinnige in the new Keichstag," can I be said to refer to reality, seeing that the purport of the ^ Brentano's Ancrktnnung. See Hillebrand, Neuen Thaorien der kategorischen SchlUsse, u. ii. IDEAS 89 remark is to deny that there is any such reality to refer to? There is still one resource. You may say, " The reference here is to the Manchester school, or to the Freisinnige party," both of which were realities, belong, that is, to the total system of reality, which is not limited by the mere present. Eef erring to them, and again to some further reality, which in the first case we may take as " the present condition of political opioion," or in the second as the constitution of the present Eeichstag, our assertion is that the two realities are incom- patible or mutually exclusive. There is, then, a reference to reahty ; but the reality in question in its full analysis is the incompatibility of one set of existing facts with another set which have existed. But there are other instances in which this will hardly avail us. Take the case of error. " The soul is a thin gaseous sub- stance which leaves the body with the last breath." Here the soul is doubtless a reality ; but where or what is the substance in question, and if it does not exist, to what does the idea of it refer ? " Phlogiston is the heat-producing substance." Where is the reahty with which this statement is concerned ? It may be said that these ideas, fictitious in a sense, have a reference like centaurs or dragons. That Polyphemus came near to destroying Odysseus is true in a sense. It is true, that is, that Homer sang of it, and perhaps believed it ; and when you or I speak of Cyclops, of sirens and centaurs, we know what we mean. We refer to the world of Homer, the world where Odysseus planned, and Achilles fought, and Penelope wove, — a world of spoken or written words, of sculptured marble, of long past thought, all of them reahties after their kind. But, then, when we speak of these things in this way, we no longer sup- pose ourselves to be in error ; and it is error which is question. If Homer really thought the sirens existed, to what did Homer refer; and when we nowadays entertain erroneous ideas, to what reahty are these ideas related ? It may, indeed, be said that the sirens were supposed to exist in the real world. The idea of them referred to reahty as the whole in which everything that is real must be found. Ajid in this sense there can be no objection to describing an idea as a content referred to reahty. But the reahty now referred to is not a real fact indicated by the idea itself. My idea of a dog refers to the real hving animal ; my idea of a centaur refers to a real world in which, in point of fact, the combination of horse and man is not found. Hence, from the logical point of view, states of mind in which we " entertain an idea " may be of two very distinct classes. Either we may be 90 DATA referring to, thinking of, a reality which in the back of our minds we know to exist, as when I think over the events of the day, or pass leisurely over the incidents of a novel or history lately read. In this sense the mere having the idea postulates logically a categorical judgment into which the idea enters as content; and it is only on the strength of such a postulate that we can venture to speak of the entertainment of the idea as an act of reference. If we drop the postulate we come to the second case, where the idea is really a suggestion. Differ- ing from assertion in point of its assertiveness, it still looks out towards a world beyond itself ; and if it does not claim that anything in this wider reality corresponds with it, it will still acknowledge itself as affirmed or denied, accepted or rejected, by a comparison with reality as subsequently given. Merely to have or entertain an idea is, if we tacitly postulate nothing more on the subject, the same thing as merely to suggest. One further point wUl clear this up, and also enable us to bring both cases into relation. Assertion (we may be allowed to assume here, though the point will need further argument in support of it) may have every degree of modal strength from certainty to the zero of pure doubt. The thought which merely entertains an idea, we may say, occupies no defined place in this scale. It is a judgment of undefined modality ; in forming it we have not even committed ourselves to a preference for or against its truth. And this will relieve us of a difficulty. A suggestion definitely adopted as a problematic judgment is thereby as definitely distinguished from an asser- torical. The problematic judgment declares its content to be possible but uncertain ; it distinguishes it from the content of the assertorical. But when the idea we entertain is a reference to a known reality, we cannot say that it is uncertain. As a mental fact our certainty of it is in abeyance ; but we do not, on that account, entertain a definite doubt on the point. We may take it, then, that the mental state called having an idea, is that of suggesting a content of reality without determining or being conscious of any degree of certainty as to thfe truth of the suggestion. The term "idea''^ can thus be applied to any content that may be asserted or suggested as real; and in this meaning a " reference to reality " in one sense is included. For if reality means the whole within which every- 1 As a verbal point, it should be noted that I have here used "idea " where, e.g., Mr. Bradley would employ the term "ideal content." That is, I have used the term idea, not to denote any state of mind, but always the content entertained in some state. Mr. Bradley's usage has the advantage of avoiding one confusion at least, and 1 shall employ it whenever it seems specially to be feared that that confusion might otherwise occur. IDEAS 91 thing real is found, it is clear that to this reality every assertion and every suggestion refers. The idea, then, is a content referred to reality; and to entertain an idea is to make a mental reference to reality. But this reference must be entertained in some definite fashion, whether as the content of command, wish, assertion, or suggestion. Excluding, then, every implication of further thoughts, we find that to enter- tain an idea is to suggest a content of reality. Lastly, what differentiates the idea from other contents of assertion or suggestion is, that it is not merely suggested of reahty, but has become known as a content so suggested, that is, as a part of your mental world or mine. Not only is it referred to reality, but it is itself an object referred to ; and, in fact, the part it plays in our thought is due to this double character. 3. The idea as thus defined is logically contrasted, but in fact perplexingly interchangeable with the idea as image. The very same content which I suggest or assert or deny of reality I may, in many cases, take simply as so much present fact. My mental picture of the Forum of Eome is something that I can call up at pleasure, something which, faint though it be, is clear and distinct almost as my perception of it as I explored it ; something which I can even examine and analyse, so as, for example, to assure myself of the relative positions of its temples or the line of the Sacred Way ; which, in short, fulfils all the functions of an ordinary presented content. All this I can present to myself without judging or suggesting any- thing. I simply see the whole thing, and I assert for the moment nothing but what is present to the mind's eye. At the same time the whole, or any portion, of this content can be transformed into a judgment. My mental vision, say, of the Sacred Way running past the Basilica Juha and curving to the right round the Temple of Saturn is transformed, in answer, perhaps, to a question, into "the Sacred Way runs," etc. Whether aU ideas can thus serve as simply presented facts, is a difficult question which we may leave untouched. All ideas of concrete things, events, and the like, appear to have this capacity ; while the same is true of abstract ideas, at least so far as they are symbolised by concrete representative images. We are forced, then, to distinguish two usages of the idea — (a) as the content of a suggestion, etc., and (6) as a presented fact without reference to a further reahty. The point of identity is that in the second usage the idea " really " refers to something further, inasmuch as it is formed from perception, and can always be used to represent the perceived object ; but so far as this usage is in abeyance, the idea falls into the second class. CHAPTEK VII General Ideas 1. Eeturning to the usage of ideas as contents of assertion or suggestion, we have to ask now what they contain. Clearly, from our definition, whatever can be asserted or even suggested of reality, can be the content of an idea, and becomes such when not merely asserted, but also referred to as the content of an assertion. It is usual to divide our assertions into Particular or General, and ideas will accordingly fall under the same heads. Ideas of particular facts will be simply the content of our ordinary memories, and constructions of memories, and their nature and genesis need not therefore give us any further difficulty. We need only remark a differ- ence between the idea of a strictly particular fact and that of an individual person or thing. The particidar fact may, at least, be given in a single act of apprehension. The individual person or thing is certainly a content involving many appre- hended data, and we shall see later that the mere construction of these data is insufficient without inference to explain all that we actually mean by ideas of this class. It will be sufficient for the present to indicate that these ideas refer to special wholes of facts connected each by its own appropriate nexus in a manner that wUl demand description later on. Passing to general ideas, and treating them as the contents of a suggestion, the question is. What do they suggest ? The answer is to be found by stating the suggestion in full, or, if you prefer, turning it into an assertion. Turn " ghost " into an assertion, and it is " ghosts exist," " there are ghosts." When, where ? The judgment does not particularise, only somewhere. There is nothing as yet in the judgment about graveyards and midnight. What is a ghost ? For our purposes it is a general content, that is, something common, or taken as common, to many apprehended or apprehensible facts, a point in which those facts are judged similar. It is not a particular content, something that was apprehended once for all, and now alluded to as " that ghost." Accordingly, the idea of ghosts means a GENERAL IDEAS 93 content common to several facts supposed to be apprehended or apprehensible, without specifying what facts. Now we have seen reason to believe that memory, properly considered, gives us a very definite assertion. It speaks of that cold I caught, that time we rowed down the Wye, three years ago. It deals with an individual fact, and particularises its content. But though memory wishes to be definite, it cannot always become so. Its contents get blurred, their angles get rubbed off, their joints and links of communication with surrounding facts get loosened. In a word, the remembered content tends to lose its definiteness, both of quality and of position. It becomes now not that thing done then, but a thing done some time. The date loses its relation to other events, and turns into a cold, experienced some time. Memory, then, in its weaker forms makes assertions with the same indefiniteness of position that we find in a general content. The remembered fact is simply located somewhere in the past, just as the general content is located somewhere in reality. It would be a mistake to conclude that a general idea is simply a blurred and degenerate memory. Memory, however it may fail, still means to recall a particular existence, while in the ideas before us generality is definitely substituted for such existence. To explain generaUty, we must revert to com- parison. Comparison we have seen to be the knowledge of likeness or difference, whether this be directly given by analysis or more indirectly by construction. Whether a comparison be " given " or " constructed " it is in its simplest form an assertion of a relation only, a likeness between two given facts. In the crudest kind of comparison, two appre- hended data A and a are related just as they were given, and are held to be more or less alike. A further step is taken when analysis is brought into play. A is broken up into p, q, r, and « into p, s, t, and a more definite relation of precise likeness or identity is asserted between the p in the A and the p in a. Now this identity is still a mere relation : " p = p" is a simple relation, just as much as " A is like a." ^ But ia dealing with analytic attention, we pointed out that the mind in exercising it can remaia quite distinctly aware of the whole that it is analysing, and of the relation of the part to the whole — so far, at least, as to apprehend that the part attended to goes to constitute the whole. Now, when such acts of analytic attention are combined with a comparison, we get a result which we may call a defined and analysed comparison, A is like a, because they are identical in p ; and there emerges 1 See below, Chap. Till. 94 DATA along with this the converse judgment that p is identical in A and in a. In p, then, the mind becomes aware of a content which may be common to more than one fact, or, strictly speaking, such that it occurs twice, as an element in different facts. Now, let p be oftener repeated, and let memory lose sight of A and a, etc., the individual instances in which it appeared, and all we retain is the assertion of p as having qualified several apprehended facts. We have not only the vagueness of position (which we found in degenerate memory), but also the definiteness of generality which we get from analytic comparison.^ One further step can, I think, be differentiated in the process of forming the idea. The memory - content; which loses definiteness of position, is left, as it were, isolated. There is distinctly less in the assertion than in a definite memory, and there is the feeling of a void. But whUe we acquire the notion of contents common to several given facts, we also, by the synthesis of memory, are building up the series of past experiences into a single whole, the order of reality as it has been presented to us. It is of this reality that the ideal con- tent is now asserted. It has quahfied facts within the given series ; while the particularity and definiteness of these facts is dropped out of sight, the wider reality in. which they were given takes their place, and it is asserted of the ideal content that it has qualified reality. This attribution gives its exist- ence all the definiteness which is required in the case of an idea, that is to say, not individuality, but a certain connection between its manifold appearances, consisting in this, that they are aU found within one and the same system of existent facts. To say this is not enough to individualise a fact, and, therefore, indefinite memory would not regain its precision by asserting its content " of reality." It is, however, enough to define the existence of a general fact. Our first formation of a general idea appears therefore to '' "We have spoken here as though analysis were conscious and purposive. This is rather the logical exposition of what is implied in forming ideas, than a psychological description of what always takes place. Dr. Ward has a right to protest that " thinking does not begin with a conscious abstraction of attention from recognised differences. . . . The same name is applied to different things or events because only their more salient features are perceived at all " (Ency. Brit. art. "Psychology," p. 77). Of course, if the common p is found without analysis, so much the more easily will the idea of p be formed. All we require is that the idea may be based on a mere element of the given, and that in the higher stages of consciousness we can be aware of it as an element. The same result is arrived at, doubtless, by the mind in many instances by a shorter and less logical road. The involuntary restriction of attention to "salient" features may have the same results as a conscious analysis, though it is only the conscious analysis which could justify those results. GENERAL IDEAS 95 rest on a particular combination of the mental activities already specified. "We detect the similar content p in two given facts, A and a, and the generality of p means primarily that it is found more than once, or, if you Hke, that two or more similar facts are found, qualifying different objects of our perception. This similarity of content, qualifying facts differing numeric- ally or otherwise, is the centre of the general idea. As long as the mind has before it the whole " p, qualifying both A and a," it is making a comparative judgment, in which an ideal con- tent is contained. Dropping A and a out of sight, and sub- stituting for them reality as a given whole, as the field in which p's existence is to be found, we have the idea of p isolated ; that is, we have the suggestion, assertion, thought (call it which you please) of a content common to different portions of reahty. In this definition of the general idea the number of times p is repeated is left indefinite. This indefiniteness naturally follows on the dropping of the individual facts A and a. The number of p's then becomes, eo ipso, indefinite. But in our ideas as we have them, there would seem to be impHed a more definite notion of generality, that is, a suggestion that p not only has been found a certain number of times, but wiU or may be found many times more. Such an idea would certainly con^ tain vsdthin it a trace of inference, of generalisation from what has been to what may be. For, in the first place, the concep- tion of a reality, extending beyond the series of experienced facts, is in itself, strictly speaking, inferential And, in the second place, when the idea is properly and strictly general, it is suggested of this wider reahty as something that may be realised again, just as it has been reahsed already. To frame a general idea is thus to suggest that a content exists an indefinite number of times at an indefinite number of points in reality. 2. Generahty then, on our account, if taken strictly, involves number, but indefinite number. It involves plurahty, because it is based upon comparison ; and comparison necessitates at least two instances. But the number is indefinite, because there is nothing in the results of comparison to indicate how many instances must, or how many can, resemble one another. This irrelevance of the nimiber of instances is what is meant by such tautologies as that " p will still be p wherever we find it." The meaning, in fact, is, that p being a general content, may be found in an indefinite number of cases ; or if you prefer it, that since in framing the idea of p I suggest it, not as existing in this or that case, but as a content qualifying reality in various parts, the particular position, number, and 96 DATA remaining character of those parts does not affect the value of the suggestion, nor the character of the contents suggested. On the other hand, some plurality seems esssential to the general content. If we take A and deny that it can exist in any case but one, it becomes, ipso facto, an individual. It does not cease on this account to have character or content. But this character is no longer general It is unique. It can be apprehended, analysed, remembered, thought of, referred to, even named, but it cannot be the content of a general idea. We may have an idea of it, but an idea that is particular and not general. It may be objected, that we do not ordinarily think of a number of instances when we use a general idea. When we discuss constitutional government, or electricity, or picturesque- ness, we are not concerned with the particular nations which are constitutionally governed, or the extent to which electricity is diifused in the material universe, or the number of scenes in existence which might be described as picturesque. We are thinking of a certain character of some reality or other, the number of repetitions of that character in reality being irrelevant. We refer this character to reality, but not to any number of cases in reality. And this analysis might be re- inforced by special instances. For it might be said we use contents undoubtedly individual in their origin as general ideas. Thus we speak of a Daniel, a Crossus, another 2nd of December. Or we form from our one known sun the idea of " a sun," and so have no difficulty in thinking of other stars as centres of solar systems. Contents of this kind, undoubtedly in some sense general, suggest an objection to our whole account. If here we get general ideas without comparison, why not in other cases as weU 1} To answer this we must understand how far the contents just taken are really general in character, and we must be quite clear as to what we mean by generality. If we adhere to the definition of a general idea laid down at the beginning of this discussion, we must admit that plurality of instances must be one of its essentials. The general content must be common to at least two instances in reality. Now, so long as a given content q is unique, however much we detach it from its surroundings and isolate it in thought, we can only treat it as general on the analogy of known cases of general contents. If n o p are known to exist each in many cases, this experience suggests that the ^ Cf. Sigwart, Logik, sec. 7. Tlie essence of Sigwart's contention will, I think, be seen to be provided for in our account. GENERAL IDEAS 97 same may hold for q. And to treat q explicitly as a general content is simply to hold this possibility in mind ; that is, to regard q as a content which may be general, just as certain known contents are general. Exphcit generahty, we may therefore say, is based directly or indirectly on comparison of instances. But there is another point. The meaning of an idea may be inexplicit and ambiguous. Let us see how this comes about. To be treated as a general content, to appear in fresh cases, q must first be detached in the manner already indicated from the instance in which it is given. By an act of analysis or abstraction we must assert q in separation from its particular context as an attribute simply of reality. Now, if we rest at this point, we have an ideal content, which, if taken strictly, is neither general nor individual. It is not fully individual, because it is referred to reality at large, and not to its own peculiar context. It is not general, because it is not suggested as qualifying reahty in many cases, or as a basis of resemblance between different points of reality. It is, in short, indeter- minate. Nothing in the idea at this stage decides whether it is a reference to " the q," or to " q." This indeterminate idea, then, is not more, but less, than the individual, not richer, but poorer. For the notion of definite position or context is dropped, and nothing is gained in return. In the general idea, on the other hand, there is a compensatory notion derived from comparison, the notion of number of instances presenting points of resemblance. Now ideas, as they pass through our heads, are mainly or the indeterminate order. Even if they have been derived from comparison, we do not put ourselves to the trouble of realis- ing their general character. The notion of generality lies ready to hand, to fill up their meaning as soon as thought requires it ; but we do not always use it. On the other hand, it makes the greatest difference whether the content of an idea is, in fact, general or not. The content which we entertain in this indeterminate fashion may be, in fact, applicable to many cases in reality, and we ourselves may at different times apply it in different contexts. Such a content, we may say, is de facto general — it is de facto used as general — even though we may never at any moment exphcitly assert its generality. On the other hand, it is de fade indi- vidual if it can only be realised in a single case, and we may be aware of this limitation without always referring to it when- ever we employ the idea. Ideas, then, are individual, indeterminate, or general The 7 98 DATA individual idea is a suggestion of some definite set of facts occupying some continuous portion of reality ; such are our ideas of Themistocles, Jack the Giant-killer, or Utopia. An indeterminate idea is a content attributed to reality at large, not to any particular part of it. Whether it exists once or many times is not stated or implied ; its individuality is ignored, and that is all ; such, ordinarily, is our idea of the romantic. A general idea is a content suggested as existing many times in reahty, as quaHfying reality at many points, constituting a resemblance between those parts of reality which contain it. Such is my idea of a horse or a mill, or, broadly, of a genus containing species, or a species containing individuals. The indeterminate idea is de facto general, if it is on various occasions applied to distinct individual cases. Lastly, as inde- terminate a content may depend merely on abstraction; as general it directly or indirectly involves comparison. 3. The numerical plurality which we take to be necessary to a general content may be held to involve, as a rule, some quaK- tative, i.e. specific, difference. But this is not universal. There may be true infimce species, and an infima species is stiU a general Thus an exactly similar shade of colour may be pro- duced in two ribbons ; two notes may be qualitatively indis- tinguishable, two figures exactly equal in every side and angle.^ Their character is still general ; it is a content appearing in different instances. More often the difference of context in greater or less degree affects the character of the ideal content itself. Thus red, we may say, is a very different red in crimson and in scarlet. Humanity seems to be one thing in Shake- speare and quite another in a Hottentot. StiU, if red or humanity are hoTid fide general ideas at all, they must have some definite and constant meaning. They must suggest some character or other, and it is only this character which really belongs to the general idea as such ; conversely, in what special form the character wUl appear, is not determined by the asser- tion of the general content as such. In this sense, then, we must contrast the generic content with its specific form, just as we contrast the specific content with its context. Only we must bear in mind that the " forms " in question quaKfy the general content in a special way, the logical significance of which we must consider later.^ For the present we may treat all difference as a matter of context. The question may be raised, whether we can carry 1 Certain difBoulties connected with the conception of an "absolute " exact ness are discussed below, Chap. VIII. ' Chap. VIII. p. 114. GENERAL IDEAS 99 abstraction a point further than has yet been done. We have spoken of ignoring the individual existence of a fact, and have treated this as a kind of analysis which simply separates off the fact in question from its surroundings, while we have supposed the fact itself to be still asserted of reality. Can we now go a step further and abstract the nature of the content from its existence altogether, its " what-ness " from its " that-ness " ? Only, if our foregoing account is correct, at the cost of reducing our content to a merely presented psychical datum, without meaning or reference to further reality. There seems to be no mean between these extremes. Either a content is suggested of reality (whether with or without definition of where and when), or it is a merely present fact. If this is false, we must find some new meaning for the idea as a mental fact. If it is the content of a suggestion or assertion, how can it be suggested or asserted but of reality? How, again, can we " mean " anything unless we suggest that thing ? and how can we suggest it unless we suppose for it a place in the real world ? I conclude that an explicitly general idea is a content found, or supposed to exist, in several instances within the real world, and that our conception of such a content depends on memory, analysis, and comparison. An indeterminately general content is one which is so separated by analytic attention from its individual setting as to be considered simply as a character existing in reality: such a content does not necessarily involve comparison ^ unless or until it is used as general ' The old-fashioned view, which is in the main that of the text, that abstrac- tion (analysis) and comparison are the two main elements in the first formation of ideas, has been attacked by various writers ; but no really vital objection has been brought against it, still less has any possible alternative theory been put forward. Lotze (Logic, bk. i. chap. i. §23) argues that, while "gold, silver, copper, and lead differ in colour, brilliancy, weight, and density," we do not find their "universal" metal "by simply leaving out these differences without compensation." But what is the "compensation" ? To our surprise, we find a little lower down that " compensation, by the corresponding universal for omission of the individual marks, is the regular rule of abstraction," i.e. for the particular weight or brilliancy of gold we substitute some more generic conception in the concept metal. But this is precisely the abstraction-theory. Differences of weight or brilliancy are left out of account ; common characters are retained. There is no substitution or compensation, but simply retention of a partial character. No defender of the abstraction-theory ever supposed that "weight" would be left altogether out of our conception of things, all of which are heavy, but in different degrees. This would be directly opposed to the whole method. Sigwart (Logik, §§ 7 and 40) is more nearly in agi-eement with the account in the text, which, in fact, owes much to his discussion. He denies, however (e.g. vol. i. § 7, 2nd ed. p. 50 ; of. p. 322), that the " capacity of an idea for being general" depends on its being derived from a aumber of individual ideas. Our account admits this, so far as any given idea 100 DATA 4 Further questions as to the nature of general ideas belong really to psychology. To logic they are important only as bearing on the nature and basis of assertions. How we come to know or believe at all remains an ultimate puzzle, for logic as for psychology, but it is a fact which must be assumed before logic can begin. Once assuming this fact, the question is, what we believe, why we believe it, and whether we can justify our belief ; and so far as the prior two of these questions are concerned, we have tried to give some account of general ideas in the preceding paragraphs. The third question, as to logical justification, must occupy us later on ; but all three are totally distinct from a fourth difficulty, which has sometimes been regarded as the point of controversy with regard to general ideas, and which must indeed remain a question of vital interest to psychology. I mean the question. What is the nature of the psychical state when a general idea is formed ? This logic need not attempt to decide any more than it is bound to describe the nature of any assertion, belief, or disbelief, as a mental fact. Granting assertions, we wish, as logicians, to know, not what they are as psychical events, but what they assert, and why. If their psychical nature from time to time concerns us, it is merely as illustrat- ing, enforcing, or indicating some logical distinction. It is sufficient, therefore, to suggest, in a few words, the easiest way of conceiving general ideas as events within the mind. Images as such they clearly are not. Berkeley showed, once for all, that a generality is not capable of being represented as an individual It does not follow, as has been shown since Berkeley, that an image may not be used in the formation of a general idea. And we may add, that a series of images may sometimes be necessary. If I take my image of a billiard ball, and attend only to the outline at right angles to the line of vision, I get the idea of a circle. I cannot see the circle separately, but I can fix attention on it and distinguish it analytically from other characters. If I compare this circle with my image of a water-wheel, and "fix" the common is concerned. On our view, it is comparison which gives meaning to generality as such, and certain contents once being known as general, any content may be treated as such. A content may be given only once ; it may be the product of analysis without comparison ; it may even be independent of analysis, i.e. be a whole datum of apprehension. But its "generality " means that that is suggested of it which has been found in other cases by comparison. Siewart seems to admit the essence of our notion of generality (§ 7, loe. cit.) : " ft lies not in the special nature or origin of that which is represented . . . but in this, that the idea {Vorstelhmg) is actually applied to a plurality of individual contents of perception (Mnzel-anschauungen), and that this plurality as such comes into consciousness." GENERAL IDEAS 101 element, I get the notion of pure circularity independent of size. The psychological process corresponds point for point with the logical, except in this, that the irrelevant matter is never eliminated. The extraneous characteristics of the image remain, however much we determine to " mean " only one element in it and to ignore the rest.^ The same process seems to go on in the most abstract or complicated cases. A " law " or " formula," say of some quantitative variation, can be represented by " taking " mentally two or three cases, representing, if possible, widely divergent instances, and realising the formula in such instances. Thus, I might realise Boyle's law and its limitations by observing or thinking of an actual volume of gas under three or four different amounts of pressure. Better still, I may take an actual process represent- ing the working out of the formula amid progressive change of quantitative values. Thus we may illustrate the effect on prices of reduced supply with nearly constant demand by the gradual rise in prices during the great coal lock-out of 1893.^ To representation by partially irrelevant images there would seem to be only one alternative — symbolism. A symbol is a content with a definite character of its own, taken as representing some other content which it may not in the least resemble. I have not called an idea a symbol, because what- ever facts are symbolic are made so by ideas. The idea is not something which I put up to act as a substitute for my representation of reality. It is my representation of reaUty. We should never speak of representing facts by means of or through ideas. Our representation of them is an idea. It is a fatal error in philosophy to take the idea as a third something that comes between the mind and reality. But this third something is precisely what a symbol is. It is substituted by the mind, on various accounts, for the direct representation of the fact. The most important case of symbohsm is, of course, language spoken or written. We may refer also to arithmetic, algebra, and the " graphic method " in physiology or social science. The lines by which Mr. Charles Booth represents the fluctuations of employment at the London Docks, the curves by which Jevons or Professor Marshall illustrates the dependence of value on demand and supply, are simply well-adapted methods of symbohsm. I would call special attention to these instances. We have said above that 1 Attention, as HbfFJing puts it (Outlines, p. 168), is concentrated on the required elements, and a " weaker light" falls on the others. ' With our whole account of. Berkeley, Prituiiples of Human Knowledge, latrod. §§ 15, 16. i02 DATA the symbol need not resemble that which it represents. But in the most fruitful kinds of symbolism (apart from that which serves human intercourse) there is also a definitely conceived correspondence of what we may call homologous points in the symbol and the thing symbohsed. This is best instanced, again, in the graphic method, where each section of an ordinate or abscissa has its definite meaning in quantity and quality. Complex relations of value to demand and supply can be expressed by a curve, precisely because each variation in the Hne is understood to correspond, in length and in direction, with a distinct variation in the factors symbolised and in their result. The case of algebra might seem an exception, since its symbols (A, B, C, +, — ) have the very barest resemblance ^ to anything they may symboHse. But it is precisely this bareness which algebra requires. It wants to deal with pture quantity, and even with pure and abstract relations of quantity (as against particular numbers). In carrying this out any concreteness in the symbols used would confuse it. It uses, accordingly, symbols which suggest nothing beyond that which it is conventionally understood that they are to signify. As mental states, then, ideas are either analysed images or symbols. Is this division final, or must aU symbols be resolvable, translatable at will, into representative images ? Here, again, the psychological question becomes important for logic in relation to particular cases of belief. But the question is rather one that demands special treatment in each case. All that I would venture to suggest, iu general, is this. Every object of belief must be either representable (by combination and analysis of images) or be taken as analogous, i.e. in some degree similar to a representable content. Thus, in mathematics, imaginary quantities or figures (which are an extreme case, since, as represented, they would be sheer self-contradictions) are formed on the analogy of real quantities. The indefinite production of the asymptote is a simple extension of its character for any given finite length. V — a is no representable quantity, but an expression formed analogically from Va ; it is, I suppose, such a quantity as should stand to — a in the relation which Va occupies to a. Further, beliefs or ideas may be very indefinite. As we try to fix them they elude our ^ It is perhaps truer to say "no resemblance at all." Of course, letters are so much black ink or so much sound, and in that sense quantity. But in the same sense they are also particular quantities, and algebra does not use them as such. As meant in algebra, they are to be compared rather to marks put on a bale of goods. They are treated as being nothing but standing each for its own quantity. GENERAL IDEAS 103 grasp. We mean something, but barely know what we do mean. To overlook the immense importance of such half- meanings, the only rays of light which reach us from some far distant regions, is a fatal blindness. It is (if I may use the expression) the scientific fallacy. If symbolism helps us to fix them, symbolism is justified of its results. But even here we must bear in mind, first, that there must be the genuine idea in the background, however indefinite it be ; and, secondly, that, in fact, the symbol has too often played the cuckoo's part and substituted its bastard self for the offspring from on high. Lastly, to develop such ideas on the analogy of symbols, to infer that such and such things being true of the symbol, similar consequences (however vaguely similar) must hold for the thing symbolised, is always dangerous, and can never be warranted except by special experience.^ We may conclude that, directly or indirectly, any content of belief must be representable by means of images, or must be analogous to one so representable. 5. We have already spoken of language as a form of symbolism. Some difficulty was at one time raised as to what it symbolised. Clearly, in a sense the name or word which I utter is a sign of my idea. I cry " wolf " because I have seen, or fancy I have seen, one ; and all the word primarily indicates is my perception, real or imagined ; the presence of the actual wolf may be regarded as being, for my hearer, a further inference. But this is taking " sign " in the sense in which it is not equivalent to symbol. The name is the sign of the idea, as any effect is a sign (gri/i^iTov) of its cause. It does not symbolise the idea in the sense of being something devised by the mind to stand for the idea. As a symbol it stands for the reality, the very same reaUty to which the idea which uses the symbol itself refers.^ Names regarded as symbols are, as Mill showed, names of things, not of our ideas of things. Taking names as symbols that " stand for " reahty, a word must be added on the logical postulates of such symbolism. Language in its origin in the individual is, I suppose, reflex, automatic, and unconscious. It is a purely physiological process. Certain mental states act on the motor nerves of the tongue and larynx, just as others act on the vasomotor nerves or the lachrymal or sweat-glands. Certain modes of conscious- ^ The fact that in mathematics calculation by imaginary quantities gives results which hannonise with those obtained, more circuitously, from ' ' real " expressions, is, I imagine, the justification of their employment. ^ This reality, of course, may happen to be the speaker's mental state, but this possibility can scarcely cause confusion. 104 DATA ness result in cries or exclamations, just as others (or even the very same modes) produce blushes or paUor, tears or perspira- tion. Not only the primitive babblings of the infant, but the ordinary unreflecting speech of the adult, is thus mechanical in its mode of production. But the organisation of symbolic speech as a method of communication involves more complicated conditions. For this purpose it is clear that every symbol used must be a fixed sound attached to a fixed and distinct content as such, and that by aU the individuals for whom it is to serve as a method of communication. Until this fixity of reference is attained there is no human speech in the proper sense of that term. The cries of an animal are significant in one sense, in that we have good grounds in observation for taking them as the effects, and therefore signs, of certain feelings or disposi- tions. But they are not significant as symbols except in so far as the animal purposely uses them as such. How far this may be done by animals is a question we may leave untouched at present. In the case of human beings, attentive observation may reveal the transition actually taking place. The child is loosely said to " speak " when it cries Mam, mam, mam, without meaning anything whatever. This is interjection, not symbolic exclamation. The same sounds when uttered only at the sight or in felt want of its mother become fixed symbols referred to a fixed content, i.e. significant speech. This fixation of meaning is, logically speaking, of the nature of an inference. When I learn that Begriff means a concept, or homo a man, I make a kind of generalisation which I have to apply in particular cases; i.e. I learn that if I want to express the term concept to a German I must use the word Begriff; or if, in reading Livy, I meet the word homo, I am to understand " man." This we shall see to be a true inference ; and in the case of an adult learning a foreign language it is almost all an explicit process consciously gone through. In the first acquisition of language by a child the conscious pro- cess is, of course, far cruder ; but even then we must admit the operation of the same connections of symbol and meaning on the infantile mind. Of course a baby does not syllogise, but (so far as he learns to speak correctly) the same facts influence him as if he syllogised. He does not say to himself, " I called this person Mam, mam yesterday (with beneficial results), and therefore will do the same again to-day." But the fact that he has once affixed the symbol to the content, operates upon him in such a way as to make him retain that symbol for that content. Now this movement of thought which connects contents GENERAL IDEAS 105 universally, we shall see later to be the fundamental fact in inference. Where such an act takes place ia thinking, there is conscious inference; where a mind arrives at results by different mental or brain processes which can only be justified by such a movement of thought, there we speak of an implied inference. ExpKcitly or implicitly, therefore, language embodies the results of a system of inferences. The spoken word or sentence becomes in this way a medium between speaker and hearer. The hearer draws an inference from the word to the fact, the speaker from the fact to the word. Confimng ourselves to the speaker, and omitting purely reflex exclamations, and lies, commands, wishes, etc., we can see that the content symbolised must be simultaneously in some way asserted, believed, or suggested by him. This assertion, or whatever it be, we call the " mental equivalent " of the spoken sentence. We might almost regard it as the premiss of which the utterance is a conclusion, since the appropriateness of the language used to " express" the object asserted involves, as we have seen, a special inference on its own account. This step taken in speech is common to every spoken sentence, and we may therefore distinguish it in thought from the beHef which forms its basis, and to which it gives expression. Now, no mental state is itself a proposition, nor does it issue in a proposition without the concurrence of the inferential process just described. But certain mental states require something more than this before they can be, properly speaking, expressed by language, while others require nothing further. Such latter states we may describe as being directly expressible in language, or as being the proximate mental basis of the proposition. 6. From what has been said of the logic of language or any symbolism used for communication, it wUl be readily clear that the only contents " directly expressible " by words must be such as are common to the experience both of speaker and hearer. To assist in communication, any given symbol must mean the same thing for both speaker and hearer, and the same thing always. It is easy, then, to see that the bulk of otu: communications must take place by means of general ideas, and that words for the most part " express " such ideas directly, while particular experiences are expressible only by being brought into relation with some general content. Thus the mass of language, adverbs and conjunctions no less than sub- stantives and verbs, is general in character. It is true that by gestures we can communicate what we immediately perceive, and direct another's attention to the same object. But whether we use speech or writing or gesture, it is difficult to see how 106 DATA we could get beyond the communication of immediately present facts to others so situated as to be able to present the very same facts to themselves, except by the means of contents common to many parts of our experience, and designated each by its own symbol. When a chUd sees a horse for the first time it will draw attention to it by pointing ; but if it sees the horse while alone, it cannot tell what it has seen unless it possesses sufficient language and power of seizing and describ- ing general characteristics. We may take it, then, that language is the symbol of a system of contents common to many parts of experience, and for the most part truly general in character.^ We may also notice, in conclusion, that just as ideas may not be always accurate, so words are confessedly inadequate exponents of ideas. You have a correct idea, but you express yourself oddly, loosely, inaccurately. Thus even in a single proposition the inference already noted as involved in the apphcation of the name may not always be accurately performed, and in arguing from the sentence to its mental basis we are assuming a correspondence which does not always exist. And in this connection we may note a special difficulty in the formulation ' Proper names alone designate contents common to many parts of experience which are not truly general. They indicate things, or persons, which are individual, and so far opposed to what is general. But, of course, the individual is characterised by certain definite recognisable attributes — he is not a subject without attributes. And, if a true individual, he persists through or reappears in many experiences, and is an object of your experience as well as mine. "London" or "John Jones" are to me (apart from inferences) names for tolerably constant characters appearing at intervals under certain conditions. No doubt I regard these characters as interconnected in a special way which constitutes them attributes of an individual. But that does not hinder them from being common to many parts of my experience and the experience of many people. Now, so far as an object is common to the experience of different people, these people can designate it by a strictly proper name, i.e. a name which does not rest on any analysis of its attributes. Thus "the sun" means the same thing wherever the English language extends, and would mean it all the world over if there were but one language. If, on the contrary, we get outside the group to which a given experience is common, the strictly proper name becomes inapplicable. The same word "John " means one person to me if I use or hear it in one company, and quite another in a different society. In such cases a designation by means of known general attributes is necessary. That which you have not yourself directly experienced, I must convey to you by a combina- tion of words representing a synthesis of attributes, each of which you have experienced. Anything, of course, even a particular event like the Three Days of Milan, or the Hegira, can be referred to by a proper name when once described. But it remains that directly or indirectly the meaning of a proper name rests on the facts common to the experience of the speaker and the hearer. So far the proper names do not differ from names of general attributes. The difference comes in a later stage. The hoiid fide explicit general content may, as we have seen, exist an indefinite number of times, and, for all we know, in indefinitely different contexts. The individual (as we shall see more fully later) is conceived as limited to a definite portion of reality, whether great or small. His truly general attributes appear in other individuals as well. Further, the strictly GENERAL IDEAS 107 of any theory of the elements of knowledge. Acts of thought do not necessarily express themselves in words; nay, the activities which have occupied us in previous chapters are not capable of being directly and as such expressed. Nevertheless, in describing them we are bound to use language. We have spoken of the apprehension of a flash of hght, the attention to a white spot on a red surface, and so on, though, according to our view, none of these acts are recognitions of general contents as such. In all such cases, then, we really mean that a content is asserted, known, or beheved which, if logically treated by further activities, would be expressed by the term used. The apprehension of a flash is the becoming aware of a content which comparison, etc., would lead us to name flash. The memory of this or that is the memory which existing in a mind stocked with general ideas, is described as a memory of this or that. Thus the description of elementary conditions of knowledge, and the contents produced by any one of these in isolation, is possible only through use of other conditions. These "corrections" once understood can easily be applied whenever requisite.^ proper name does not indicate him by any one of his attributes singled out for that purpose. In the degree in which any such name does " connote " such an attribute (as, e.g. John may be said to convey English-speaking and male), it becomes an ordinary attribute name. Nor does the proper name cease to be applicable, however much its subject may change. Hector is still Hector how- ever changed from the triumphant spoiler of Achilles ; and even the nickname, though attributive in origin, "sticks," as we alt know, throughout life. These considerations, which must depend for their further support on our views of the general nature of the individual, seem to have given rise to Mill's much mis- understood doctrine (Logic, bk. i. chap. ii. § 5), that proper names are non-con- notative. Mill certainly does not mean that the individual has no attributes, but that the proper name in designating him does not rely on his possession of any special attribute. It refers to the object as individual, not to his attributes, which are general. Mill pushes this point too far when he says that proper names have no "signification." That proper names are full of "meaning" is well brought out by Mr. E. C. Benecke {P7-oc. Arist. Soc, forthcoming volume, 1895) ; but that they have meaning is one thing, that this meaning is gaieral is quite another. The name of an individual means all that that individual is, but precisely on that account it is not as such a general name. ^ We may fully agree with Mr. Bosanqiiet {Essentials of Logic, pp. 94-97) that the view taken in this chapter is ' ' not the only way of regarding " general ideas. The "generic" can also be ti'eated as containing the "promise and potency " of the specific, as a plan which may be filled up in more than one way. But so used it is scarcely a single idea any more, but rather a synthesis, explicit or impHed, of related contents. We have passed beyond the "moment" of abstraction as such to that of subsumptive classification. As to the "particulars" of which the general "consists," a word maybe added to obviate misunderstanding. A concrete whole (a or a) has an element Pj. This Pj is a case of a general p. And of tJiese particulars, pj, p2, etc. , the general consists. But the wholes, A, a, etc., are also particulars, and in them Pj, P2, etc. are mere elements. In this sense the general does not consist of, l3ut is contained in, the particulars. CHAPTEE VIII Eesemblance and Identity We have explained general ideas as resting on the notion of resemblance. But resemblance itself and its companion, difference, are relations which have been no small stumbHng- block to theories of knowledge, and therefore demand our attention. 1. Though the term resemblance admits of confusion, and therefore demands analysis, the facts of resemblance can only be analysed a very httle way. It is simple matter of fact that I see resemblances and differences, but I cannot resolve this characteristic of the world into anything more simple. One step, however, I can sometimes take. Beginning with a vague perception of resemblance, I can analyse out a common quahty in two objects presented to me, and see that whUe precisely alike in that quaUty they are different in other respects. That is to say, I can resolve likeness into identity ^ in difference. Two architectural styles, two pictures, two faces, two landscapes, two constitutions, two historical situations resemble one another ; they " impress " us as aUke, we vaguely say. Then comes analysis, and points out a common quality — the same development of constructive knowledge, the same technique, pose of the head, prevalence of democratic sentiment, decay of civic morality in the presence of a spirit of faction. Now it is explained — the common quality is clear, and the slight mystery which attends vague resemblance is dispersed ; the remainder is mere difference, and does not interest us. Which, now, is the ultimate of these relations — likeness or identity ? In the instances given we proceed from a know- ledge of likeness to that of identity, a fact which may tell either way. We may infer that identity is an abstraction ' The word identity is used here as = precise or complete likeness. That this conception is radicaUy distinct from that of numerical identity or continuous identity I shall ai-gue lower down, but the double or triple usage of the term seems unavoidable in English. 108 RESEMBLANCE AND IDENTITY 109 of likeness, an idea derived from reflecting on likeness and difference, seeing that most likeness involves or includes difference, and conceiving the likeness in abstraction from the difference. Or we may urge that if vague knowledge begins with likeness it rests really on identity. Likeness is always logically analysable into identity in difference, and therefore these ideas are its logical basis, that is, its ultimate basis in fact. Both views, I believe, are too extreme, and they fail in distinguishing the perception of likeness and identity on the one side from the analysis of these ideas on the other. Both Ukeness and identity are matters of immediate apprehension, that is, reality presents us with both relations. If I consider the colour, shape, weight, " feel," etc., of a number of small shot run from one mould, they are aU in these respects identical to my apprehension. A minutely accurate balance might detect a difference of a milligramme, but that is no difference to my hand ; or a micrometer a difference of a millimetre, but that is no difference to my eye. The relation of perfect resemblance is thus given to my apprehension whether or not the shot, regarded as something physical {i.e. as existing apart from my consciousness or for some higher consciousness), resemble one another thus perfectly. The idea of identity is generalised from these resemblances, and they are just as truly perfect resemblances of the object as given as the rheumatism of an amputated leg is really pain. Just as the idea of identity is generalised from apprehension, so is that of mere likeness. Blue or green are something ahke ; orange and red are some- thing aUke ; those two faces, figures, sounds are nearly alike. All these are facts that I perceive long before I can analyse them ; and even when I can analyse them the original likeness in general remains,^ i.e. the likeness though analysed iato identity and difference is not analysed away. Likeness is not an unreal or even an evanescent relation of which identity in difference is the only genuine or permanent groiind. Where there is likeness there is generally ^ identity in difference ; but the likeness does not in the least bit cease to be real because it is then analysed. Brown does not look less like Jones because you have discovered that each has a Roman nose and a receding chin. ' I.e. unless some new turn is given to attention by the analysis so that we "cannot see the resemblance any longer." If the identity exists it is certainly not always discoverable ; and if not discoverable, why is it assumed ? It certainly, as Professor James has shown, contributes not a jot to the " explanation " of resemblance in general. See his controversy with Mr. Bradley, Miiid, N. S. Nos. 5-8. ' '^ It is a favourite doctrine of some authors that all likeness involves identity in dilference. But what is the identity and what the difference between blue and green ? I speak of the colours, not of the physical stimuli. 110 DATA So far our result is that relations both of identity and of likeness are matter of apprehension. Both terms will then be the names of ideas generalised from apprehension. The ideas thus formed are, as the next step, compared, and the result of the comparison, about the method of which we shall have more to say presently, is to make clear the relation between them. Thus identity becomes known as likeness without difference, and likeness as identity plus difference. These definitions or analyses of the two terms mutually iavolve one another, and hence make it equally plausible to argue that either is ultimate. The truth is that the given is the ultimate ; that both are given, but that they are analysed and understood by comparison with one another. 2. General ideas rest on comparison, and comparison reveals sometimes identity and sometimes hkeness. Which, then, does an idea contain ? " A " is a general content suggested of reality by an idea. Then does A mean Aj Aj A3 all identical with one another ; or does it mean A a a and a, all resembling one another ? It is reasonable to suppose that idea follows comparison, and that thus there will be two classes of general ideas to cor- respond with the twofold relation of comparison. Perhaps it seems difficult at first to attach any meaning to a general content which shall include not merely identical but similar facts within it. For, it may be asked, where are we to stop ? If a heap is a hundred grains, " more or less," i.e. if it refers to a hundred grains or any similar collection, do ninety-nine grains form a heap, do ninety-eight, and so on, as the puzzle goes ? In short, there is nothing precise or definite in our content. But this is just what we really find. There is a complete want of precision and definiteness about the majority of our ideas ; they are kinglets whose territories are very ill defined, and whose boundaries are the happy hunting-ground of the sophist, the punster, the rhetorician, and many other knaves and fools. The idea is really king only in his own capital. The centre of the territory is definite enough. This is just ; but push the principles of the action a step — is that just ? "We are not quite sure. A step further — that is unjust — clear daylight again. Now it is night. Now it is morning : both propositions are equally certain. What was it just between times ? The only lesson that so many weary controversies have left us is that ideas are not as definite as we could wish. We make them, if we are honest, as definite as we can, but that is not saying much. There are ideas definite and ideas indefinite, and one object of scientific reflection is to transfer as many as possible from the second to the first class. The definite idea RESEMBLANCE AND IDENTITY 111 suggests a content which is identical in all instances ; the indefinite idea one of which all instances resemble one another. There are two sources of vagueness in the mass of our ideas. The first is that they are often generalised from contents which are not identical. Two facts, M and N, resemble one another in p, and p being asserted of reality, becomes the content of a general idea. But, now, suppose the Pi of M and the pj of N are not identical, but only alike ? Then the general idea p already has a loosely defined content, which, 'at least, may alternate between p^ and pj, and over all the distance between them. That is to say, the mind, in applying such an idea, will consider anything to be " a case of p " which has either of the qualities pj or pj, or has any quahty p which is " something between " the two. In all this the mind is probably not conscious of any difference between Pj and P2, the distinction being drawn by later analysis. It is not so much that we take them for identical, as that we do not at this point distinguish between identity and resemblance. And here is our second source of vagueness. Supposing p a real identity (i.e. a resemblance in which no microscopic analysis can find a difference), it does not follow that it wdl be made a content of a definite idea. If the mind which asserts it of reality does not distinguish between identity and resemblance, it does not remain for that mind a clear cut content, nor wiU its appUcation be restricted to contents exactly aUke it. It will be "loosely" appHed. A vague idea, then, is one which suggests of reahty a quality more or less resembling X ; or, if you prefer it, which suggests that contents more or less hke X qualify reahty as an indefinite number of points. A definite idea suggests that X and contents exactly like X are found in reahty. Ideas ought to be definite, but mostly are indefinite. The postulates of definiteness in an idea are, first, the general condition that the mind should have arrived at the distinction between identity and likeness, or at least should not assert them indis- criminately; and second, that in the special contents con- cerned analysis should have arrived at a point of identity. This definiteness is not reached all at once. Just as the general condition of definiteness is reached by stages, so with the actual definiteness of any special content. If p is common to M and N, p is a temporary resting-place for the mind ; but further analysis may show (as above) that M had pj, and N pg; that they only resembled one another, and that their resemblance was based on a common point v. The same process may or may not be repeated ; but the goal is in any 112 DATA case a point of identity resisting further analysis, asserted with absolute definiteness, and appKed always with identical meaning. 3. But this is not all. As we discriminate degrees or forms of likeness, we become able to make comparisons or sub- sumptions which are not identical but yet are definite. Identity is only one case of definite likeness. It is hkeness without any difference at alL Substitute for it a resemblance admitting a definite degree or hind of difference, and we still get a definite assertion. Twice as loud, twice as tall, fix, or attempt to fix, relations to some given content which are definite and yet not relations of identity. But in getting definite ideas we are able to assert with precision both identity and kind or degree of resemblance, identity itself being only a special kind of resemblance, viz. the maximum up to which degrees are measured. The advance of definition thus sub- stitutes for a vague, indiscriminate identity-or-likeness, a precise determination of resemblance, according to kinds, one of which is identity. A kind of resemblance is itself merely a general idea formed by a combination of comparisons. " This is brighter than that." Here is first a recognition of resemblance or difference — it does not matter which we call it. Then the resemblance itself is compared with other resemblances, and a general idea "brighter" is formed differentiated from other resemblances to the same qualitative content, such as " less bright," or, again, " as bright, but of different colour." Again, "brighter" breaks up by analysis into " much brighter " and " a little brighter," and so on. How far we can carry analysis by such simple comparison depends on circumstances. We shall see later on that a mediate com- parison is necessary when we require mathematical exactitude. Meanwhile there is progress in another direction. " Brighter, louder, heavier," all involve the general relation expressed by the word " more," and " more " and " less " have also a certain community of content, which we express by saying that they give quantitative difiierence as distinct from qualitative. These are the summa genera of resemblance and difference into which aU our apprehensions of likeness and difference fall. Thus the conceptions of quality and quantity are simple generalisations of the various resemblances which we find given among the facts of .apprehension.^ ' It is, perhaps, best to make these two the only ultimately distinct kinds of resemblance and difference, and to treat difference of degree as a union of qualitative and quantitative difference — a quantitative difference which is also qualitative, or a difference in quality which is merely one of quantity. It RESEMBLANCE AND IDENTITY 113 4. We can now understand that an idea may be definite and yet admit of much difference. Take a content like " green." All greens are not identical ; but green is a definite idea, for one green differs from another ia certain determinate directions, e.g. in saturation or in intensity. Greens may also differ ia actual greenness, in quality proper, within certain limits. ISTow the idea green asserts or suggests any content within these limits indiscriminately, and if you say " The sea is green," you assert only that the colour of the sea falls within these limits, without assigning it a more definite place within them. Ifevertheless, so far as this is concerned, the idea is precise. It is indefinite only so far as its Hmits in any direction are not precisely fixed. For example, where is the minimum saturation point below which green becomes white ? or where is the line which marks it off from blue and yellow ? In neither direction can the limit be fixed with absolute precision. But a very small step in either direction along the spectrum wiU make us at once say " blue," or " green," as the case may be. The idea is definite in this direction in proportion to the narrowness of this debatable ground ; and, as we have already seen, the exist- ence of such debatable ground does not in the least make green less truly green, or blue less truly blue.^ It may be said (and up to the present chapter we have our- selves assumed it) that what makes an idea definite is the presence of some point of identity. In aU green there is an actual point of identity " which makes it green." In aU colour there is a more attenuated identity which makes it colour. This may be so, but we still require analysis to point it out. If I ask you what then is the common point in aU colour, you •will answer probably, " Why, it's — colour." You will not be readily able to isolate this "colour" in the concrete colours given you, and say what part of the given is to be set down to its account. If you make a further effort to define it, you will come back to the point you started from, and say that it is precisely that in which this tint is identical with all other would be an error, however, to suppose that the conception of degree could be constructed out of quantity and quality in the abstract. Its value is merely that it recognises certain given facts of a special character, and it is from these facts that it is derived. In the genesis of all three conceptions we may note two movements : (1) the discrimination of the point of comparison, e.g. of the quantitative as opposed to the qualitative aspect of the thing ; (2) of degree of resemblance in the points compared, e.g. quantitative proportion. The con- ception of quantity and quality could not be called complete without this power of measuring differences within them ; and so far the conception of degree (in the sense of nearness and remoteness of resemblance) is involved in that of quantity or quality. 1 Of. Lotze, Logic, bk. 11. chap. ii. § 183. 114 DATA colours, as against those properties which it shares with some only. Meanwhile, if you have studied the matter a little, you will be able to tell me what resemblances this tiut exhibits. It has its own place in the circle of colours somewhere between red and blue ; it has such a degree of saturation, and so much luminosity — all of them definite points of comparison between it and other colours, and the general idea colour includes all contents differing from one another in these ways only. Now, I am not arguing against the existence of an identical quality in all colours, but I say that in the existing state of our know- ledge such an identity is less definite and less easily assign- able than the resemblances and differences in which all colours stand to one another ; and that the colours themselves, in their analysed relations of likeness and difference, form the most definite content for the general name colour.^ I conclude that when you say that a thing has colour, you assert of it a content which may vary within the whole range thus specified ; and the idea of colour taken by itself suggests of reality an indefinite number of facts resembhng one another in certain definite ways. To put the point in a slightly different way. Admitting an identical character in all colours, and calhng it, without attempt at definition, simply colour, we must admit that in the different tints which we see this common character is itself modified. Colour itself is differently qualified in red or in green. The scalene and the equilateral differ as triangles in those very features, relations of sides and angles, on which their character as triangles depends.^ Contrast two patches of sunlight which differ only in the place on which they fall, or two notes which are distinct only in time. Here the time, place, or other characteristics qualify the whole which is given, but can scarcely be said to modify the colour or the sound, as colour or sound. We have come once more on the contrast between specific modifications on the one hand and mere differ- ences of context on the other. The first may be said to qualify ' This, it must be remarked, does not make the conception of colour more, but rather less useful in thought. Though I treat colour as a reference to any and every kind of shade, this reference remains indefinite, or, as we might put it, disjunctive in character, and, accordingly, when I predicate colour of an object, I assert only that its character falls within the limits of this disjunction. This is not fuller, but, if anything, poorer information than would be contained in the predication of a definite attribute, however abstract. This, however, seems our only resource when the universal is not capable of being constituted a distinct element for analytic attention within the whole which it qualifies. " This is illustrated, e.g., by the fact that the straight line is the limit of the obtase-angled triangle. In the same way the ellipse, as we modify the relations on which its elliptical character depends, passes into the straight line at one extreme, or into the circle at the other. RESEMBLANCE AND IDENTITY 115 the general content itself ; the second, to be further qualities of the sensible wholes to which they belong. Now we cannot draw a hard and fast hne between the two cases. The merest difference of context tends to assume a specific value, and to become a modifying character. Thus the texture of the coloured object would be naturally taken as mere matter of context ; but the scarlet of a smooth ivory ball and of a soldier's coat, scarcely " look " the same. Even the heat of the sun and the heat of the fire might be said to have distinguishing charac- teristics ; and the " same " note on two differently built instru- ments will, of course, present distinct peculiarities. It is enough to notice that the different " cases " in which a content may be present vary in the way in which they affect the content itself ; and that in proportion as this affection diminishes, the easier it becomes to get at a distinct general content of precisely similar character in all cases in which it is reahsed. While in the converse cases the general idea tends to mean a series of contents which, while retaining a common character, must also differ in point of that character along certain definable lines. To sum up. Both identity and likeness (of all kinds) are relations originally given in apprehension. Ideas may be founded upon either, and so long as different forms of Likeness are not distinguished, ideas are vague ; that is, the mind does not discriminate their contents from any similar contents. Forms of resemblance are compared, and give rise to ideas of them, discriminating different forms with increasing accuracy, and also discerning resemblances, with the result that differ- ences are finally grouped under the heads of quantity and quahty, differences of degree coming under both. Differences in any point admit also of being classified according to the nearness or remoteness of the resemblance, and identity is distinguished as the maximum of resemblance. When these distinctions are clear, ideas also become definite ; their con- tents are either identical in every application, or vary within known limits, which can be defined with an exactitude varying according to the nature of the subject and our know- ledge of it. We thus get two great genera of definite general ideas, those with an identical content ^ {e.g. the middle C of a •piano, cobalt blue), and those admitting definitely ascertained differences {e.g. a musical note, colour). The knowledge of identical contents is the basis of measurement, and, therefore, of mathematics; the knowledge of degrees of quahty, and affinities among qualities, is the basis of any systematic science ^ More strictly a content as nearly identical as possible. Absolute definite- ness is, I suppose, an ideal. 116 DATA of nature. And this definiteness of knowledge rests simply on further combinations of the comparative judgment applied to the comparative relation, as weU as to the things compared. 5. The simplest instances of likeness of any kind, exact or inexact, are, of course, those which we call purely " sensible " — the taste of two sorts of jam, the matching of two colours, the " identical " pitch of two notes. "We have already seen that some degree of analysis is requisite for the detection of these simple resemblances, and it is a further stage of analysis — further, because deahng with a more attenuated character of the whole — when we attend to resemblances of quantity, equality, or proportion. Yet another stage of complexity is reached where the data of comparison are themselves complex. The contents compared are then results formed either by construction or analysis, and on this the analysis which con- stitutes the comparison has to supervene. Thus the judgment, " In these two triangles the sides about the equal angles are reciprocally proportional," involves attention first to each pair of sides, and then (abstracting from the actual lengths, etc., of the sides) the selection of the proportions of each pair as the point of comparison. Construction and analysis may go to any degree of complexity in affording us points of resemblance. Thus it is right to say that two systems of forces which produce the same motion have a common character. But what is this character ? Not any one direction or quantity of any one force. We may have only one force in the first system and a hundred in the second, or we may have a hundred forces in each, acting at first sight in aU manner of directions. There is stiU. this one common point — that, if we sum up and consider together the totals of the forces, their directions and amounts, there will be as between all the components of each total a relation expressed by the fact that their resultant is of such an amount and direction, and this resultant will be common to the two. In cases like this we can in some degree " reconstruct " the totals, assigning their elements and the acts by which they are brought into comparison. But who can analyse resemblances of face, of personality, of style, of national character ? The data here, the constructions and the analyses, are too subtle for recognition j but there is no need to regard them as funda- mentally different. We may then look on analysis as an essential feature in comparison, and construction as commonly concerned in it; and calling those comparisons "sensible" which rest on the simplest and slightest analysis, we may say that resemblances become "intelligible" in proportion RESEMBLANCE AND IDENTITY 117 as the constructions and analyses involved increase in com- plexity. 6. A word must be added here as to the senses, already referred to, of the term identity. I have used it in this chapter as a synonym for precise or exact resemblance (Gleich- heit), and I think that that usage is in English unavoidable.^ But I should be sorry to give any colour to the charge of con- fusing this kind of identity with that which we predicate of one thing in two relations, or of one person at different periods of his life (Identitat). Quite different contents of perception or thought are before us in these cases, according to my view, which I will state, avoiding controversy as far as I can.^ "We have then three relations. (L) Exact hkeness. We have seen that hkeness in general may be often resolved into partial identity, which we must now call an exact likeness in some one point ; and, for the sake of argument, we may assume that in theory this must always ultimately be possible. In any case, any consideration of such likeness as still admits partial difference will force us presently to the consideration of a likeness which is more precise or com- plete. What, then, is to be said of the relation of complete likeness ? Take the objects which have served as a proverbial example of this relation — a couple of peas. These two peas are precisely, in all respects, alike. Can this be so ? It may be said — (a) it is impossible. The chances are infinity to one against it. That they should differ in weight or colour, or size or texture, by ever so little, is infinitely more probable ; and, however little the difference, difference it will stiU be ; and if there is difference, then resemblance is not complete. This may certainly be true of the actual peas in their entirety, but can scarcely be said of such elements or characters of them as we perceive. The differences of weight, colour, size, or texture, if there, are imperceptible to us. So far the argument would not militate against complete resemblance between contents of our perception, memory, or thought. And even apart from this, if two contents, M and m, differ in some respects, they may be precisely alike in some others, as /i, and thus the ^ See on tlie terms, and for a general discussion of tlie subject, Mr. Bosan- quet's Knowledge and Reality, pp. 97 ff. ' This method seems best in view of the manifold verbal misunderstandings which have inextricably intertwined themselves with real differences of meaning. It is, however, as well to state that what follows in the text is written with reference to Mr. Bradley's Logic, esp. bk. ii. part i. chap. vi. ; and Appearance and Reality, p. 347 ff. ; James' Psychology, vol. i. chap. xiii. pp. 528 ff. ; the above cited controversy between James and Bradley, and the above passage cited from Mr. Bosanquet. Cf. also MOl, Logic, bk. ii. chap. ii. § 4, and Mr. H. Spencer, Principles of Psychology, pt. vi. chap. vi. pp. 58-64. 118 DATA resemblance though the product of a further abstraction is stUl precise.^ But (/3) is not complete resemblance a contradiction in terms ? For resemblance surely involves two terms that resemble one another ; and these terms, if two are distinct, and if distinct then diiferent, and if different then not completely alike. But the attribution of resemblance to two objects, of course, involves distinction. That I imagine to be taken for granted by anyone who uses the words, understanding the English language. But what is the distinction? It is one which we call numerical. There are two peas, or two contents fj., and as two they are distinct. But then are they not differ- ent ? Certainly, in one sense. They are two. But as regards their character or quality they do not differ. The two peas do not differ (for our perception) at all : M and m do not differ, so far as ,a is concerned. This is expressed by saying that the peas are completely alike, M and m completely alike, so far as jh is concerned, or precisely similar in the point /*. Then, have we two contents which differ without being different? Well, we have two contents which are distinct in niimber or in existence, but are not different in quality, and if you like to make a verbal puzzle out of this you can. But is it only a verbal puzzle, or does not numerical dis- tinction involve some kind of qualitative difference ? Go back to the peas. If they are two, clearly they cannot occupy the same space at the same time. Conversely, if two contents really do occupy the same space at the same time (as we might say the colour of that marble and its coldness are referred to the same space) then, ifso facto, to be two they must be qualitatively different. If, therefore, we speak of contents as being two and yet qualitatively alike, we must clearly admit them to occupy a different position in the space-world or in the time-series, or in both. But difference of position means also difference of relations ; and are not relations attributes of contents ? We are again in a dilemma. A, and A^ are exactly aHke : but as alike they are distinct ; as distinct they are differently related, say in space, to B. This difference of relation is a qualitative difference ; therefore Aj and Ag are not exactly ahke. The puzzle might be answered on more than one line. We might say, "It is true that Aj and A2 do not completely resemble one another, if you take those words strictly. Any two contents must as two differ in something ; but when they differ only in space or time relations we call them exactly alike, because this is the minimum difference possible." Or ' The attempt to deal with the question empirically is justly ridiculed by Hegel, Wissenschaft dcr Logik, vol. iv. p. 44. RESEMBLANCE AND IDENTITY 119 again, to justify our language, we might question the propriety of treating a relation as a land of quality. The qualities of A, we might say, all belong to it as such. They appear when we attend to A, and would appear just the same if we could con- centrate our attention on A to the exclusion of all the rest of the world. Its relations, on the other hand, depend on B or C as well. Now, what we meant was that A^ and Aj were exactly alike in their qualities, although their relations are different. But neither of these answers — though the second, at least, is just — goes far enough. We must insist that resem- blance not merely admits of difference, but implies it. We have been told this in slightly different language (identity being substituted for resemblance) often enough ; but what has not been made sufficiently clear, I thitik, is what sort of difference is implied. A loose or inexact resemblance (Aehnlichkeit) may go along with qualitative difference; a complete, perfect, or exact resemblance impHes a difference of position in the spatial or temporal series, and in that alone. It is false, then, to say that resemblance cannot be complete because the positions of the resembling pair must be different. For the relation of complete resemblance implies and contains this difference of position. (ii.) Now take identity, and observe the contrast. I predicate identity when one whole has many attributes, or when one content stands in two relations. " The triangles A B C, B C D have the side B C in common." What is asserted here is not that there are two sides B C quahtatively alike, equal, but that there is one side, B C, common to two triangles. That is, two wholes (A B C, B C D) have one part actually in common, are partially identical.^ Now take the M and m, which are partially identical, as each having ^, and what do we find ? Two cases of /a. Take A B C, B C D partially identical, as having B C, and what do we find ? One B C. We express the differ- ^ We may think of the identity as predicated (a) of the wholes A B 0, B C D. Then it is a partial identity, an identity in the part B C. Or (/3) of the part B C. Then we are taking B C as a whole, which has two aspects, its relation to A B C and to B C D, and our judgment is analytic — that one whole contains two aspects. What we cannot do, as I think, and as most authorities seem to hold, is to judge B C=B C, without taking B C either at successive moments or in different aspects. I say "judge" advisedly. Of course we can say B C = B C, and take it in no sense at all. We must therefore accept Hegel's doctrine, op. cit. bk. ii. 1, chap. ii. A, Werke, vol. iv. pp. 29-36, that all genuine identity (in whatever sense) involves some difference or distinction. Hegel's result here is sound and valuable, though his reasoning cannot always be taken seriously (see, e.g., p. 32). It is unfortunate that the phrase identity-in-difTerence should have passed into a kind of catchword applied to every conceivable content of thought ; especially since, as a rule, no attempt is made by those who use it to specify the kind of identity or difference in question. 120 DATA ence by saying that the two instances of ix are exactly alike, while B C is one fact in two relations ; or that the identity of IL is qualitative, that of B numerical. The two cases are as distinct as one is from two. (iii.) Identity is predicated in yet another sense, when we say, " That is the same man whom I saw at this very spot yester- day." I should consider myself to have been wrong if you proved that it was his brother, and only very Like him, though I might still say, " Well, it's the same face," meaning now a qualitative sameness. That is to say, however much likeness affects recognition, I do not, by the same tnan, mean a very similar man. I mean one man; I mean that the man now before my eyes and the man of yesterday are one. It is, again, a kind of numerical identity that I assert, but with this differ- ence, that difference in time (and perhaps in space) is not excluded. Before, when there was numerical identity there was actual overlapping in space and time. We had two wholes with a part in common. Now we have two contents separated in time. The oneness in this case, then, must be something extending in time or space, or both, beyond these contents, and includitig them. It is the sort of oneness which we call continuity ; and where continuity is excluded, we do not attri- bute identity in this sense. This cannot be the same table that I had in my old rooms, for how could it have got here ? I must be convinced, not of the closest resemblance, but of continuity of existence in a single unbroken thread, before I allow it to be the " same." The metaphor is not inappropriate, since material continuity in space is also a ground of "identity." We are holding the same thread in a tangled skein, not if both ends are qualitatively ahke, for presumably many of the threads are that, but if there is a physical con- tinuity from my end to yoxirs. It is beside the mark to answer that continuity implies likeness. It is true, I imagine, that some likeness exists between the oak and the acorn, or between nineteeth-century England and the England of the Conquest, or between the Thames at London Bridge and the Thames at Lechlade. But the resemblance may be far less than that which unites " numerically different " things or persons. Two babies are more ahke than either baby to his grown-up self. And dimness of resemblance does not interfere with complete- ness of continuity in development. In short, complete resem- blance does not prove continuity.^ Continuity does not prove ' When you "swear to identity" on the ground of resemblance, the infer- ence, notoriously unsafe, ia based on the rarity of certain combinations of qualities. Probably there are no two human faces exactly alike, so that RESEMBLANCE AND IDENTITY 121 complete resemblance. And even if you could argue either way, they are different in idea. Continuity, numerical oneness, and complete resemblance, then, seem all to be different ideas. But is it not aU a matter of abstraction ? Go back to M and m, and consider only the element /i. We have two /i's. Yes, but disregard their setting. Then we have identity ; and thus it may be said the reference in a general idea is really to an identity, not to a plurality of similar objects, since the idea considers the context apart from its setting. Should we not say, then, that identity in one kind of setting works out as resemblance, in another as continuity, in a third as numerical oneness ? Well, we may say this if we Mke, but we shaU be ignoring very fundamental differences ; and, what is more, we shall be carrying abstraction further at one poiut than at another. For in the case of numerical identity, the unity of the connecting link is given at once by the analysis of the pre- sented content. Nothing has to be ignored in order to recog- nise it. In the case of resemblance you must determine to overlook the duahty in order to get at the unity. And as to founding any serious argument on that unity when you have got it, you might as well argue that you have had no cake, on the ground that you have eaten it. As to the idea, it certainly disregards quahtative peculiarities of different " contexts " ; but if and in so far as it disregards all numerical plurality, the generality of its content is not expUeitly realised. The content may be called general when regarded in isolation, because, so regarded, it is the basis of the resemblance which constitutes generality. We have therefore called it potentially general. But if there were no resemblance there would be no generahty. You might still take things in the concrete, or take their elements in isolation, but the one would be as " particular " as the other. The quasi-generahty of actually iudividual contents (Solomon, Coeur de Lion) rests, as we have seen, on this, that other thiags, taken as isolated contents, become general, and the same possibility is transferred to them. If, then, the ideal content is a numerical identity, it is not general ; if general, it is not an identity. The three ideas of complete resemblance, numerical identity, and continuity, all tending to be expressed by the same phrases, are to be kept clearly distinct, and we shall use the above three phrases to distinguish them whenever necessary. ' ' identification " is more possible there than in most instances, though we have all experienced comedies of errors. If you swear to a marked sovereign, your accuracy rests entirely on the improbability of anyone else affixing an exactly similar mark. CHAPTEE IX I. The Qualitative Judgment The term judgment is frequently used as a general expression for any kind of cognitive act. But two characteristics com- monly attributed to the judgment appear incompatible with so wide a use. The judgment is generally taken to be an act of thought which employs ideas/ and which is directly expressed in the proposition.^ I have tried to show in the preceding chapter that there are cognitive acts which do not employ ideas, and which are not directly expressed in propositions. Thus the apprehension of the present fact is (on my view) a form of knowledge, but quite distinct from the judgment which describes it, and needing some further intellectual act to render it expressible in the proposition. I have therefore thought it best to use the colourless term assertion for the general expres- sion required, restricting the term judgment to the species of assertions which employ ideas, and are directly expressible in-a sentence. Taking the judgment in that sense we have now to consider its general characteristics, i.e. its contents and con- ditions. We shall raise the questions thus defined for certain great classes of judgment separately, and then put our results together. THE JUDGMENT OF QUALITY 1. Beginning with the qualitative judgment, we may put aside all difficulties as to its form. " It's pouring," " Fire ! " " Too bad ! " " Row it hurts ! " " What a pity !"— are all of them as much judgments descriptive of a quality of a present fact as the orthodox S is P. That is to say, they are so if they are meant so. The question between judgment and exclamation Hes in the intention rather than in the form, though he who uses the set form commits himself, as it were, and cannot so well plead that he does not make a statement. At the same time, the full , ^ See, e.g., Bradley, Logic, I. i. 10. " E.g. Sigwart, § 5. THE QUALITATIVE JUDGMENT 123 form, " This is a hippopotamus," " This is blue," gives us the different elements in their most analysed form. Let us ask, then, what is the content of such a judgment ? An obvious answer would be something of this kind. The fact referred to is something present to our observation (" this ") ; its character is expressed by the predicate ("blue"); the copula ("is") being the sign of affirmation. We are asserting a definitely characterised present fact. If it be asked, how, then, does judgment differ from simple apprehension ? the answer might take two forms. First, it may be said, the detection of the character " blue " implies analysis of the given ; and if, secondly, it be objected that still this is only analytic attention and not judgment, the answer may be that there is, in fact, no difference at this point. Analysis, it might be said, is a judgment ; a judgment becomes a proposition when we name what we judge. Naming, then, in the sense of applying a term already significant, is the new activity involved. Here, then, we have arrived at a point of departure, and now at once a deeper question arises. What is the act of applying a name ? What does it assert ? The name we found above to be a symbol, and he who names a thing asserts that that symbol stands for that thing. So far, then, our result would be that the judgment recognises (a) the character of the present content, and (&) the appropriateness to that character of a certain symbol. There is this much truth, then, in the old nominalistic theory of the proposition thsXprimd fade its content is the relation of a symbol to a reality. This relation, again, is present simply as a felt appropriateness of word to object. And so much at least the judgment must assert. But if this is the beginning, it obviously cannot be the end of our account. For what, analysis must first ask, is this felt appropriateness of a symbol to a given object ? On what does it rest ? A symbol, we have seen, expresses or stands for an idea ; when we present a symbol to ourselves we mean some- thing else ; instead of directly and explicitly representing this something else, we fasten on the symbol. The symbol, then, or name is a mere cover for an idea ; and if a symbol is appropriate to an object, it must be because the idea whose place it takes corresponds to that object. Here, then, at the second stage, we come to another old theory, that a judgment asserts the correspondence of a fact to an idea.^ And this view, again, expresses at least one side of the truth. When I judge " that is a protococcus," the idea of an organism of that kind must be in some way present to me, however much it tends psycho- ^ logically to be merged in the perception on the one hand and ' See, e.g., Sigwart, § 9, pp. 63, 64. Each is " one in content " "with the other. 124 DATA the name on the other. So far, we do not go beyond an apprehended correspondence of perceived facts on the one hand, and our idea represented by a name on the other. But this account again cannot be ultimate. For the idea which we use must have some definite basis, and we must have some purpose in using it. Now an idea means something, that is, contains some sort of reference to or suggestion of reality. This reahty must then somehow fall within the judgment, or be by it brought into relation with the present fact. What this reality is, and what the relation is, we may discover by attending to the proposition, and considering now the value of the symbols, i.e. the full meaning of the terms which it employs. Let us take the three words, " this is blue,"^ and begin at the end. Blue is a general name, the name there- fore of an ideal content. That is, the word taken by itself asserts or suggests a content common to various parts of the series of given facts, without specifying what facts. " This " is the name for the present as present. It has, that is to say, a general meaning like any other term, and its equivalent is " present." When a thing is " this " it is present, the general quahty of being present is expressed by the word. So far, then, we have " this " = the present fact, " blue " a content already otherwise known to qualify reality. The connection between them is given in the copula. What does the copula assert ? That may be got either by analysing the verb " to be " independently, or by inquiring what relation we are actually aware of between " this " and " blue " ; and then (since our proposition is simply the attempt to express this relation) inferring that the use of the copula means or can mean (we need not hastily assume that the copula always means the same thing) just that relation. Take the second method first — what is the relation ? Here is a content quahfying reality in an indefinite number of instances ; and here, on the other side, is a particular individual fact. How are they connected ? Is it by resemblance ? This will carry us a certain length. " Blue," it may be said, is a reality already known as existing. It has been presented to me at sundry times and in divers contexts, and from these presentations I have by comparison and retention formed it into the content of a general idea. It means to me a fact which has qualified my reality. Now " this," again, is a fact of apprehension, and what do I find ? That it resembles the fact already determined and ' Judgments of this type, which are real acts of thought only for an infantile intelligence, form the best examples of the qualitative judgment. Other instances used in this chapter, though suitable for present purposes, often con- tain implications which would in strictness carry us beyond judgment proper. THE QUALITATIVE JUDGMENT 125 named " blue." " This is blue " then should mean, " This re- sembles the reality to which the name blue refers." This account would not (I believe) lead us far wrong. But it omits a point of importance. It tacitly treats the idea (or name) as standiug for a given reaUty — the experienced instances of the general attribute. To these experienced in- stances the present fact enters as a new case, and the relation between them is, truly, that of resemblance. But the idea and name, it must be recollected, are general. They refer to no definite section of experience, to no single set of cases or period of time, to the exclusion of others. The general content is already suggested of reality as a whole. Future or possible cases, as well as actual or past instances, are within the terms of its reference. We are therefore bound, as it would seem, to take the new case, not as an outside fact related to it, but as actually falling within and exemplifying the general content itself. The relation, then, is rather that of identity than resemblance. But the identity is not absolute. The general content is not confined to this particular case, but extends to others — what others, how many, when and where found, is not in question, but others. The present, then, is one case of the general content. It is, we might say, identical with one part of it, and so the relation expressed is one of partial identity, or subsumption ; or starting from the side of the general, we may say that it is applied to the present instance. Our result, so far then, is, that the quahtative judgment, taking the full meaning of the symbols used, asserts that a present fact is in virtue of some of its features a case of a general content. But, now, if we examine this result we shall see that it is not so far removed from the interpretation of our judgment as ex- pressing resemblance. For what is the general content ? You may take it, on the one hand, as something existing " in my mind," and expressed by the class term. Then the " subsump- tion " would assert the correspondence of this present fact among others to the "mental" content or its symbol. But this analysis is substantially that from which we started. We saw at once that the judgment expressed the relation of a symbol (and that imphes an idea) to a real present object ; and our question has been, what more this symbol means. Considering this meaning, we found that it is a reference to a general content ; and what is a general content ? Something which is realised in many individual cases, or, to put it the other way round, a number of individual facts resembling one another. What, then, is the real fact asserted when we subsume a new case under a general ? We may phrase it so that the new fact 126 DATA appears as one of a number. But it would be misleading to put it in this way if it suggested that the number was a more or less definite series in which the individual had some place more or less definitely assigned it. There is no question of " inclusion " in a class, if a class is like a bag into which you put your sponge.^ What, then, is asserted ? Simply resemblance to other individuals.^ That is the true character of reality, with which the qualitative judgment deals. Then why not have accepted our first analysis ? Because that limited the individuals to which the judgment refers, and defined them too far. The resemblance asserted holds not only between the given and certain facts already presented, but is valid for an indefinite number of facts past, present, or to come. This potentiality of resemblance is the point at stake when, as in this judgment, we treat an individual fact as general. It is a stage in the reduction of facts to an order of resemblances and differences, a stage in which the mass of facts to which the present is correlated are stiU left indefinite. This indefinite- ness we shall see in part removed by the comparative judgment which so far renders the content in question more explicit. 2. So far, then, for the content of our symbols. If, in the qualitative judgment, we " mean all that we say," we are taking an apprehended fact, analysing it, and discovering it to be, through one of its elements, an instance of general content.^ Beginning by treating it as an act of analysis, expressing itself in a name, we have been forced to consider what this name implies, and to include its implication in the content of the judgment. The judgment, then, has a dual character; it is first an act of naming an analysed content ; and, secondly, if we examine it further, an act of subsumption. But this position is not free from difficulties. The subsumption (assuming the correctness of our account) is implied by the terms used in our proposition. ' This, of course, is the oonoeption of class predication against which Mill's polemic {Logic, bk. i. chap. v. par. 3) is, quite rightly, directed. The class is simply- constituted by and dependent on the possession of the common attribute, and far from being a definite collection, it is of indefinite extent and destitute of order. On the other hand, the ideal content has extension, i.e. plurality of application, and this makes it a basis of resemblances. And this element in its meaning must not be neglected, but must form part of the whole implication of any judgment which employs it (cf. Bradley, Logic, bk. iv. 1, chap, vi., esp. the summing up in par. 21). ^ Resemblance, more fully, of this element in this given content to elements in other wholes. ^ I speak indifferently of the concrete fact or its analysed characteristic as being an instance of, or subsumed under, the general. In the same way we speak indifferently of the subsumption meaning ultimately a (relatively loose) resemblance of this wJwle to other wholes, or a (relatively exact) resemblance of this element or attribute to other elements. THE QUALITATIVE JUDGMENT 127 But is what is implied to be taken as actually asserted ? If, from the spoken proposition, we go back to its mental equivalent, what shall we find ? Shall we get a direct reference to a general character of reaUty as including this instance ? Shall we get the content of our symbols realised adequately, or even at aU ? And if not, can we strictly say that that content is actually asserted by him who utters the proposition ? The difficulty is not an idle one, and arises, I imagine, on any theory of the judgment and its import. We wish to measure the content of the judgment by means of the proposi- tion, and we feel that the two ought for a careful thinker to correspond. Yet everyone knows that words are used and sentences uttered habitually, with a very imperfect reahsation of their meaning. It might be objected that such sentences no more concern us as logicians than Aristotle's drunkard who could roll off lines of Empedocles, or Mrs. Gamp's patient making up a string of names. But to take this line would be to ignore what we must almost caU the normal relation of thought and language, and to omit from our view the great majority of the judgments which men actually make. For, however much logic might demand that every assertion should directly, explicitly, and completely reaUse the content which it asserts, our actual thoughts as often as not occupy themselves wholly or partially with symbols. Just as in Chapter VII. we saw that symbols acquire a fixity of meaning by a process which is gradual and at first unconscious, so here we must admit that in their employment by the adult, words may be used with imperfect consciousness of the meaning which is the only logical reason for uttering them. Analysis may show that a proposition would be meaningless or impossible unless certain things were true and known to be true. Logically, then, those things are asserted ; but it does not follow that they enter into the explicit purport of the judgment which expresses itself in that proposition. So it is in this case. The content of a general idea is one which must be applicable to many instances in reahty. But it does not follow that that plurality of appli- cation is mentally referred to whenever we employ the general idea. On the other hand, the idea, as we have seen, may merely suggest a content of reality without reference to its repetition in many instances; but if the content is, in fact, known to be repeated, if we at different times do actually apply it to case after case, then it is a de facto general content. Now this is the case with the idea used in the qualitative judgment. The present fact is identified with a content which is de facto general. If we give the whole meaning of this content, its 128 DATA generality must be brought out. But we may use the ideal content without actually realising its whole meaning. Nor is this all. What we actually use in the judgment is not necessarily the ideal content at all, but only its symbol, the name. The symbol takes in our thoughts the place of the reality for which it stands; and thus in the judgment our actual consciousness seems often to be concerned, on the one hand, with the given and its character as detected by analysis ; and on the other, with the feeling of familiarity attaching to this character, and the consequent appropriateness of the term used. But, now, whether or no the full imphcation of the words is actually represented by the mind in the act of judgment, it must be admitted to influence and, in fact, determine that act. This holds even for the exclamatory or interjectional use of language. The child who cries " gee-gee," or the man who exclaims " lightning," make no conscious reference to a general characteristic of things. They are concerned with this horse, this flash only. But, first, why do they utter these exclamations and not others ? Because of previous experiences in which the same general content has appeared and has had the name applied to it. Thus, whatever they know or think on the subject, the de facto correspondence of the general and particular is de facto influencing them. Secondly, why is the name understood ? Again, whatever may be thought by the hearers, the de facto conditions are precisely the same. The content symbolised, then, is at least the condition both of the use of the symbol and of its being understood. We have then before us the upper and the lower limit to the meaning of the qualitative judgment. Taken as an ex- plicit assertion of all that its words mean, it is a recognition of the present as a case of a general content, that is, as a centre of resemblance to an indefinite mass of facts. Taken at its lowest, it is an assertion of the appropriateness of a name determiaed by the fact that the present is a case of a general content. In either case the relation of the general content to the present object is the really operative condition ; but how far it actually enters into the sphere of conscious thought is a question which would require a different answer for every judgment which we make. The actual judgment moves wit hin the limits assigned. At its higher stages, where the generality of the idea used becomes explicit, a definite reference to other cases begins to come in ; and as soon as these cases are defined or individualised we pass into the comparative judgment. On the other side, where the felt appropriateness of name to object gives way to merely mechanical utterance, we fall from THE QUALITATIVE JUDGMENT 129 judgment into the sphere of exclamation. Between these limits the qualitative judgment is to be foimd. 3. Certain difficulties in the above view remain to be dis- cussed. To begin with, how can we " identify " the present fact with the general content ? What is the present fact ? It is not only blue, but various other things as well. It is rough, oblong ; it is placed in such a position, it is a particular shade of blue ; and, again, it is not all blue, but has spots of black ink on it. These are serious drawbacks to calling it blue without any qualification. Still they do not interfere with the apphcation of the general attribute properly imderstood. Every fact which I can call blue, from the summer sky to a pair of wintry hands, has a certain vague resemblance ; and so far as the idea of blueness is confined to this vague point of resemblance, it may be correctly applied to any one of them, differences being left out of account. But to effect this we need an act of analysis to pick out of the whole that is given the quality blue which is common to other objects. When this is considered, the relation is seen to be a degree more complex. There is the selection in the whole presented of a certain element, implying a distinction of part and whole, and then a subsumption of the part under the general content. The relation then becomes a partial identity in a double sense. The given as having such a quality or element is a case of a certaiu general content — that is now the analysis of our judgment. The one term of the relation then itself involves a relation. This relation, however, is merely the selection within the present fact of one feature marking that fact. That is, to determine the subject of the judgment we do not need to go beyond the present. The ultimate starting-point on this side is the present fact. It may be objected with some cogency that the present fact is rather a vague term. If I mean by it something definite, like the back of a book which I am looking at, can it be said that that is aU that I am aware of at present ? It may be occupying my attention, but even so there will be a " fringe of consciousness " beyond it ; and, further, does not the formation of the quahtative judgment precisely correspond to the con- centration of the mind on one part of the present, the selection, in short, of "this" from its surroundings? We may admit much of this, but observe at the same time that there is a change in the process of selection corresponding to our description in Chapter III. The picking out of the book from the vague mass of the present is a simple concentration of attention. A fringe of consciousness no doubt remains, but has no logical connection with the content apprehended, and 9 130 DATA has no interest for the attending consciousness. But when in the content now attended to, the book, we pick out a characteristic blueness, the whole content remains a matter of interest to us. It is of it as a whole that we make our asser- tion. The analytic act of attention gives us an element in a whole, and the qualitative judgment asserts an identity based on this element. The judgment is about that whole which is occupying attention. If we are asked, then, what is the ultimate subject in the qualitative judgment, we must answer that in the simplest case it is the whole present on which atten- tion is concentrated. The mind does not here make any reference beyond the present ; so far as the subject is concerned no knowledge is necessary for the mind except the knowledge of this whole. It is not determined or made clear to the mind by its relation to anything else. But must it not be distinguished at the very least from other contents ? It must certainly be distinct, but it does not follow that it must be distinguished. To distinguish a thing may mean simply to contemplate a thing " by itself," not to confuse it with other things. This is certainly needed, but involves no presentation or representation of a relation between this thing and others, being, in respect to other things, a purely negative state of mind. To distinguish a thing in the sense of knowing its distinctness, of knowing how it is distinct, and from what, involves knowledge of its relations to other things. Now I must distinguish the present fact in the first sense, but I need not in the second. The apprehension of the total present or the concentration of attention on a part of it, is not the same thing as apprehending or knowing its relation to other contents. These relations, and the distinctions involved in them, become clear when the facts are brought together in one act of thought, as by memory. The distinction depends on the bringing together of two facts given separately ; their being given does not depend on their being known as distinct. My apprehension of the present cannot in anyway be con- stituted by the relations between it and other things. They do not determine it, but it determines them. The position of the present is not known as being after something which was, but that which was is known as before that which is. I do not buUd up my knowledge of the present by finding out relations between it and other things, but I start from the present in determining other things. These simplest judgments are represented verbally by the impersonal form or the interjectional judgment. " It's a bad job "or "first!"; or, still better, a baby's "da-da," "gee-gee," THE QUALITATIVE JUDGMENT 131 contain no symbol specifying the position of the content in reality. The interest is concentrated on the content and its character, that is, on an element of the present fact, and nothing further is under consideration. When the subject is designated by "this" or "that," it must be allowed that a shght change takes place. "This," we have contended, has a general signification, viz. that of presence. So far there is no indication of other things. But bearing in miud that words are used for purposes of communication, we must ask why we have to designate the present as " this," and we shall have to answer, that it is because the present is not the only reality, and that our hearers' attention may not be concentrated upon the fact which interests us. So far, then, a distinction from other facta is implied in the use of "this." But this distinction implies no reference to the definite character of such further facts. The present is taken as a fact within a wider reahty from which it is marked off. What that reality may be does not concern the truth or value of our judgment. Nor does the reference to it belong to the genesis of the judgment as such, — for the simplest cases are without it, — but to the wider con- structions of reality into a spatial and temporal order which go on fari passu with the formation of the judgment, and force it to define itself with reference to them. The qualitative judg- ment, then, takes a whole of apprehension (which in the most exphcit case it distinguishes from a wider reality), and, analysing out some element of this whole, subsumes it under a general quality ; or if we start from the other side, it appUes a general quahty to an element taken as before. As to its explicitness, this analysis is in much the same case as the general idea. There is a parallel development. From the beginning the given must really be analysed so far that the quality named is distinctly present to the mind ; but that it is a quality, an element in a whole, which is the " this " that we see, becomes explicitly admitted only as we realise that the object attended to is more than that which we predicate of it. The form appropriate to this stage is that in which the (grammatical) subject is designated by a class name ; when for " It is hot," we substitute " This water is hot." There is a still further develop- ment, but in a direction which soon takes us beyond the q[ualitative judgment when the perceived object is taken as related to others. The lowest grade here is a simple but explicit distinction, " That book (not ihis) is the one I want." This is stUl in the region of the qualitative judgment. 4 We have assumed so far that the judgment has only to analyse the given in order to bring it under the general idea ; 132 DATA and this may perhaps be taken as holding universally for the class under consideration. But we must observe that the relation of the idea employed to the fact given may vary materially. In " It is quite warm," the attribute subsumed under the general idea is an actual element in our perception ; nor is anything further stated about the present content and its remaining attributes than is already present. In " He is livid with fury," his appearance is given, but not the emotion prompting it. On the strength of the appearance you apply an idea which carries you beyond the given, and asserts of the present fact some further characteristic not strictly observed. Ordinary judgment does not observe this distinction, but logically it carries us over the boundary line into inference. In concrete thought the distinction between ideas which do and those which do not "extend" the present, i.e. assert of it attributes which are not given, is difficult to draw with precision. It is often hard to say how much is given and how much the idea really contains. The theoretical distinction is clear enough. A Subsumption which adds nothing but itself to the present, i.e. which states the conformity of the present to a general attribute, is judgment. If it adds more it is logically inference. But the inferences do not cease to be judgments ; they still subsume, though they do so on a different basis and with further results than the judgments hitherto considered. This understood, we need say little of the case where the qualitative judgment does not rest on observation at all, e.g. when I judge the character of the present or past on the strength of another's statement. The basis of the judgment is altered, the judgment is the same, viz. that the present ^ or past fact contains an element falling under a general content. In this case we should call it, not a subsumption (as of some- thing already given), but an application of the idea to a fact occupying a position in reality determined by the demonstrative taken in connection with my relation to the person using it. Lastly, recognition does not differ in its elementary form from a qualitative judgment. "We recognise primarily by character, and so the act of recognition is a subsumption of the present under the already experienced content which the proper name means for us. " Da-da " is properly a recognition, " gee-gee " or " puff-puff" a qualitative judgment ; but either of these last are recognitions, if applied day after day to the same toy. Obviously at this stage the difference only exists for a more developed consciousness, i.e. it depends on the distinction ^ The present here should mean present to the speaker, not to me. The distinctive force of "this " is here at least essential. THE QUALITATIVE JUDGMENT 133 between the natures of the individual and universal, which is not contained in the judgment as such. 5. The content of the judgment now being imderstood, let us consider its conditions. These are, first, the apprehension of the present fact; second, knowledge of the general content; and, third, the application of this content to the fact. The last two demand further analysis. As to the^ideal content, we have already seen the conditions of its formation, viz. analytic attention to be given, comparison (resting on the constructive activity of the mind, or on mere apprehension of similarity), and, of course, memory. As to the presence of the idea in the mind, we must not be led into assuming too much. The case is similar to that of memory. An individual apprehended fact is retained, not in the sense that it continues to exist as a perma- nent state of the mind, but in the sense that it leaves permanent effects on the mental structure, such that an appropriate stimulus will cause it to be asserted as a past fact. At least no further condition than this is impHed by memory. As it is with the individual, so it is with the general content. The idea is present or continues in the mind in the sense that the mind can again assert the same content. When we speak of the presence of the idea as a condition of the qualitative judgment, we accordingly mean that perception must act upon a mind modified by the past assertion of an ideal content in such a way as to be capable of reasserting that content, and that the act of perception stimulates to such reassertion. The third condition also demands notice. The idea must be applied to the present content. The idea itself is the suggestion of a certain content, the apprehension is the assertion of another. The application of the one to the other means the assertion of the two as one whole. General and particular content with the partial identity involved are asserted together. That is to say, we have another case of construction, the assertion of a whole of which the elements are or have been given. I do not mean that in a qualitative judgment you necessarily place the idea before you, as though it were an image, and so compare it with the given. I mean only that just as " this " means the present, so " blue " means the general quahty; and so also the whole judgment means the subsumption of the present under the general quality. The act of forming the judgment, then, as distinct from the antecedent conditions, is an act of construction joined with an act of analysis applied to the given content. Lastly, in choosing a name, that is, in connecting a special symbol with a given content, judgment involves inference. But 1.34 DATA here we may make a diBtinction. So far as the process under- lying the choice of words is concerned, inference has no place. The knowledge of the relation of the given content to the general attribute, or of its correspondence to the idea as a mental state, is given, not by inference, but by memory and construction. Inference comes in with the choice of the name. So far as a fixed symbol uttered or not enters into judgment, so far inference is involved. So far as the comprehension of the real relation on which the symbol is based can be separated from the symbolism, we may speak of it as judgment proper, and deny that the judgment - function as such depends on inference.^ The quahtative judgment, then, would be ex- plained by the factors of knowledge already distinguished being the result when they are combined in a particular way. To sum up. The qualitative judgment overtly and pro- fessedly names the present content as something familiar. In BO doing it imphes the appropriateness of the symbol used; and this involves the presence to perception of a character corresponding to an idea already entertained : this correspond- ence involves the subsumption of the given under a general content ; and this subsumption, again, means the resemblance of the given character to any other case in which the ideal content may be realised. Any part of this content may enter into the explicit purport of the judgment. In its higher stages the judgment assigns to the present a definite place in the series of given facts. The conditions on which it rests are apprehension, analysis, memory, and construction ; while, as correctly expressing itself in a proposition, it involves infer- ence. An essentially similar judgment may be based on remembered or constructed contents, instead of simple analysis of the given.^ II. The Compaeative Judgment 6. In the Quahtative Judgment the second or non-pre- sented term is a general content attributed to reahty without specification of when and where. Substitute now for this an ' Inasmuch as symbolism or verbal utterance is rather the mechanism, and the relation of ideal and present content the essence of the qualitative judgment, this use of terms seems justified, and will be adhered to. For this reason we have already distinguished judgments which do from those which do not involve inference in the real relation which they assert, as well as in the usejof the terms whereby they assert. The former class are inferential in respect of their most important features. 2 My chief debt in the above account is to Messrs. Bradley and Bosanquet, though I also owe much to Sigwart, and, of course, to Mill. THE QUALITATIVE JUDGMENT 135 individual fact apprehended or remembered, and we get the comparative judgment. The qualitative judgment implies the existence of individuals resembling the present fact, for without them the idea would be nugatory, as an idea of some- thing never realised. But it does not specify any such facts, it does not hold them up to view together with the present. This is the work of the comparative judgment. We have already touched on this form of assertion, but must now treat it rather more systematically. Simple or indefinite comparison deals merely with the relation, the resemblance of the two contents compared. To effect this it is not necessary to use a general idea. The resemblance may be given or may be " con- structed." In either case it is an individual relation, if we can speak of such a thing, existing between two individual facts. Nothing general or common to other facts enters into considera- tion. It follows that this assertion does not strictly faU within the limits of the judgment as we have defined it. When I say, " That leaf is darker than this," I make a pro- position ; but then I am designating the contents compared by general names, which imphes that I view them in the hght of general ideas. Besides, it is worth noting that the proposition just quoted is'scarcely a fair example of indefinite comparison, since the word " darker " implies an analysis of the points of resemblance and difference. This shows us that only the crudest comparisons, involving simple hkeness and unhkeness, fall strictly within the province with which we are dealing. " These hats are like the fashion of ten years ago," is a fairer example. Here, then, all that turns the assertion into a pro- position is the designation of the contents compared by the names of the hats of to-day and the hats of ten years since, in addition to which it must be said that the relation of vague hlieness has itself become an idea, and is symbohsed by the term "resemble" or "hke." But every act of mind, from apprehension upwards, is turned into a judgment by applying general ideas, and into a proposition by applying general names to its content. And the question whether an assertion is a judgment, is to be settled by asking, not whether it is expressible in a proposition, but whether it is so expressible without the mediation of ideas unnecessary to the assertion itself. According to this test, simple or undefined comparison is not a judgment, but is antecedent to the formation of judgment, inasmuch as it has a hand in the formation of ideas. Defined comparison not merely asserts a resemblance between two contents, but asserts it on the strength of an analysis. Its scheme is A x, as having A, is like A y, or the A 136 DATA of A X is like the A of A y. " These colours are alike in tint, or in intensity, or in saturation." " These notes are of one pitch, of different timbre." " John is as tall as James " ( = is like in height). All these cases involve analytic attention, and com- pare the wholes on the strength of the analysis. But even among these we must make a further distinction. If I judge A X to be like A y in A, that is a true judgment, because I apply the general idea A, for which I have a general name, so that my judgment is at once the basis of a proposition. But if the point of resemblance is not an idea already known to me, the comparison is not a true judgment. Doubtless it results immediately in the formation of an idea for which I endeavour to fashion a name, an endeavour always made by language when new observations give it new general contents. But the idea beiag formed pari passu with the comparison, cannot be regarded as applied by the comparison. Whence, if judgment involves the application of an idea, defined comparison in these cases is not a true judgment. Let us then distinguish the cases in which an idea is applied as comparative judgments from both defined and undefined comparisons in which an idea is not applied. With regard to the conditions of these forms of assertion, comparison (defined or undefined) has already been shown to depend on an act of construction. The comparative judgment involves a repeated construction — of the relation of the two quaUties to one another, and of the conformity of both to the general quality contained in the idea. 7. Comparison and the qualitative judgment in their several stages imply one another. If " This is A " means anything, A must be an idea already referring to some other reality, Aj, and Aj must be like A. Conversely, if A is like Aj, it is generally to be supposed that they both can be subsumed under a general idea a. Here the undefined forms of com- parison and of the qualitative judgment are seen involving each other. Passing to the higher forms, " This contains the quality A " equally implies resemblance in point of A to other things, and conversely. Finally, the comparative judgment proper is an analysis both of the comparisons and the qualita- tive judgments preceding it. " A is the common property on which rests the resemblance between A x and A y." This justifies the qualitative judgment, "This (A y) is A," by explicitly declaring the comparative relation to another indi- vidual fact necessitated by it. Similarly it fixes the point of resemblance in A x and A y as the definitely known content A. The set of facts with which both qualitative and com- THE QUALITATIVE JUDGMENT 137 parative judgments have to deal is the presence in reality of a general quality existing in an indefinite number of facts, forming, in general, a part only of the content of each, and constituting a resemblance between all of them. We may dis- tinguish two main aspects of this set of facts — (a) the exist- ence of the quality ; (6) that of the relations of resemblance. With one or both of these aspects all the mental operations of which we have treated in this connection are concerned. Thus— (i.) Analytic attention asserts the existence of the quality of the given, without deahng with its resemblances or thinking of it as a general quahty. (iL) Undejined comparison asserts the relation of resem- blance between two facts present or past, without specifying the quahty on which the resemblance rests, (iii) Defined comparison rests the resemblance of two facts on a common quality, without referring that quality to a general idea, (iv.) A general idea is a reference of a quality given in defined comparison (as common to two facts) to reahty as a whole, (v.) Qualitative judgment asserts a quality of the present as conforming to the content of the idea, (vi.) Comparative judgment asserts resemblance of two or more facts in point of a known general quahty, or asserts a general quahty to exist in two or more facts. This order represents the increasing definiteness or exphcit- ness of knowledge in this direction, the higher forms at each point making use of some or all of the lower. In the final stage of the developed comparative judgment we have, in a kind of miniature, the whole accoimt of that part of the nature of reahty with which this series of operations deals ; we have, namely, the explicit recognition of the general content, present over and over again in the world of existence, determining resemblances between the particular facts in which it is found. The lower forms of assertion lead up to this by expressing various parts or aspects of the general con- ception. All these assertions rest ultimately on the four con- ditions of knowledge hitherto distinguished — apprehension, analysis, memory, and construction. I do not mean that many actual quahtative or comparative judgments may not involve further factors, such as inference. " That is a man " always, I think, does, and yet it would generally be classed as a very simple qualitative judgment. But these judgments do not, apart from their verbal expression, necessarily, or as such, 138 DATA involve inference; in many cases inference supplies part of their data, but not always. These forms of thought would remain to us if our powers of inference were paralysed; to analyse their nature and constitution it is necessary, if we take inference into account, to observe carefully the lijnits of its function. CHAPTER X The Judgments of Eelation and Desceiption i. the eelative judgment 1. We have seen the qualitative judgment rise to its full degree of explicitness and then pass into the judgment of comparison. This transition is necessitated by the character of the general content, ■which, to be definitely recognised as general, must be taken as applying beyond the bounds of the particular case. Here is already a vague reference to other cases, some of ■which are expUcitly designated in the judgment of comparison. This transition, then, rests on the predicate — to give that name provisionally to the general content employed in judging. An analogous transition is determined by the subject — the individual presented. We have already seen that the subject is the present fact, or a portion of the present. In either case it exists in reality as an element in a continuous world of perception. We have argued that in the simplest form of the subject no reference is involved to this wider reality. Nevertheless, for purposes of communication it is impossible to go far without at least so much reference as is involved in distinguishing this subject from others. And whatever the contents judged, in reality the surroundings must exist. A step onward is taken when they are brought into the judgment, so that the subject is now further deiined, not merely by the attribute assigned to it, but by its position or relation to other things. At this stage we have not, " That book is Pickwick" but, " The volume next to Vanity Fair is Fickioick." The purport here is still to point out Pickwick ; but it is essentially the same judgment, with the shghtest shifting of interest, when I say, "My volumes of Dickens and Thackeray are on the same shelf." We have here a new complication introduced. The perceived fact, which forms the starting-point of the judgment, is no longer a simple quality, but a relation involving two terms. 139 140 DATA The first form of judgment in which this complication arises is that which deals with the relations of facts as dependent on the order of their apprehension. A was before, is simultaneous with, or after B, above, to the right, to the left of B, and so forth, are simple judgments of relation or construction upon which more complicated ones are based. We confine ourselves for the present to judgments whose data are apprehended facts, so that we have only the simpler forms of relation before us. Let us consider how these judgments differ in content and conditions from the qualitative judgment. In the judgment " A before B," when the whole A — B is present to apprehension, we are clearly asserting two distinguishable parts of the given whole, and also the relation between them. Moreover, since each of the three words used (A before B) is of a general character, we are comparing both the parts A and B to some general qualities of reality, and the relation to some general relation. It is not necessary that the whole A — B should be capable of subsumption under some general content a — B; it is only to the constituents of the relation that the ideas must be applicable. Further, A - B taken together will not probably be found to exhaust the whole of the present fact; there is a remnant X which is more or less clearly present to consciousness, as going to constitute the whole out of which A — B has been selected by the analysis of attention. Thus in uniting A and B the judgment might be called synthetic, but in distinguishing qualities in the whole it is even more analytic than the judgment of quality. The reference to the whole may be inexplicit, but may be pretty obviously impKed by the nature of the case. " The cylinders are underneath the boiler," would imply in most cases that a locomotive was the true " subject." To bring the locomotive into the judgment is clearly a very small step. We have, then, as our content, two given qualities as cases of two general qualities in a relation which is a case of a general relation. This at least is the full implication of the terms, which, as in the qualitative judgment, is more or less realised in different instances. Each element is " felt " as familiar, or recognised as corresponding to our ideas. From the content of the judgment the conditions are clear. We have the same factors as were found in the qualitative judgment, excepting only that the act of analysis is repeated. We must, in order to assert a relation, analyse out of the given, not only A, but B, and the relation between them. This repeated analysis gives ground for a repeated comparison, and JUDGMENTS OF RELATION AND DESCRIPTION 141 this is the only new factor introduced by the judgment of relation.^ II. THE DESCEIPTIVE JUDGMENT 2. We may perhaps group somewhat more advanced cases of judgments which we have already had imder this name. In the qualitative judgment we deal with a part of the given whole ; in the relative judgment, with a relation of two parts ; there remains the relation of part to whole, the constitution of the whole by the parts, which is the work, never perhaps adequately performed, of the analytic or descriptive judgment. This judgment combines, in a way, the characteristics of the two others. For the qualitative judgment states a quality of the given whole. But it concentrates attention on one element, and does not attempt to describe the fact as a whole. The relative judgment, again, puts different elements together, but tends to lose sight of the whole to which they belong. The descriptive judgment keeps the whole in view while detailing the parts. Its ideal would be to exhaust the whole nature of the given ; but it is the continual mistake of the analytic mind to imagine itself to have succeeded in this Sisyphean task. We must not therefore confine the name of descriptive judgment to assertions of an equation between the parts and the whole, a complete construction of wholes by parts, lest haply we shall have a class without members. We should caU all judgments descriptive which involve, like the relative judgment, repetition of the analytic act ; but, unHke the relative judgment, explicitly designate the whole to which the parts so selected belong. We have seen already that the relative judgment passes by easy transition into this class, and the transition is represented verbally by the change which makes the whole fact the grammatical subject. The quahtative judgment passes into the descriptive as the qualities selected become complex. Such complexity involves plurality of attributes and relations between them, and thus the descriptive judgment is simply a completed form of the judgments of quality and relation. Any description of a person or landscape, or scene, might be taken as illustrating this judgment. We may add that there is one judgment requiring to be distinguished from the above. It also involves a repeated 1 Cf. on the whole subject, Sigwart, §§ 10 and 12. The judgment ex- pressing the "unity of a thing and its property," etc., in which he finds a "double synthesis," I have noted aa transitional between the simple qualitative and the relative judgment, 142 DATA analysis, but it is a second analysis of the quality already selected. Thus, " That is bluish-green " ; " That is grass-green." Here " bluish " and " grass " seem distinctly to qualify green, and to describe the whole only through its greenness. Green here takes the place of the whole as the " subject " of the judgment, so that the assertion is rather a secondary judgment of quality than anything else. 3. We have already noticed that memory and the synthesis of memories form a basis for judgment equally with apprehen- sion. If I can represent a content in a memory -judgment, I can do with it all that I could do if it were a present fact. I can analyse it and describe its qualities, or I can note its rela- tions to other facts. Every such operation, present or remem- bered, involves a construction or an act of analysis ; but so also would it if it were performed on a present fact. As we have seen, memory-synthesis gives us wholes which we could not have presented to us. One case of such wholes may be noticed here in connection with the judgment based on it. Ordinary memory synthesis puts together facts given in continuity; but our constructive activity is not content with these simple syntheses, but will form a conjoint content of any portions of our memory which may in anyway suggest one another. From this arise the subjects of collective judgments and all judgments of number. " The last three Saturdays have been wet," clearly is not matter of immediate apprehension nor of continuous apprehension ; but the wetness of each Saturday is given by memory, and the combination of them is a simple construction. Thus numerical and collective judgments have their subjects supplied by construction working on memory. It is different when the word " aU " no longer refers to a definite number of recollected individuals, but to an indefinitely extended class. No judgment containing such an idea will be explained from mere memory, or any construction of memories, for it carries us definitely beyond what is either given or remembered into the region of what is to be or must have been. In a word, it rests on inference, and to explain it we must first understand inference. Less obviously, but with equal certainty, every predicate involving a universal conjunction of attributes also involves inference. That X is a man cannot be a matter of immediate apprehension, and scarcely even of memory. Por the conception of manhood involves a complex union of many attributes which cannot be present to a single act of conscious- ness, but which are asserted of the present or past on the ground of their universal inter-connection. Thus so long as judgments rest on the conditions hitherto explained, they would JUDGMENTS OF RELATION AND DESCRIPTION 143 carry us over a limited' field of reality ; but just the same factors and processes, which built up these judgments from the facts of apprehension, are repeated, with various complications for data supplied by inference ; and thus to treat them once is to treat them once for all. It remains, then, to sum up the forms of assertion which we have hitherto described, and to give a general view of their content and condition. We shall then have a general conception of the character of knowledge in isolation from the factors introducing inference. 4. We have had, then, (a) simple apprehension, (&) analytic attention, and (c) memory. All of these may be regarded indifferently as forms of assertion or as conditions of knowledge. The first two assert the present fact only, and give us truth. The third asserts a content which is not present, and may give us falsehood. As condition (d) of knowledge we have had construction, which in its various operations on the contents supplied by the first three factors produces many various forms of assertion, viz. collective and synthetic memory, comparison indefinite and definite, and, lastly, general ideas. Fuither, the combination (a constructive act) of the idea with analytic attention to a part of the present, gives us the qualitative judgment, and, when it asserts the relation between some of the individuals to which the idea applies, the comparative judgment ; with the same attention to a relation of facts it gives the relative judgment, and with the same applied to the relation of wholes and parts the descriptive judgment. All these judgments concern the present. Again, applying analysis to memory-contents we get the same three judgments concerning the past. According to the construction made of memories and apprehensions, we get plural or collective judgments, which, again, may be quahtative, relative, or analytic. Thus, with apprehension and memory as relatively constant factors, the increasing com- plexity of the judgment results from the repetition of the acts of construction and analysis. Such being the factors, what is the result so far ? Briefly, the knowledge of the order and resemblance of facts that are and have been matters of apprehension. A mind equipped with the methods and forms of knowledge which we have so far taken into account, would, if we suppose it to have applied them with ideal precision and completeness, be in much the same case as if it were able to take a bird's-eye view of all that it had experienced up to any given moment. Of this whole, every element would have been given at some time or other ; every part would enter into a continuum, spatial or temporal, or both, and any two or more 144 DATA facts being considered together would appear in a definite relation of time or space, or both; general characteristics would be observable among many parts forming the basis of relations of resemblance and difference ; and, lastly, the " part " considered might be of any magnitude, and not necessarily continuous. Such, broadly, would be the aspect of knowledge apart from inference. The judgments which we have described are distinguished mainly as laying stress on various aspects of the whole. In the actual usage of living thought such judg- ments are made always with more or less reference to such a whole (or even, strictly, to the still wider whole to which inference contributes so much). The qualitative, relative, comparative judgments are all, then, more or less abstractions to which nothing precisely corresponds — types to which thought more or less nearly approximates at certain points. Their affinity and their distinctness are both more clearly seen by a reference to the whole which they constitute, for it is with some special aspect of this that each judgment is peculiarly connected. Starting from any point of thought, we are soon led on to take some sort of view of its whole kingdom. The connected view, extending, so far as memory goes, over the whole of our experience, and analysing and correlating its constituent parts according to their order, their resemblance, and their difference, is the stage on the road now reached. But correlation of apprehended facts takes our belief beyond the present into the past, and therefore renders it an assertion jof a content distinct from and independent of itself. Hence from another starting-point the judgment leads us to inference, for it is only by correlating judgment with judgment that we can find any test of truth leading us beyond momentary apprehension. To sum up, then, the system of belief, so far as it rests on the conditions hitherto assigned, consists of assertions of con- tents which may or may not be real : they rest on one or all of four conditions, apprehension, analytic attention, memory, and construction. The system of knowledge as formed by them, taken alone would consist of a mass of facts classified according to resemblances and differences, coexisting or succeeding one another in a definite order, the relations within which would be likewise classified by their resemblances. To give a newly apprehended fact its position in both these orders of relation, or to determine further resemblances or fresh relations of spatial and temporal order between facts already known, is the work of a new assertion. JUDGMENTS OF RELATION AND DESCRIPTION 145 The whole of this account postulates that judgment and belief are concerned with reality. Eeality, we have argued, means primarily to the mind the fact that it apprehends, and every one of the assertions with which we have been concerned is formed according to our account either by analysing or retaining what is given, or by uniting different given facts in one assertion. All the assertion we have yet had, then, is either of the present or of what has been present, the only quahfication of the latter being that in reasserting facts we tend to take all that has been given as one whole, aU or any parts of which we may assert together. It is clear, then, that all behef is con- cerned with reality, though it is not all true, and there can therefore be no objection to speaking of belief or judgment as a reference to reality. The only mistake to be avoided is the supposition that the contact with reality begins with the judg- ment. Apprehension is already the assertion of fact, of what is real, and judgment only follows in the track of apprehension. The mind is given reality in the first place, and the whole of its effort so far as we have yet traced it is to retain and to sum up the reality which it has been given. CHAPTEE XI General Nature of Judgment Although we have not yet dealt with the higher forms of judgment, we have reached a stage where some of our results may be provisionally summed up, and certain difficulties that have been urged by various thinkers may be considered. Restricted as our view of the judgment has been, it may yet be enough to show us the broad characteristics of that act of thought. For we have in effect explained the essentials of the categorical judgment. It is true that having an eye to the conditions of thinking as well as its content, we have confined ourselves to cases in which the data are supplied by apprehen- sion, memory, analysis, and construction. But the special function of the judgment is not altered by the source from which its materials are derived, and so if we understand what the categorical judgment does with its data in any one case, we understand it in all. Thus a simple assertion like "He is suffering from heart disease," falls outside the classes of judg- ment that we have been considering in respect of its conditions. Heart disease is a conception that could only be built up by means of a concatenation of inferences, and obviously the symptoms on which the diagnosis rests in the present case are known as symptoms infer en tially. But the general content is applied to the individual in the same way as before, though for different reasons. The individual is a case of the general, as before — only the nature of the individual or general contents used is different, and the grounds on which we connect them less immediate. The movement is the same in every cate- gorical singular judgment, and we can now treat of the content of such judgments (apart from their conditions) in general.^ 1 Mucli of what we say will apply also to the universal judgment as far as it is categorical, and even to the hypothetical and disjunctive so far as they involve the categorical as an unit. In fact we treat of the categorical judgment qud categorical, and our results will be applicahle to all judgment forms so far as they involve the categorical. 14G GENERAL NATURE OF JUDGMENT 147 We have then to ask, what peculiarities can be attributed to the categorical judgment, or, as we will briefly call it, the judgment, as such ? What distiaguishes it as a mental activity ? What can be said in general of its content ? 1. Comparing the judgment with other forms of assertion, it is distinguished at once by the use of ideal contents.^ If we suppose — as has been supposed in preceding chapters — that it is possible to apprehend the present or remember the past without bringing the contents so given into relation with ideas, then in memory and apprehension we have forms of assertion that are not judgments, and are distinguished from judgments precisely because they do not make use of ideas. And if we deny the possibHity of making mental assertions without using ideas, that would not modify our present accomit, but would be merely another way of saying that every assertion of whatever kind is, in fact, a judgment. Eetaining the doctrine of the preceding chapters, we may illustrate the character of the judgment by contrasting it, for example, with apprehension. Thus, I listen to the cawing of the rooks outside my window. This, as I describe it, is a judgment, and a judgment because the present fact is brought under an ideal content. Consider my state of my mind as it is (in thought or in actual time), apart from this subsumption, and we have simple apprehension. The application of the ideal content turns apprehension into judgment. Judgments differ according to the ideas which they employ, and the way in which they assert them. But in all cases they assert in one way or another the content of an idea. Thus the judgments considered in Chapter IX., apply an ideal content to data of memory, apprehension, etc. Here an individual fact is given, and its identity with a general con- tent is asserted by the judgment. In other cases, two ideal contents may be brought into relation. " Twice two are four," " All the radii of a circle are equal," " Honesty is the best policy," assert relations between general contents, without applying them to any particular facts. Or the validity of the idea itself may be the point in question, as in the existential judgment, " Faith-healing is a reahty." More will have to be said, and many difficulties may, of course, be raised about these judgments and others ; but in this all agree, that they make assertions containing ideal contents, and this it is which renders them at once expressible in a proposition. Comparing judgment now with the idea itself, we find, amid a multitude of minor differences, two main types of ^ Ideal, that is, in the strict sense of contents which have become definite and constant objects of reference, and therefore nameable. 148 DATA theory as to their relations. To begin with, we have the view, partially adhered to by Sigwart,^ that the essence of the judg- ment is synthesis, — synthesis of two ideas, or of idea and per- ceived fact. " Night," that is an idea, not a judgment, not an assertion, — ours aXn^i's oun -i^iZhoi;, — because not yet brought into relation with any other fact conceived or perceived. " The night is fine," that is a connection, a putting into one of two contents, a avvhai; voTifj,a,Tiiv ; hence there is something asserted, that is, there is judgment. As an exhaustive account of the essence of judgment, this would labour under the defect pointed out by various writers from Mill to Hillebrand, that (a) a synthesis of ideas may remain merely ideal, and (b) a given idea, whatever its degree of complexity, may become the content of judgment without entering into any further connections with other contents. As to (a) it is clear that " the fine night" is no more of a judgment than " night " or " fine." To prove (6) much stress has been laid on the " existential judgment " ; but needlessly, since the case is clear from other instances. "Liberal victory," "The Liberals have won": the connection may be entertained as an idea, suggested to another as a question, affirmed as a fact, but it is the same connection throughout. This brings us to the second main theory of judgment, which defines it as the reference of an ideal content to reality, or the quaUfication of reality by an ideal content. With this defini- tion, as will be clear from what has already been said, we cannot in the main have any quarreL One point, however, should be noticed. According to our view, judgment asserts an ideal content, and to assert a content is for us to assert it of reality. There is no assertion but is a reference to reaKty 6r an assertion of reahty. But it would, on our view, be a mistake to regard the judgment as first introducing the refer- ence to reahty into the idea. We have seen that an idea may mean one of two things. Either it may be a content, picture, image, or in some other way (if other way there be) presented to the mind. In this case it is simply so much present matter of fact, with no reference beyond itself. Or it is itself as such something suggested of or referred to a further reality. If we take the second meaning, it is clear that the reference is abeady contained in the idea in whatever form we entertain it, and is not first introduced by the judgment. Here the judgment merely affirms the idea. Taking the first meaning, the judg- ment does not refer such an idea to reality at aU, but asserts a reality to which the idea or image corresponds. Thus, " Gibbon ^ I do not mean that in Sigwart's view this is the whole of the question. For qualifications, see below, p; 152. GENERAL NATURE OF JUDGMENT 149 formed a very just conception of the character of Julian," confirms a reference to reality already named (i.e. Gibbon's conception) ; " He is the ideal labour-leader," asserts a corre- spondence between a real person and an imagined content which may hitherto have remained a mere imagination, without question of the possibility of its being realised. In neither case does it seem quite accurate to speak of the judgment as instituting the reference to reality. Either the reference is already there, or what is asserted is a correspondence between two kinds of real fact, one of which is a mental image. These qualifications being understood, we may subscribe to the definition of the judgment as the reference of an ideal content to reahty. Nevertheless, some connection of contents (one of which at least must be ideal) is so intimately bound up with the work of the judgment, that it may be fairly regarded as of the essence of the matter. Both the form of the proposition and the history of logic are witnesses to this. In the simplest categorical proposition, both terms are signifi- cant apart from the proposition itself. That is to say, each designates a certain content, and the effect of the judgment is to bring these contents into relation. Thus in " Balbus is building a wall," the subject Balbus refers at starting to a certain reality, and this reality is connected with that referred to by the predicate. Subject and predicate alike deal with ideas already otherwise familiar, the only logical distinction between them being that the subject corresponds to the starting-point of thought,- and the predicate to its further movement. Considering the whole process of judgment from this point of view, we find it to be an act in which the mind begins by a reference to a content, real or supposed, given, remembered, inferred or imagined, and goes on to assert its connection with some further content. 2. Now, are these two theories of the judgment compatible ? If judgment merely affirms an ideal content, can it also be said to connect it with something else ? If it connects it with something else, does it not do more than merely affirm it? The answer is to be found by asking, what idea is it which we are comparing with the judgment ? If the judgment be, " It has been raining for an hour," the whole content might be regarded as a single idea. I may suggest that the rain has lasted an hour, and confirm the fact by looking at my watch. From the entertainment of this idea, judgment differs merely as assertion from suggestion, and thus taking the whole matter, subject, predicate, and their relation as the ideal content in question, judgment is the assertion that this con- 150 DATA tent is real. But " raining," taken by itself, is also an ideal content, and tliis content is connected in the judgment with other facts. Thus, in spealdng of the relation of judgment to idea, you must know which idea you mean. Judgment is the assertion of a content which is ideal, or includes an ideal element.^. This relates the judgment to its total content.^ Judgment correlates an ideal content with some other content ideal or perceived. This relates the whole content to one necessary element, which it includes. In two cases the element of connection seems to fall out of the judgment. The first is that of exclamation, or the imper- sonal judgment. " Freezing ! " " It's lightening ! " may be said simply to affirm an idea, or simply to qualify the present, and on this account some would exclude them from the judgment altogether. We have already seen that the form of expression is not decisive, and that in point of fact the process underlying these expressions often differs only in degree of explicitness from the thought corresponding to the formal sentence. We may note here that the difference of explicitness affects the relation of the elements in judgment. Eeally the data before me, and my thought about them, are much the same whether I say " freezing " or remark, " There is a sharp frost." In either case I have the character of the present given me, and I note its correspondence with a known general quality. These are the elements, and this the relation asserted ; and as soon as the relation begins to be realised, we have the beginnings of judgment. Eliminate the thought of the relation altogether, and we have mechanical exclamation. So far, then, the con- nection of contents is coextensive with the judgment itself. Where no connection is realised in thought, there judgment fails. The second case presenting difficulty is the existential judgment. Defenders of the "synthesis" view have iasisted that we have here a synthesis of the idea which forms the subject with that of existence in general. To this more than one objection has been taken. Can existence, it may be asked, serve as an idea for this purpose ? And if it does, must we not regard other judgments as a double synthesis of subject with predicate, and of both with existence ? And, lastly, is it the fact that judgment introduces the idea of existence, or is that already contained in the idea of the subject ? Starting from the last point, we must at least admit its ' The wTioU content is not always strictly ideal. In the simplest qualitative jndgment, one element is merely apprehended fact. But it must include, and may be entirely composed of, ideal elements. ^ Cf. Bosanquet, Essentials of Logic, Lect, vi., esp. p. 108, GENERAL NATURE OF JUDGMENT 151 possibility. My idea of the ether is not of something non- existent, or existent merely in my head, or, again, "ia some place above the heavens " out of relation to other things, but of an imponderable substance diffused in my actual environ- ment. If you tell me " the ether exists," you do not add the notion of existence to the idea I had before. You merely con- firm a suggestion. You tell me that that is true which I thought possible. Nor is it enough to reply that existence in the judg- ment always means some definite kind of existence {e.g. in space and time, as material, or what not) ; for we should then have to say that the idea forming the subject of such a judgment is really itself a reference to existence of that very kind. The child's idea of a fairy refers to the same real world in which its parents move.^ The idea is a reference, not only to reality, but to the kind of reahty contemplated by the judgment. It would seem clear that it is not synthesis with the idea of reality that turns the subject-idea into a judgment. It is simply the recognition of the suggestion involved in entertaining the idea. In fact, the reference of the ideal content to reahty is here the explicit or formal purport of the judgment. It does not follow that the element of synthesis or relation is absent from the content. Por the idea is not only a sugges- tion, but something that exists on its own account, viz. in the miad of this or that person. The existential judgment refers ia its subject to the idea as such, and affirms its correspond- ence with some further reality. We have iusisted that the existential judgment (like others) confirms a suggestion. It is merely stating the same fact in another aspect when we say that it refers to a suggestion as a thought in your mind, and asserts its correspondence with a reality. Thus, " The hypnotic trance is a real state," exphcitly affirms an ideal content to be real. This may be broken up in two ways : either (a) " Is the trance real ? ■ Yes ! " or (b) " The idea of the trance (already in my mind) corresponds with the reality." And (a) and (&) simply represent the same content split up at different points, for the " the trance " of (a) is nothing else but a reference to my con- ception or someone else's. The existential judgment is, in fact, a case of the judgment which recognises the truth of some other belief. " What you suppose is true," is much the same as, " The thing you imagiue really exists." The existential judgment thus asserts a relation. But the relation is no more than the reference contained in the subject-idea itself — the relation of a mental act to a reahty beyond it. Hence this judgment is the ^ I know a child who wants a pumpkin in order that the fairies may change it into a tram ! The mixture of poetry and prose is instructive. 152 DATA limitmg case where the assertion, on the one hand, and the relation into which the idea is brought, on the other, coincide. The element of relation still remains in its content, but it is merely the relation (of reference to a reality beyond itself) already contained in the subject-idea. It would be false to describe this as either a synthesis of two ideas or a connection of two ideal contents. It is simply the affirmation of a reference contained in a single idea. The peculiarity of the judgment is that an idea (as something in your mind or mine) is itself the object of reference in the subject, and then some- thing further is said of the idea, viz. the reference it contains is affirmed. This judgment, then, like others, while affirming an ideal content, stOl says " something of something," predi- cates, affirms a relation ; but not a relation of two ideas or two ideal contents. In particular, it does not predicate anythtag of the content which it asserts as real.^ Hence, if the question be, what is the relation of judgment to idea ? our answer must be that an idea becomes a judgment when its content is no longer suggested, but asserted of reahty. On the other hand, the content asserted, or some part of it, must, if it is in the strict sense ideal,^ be already in some way known — and that is why it can be referred to by a fixed name. A necessary incident of the assertion is therefore a correlation of what was previously known of the content with what now be- comes known. Hence the necessary distinction of subject and predicate in the judgment, of which we shall presently treat.^ ' The existential judgment may be said to establish a reference of one kind of reality to another. We get a close parallel in "Lord Steyne was a real Eerson," " The execution of Bernardo del Nero is historical," for these characters elong to an "ideal world" of their own, and only by these judgments are brought into relation with our ordinary "real" world. They already present the relation of ideal and actual, and shoidd not be confused with "CHve Newcome really marries Ethel," which merely affirms a point left doubtful by the novelist, but refers always (as Mr. Boaanquet says) to the ideal world of Col. Newoome and Lady Kew. ' Ideal contents, we have seen, are normally general, and hence we may speak broadly of the judgment as necessarily implying a general content. But what is actually essential is that the content predicated should be an object of fixed and determinate reference, common to the knowledge of speaker and hearer. This is the case with the individual, which is common to many facts of ex- perience, and many experiences, but is not bond fide general. Hence the proper name judgment, "Here is Leeds," "That is Mr. Gladstone," employs an ideal but not a general content. ' This account, though mainly based on Bradley {Logic, bk. i. chaps i. and ii.) and Bosanquet (Introduction and chap, i.), is not, on the whole, opposed to Sigwart's, to which it also owes much, if we take the doctrine of §§ 5 and 9 in close connection with the insistence (§ 14) on belief in the objective reality of the content. Here, at least roughly, we have all the elements requisite. Brentano's view, adopted by Hillebrand {Neuen Theorien der Kategorischen Schlilsse, pp. 26, 27), that judgment is essentially the Anerkennung of an GENERAL NATURE OF JUDGMENT 153 Our conclusions, so far, may be briefly restated. The whole content of the judgment may generally be put as an idea, and from this idea the judgment merely differs as assertion from suggestion. Again, in the content, one element at least must always be ideal, i.e. an object of fixed reference, and so nameable. The content involves a relation of this element to some other, and thus assertions, not involving a relation and an idea, fall outside the judgment. 3. Treating judgment as the acceptance or assertion of an idea, and " idea " as involving a suggestion of, or reference to, reahty, we see that the difference between judging and enter- taining an idea turns out strictly to be one of modality, and modality enters into the essence of the judgment. The mere idea is the reference simply taken up and entertained by the mind. This is ou^rw B to denote that A is always followed or accompanied by B, and ^ .' to denote a variable relation) — (1) M— -►N (2) (3) K /\ M N I (5) ,^U NUMERICAL PROBABILITY 305 of inference. To use it, we should have to know not only the frequency of N and 0, but the extent to which their conditions coincide with those of M, and the absolute frequencies of those of their factors which do not coincide with those of M. But in one particular case the law becomes very simple, and by starting from this simple case we may deal with others which are more complex. For supposing M and its antecedents con- tain no conditions at all which would lead to IST rather than 0, or to rather than N, all further inquiry into antecedents may be dispensed with, and, according to our law, the frequency of M — N and M — will depend solely on the frequency of IST and themselves. This, then, is the law of probability in its ordinary and workable form: the frequency of a con- junction between elements in no way connected with one another^ will be proportional to the frequency of those ele- ments themselves.^ The converse law is also applicable — if ^ More strictly, in no specific way. M's causes may contain conditions which go towards producing both N and 0, but this for our purposes will be equivalent to "no connection at all." We need only that there should be no element leading to N and not to 0. '^ Jevons' argument (Principles of Science, ii. 10), that probability can give no guidance to actual frequency, fails to distinguish two very different cases, (a) I may know very little about the degree of connection between two events. They may, in fact, be rigidly connected, wholly incompatible, or related in any other way. But, so far as my knowledge goes, it favours their conjunction as much as any other. Now here the true theory certainly does not assume that the rate of frequency can be known. But (;3) without knowing all the con- ditions of two conjunctions we may know just this much, that the closeness of their connection is equal. Then the theory does say that the frequencies will be equal. And, conversely, as we shall see more fully later, if the observed frequencies are unequal, we deny that the degrees of connection can be alike. Jevons himself slides into this admission when narrating his own experiment with coins ; he concludes: "The coincidence with theory is pretty close, but considering the large number of throws there is some reason to suspect a tendency in favour of heads." When I add that the actual figures were 10,353 heads instead of the calculated 10,240, we see that Jevons is influenced by so small a deviation as 113 in over 10,000 throws. Sigwart (Logik, § 85) draws the distinction missed by Jevons, but rules the case of known equality of conditions out of the true theory of probabilities. But how in this case he gets at his process of reduction by which he argues from given frequency of combination to its most probable cause in the conditions which would most likely give it, I cannot understand. Grant that the conditions, if real, would most probably give that frequency, what we want to know is, whether that frequency most probably postulates those conditions. To be sure of this we must postulate that frequency depends on certain definite conditions, namely, closeness of con- nection or absolute frequency of the members conjoined. If we do not make such a postulate, I do not see how we can argue from the fact of frequency to any conclusion at all. Has not Sigwart been misled by his "reduction" theory, which involves the conversion of the hypothetical judgment ? In fact, at a later stage (§ 101), when dealing with reasoning from statistics, Sigwart distinctly lays down the principle for which we are contending (see esp. pp. 518, 519, vol. ii.). But if this principle is not the law of proba- bility (and Sigwart still distinguishes it), on what does it rest ? 20 306 INFERENCE the elements are equally frequent the degree of connection will be proportionate to the observed frequency of conjunction. That is, if M - N is more common than M - O, either the ante- cedents of M and N" have more in common than those of M and 0, or the elements which they do not share in common are the more frequent factors in the conditions of N. How far this deduction is of value in inference we shall consider later. But is it so ? Toss a penny half a dozen times. Heads and tails are always " there," and what is there in the tossing to bring down one uppermost rather than the other ? But are we bound to get three heads and three tails ? Do we actually find the equality postulated ? And if not in six instances, do we find it in ten or twenty or in how many ? We must answer : (1) Exact correspondence is never expected, and may never take place ; (2) approximate correspondence is not expected for small numbers ; but (3) where the chances are really even, the actual numbers approximate to those calculated as the total number of instances taken increases. This statement may be formulated, that if in any series of trials the actual and the calculated numbers do not correspond, a larger series can be found in which they approximate more closely.^ (4) For our own part, if we do not find this to be the case, we give up supposing the chances to be what we thought them. If, as ^ It has been urged by Lotze {Logic, bk. ii. chap. ix. § 286) and others, that the correspondence of calculated and actual frequency can never be "a real fact of observation," since it is only realised in the infinite series. Lotze adds, rightly enough, that if " in an experiment we reach a point at which the two numbers coincide ... it would be a very arbitrary procedure to break off the series just at this point." But granting that exactitude could only be found at infinity, that is neither here nor there. We have said nothing about exacti- tude, but deal with approximations. And even as to these approximations we make only an approximate, i.e. a rough statement. I have tried in the text to make that statement as exact as possible. Another way of putting it would be, that the fluctuations of observed events about the calculated frequency can be expressed by some such a curve as below — where the "trials" proceed from left to right, and the calculated number of "successes" falls always in the lineAA'. From what follows, it will appear ultimately that the approximation must be close for finite areas, if the conditions are given as equal for those areas. Lotze's argument {loc. cit. Eng. trans. § 286), that you cannot argue from experience to the permanence of the approximation, is accepted in the text. But we shall see later that, given the theory, we can argue from experienced frequency to a similar rate in other oases. How Lotze, while denying the theory, can tell us that the frequency of an event must have some kind of constant cause (see § 287), I cannot understand. The whole point of our NUMERICAL PROBABILITY 307 the result of 1000 trials, I threw sixes 56 times (i.e. about double the " right " number), I should infer pretty confidently that the dice were loaded. If I threw them 100 times I should be " sure " of it. If you ask me at what point I become sure, I can only say that you may as well ask me, like the old sophist, how many grains constitute a heap or how many times form a " lot." All I know is, that I " begin to suspect it " pretty soon, and my suspicion grows by slow degrees into certainty. It is a matter, not of definite certainty at any one point, but of a gradually growing strength of conviction. 6. Still, it may be urged, this does not answer the real ques- tion. Granting that the law of probabUities only exacts an approximate conformity to calculated results, and that even this conformity is only to be found over a wide area, and grant- ing that such conformity is on the whole found in some iastances, what proof have we that it will obtain in all ? Granting, once more, that we for our part postulate it in all cases, it still does not appear that we are justified in doing so. It might even be urged that this argument involves us in a vicious circle, for if any given collocation does not correspond to our calculations we at once reverse our judgment about it. If A - D is on a long series of trials more frequent than A - C we conclude that the chances are not really equal in the two cases, but that A " favoiirs " D. Hence the very instances that would negative our law are put out of court by our arbitrary assumptions. There are, however, two possible ways of proving a general assumption. One is by enumeration of iastances — and thus the law of chances would be proved by taking all, or some very large number of cases, and showing that the calculated results are verified in them all. This course is obviously impossible in our present case, and would undoubtedly involve the circle just suggested. In dozens of cases we should find that things which we set out by supposing indifferent to one another turned out to be very frequently conjoined. Such cases are primd facie exceptions to our rule ; unless or until each one of them were disposed of by some quite different method of investi- gation, we should have to admit them as exceptions. In fact, tlieory is that the frequency of a oonjunotion, like anything else, must be determined. Sigwart's argument {Logik, § 85) against Mr. Venn's admirable ■work is ingenions but scarcely fair. It is true that the calculated average will be exactly realised less often than it is approached, taking all cases of approxi- mation together. This does not militate against the view that approximations will be realised, and that after any deviation the series will return towards the average. I should have thought Mr. Venn's statements on this point were sufficiently explicit (see, e.g., Logic of Chance, pp. 90-100, and in {a.ct passim). 308 INFERENCE the general truth of the law of probability cotild not possibly be proved by observation until we knew everything about all manner of causal relations. Another resource remains — that of connecting the present assumption with some other established principle. Such a principle we may for the present take the law of the ground to be. Not that that axiom may pass unchallenged. It will have to give some account of itself in its own turn later on. But for the moment it may content us that the said axiom is less likely to be challenged, and in fact (if our analysis is correct) it cannot be denied at all unless reason itself is rejected. If, then, we can connect the law of probability with this axiom we shall explain it, and justify those who hold it, and judge of things by it rather than of it by things. According to this axiom, every fact must have an universal antecedent, in the widest sense of the word fact and of the word antecedent. Now, any given conjunction A - B is a fact, and so again is the frequency of such a conjunction in a given area of reality. Such frequency, e.g. the repetition of so many wet days in a month, is as a single fact no doubt the result of a construction, but that does not exempt it from the necessity of following some imiversal antecedent. The same is true of comparative frequency ; that, again, is a fact requiring explana- tion, as we recognise when we ask why there are more wet days in the West Eiding than in Lincolnshire, or why there are more male births than female. Now compare any two " indifferent " relations A - B and A — C in a given area of reality, and let the frequency of A - B exceed that of A - C. What can be the cause of this ? There are three alternatives. Either 1. The internal character of A — B and A — C, which must be such that pairs of facts so characterised must always ^ obtain the given frequencies of conjunction ; 2. Some external fact P favouring A — B ; 3. The absolute frequency of B and C. The absolute frequency being given, the question is between the character of the facts related and a possible outside cause. But the first of these alternatives is impossible. If neither A nor any of its antecedents is such as to produce B rather than C in any given case, how can they have this effect in a ^ I.e. either in any area in which they are examined or in the universe as a whole. We shall see that only this second meaning can be actually fulfilled by other than universal relations. Merely "general " relations preserve the same proportion of coincidence in every area only under equally favourable circumstances. NUMERICAL PROBABILITY 309 plurality of cases ? how can they account, then, for those cases by which the frequency of A - B exceeds that of A- C ? The supposition contradicts itself. If two conjunctions be indifferent, and one of them more frequent than the other, the cause can- not lie in the nature of the conjunctions themselves. It remains that the greater frequency of A - B is due, not to A and B as such or universally, but to a third fact P. Then if P makes A - B more frequent, — adds to its frequency, — it must clearly cause it either universally or in certain instances. That is, it must be an antecedent or part of an antecedent of A or B or the relation between them. Then take A as given, and we may have A in the presence of P producing B or bringing B into the given relation with itself. Or again, A may follow on K, and K be such as with P to produce B. In either case the frequency of A — B wUl depend on the frequency of P ^ when P is the single condition required. If more conditions Q R are required, the result will depend on the frequency of Q and E as well as P, but must in any case be less frequent than before, depending on the conjunction P Q E instead of P. Then the frequency of A — B will depend on the closeness of their connection, as before defined, and our general "law of probabihty" is justified. If we know, by whatever method, that the " chances " are equal for B and C, we have a right to infer that they will be equally frequent. A converse application follows. From the facts of frequency we can argue to degree or nature of connection. For in any given area, i.e. in any number of instances or in any particular part of space or time, the frequency of A - B must have its determining cause. And the frequency found must either be universal or it must be due to some P which favours B rather than C. Hence the variations in the frequency of a conjunction foUow the varia- tions in the other characters of different areas. And if no " P " can be assigned for the area given, we ought to generalise the rate of frequency for all areas. 7. But here an important distinction arises. P itself may be an expression for some single fact or for a collocation of cir- cumstances. By a single fact I mean one which, whether simple or complex, is universally coherent, so that if we have ' For let Q give the contrary result (A - C) and be equally frequent ; then by our first argument the combinations K - P and K - Q wiU be equally frequent. It might be said that P may be specially connected with K by some E ; but here, again, the same question will arise. K-R will not be more frequent than K - Q, unless either K is more frequent or K contains conditions of E. In the first case, P wiU be more frequent than Q, which it is not ; in the second, there will be a further link of connection between A and B, which we assumed there was not. 310 INFERENCE any one element of it we have all the rest. If P is of this character we have our single cause to which to refer the fre- quency of our conjunction. Thus, in an earlier instance, frequency of fever was explained by bad drainage, i.e. a single permanent set of facts which once begun continue of them- selves, i.e. under certain negative conditions, universally. In such a case a variation is " explained," i.e. resolved into one of the known unvarying causal sequences. But P may also, ia its turn, be an expression for a certain individual collocation of facts, a^y & . . . none of which deter- mines another,but which have come together in this instance, and make up the individual character of the " area " under investi- gation. Thus, when we begin a game of backgammon, the dice are lying on the board in such and such a way ; you take them up with such and such a movement, depending on this and that stimulus of sight or touch. This determines how you throw them into the caster ; and they describe a curve in falling which determines how they are turned in the caster itself. Similar combinations infinitely subtle follow on, determining every step until the die is cast. Here, again, we have a combination of apparently disconnected facts, yet each with its own train of connections working upon one another. This double possibility as to the character of P introduces a difficulty into probable arguments. At first sight it appeared that, if I found a certain rate of frequency for a given com- bination, I could either generalise that rate or lay down that some special cause existed in the area examined, determining it for that area. And this cause, at least if the variations in fre- quency were great, so that its operations would be on a large scale, ought not to be difficult to detect. But we now find that the cause in question may be no single fact on which we could at once lay our hand, but a concourse of dis- connected events which come together here but perhaps nowhere else. How then are we to tell, in any case, whether such a " congeries of events " exists or not ? How far this difficulty can be surmounted in arguments from frequency we shall consider further in the next chapter. We may suggest here some considerations to which the theory already laid down would seem not unreasonably to lead us. Take any conjunction a — b. We have shown that in the absence of a connection it depends on the frequency of a and b separately. Let it occur m times in a given area. Similarly, b - c may occur n times. Clearly, either of these combinations must, if each be indifi"erent, exceed in number the more com- plex combination a - b - c. Similarly, a - b - c will be more NUMERICAL PROBABILITY 311 frequent than any a - b - c - d. Hence, in the absence of any connection, the more complex combination is invariably less frequent (and, as calculation shows, very much less frequent) than the more simple. Hence, if a given result involves a complex combination of many antecedents, it will be rare. And conversely, if a given " casual " combination is frequent in a given area, it is more probably due to a " single " cause (as above defined) than to a combination of causes.^ Thus the recurrence of a particular hand at whist is vastly improbable, owing to the great complexity of the circumstances which pro- duce it. And conversely, should it recur, it is a lamentable, but probable inference, that a single human agency has pro- duced it in both instances. It would require a very complex com- bination of undirected bumpings and rubbings to shape one piece of flint into an arrow-head, so that arrow-head flints so formed would be rare. And conversely, if many are found together, the probabilities are great that all the rubbings and bumpings that produced them were due to a single connected cause. Lastly, if a collocation C is operative in a given area, the more complex it is the less frequently will it recur in other areas as weU. If the conditions are really equal, it will, in some other area, give place to r, which results in a - c instead of a - b. And hence, over many distinct areas, equal conditions will produce equal frequency. The same holds in theory of a single disturbing cause P, but we shall presently notice a practical difficulty in applying the theory in this particular. If, then, we are comparing conjunctions for which the con- ' We cannot here enter into details with regard to the degree of probability assignable to the inference, but we may remark — (1) supposing our choice to be between two hypotheses to account for the abnormal frequency of a combina- tion, the first involving a single, the second a combination of n causes ; and assuming, further, that a cause of the combination is as likely to occur as not, then the first case ia more probable than the second, in the ratio of -^ ^""^ ! but (2) this second assumption may be very unreasonable. If a combination a - b is rare — if, say, it only occurs once in ten instances of a — it follows that a cause of a - b occurs only once in ten instances of a cause of a. The ratio of probabilities now is rjr to r-77j, a ratio which gives a high probability to the first alternative even for low values of n, and for high values an overwhelming probability. If (3) we have not to do with rival hypotheses, but have no hypothesis to offer, then, in any case, («) the inference to some single cause is more probable than any other single inference ; (/3) taking the probability of the occurrence of any cause as J, the supposition of a single cause is as probable as all remaining suppositions combined ; (y) taking it as ^° ^^^ ^^ °^^ evidence goes, we have every reason to take their effects in the new context A as still different. The counter suggestion, that just in the context A they might in some respect work out a similar result, is thus ungrounded. It is an unmotived possi- bility. If it rests on anything, it must be some concrete feature in the character of the facts concerned, against which those who applied the method in such a case would of course take their precautions. Apart from this, it may be dismissed as ungrounded. And that their total effect should be similar is impossible. From this point of view, then, our method seems capable of establishing; a true universal relation to the full degree of unchallenged certainty which we require. To illustrate. The D line appears in the sodium spectrum whether the sodium be pure or an ingredient in another substance. Yet the different substances in which sodium might be present, so far as they contribute to the spectra, give each of them, so far as our evidence goes, different bands. If we supposed any two of them to co-operate with the sodium in forming any portion of the spectrum, the two spectra so formed should, in respect of that portion, be different ; but in fact the yellow line is constant. Similarly, take any law you please, holding true of energy in different manifestations, of substance in different forms, or of life under different circum- stances ; to attribute the common result whether wholly or in part to the difference in the manifestations, forms, or circum- stances, is obviously the height of unmotived absurdity. If the law of multiple proportions holds for all substances examined, that is obviously not due to the special character of those substances, for qua special each substance has its own peculiar (i.e. different) effects. If the rate of expansion is equal for all gases, this cannot be due here to the lightness of hydrogen and there to the density of carbonic acid gas. If the mercury rises when the pressure increases, this could not be due to a simul- taneous rise and again to a fall in temperature, for the effects of heat and cold are not alike. It will be perhaps better to turn from these instances where the suggestion of failure in the method is really unmotived SCIENTIFIC INDUCTION 375 and fantastic to a case when the alternative has or has had more actual interest. To determine the rate at which an excitation is propagated along a nerve we make a double experiment. In the first we stimulate a nerve close to a muscle. In the second we stimulate the same nerve at a remoter point, and find that the muscle contracts later. Here A (the suggested cause or ground) is the extra length of nerve which the excitation must traverse, and D (the effect or con- sequent) is the difi'erence of time. Now, if the first experiment be made close to the muscle, it may be suggested that the stimulation involved diminishes the excitability of the nerve, and that this concomitant fact (B) accounts for the whole or part of the difference in time. Or equally if the order were different, i.e. if the stimulus had been first applied to the remoter point, it might be suggested that the stimulation increased the excitability, and that this concomitant (C) ac- counted for the diminished time. But when, varying the order of the experiments, we find the result constant in both cases, we dismiss both of these suggestions at once. The narcotic effects (D) of opium are familiar. Now, opium contains morphine (A) along with other substances, sometimes codeine (B), sometimes other alkaloids (C). Neither codeine nor the other alkaloids could be shown to produce narcosis in isolation ; while, conversely, morphine, whether combined with codeine (A B) or with other alkaloids in which there was no evidence at all for the presence of codeine (A C), had a narcotic effect (D). Hence it was reasonable to conclude that morphine is the operative element in opium, an inference which is corro- borated by experiment with morphine in isolation. Our result is, that if we find no common element in the various sets of concomitants we can argue with great prob- ability to the universality of the relation A - D. (h) Now taking our two sets of antecedents, ABC T, A EFT, and neglecting T as not now in question, we have to ask, first, whether BC, EF can be the whole of the concomitants, and secondly, whether they have no identical point. As to the first point, we may say that any unobservable fact XJ must depend either on T, in which case it ranks along with T among the permanent elements of nature ; or it is a concomitant repeated with A, and must be somehow connected with it. Its case is then parallel to that of the unobserved concomitant in the method of difference, and may be treated in the same way. The second question remains whether B C, E F contain any point of identity. The difficulty of this question is best felt when we think of the case of " counteracting causes." A force 376 INFERENCE P produces motion M V, as is shown by the fact that motion follows under circumstances which have " nothing " in common except that force. But another case presents itself in which P produces no motion at all, because it is " prevented hj a counteracting force " Q. The set of circumstances in which P appeared had, it would seem, this much in common, that Q was absent. They agreed, as Mill would put it, in certain negative conditions — they agreed in differing from a further case, now apparent, in which Q appears. Now this result may be unobjectionable in point of pure theory. Its difference from another antecedent is in a sense a characteristic of this antecedent; the absence of certain features from a totality characterises that totality. The significant negation expresses a difference or rests on a difference, as we have seen. Hence if we call Z the ground of difference from any cases containing " counteracting causes," i.e. conditions leading as such to con- tents other than D, we must admit that if A is the sole ground of D, A must contain Z ; and conversely, if B C and E F have any Z in common, the security of the generalisation A - D is impugned. But an analysis so accurate as to detect such elements of identity may be a theoretical ideal, but must come rather at the end of science than in the early stage occupied by the inductive process. "We must then have a different method of dealing with counteracting causes. Applying our principle of causation, we know that A - D will be universal unless the change of D to A has an universal antecedent in some change accompanying A. But now a change, we may put it, must consist in one or both of two points. Instead of the concomi- tant B we have E. This means (a) that B which was present is now absent, and (6) that E which was absent is now present. Now we may go on, if a content E is such as to be always followed by some A which excludes D, i.e. is such as to "negate" D, then the mere fact of E's absence may be regarded as a condition of ~D. But if not, not.^ Unless, that is to say, E negates D, the mere absence of E or the mere presence of such general and abstract characteristics of the surroundings as are involved in the absence of E cannot be a condition of D. Now between two cases AB-D, AC-D let there be what appears to analysis a total difference. Analysis may say to itself, " I still cannot be sure that there is not this much in common, that both these contents are exclusive of some fact E which ^ For we may put it, either E as such is ground for negating D or it is not. If it is, then its absence as such must be one condition of D. If not, its presence is not a final reason for negating D, nor therefore can its absence as such be postulated by the assertion of D. SCIENTIFIC INDUCTION 377 might be a concomitant in another case. But granting that this is so, it will not affect the result before me unless E is such as to be always followed by the absence of D." E must be what we call a counteracting cause. Now, of the existence of E we shall require evidence : first, evidence that E exists at all ; secondly, evidence that it is found in any given case in which we are interested. And we can apply our generalisation with a probability inversely as the probability of E.^ "We have arrived here at a more definite meaning for the term " counteracting cause " than we were able to affix to it in the earher stages of the discussion. A total cause, we may say, is that from which a consequent follows universally. A positive cause is that from which it follows in the presence of con- comitants which do not of themselves produce it or any element of it. A counteracting cause is that from which some second effect follows, of a character related but opposite to that of the first. Thus when a positive cause is totally counteracted, the total consequent, being such as to correspond to an ideal con- struction of the two effects, presents no apparent element of the first effect ; if counteraction be partial, some elements only of the first effect will appear. Now, with some reservation, we admitted the term "counter- acting cause " as applicable to any abnormal concomitant in which a familiar result fails. We cannot, it would seem, deduce from the theory of causation, but we may perhaps infer from general experience that in their application these two usages would coincide. A relation holds in a great variety of circum- stances, but with certain concomitants it fails. Now, there are two ways of explaining this. Either all the circumstances of the first set are favourable to the result, or those of the second set counteract it. The second hypothesis can be tested by con- sidering the effect of those circumstances apart from the antecedent under trial, and if they give effects of " contrary " quality they are counteracting causes. We may suggest that common sense — which means the result of thought acting on masses of experience too great to be perfectly articulated — takes the second hypothesis as more probable in proportion to the extent and variety of the circumstances in which the ' It may be said that E, the strict universal antecedent of a change, is as difficult to discover as A itself. That is true of the precise definition of E. But the denial of our inference only requires some degree of evidence for the existence of E. This would be obtained definitely by a negative instance of A without D in the presence of some E, or by analogy from cognate cases. In fact, we could discover E to be a partial or "positive" cause, just as we can discover A to be. Which, then, is a true ' ' total " cause can only be determined by discovering the case A E. 378 INFERENCE relation liolds. That is to say, analysis constantly resolves the " exceptional circumstance " into a counteracting cause in the strict sense. And so the two conceptions tend to coincide, and the relation which holds normally is taken to hold always, unless counteracted in the sense in which we understand those words, and our first account of the logic of the method tends to the same point as our present more detailed analysis.^ It is not necessary to illustrate the conception of " positive " and "counteracting" causes at any length. The simplest and most obvious illustration is the one taken above of mechanical forces. We might also refer, in physiology, to a reflex which is subject to inhibition, or in political economy to the tendency of increased demand to augment price, unless met by an equiva- ^ Mr. Bradley (Logic, ii. 2, par. 3) argues from the fact of plurality of oaiiaea that ' ' the generalisation " resulting from the method of agreement ' ' is vicious, and the canon which regulates it is false. " As to the canon, it is a case where a principle is true on a certain condition or with a certain limitation. To hold Mill up as a horrible example of intellectual obliquity, because for the convenience of exposition he states the canon without that limitation in one chapter, while he carefully explains it in the next but one, seems an excess of zeal. As to the generalisation, Mr. Bradley gives only one side of the case when he says crudely that it is " vicious." Mill himself saw that it was vicious if regarded as a con- clusion fully demonstrated by a single set of instances, but he explains it (and rightly from his data) as a probable argument, the probability being as the number of the instances {Logic, iii. 10, 2). Mr. Bradley is equally unhappy in his criticism of Mill's instances. "Let us take once again the very first instance. The universal which you come to is, ' that the combination of an oil and an alkali causes the production of soap.' The universals which you start with are that an oil and alkali, if combined under certain conditions b c and d e, in each ease produce soap. But how can you deny that these latter are universals ? " We do not deny that the premisses are in this case universals ; but they are relatively narrow and concrete universals, while the result is wider and more abstract. That is, the method obtains a more general from less general truths. Mr. Bradley's statement obscures this, for he puts the premiss in such a form that the work of the method appears already done. The true premiss is, "This pair of substances ab, and this ed and thisef, all in combination produce soap." Then comes the work of the method, which is to analyse and compare them so as to find that they agree only in a (3, the fact that in each case the pair are an oil and an alkali. Then we have the wider universal "oil and alkali as such give soap," which is our conclusion. The method here starts from true universal relations, and goes to a higher universal. But at a lower stage it starts from a true particular. Mr. Bradley thinks this cannot be, since, as soon as you have reduced the particular to a "perfectly definite set of elements, existing in relations which are accurately known, you have a judgment as universal as the result of your induction. " But this is a confusion between the general content and the universal relation. If I know precisely that I have here A in the con- text B C followed by D, I have a definite content before me consisting of so many clear elements, each of which may be called a general attribute or form the content of a general idea, that is, which Tnay recur anywhere else. I hare not yet any universal relation, i.e. I cannot yet say that D will recur when A recurs : and I cannot say this without that comparison of instances which induction requires. Jevons (Principles, vol. ii. chap. xix. p. 23) argues against the possibility of proof by experiment that " we must not assume an independence to exist among SCIENTIFIC INDUCTION 379 lent increase of supply. It will not be amiss to dwell on the last illustration for a moment. For when demand has been shown to be a merely positive cause of price, and the conception of the equation between demand and supply has been brought in to supplement it, we might be tempted to think that we had the true total ground of price. Really, there are still further counteracting causes, such as custom, prejudice, stupidity, or good feeling, all of which may or might on great scale or small influence prices.^ These, then, must either be set down as counteracting causes or taken up into the previous formula by some such device as that of limiting demand to effective demand, and so on. (c) We may notice here a special case of some interest. "We the conditions." Discussing the proof that heat is produced by friction, as grounded on the experiment of rubbing two sticks together, he mentions the Tarious "conditions" capable of being eliminated, e.g. conduction by Davy's erperiment, and proceeds : ' ' Previous to experiment ■we have no right to say that the rubbing of two sticks will produce heat in the same way when air is absent as before. We may have heat produced in one way when air is present, and in another when air is absent. The inquiry branches out into two lines, and we ought to try in both cases whether cutting off a supply of heat by con- duction prevents its evolution by friction." As the result of this assumption he is easily able to show that the business of elimination is in the simplest cases infinite. Now, this reasoning rests on the plurality of causes. We have A (friction) B (conduction) C (presence of air) d (heat). And we have ABC AEF d d (where E is absence of hotter = presence of as cold or colder surroundings, and F a vacuum). It is suggested in effect that while B and C together produce d (or are contributory conditions along with A to producing d) in the first instance, E and F perform the same function in the second. That is in reality, that B and E F are two fundamentally different causes of d. Jevons, in fact, makes the assumption combated in the text, that con- ditions of which all we know is that they are different, and their effects different, will here out of pure malice give an identical result and so thwart our induction. Unmotived scepticism will not easily outdo this. In fact, we aim at varying a single condition by itself (e.g. temperature in a physiological experiment) only when there is special reason to suppose that that condition interferes with our result. Otherwise we vary not as little but as much as we can, the strong presumption being that whatever varies without aflfecting the result is irrelevant. Sigwart's criticism (§ 95, pp. 419, 420) could only be relevant if the method of agreement set itself up as a guide to discovery. When he says that the only result of the method as applied to the causes of death is that "that which is to die must previously have lived," this may be true in the existing state of our knowledge. But this may only mean that we do not yet know the final analysis of any of the modes of dying. The common point in death and its antecedents is still to seek. Assuredly no one ever supposed that the method of agreement was an open sesame ! to the secrets of nature so potent that by crudely applying it to any mass of raw fact you would at once get any causa' relations you might require. ' I am not, of course, thinking of the remoter causes (such as cost of pro- duction) which influence demand and supply themselves. 380 INFERENCE have already seen that a persistent identity is as such a basis for a certain hypothetical inference. If the fact A persists for any time, it will do so always, unless it meets with a con- comitant C having a change in A as its necessary consequent. Now, if experience suggests certain changes C, D, E which may have such a result, the inference to A in any case is doubtful. But if we test A in all these circumstances and find it un- changed, — if every analogy which experience suggests for a change in A is thus taken account of, — the suggestion that A will change is reduced to an unmotived possibility. Similarly, if only C can be found to change A, the suggestion that A will change under any other circumstance is unmotived. Thus the weight of a substance is permanent for the sum of its parts, since no known change of chemical form affects it. This infer- ence rests on an exhaustive negation — exhaustive, that is, of all possibilities which any analogy can suggest, and hence is used in chemistry (as noted above) almost as an axiom. And prob- ably all the great masses of induction establishing permanence could be reduced to this type. So far we have treated the joint method as essentially a combination of the methods of difference and agreement, the former proving the antecedent to be a factor in producing the effect, the latter showing that no other conditions are required. We nowsee that the former function maybe supplied by the argu- ment from continuity. If we have A - d a continuous process, or still better A - A a persistent identity, this indicates at once with high probability that the antecedent is at least a factor in the production of the consequent, and hence the only question remaining is whether there are any other factors ; so that for relations of this kind we do not practically need to go beyond the method of agreement. A great mass of our common know- ledge seems to rest on these considerations. The substances or " objects " of everyday life form connected wholes for us (are thought of as substances), because maintaining their character through changed surroundings, and so far as these changes are exhaustive we have warrant for thinking of them as " really " substantial. So also with the ordinary processes, — motions, qualitative changes, and so on, — we think of them as self-deter- mining or conditional, according as they stand or fall before the test of the method of agreement. By the "joint method," then, must be understood a combination of " agreement " with either " difference " or " continuity," as the case may be. (d) Generalisations to the effect that one event is always followed by another, except in the presence of one which is always (or always unless in its turn counteracted) followed by a SCIENTIFIC INDUCTION 381 change in that other, are the normal generalisations of science. They can be applied to any case with a probability proportionate to the weakness of the reasons for supposing a counteracting cause in that case. We shall show in the next chapter that such partial knowledge of causes as is supplied by the method of difference and the joint method tends to multiply itself, and the same processes that give us knowledge of what we may call positive causes make counteracting causes known to us too. And with such knowledge we can apply generalisations derived from the joint method with considerable certainty. In point of fact, the results of the methods are probably taken as certain, and used with success at an earlier stage than our theoretical analysis would suggest. In the actual usage of science it is, I take it, only so far as there is some definite ground for suggesting an alternative that either the method of difference or the joint method is doubted. So far as there is reason to suspect some unobserved concomitant, so far as there is ground for supposing some coincidence with a cause of a different kind, the respective results of the methods are called in question, and when these grounded doubts are removed they are treated as certain. The abstract considerations which we have gone through represent in fact only certain bare analogies from experience, which can be urged against their ideal certainty. They are the last remnants of the counter sugges- tions of experience, and at the point when they are overcome — i.e. where the failure of our result would involve a combina- tion without parallel or analogy in our experience — we come to proof proper. We may notice at this point that every complete induction which is to prove causation really falls in the last analysis under the joint method.^ For every observed relation would be an immediate basis for an universal judgment if it was not for the possible influence of the concomitants. Hence all scientific induction must aim at eliminating this possibility. And there are two obvious methods of ehmination. The first is by getting a single point of change or difference in the ante- cedents, and seeing what follows. This is open to the objections that there may be an unobserved change, and that the un- changing concomitants may combine with the point of change to produce the effect. The second is by finding differences in the concomitants, and this is open to the objection that they cannot all be changed, and that different causes may produce the same efi'ect. The combination of the methods removes ' Concomitant variations is scarcely an exception, for it rests on variation and requires attention to the concomitants, 382 INFERENCE both sets of objections. It destroys the possibility of indirect causation by showing that the permanent conditions do not suffice for the effect, while it puts aside the influence of the observed concomitants by varying them, and of the unobserved by the unlikelihood of a repeated coincidence in divergent surroundings. Lastly, it may be noticed that the method required is really that of agreement and difference in the sense that a simple combination of a negative instance with agree- ment is insufficient. If I have A in many contexts with D, and without A no D, I must still know that A is the only point of change, and not part of a whole A C. For in this case C might be the true factor, and though by a secondary application of the method of agreement itself to the points of change A C, A E, I can eliminate and E and reduce the common factor to A, yet this postulates that originally A C and A E respectively are observed as the sole point of change. I conclude that the exhaustive observation of the changes which are, and of the changes which are not, followed by a difference in the result is the basis of scientific induction, which consists essentially in a combination of these observations. On particular occasions we may speak of employing the method of difference or of agreement, but that is because the work of the other side of this logically inseparable whole is tacitly presupposed. A may be already well known as a factor in B, and all that is required is to know whether or how nearly it is the total cause of B. Or the cause of B may be known to be within the whole A X, and it is only necessary to see what in this whole can be eliminated. But in both cases we assume knowledge derived from the reverse side of the method which we are now pursuing. The certainty of the joint method, i.e. of any complete in- duction, is of course absolute, granting it its hypothesis, namely, that all the relevant facts have been taken into account. "When we push the question further, and ask how we can ever be sure that observation and analysis have gone far enough and taken enough facts into account, we can only deal fairly with the method by asking, as before, what ground' there is for doubt ? So viewed, the answer takes a fairly simple form. Wherever we can find a case of failure we may argue that failure is at least a possibility in a parallel case. A ran we of instances that has once proved too narrow may prove too narrow again. A method of " ehminating " casual concomitants that has failed here may also fail there. Conversely, if a method, or application of a method, has never been known to fail, there is no rational ground for disputing its validity in SCIENTIFIC INDUCTION 383 any instance. If, for example, we can take the joint method as applied with certain precautions over a certain width of instances, and can find no instance of its failure so applied, we have no ground for doubting its results. Now to discover and make use of such application is the business of each special inductive science, not of logic in general. As the required tests in any subject matter become known, the knowledge of that matter assumes a stable form and becomes a science. Different investigations no longer lead to conflicting results, but corroborate and supplement one another. Wherever, then, a stable inductive science has been formed, there the appro- priate use of induction has been, for that body of matter, found out and applied, and the inductions of such a science can no longer be matter of legitimate doubt. Briefly to sum up our theory of the inductive methods. Starting from any single case of a relation A-B, we saw that the attempt to generalise it would be met by a counter consideration. This would rest on the fact that any relation will have manifold concomitants, and that changes in these constantly modify observed conjunctions. To meet this con- sideration we tried first an increase in the numbers of conjunc- tions observed. We found that on the theory of chances this proved some connection, close in proportion to the number of conjunctions observed, and we found that generalising such a conjunction, and testing the generalisation by wider experience in parallel cases, our deduction from the theory of chances was borne out, and we got a higher probability as the numbers taken increased. But still in this method we laboured under the initial difficulty. There must always, according to our experience, be concomitants, and nothing could be said, on the ground of any rule of probability, against the repetition of the same concomitants many times over. Our arguments there- fore at best proved only some connection without specifying what. It remained to eHminate concomitants altogether by observing, first, their absence. This could be applied only to the facts of change, and even then it was necessary to show that there was no ground for supposing an unobserved con- comitant before we could conclude to a direct connection. Moreover, we could not in this way arrive at knowledge of the whole conditions of a sequence. And thus, secondly, we appealed to a complete variation of concomitants. The con- comitants thus eliminated, and there being no reason to suppose a further unobserved factor, we could conclude ideally to a total cause, more readily to the total positive cause from which the effect could be inferred in the absence of counter- 384 INFERENCE acting causes. Important subsidiary arguments were derived from continuity and concomitant quantitative variation. The development of science from this basis, its growth in cer- tainty, insight, and completeness will be the subject of our next chapter.! ' The above discussion of the Joiut Method is based on Dr. Venn's amend- ment of Mill's account {Empirical Logic, p. 430). CHAPTEE XVI The Interconnection of General Truths So far the generalisations we have accounted for have been isolated, or as they are sometimes not very happUy called, empirical, laws. This would matter less if their certainty could be regarded as complete, though even in that case we might have to ask how we were to apply them to the complexities of nature. But they are not as they stand absolutely certain ; in many cases the degree of uncertainty attaching to them is practically appreciable, and in all cases it is of theoretic interest. We have therefore to inquire whether, by connecting these isolated generalisations with one another, we can wholly or in part eliminate this element of doubt ? Suppose we have a generalisation a — b groimded on an induction strong enough to make it probable but not strong enough to make it certain. Suppose, further, that we can connect this induction with another a - ^ which is also probable. Suppose, first, the connection to be such that if « - |S is true a - b must also be true, and assume that the evidence for a - j3 is entirely independent of that from which we inferred a - b. It is clear that the probability of a - b is increased. A fresh and independent consideration is ad- duced in its favour. The nature of the increase is best seen by putting it arithmetically. Let both the generalisations have an independent probability of |. Then the probabihty that a is not b is :i before we investigate it on its own merits. The result of our investigation is independently to reduce the probability to \. The actual resultant probabihty that a is not b is therefore \x\, i.e. the probability of a - b is l-(ixi) = it. But there is a further possibility. The inductions a - /3 and a - b may be so related that they imply one another, i.e. that not only does a - b follow from a - 13, but if a - b is true it follows also that a - 18 is true. In this case it appears that the prob- ability of both generalisations is increased.^ The fact that they ' If we wish to put the increase matliematically we must in this case use a different formula. For not only does the probable truth of each generalisation 25 386 INFERENCE coincide is fresh evidence for both of them. In the world of knowledge, as elsewhere, union is strength. Two judgments relatively weak in isolation gain strength when seen to cor- roborate one another. Each has its own ground and each is ground for the other, and therefore increases the considerations making for the other. It is clear that this relation need not be limited to two judgments. A third and a fourth may join the band and add to its strength. And, lastly, each judgment may be connected in one relation with this, in another with that, independent belief, so that ultimately our thought might form a single system in which all parts should be interconnected. It will be our business in the present chapter to explain the various ways in which inductive results can be thus inter- connected. 1. Variation of the cause. (a) General principle. The first method of connecting inductions may be put in general terms as follows : — By the inductive methods I can get a high degree of probability for the generalisation a - b. Similarly, I have a highly probable generalisation c - d. Suppose now I have a fact qualified by both a and c, I shall expect a consequent qualified by both b and d. Of course, a and c may be related in very different ways. They may stand, as we sometimes put it, " side by side," so that the whole formed is more appropriately symbolised as a + c. Two forces applied at different points but tending to move a body in the same direction, e.g. two weights in one scale might serve as an instance. Or a c may be a whole in which c, a determinate difference, qualifies a. And here either c or a may be abstrac- tions, facts not capable of presentation independently of some qualification, whether that which they exhibit in this instance or in some other. Thus a might be a volume of water at a given temperature and c a definite change of temperature ; a support the other, but in this case the probable falsity of either would be an argument against the other. "We may perhaps compute the probability after this fashion. Let a - b and a - /3 have each a probability of f . This means that inductions of such a kind are ooiTcct three times out of four, and incorrect once LQ four times. That of two such inductions both will be true has then in general a probability of 5 x|=T^, and that both will be false a probability of I X J = ,5j.. But by our hypothesis one or other of these alternatiyes must hold, i.e. the remaining cases in which one might be true and one false are put out of court. Hence of the only possible alternatives, one is more probable than the other in ratio of 9 to 1, i.e. the combined inductions have a probability of ^. I am much indebted to my friend, Mr. A. E. Jolliffe, for valuable criticisms and suggestions on the application of the mathematics of probability to this' point. I should say here that I conceive such an application to be of use merely for purposes of illustration. It is not, I think, the real basis of the argument before us, but it illustrates the rate at which probability increases. INTERCONNECTION OF GENERAL TRUTHS 387 might be a " typical " cell (of course an abstraction) and c the particular development (elongation, etc.) constituting ac the cell of a longitudinal striped muscle. But in any of these cases we may have evidence of the behaviour of both a and c from the joint method. As long as we have this evidence the relation between a and c is immaterial It does not primd facie matter whether c qualifies a or is a part of a or vice versd. All we are concerned with is that we have ac, and that accordingly, if our previous generalisations were good, we must expect b d to follow. It may be objected that the presence of c may " affect " the action of a or vice versd, but the point is that if the inductive tests have been properly ap- plied we already know the way in which c will affect a, namely, by introducing the modification d. Hence if both consequents b and d be known, and if we are capable of making the con- struction, we can infer the result b d. And so far as b and d are probable, so far b d, the whole, is probable. Of course, the new case may be just one which will throw some quite new light on the consequents of a and c. It may be the exception which redetermines the rule. But if the joint method has already been applied with due stringency, we have strong probability that b and d are the true consequents in any case. We have ground for believing that they will not fail at all ; and that they will fail just in this case will be still more improbable. Hence we get a very strong antecedent prob- ability for the effect b d.^ Thus a and c may be two mechanical forces operating on the same body, the resultant (r) of which can be determined ^ Thia is of course subject to the limitations laid do-mi in explaining the joint method. If there is any evidence that the new concomitants are counter- acting causes the inference still holds, but in a special shape ; for in the total b d, b and d will tend to reduce one another to zero. One misunderstanding must, however, be guarded against. The effect of a may be to modify c, and that of c to modify a. If we thoroughly understood the nature of a and o as " positive " causes we should expect this beforehand. But the new whole b d=m may have further consequences or enter into interactions with other agents in a manner quite incalculable from the behaviour of b and d taken singly. This is the case {inter alia) of chemical combinations. Of course, the fact that carbon and oxygen form carbonic acid depends on the character of oxygen and carbon (together, in strictness, with the conditions under which they are brought together), and would be inferable therefrom if we had enough knowledge of those elements. It is only the further behaviour of this new whole — its reactions with other substances or its behaviour in varying conditions — which we can in but a slight degree determine or explain from our knowledge of the components. And this whole, we must remember, does not consist of the free oxygen and pure carbon, whose properties we have determined, but of oxygen and carbon in some modified form. Strictly taken, then, composition of causes holds universally, and thus so far as we know the character of a cause we may apply our knowledge when the cause is acting in any fresh combiuation. 388 INFERENCE by combining the effects b and d of each. Or a may be a freezing mixture which cools (b) a body immersed in it, and c the liberation of a gas from pressure which also lowers the temperature (d). The liberation of a gas already cooled by a freezing mixture (a c) will reduce the temperature doubly (b d). Cells in general exhibit some contractility on stimulus. Imagine a contraction taking a determinate direction length- wise down an elongated cell and you have the rudimentary form of muscular contraction exhibited as a simple modification of ordinary cellular processes. An important result follows affecting the whole problem of induction. By separate inductions I have a probability (say of-^g) for the generahsations a b and c d. The probability, then, that Ijoth these generalisations will hold true is -^^ Xfn=^ ^^ = approximately ^. Then ^ measures the antecedent prolahility of the sequence a c-b d But now suppose that I examine this com- bination in the concrete, that I test it in turn by the inductive methods and get the same probability (A) of its truth. This probability will be independent of the other, being arrived at by independent observation. Hence the total probability of a c- b d will be as the joint probabilities which here converge upon the proof of it. Mathematically it will be as f X ^ : ^ X -j^, i.e. as 36 to 1, a very much higher certainty than before. That is the combination of two probable generalisations, and the sub- sequent verification by an independent induction of their joint result very greatly increases our certainty of that result as compared with the certainty we could obtain by either cal- culation or induction separately. Nor is this all. a c-b d has an independent probability of ^, and c - d has a probability of ^jy. But if a c - b d and c - d are both true, a — b must be true also. Tor if the whole a c causes the whole b d, and of these the part c causes d, it remains that a causes b. Hence the argu- ment applied to a c - b d may be in turn applied to a - b. It will have a probability of ^ in addition to the probability of -j^ derived from its own induction. And so with c-d. Hence the combination of the three generalisations materially raises the probability of each and all.^ (6) Application to quantity. If now we put c = a, we have the case of quantitative variation aa or 2a. Thus a is a force communicating a certain momentum to a body, 2a produces twice that momentum. Or ^ Of course we cannot apply the whole increase of probability to each of the three in turn, or we should have a self-multiplying process. But each general- isation, if not already certain, must be in its due degree rendered somewhat more probable by coinciding with others. INTERCONNECTION OF GENERAL TRUTHS 389 a is a change in the direction of a force which alters the direction of the moving body. Move the force through the angle 2a and you alter the direction of movement in the same degree. But here arises the question left over by an earlier dis- cussion. Quantitative variation does not always take place by simple laws. It is pleasant to get warm, but it is not twice as pleasant to get twice as warm. To put the same objection on grounds of theory, it may be urged that here the inference from the method of agreement breaks down. I have tried the effects of a in the context p, q, r, s, etc. But I have not tried it in the context a. All the other contexts have the common point of differing quahtatively from the agent a itself. Accordingly, I cannot infer d, priori to the conduct of a when combined with another a to form the quantity 2a.^ In point of fact, what we call " causes " and " effects " do not always vary in constant proportions. Nearly aU physical stimuli, as their intensity varies, pass rapidly from the pleasure- able to the utterly intolerable stage. Nor can we, in face of countless familiar phenomena of "periodicity," lay it down that the variation will be always in one direction. The upper C resembles the lower more nearly than any intervening tone, though the vibrations increase regularly in frequency. The outermost violet of the spectrum is to the eye nearer red than is green, though again the wave-lengths continue to diminish from red through green to violet.^ Size of brain is almost undoubtedly connected with degree of intelligence, but a frog •^ A special caution is required here. "We saw above that if the general qualities A and B (including all their degrees a-btona-nb) were connected as such in the strictest sense, their variations ought to foUow a law of simple proportion. But here we are starting not from A — B, but from a — b. The latter connection is taken to be substantiated in the sense that a is the total positive cause of b. Now if this is true, and if the whole of a varies, I imagine that the law of simple proportion must hold ; and we can convert the connection and say, If a - b, A - B, and if A - B then a - b. In fact, we make this inference in the laws of energy and of the permanence of substance. But if the total cause contains an element which does not vary {e.g. if a = aa, and if a higher degree of a means really an increase of a while a is stationary) there is nothing in the connection a - h to indicate the quantitative result of 2a or n a. And this corresponds to the ordinary case in which we speak of varying the cause. For what we call "the cause " is in fact as a rule a part of the true ground "acting on " another part, e.g. stimulus on nerve. Increasing the stimulus, the nerve remains constant (or if altered, e.g. in excitability, is not necessarily altered in the same direction as the stimulus), and the question then arises as to the residt. Conceding then that our general principle gives us guidance in the very simplest cases, in aU but these we require specific experience to help us. " In the instances quoted, and no doubt in countless others, the periodicity can be ' ' explained. " In the simplest case the return of the effect at a higher stage to something like its character at a former stage is in direct parallelism 390 INFERENCE with a large head filled with brain substance is perhaps as stupid as a crayfish with its insignificant ganglia. We cannot, except where our knowledge is exhaustive, say much a priori of causal variations of degree. But the method of agreement does not altogether fail us, for we can apply it to the varying degrees themselves. If we have a 2a 3a b 2b 3b it is obvious that variation of quantity as such makes no difference to the sequence a b. We may accordingly (from a few variants) expect to find any a followed by b. But here two cautioDS are necessary. First, we must consider (in accordance with the ordinary canons of this method) whether there is any common point in the degrees selected for examina- tion. If so the inference will not be safe to other degrees, especially to those which are widely divergent. Thus the degrees above instanced agree in being low. It is possible, then, that 12a or 20a, it is even possible that 4a, may have a different kind of effect. Nor is mere lownesss (or height) of degree the only possible form of identity. Any " periodicity," such as the choice of the squares, should be avoided if the inference is to be sound. But if we take both low and high degrees, avoiding any special point of resemblance, a few instances give us high probability for all intervening cases. Inference beyond the extremes observed — what Jevons calls extrapolation — is always uncertain, and a broad experience has shown us that the highest degrees of a quality are very liable to be followed by qualitatively different effects. Confining ourselves to "moderate" degrees, a very wide range of instances would assure us of Boyle's law, and the generalisation seemed sound until examination of much greater pressures proved a deviation. Similarly, Weber's law holds for certain stimuli {e.g. sound) within tolerably broad limits and then entirely breaks down. Notice, secondly, that it makes a great difference whether the inference you wish to draw is merely that any a will have soTM b as its effect, or that the degrees of a and b will in all variations observe the same proportion. The first inference is obviously much the safer, i.e. is substantiated by fewer instances. Thus if Boyle's law merely stated that volume witli a. like return of tlie cause. The vibrations of the octave are just double those of the original note, and perhaps the same explanation may apply to colours (see Wundt, Vhys. Psych, ii. cap. ix. § 4). There is the same sort of resemblance between the causes as between the effects. But that just this kind of resemblance would operate in just this way could surely be proved only by specific observation. INTERCONNECTION OF GENERAL TRUTHS 391 decreases as pressure increases without further assigning a direct proportion between the two facts, it would not be falsified by any known instances, though of course it would be less valuable. I conclude that our real guide in estimating the effect of quantitative or qualitative variations is, apart from the simplest cases, nothing but the method of agreement applied to the examination of instances of those very variations. A priori, we may know nothing of the difference which any variation will produce. But when we have tested it we may apply our results to new combinations with a certainty proportionate to the thoroughness of our test. It follows that if one series of inductions goes to establish a connection between a and b with a certain law of concomitant variation, and if a second set of inductions go to show that m a gives n b ; then if the quantities in the two cases tally according to calculation with one another, these sets of inductions confirm one another, precisely as the inductions a — b, c — d, and a c - b d in the cases first taken. In the first case we combined inductions of different character ; now we connect results differing only in quantity. Such combinations clearly articulated or obscurely felt seem to form the backbone of our confidence both in scientific and in common-sense results. We have, in fact, here the con- verse case to the interference of counter considerations which has hitherto guided our account of induction. A belief rests on such and such considerations, and if these are the only evidence bearing on the subject, that beUef must be provision- ally accepted. But it may yet encounter other results drawn from equally good evidence. These may conflict with it and then we have to balance probabilities, or they may support it and then we have an added confidence. The business of induction is to eliminate the first contingency and provide for the second, — to put counter considerations out of court and to find considerations with given support. This second operation is as applicable to "unscientific" as to "scientific" inductions; the common-sense generalisation or the analytic comparisons of the experimental methods equally gain strength by union. (c) But are the probabilities of connected inductions really independent ? Suppose (it may be said) that the induction a - b laboured under a doubt arising from the possibility of an unobserved concomitant X of a. Why should not that very same concomitant X be present here in the case a c ? Again, granting a - b universal in certain contexts, the method of agreement converts the relation into a strict universal by 392 INFERENCE varying the contexts, e.g. by trying it in company with p, q, r, s. Suppose now that ac — bd has been tried in just those contexts, or in some of them, over again. Then the inductions will not be independent. The objection has force, and we can deal with it only by careful consideration of the nature of the facts connected. The answer wiU best be understood by dealing with our two main cases separately. (i) Quantitative variation. If a c is qualitatively like a but much greater in quantity, it is clear that the conditions under which we observe its effects wiU differ in some important particulars. For example, operating under the method of difference, I perform the act p in order to produce a, and I find b following. Now p may have introduced q, which was too small for my powers of observation to detect. For example, a given chemical sub- stance might owe certain of its reactions to the presence of a foreign substance too small to be observed. Or again, in stimulating nerve A I might slightly excite B as well. At the given degree of intensity this second stimulus might not manifest itself. Now, if I wish to try a higher degree of a, I must also either increase p or bring about a by other means. But increasing p will probably increase any other effect it may have as well as a. Hence if q really existed, and was un- observable on account of its minuteness, it should now become evident. If it does not, the probability that it is non-existent gathers strength. Thus increasing the quantity of the sub- stance used I should also increase the foreign substance which might now exist in sufficient quantity to be manifest. Or in increasing the stimulus to nerve A, I should increase that of B, which would then give some palpable sign of itself. Here, then, the two inductions are at least in part inde- pendent, and so far as this independence goes the probability both of a - b and a c - b d, and therefore of the general A - B, is increased. But this is not all. Suppose the original induction an error. The relation a - b was then really due to the presence, say, of m. This supposition has a certain probability, high or low, as the case may be. But if it is true, it is clear that m must be present in the new case (a c - b d) also, and that in the due proportionate quantity c m. That is to say, the quantita- tive changes a c, c m must coincide in time and space, and for this coincidence no reason appears. Its probability is wholly independent of the original probability of m, whatever that may be. The resulting probability that m really exists will INTERCONNECTION OF GENERAL TRUTHS 393 therefore be the product of these two probabilities, and will be proportionately diminished.^ In two ways, then, the probability of the original induction is increased. On the one hand, the operation of a is observed under materially different conditions, eliminating certain oppor- tunities of error. On the other hand, the hypothesis of error involves more complex suppositions than before, and these new suppositions are not such as to lend any support to one another. The separate inductions may therefore be taken as independently probable ; and since the truth of one involves that of the other their joint probability is increased. (ii) Qualitative variation. If a c is a special combination of two causes known in separation, the above arguments are even increased in strength. An instance will best show the kind of combinations referred to, and the total independence of the elementary and deriva- tive inductions. That liquids distribute pressure equally in all directions (a — b) results from certain simple experiments as at least an approximate truth. That either solids or liquids exert a downward pressure on their supports (c - d) is a familiar generalisation. That bodies lighter, bulk for bulk, than water will float (a c - b d) is another familiar fact which we know from observation, but which we could also infer from the two previous laws. In this case the resulting law (of floating bodies), taken in conjunction with the elementary law that an unsupported body falls, is confirmatory proof that liquids exert pressure upwards as well as downwards ; for were it otherwise, we should have a contradictory result. Now, in this case, if we assume an error in either of the simple laws (a — b, c — d), we should have to assume an exactly compensating error in the complex law (a c — b d). Or if we assume that m is the true cause of b, and n of d, we should have to suppose a combination m n to exist, and that in just the relation required, in order to give us the effect b d. In Pascal's experiment proving the equal distribution of pressure, the pressure is applied by a piston. Suppose the error to originate here through the introduction of some unnoticed force m, we should have to suppose a second error m n, originat- ing in a different manner, and accurately adjusted in quantity and direction to explain the laws of floating, a supposition which would be clearly gratuitous. ' The argument of course implies that we can find no ra and n which vary concomitantly (cf. above, p. 364). We have then, in fact, a combination of the method of concomitant variations with the joint method as applied to each degi-ee of the qualities. 394 INFERENCE Take another instance. Stimulating a nerve (a) we get a certain reaction (b). This reaction is a part of some wider function, say, of respiration or digestion. After section of the same nerve (a = a c), though the general process goes on as before, the particular function ceases (i3 = b d). The two experi- ments clearly confirm one another, and are as clearly inde- pendent of one another. An error which should affect the one would not affect the other. And the argument here is really the same as before, except that c is now a reversal of a — a being the introduction of the stimulus into a quiescent or normal state of things, and a ( = a e) the removal of the same. Clearly, if a is the true cause of b, the removal (c) of a should also bring b to an end. Whence, from a — b we infer a - /3, and from a — /3 we infer a — b. Another case, in which a c means, in fact, the non-appearance of a when it would otherwise be expected, is the following. The attractive force of an electrified body (a) is inversely as the square of the distance (b). This is proveable by direct ob- servation, namely, by means of Coulomb's torsion balance. That a charge is equally distributed on the surface of a sphere and tends to accumulate on points and edges is an independent induction (c — d). That no electric attraction is manifested within an electrified body (a c - b d) is also well known, and geometrical considerations prove that, granting the laws of surface distribution, this is only possible on the assumption that the attraction is inversely as the square of the distance, i.e. the second and third inductions necessitate the first. But they are obviously independent, not only in the sense that they take place under different circumstances, but that they are actually different laws.^ Essentially the same principle appears in a somewhat different light in a very wide and important class of cases. Suppose we have a number of highly probable inductions, M - ISr, - P, Q - E, and so on. We set about the analysis of these results, and we find that M - N" may be analysed into ac-bd, 0-P into ae-bf, P-Q into a g - b h, and so forth. The result is a secondary induction, based on our first general- isations, showing that the relation a - b is universal. The very same inductions go to show the precise modifications d, f, and h introduced by c, e, and g respectively into the relation a - b. Then a - b becomes a true universal, and we use it now as a major premiss from which we deduce other relations S-T. But thisis not aU. If S - T can be analysed into a k - b 1, and if k - 1 is known from other sources, the new case S - T is a ' The atove example was suggested to me by Mr. C. H. Oldham. INTERCONNECTION OF GENERAL TRUTHS 395 further confirmation of the principle a - b. And this may be stated generally. When we apply a principle to a fresh case, and find our calculations verified, if the context is such that it could not give the result found unless our principle were true, this is confirmatory evidence for the principle itself. In this case deduction is evidence, not only for the conclusion,'but for the premisses. Thus primitive experience teaches that by pushing and pulling we can move bodies (M — N) ; we also see bodies moved by the impact of others (P — Q) ; insufficient force fails to move a body (K — S), but has its effect, as is manifest when it is combined with another force (T-V). We form a mass of such crude generalisations. Then analysis begins, and we form certain simple generalisations concerning the relations of force and resistance, composition of forces, acceleration, momentum, etc. These principles, one or more of them, explain our common-sense knowledge, and enable us to infer further results as well. And if, further, we deny any of these mechan- ical principles, a contradiction will ensue. If we conceive any one force or law taken out of our system of principles, the remainder will fall to pieces, for we shall find effects without causes. If I can explain a motion m by the composition of two forces p and q, I cannot deny p and leave the rest stand- ing. For if I know the effect of q, I must be aware that it would not produce m without p. So is it with any application of the mechanical laws, whether singly or in combination. I can infer the path of a projectile by calculating from the "impressed" force, the law of inertia, the action of gravity, and the resistance of the air. Ordinarily we assume these principles, and think only of the result as the thing to be proved. But if experiment confirms our calculation, it is also indirect evidence for the principles themselves. For, take away any one of the laws used in our calculation, and the effect of the remainder must be different. Suppose the law of inertia false, and there would be no curve described at all. Suppose the medium to offer no resistance, and the curve would be a perfect parabola, which it is not. No single result can prove the principles from which it is calculated, but a combination of results may necessitate all the principles which we also use to explain them. The logic of the matter is simply this. We have first a set of crude and simple inductions which we may call primary. Comparing two or three of these, we arrive by a secondary induction at a law or principle. Another group gives us a second principle, and so on. Let our first principle be the connection a — b. 396 INFERENCE Now find a case N' = ac where by a second group of inductions is shown to have the effect d no more and no less. If we find b d here, b must be due to a, and is therefore confirmatory evidence of the original principle. Of course, the belief that c will not give b is an induction, and may itself require con- firmation, but this confirmation may in its turn be found in other instances. In this way a mass of primary inductions may tend to support one another through the medium of certain secondary inductions formed from them. These "secondary inductions" become in the order of logical ex- planation the first principles of the science; they are fveu wpoTipa, though not so ^^7)/ ; and their strength is not that of any single induction, but of a concurrence of inductive results. We can therefore corroborate our single inductions by com- bining them in two ways,'namely, by examining the causes under investigation in different degrees or quantities, and again in composition with one another. To the variation of concomitants we have thus added variation in the causes examined them- selves, and the errors which might affect inferences drawn from the one method would not apply to the other. Hence the more our results are interconnected after this fashion the higher their certainty becomes. 2. Composite inductions. A simpler but in some respects weaker form of corrobora- tion may now be described. We have hitherto considered the " context " of a generalisation a — b as modifying the relation considered in degree or in kind. But there are many cases more naturally described by saying that the context makes " no difference " to the relation a — b. We then have the rela- tion perhaps in very different " forms," but without the kind of variation discussed above. The simplest form of corroborative induction is as follows. We have a number of inductions, m — n, o - p, q — r, s — t, all of them taken to be sufficiently established by the joint method. Then, by analysis and comparison we find a relation a - b running through all these, and we infer this relation to be universal. Now, from one point of view, a - b might be regarded as resulting from a single induction in which aH the instances from m - n, o - p, and q - r, s - 1 are premisses. But it is also a link between four separate inductions, confirming them and justifying our view that they were adequately grounded. For the relation a - b can be inferred from m - n, and o - p alone ; and using it as a principle we can (at least in part) determine the relations q - r, s - 1 by deduction. And conversely, we can infer a - b from q - r, s - 1, and deduce INTERCONNECTION OF GENERAL TRUTHS 397 m - n, — p from it. The result is that (so far at least as the connection of the elements is concerned) the four inductions stand or fall together — that is, they confirm one another. "We may say that this merely means that they together form one wider induction ; hut this misses the essential point, namely, that the adequacy of the test used in each separate induction is con- firmed by the remainder. If our different inferences collide with one another, that is a sign that they are inadequately tested. If, conversely, they support one another, this shows that the grounds on which each has been asserted are adequate. Thus, e.g., the broad principles of chemistry, the law of multiple proportions, and the principle that weight is per- manent in changes of form, are usually treated as major premisses by which new experiments can be tested. But every new experiment is also an instance in support of them. A small proportion of the instances in which these principles have been verified would be a sufficient inductive proof of them. And every additional group may be regarded as a fresh induc- tion converging upon the same result, and justifying the method already used. When a relation is generalised by the joint method, every fresh instance in which we find it is in some sHght degree a confirmation : not because number of instances is as such a basis of generalisation, but because in every fresh instance the context is in some degree varied and the chances of error are thus diminished. But if a set of instances X is held sufficient to prove a law, and the same force is attributed to a quite different set Y, when X and Y are found to coincide in their results our original confidence in X is confirmed by a second induction of equal strength. We cannot, indeed, hold these two inductions to be as independent of one another as those previously discussed. It is conceivable that the same error might vitiate every instance observed. But we must remember that the suggestion of error must have its ground in experience of the failure of our tests. Hence, when inductions resting on a given test collide, that test is proved inadequate. Conversely, the adequacy of the test is guaranteed by success in different cases. Hence, when separate inductions resting on a similar test support one another, the credibility of the test is confirmed. 3. Corroboration of particular facts. Any given content stands in many relations, and has many points of connection with reality. It has its grounds as well as its consequent, and it may have more than one consequent peculiar to itself, i.e. there may be more than one fact for 398 INFERENCE which it is in part responsible, which would not now exist if it had not been. Any one of these " points of attachment," as we may call them, may serve as an argument for the existence of the fact in question ; and if any one such argument is insuf- ficient, a combination of them may give us certainty. I believe the station wliich we have just passed is Didcot, because it is the first large station west of Eeading. On looking at my watch I find that it is just an hour since we left Paddington, and I know that we are due to pass Didcot in that time. The inferences corroborate one another. A statement of Herodotus may be received with some caution, but if supported by the evidence of an inscription we doubt it no longer. That the earth is spheroidal we believe on several very distinct grounds. At the seaside the horizon grows more distant if we climb a cliff; aud the masts of a ship appear before the hull. This might not be enough by itself, but it is reinforced by considering the apparent changes in the position of the stars, and so on. From the laws of evaporation we should infer that the air on the surface of the sea would absorb moisture. From the rain which the west wind brings we infer that it has absorbed moisture, and we find that it comes from the sea. The argu- ment from the effect (rain) confirms the argument from the cause (the sea), and proves evaporation to be the link between them. Putting the matter symbolically, we may have a b c d where all the relations a-b, c-b, d-b are probably universal. If this is so, and if we have ground for believing a, c, and d to exist, we have three independent proofs of the existence of b. 4. The froof hy construction. Both particular facts and general laws may be corroborated by the nature of the systematic whole which they form. To take the simplest case, let the sequence A - C be certain or probable, but not immediate. Suppose we find B intermediate between A and C. Here alone is ground for supposing that the true causal sequence is A - B - 0. Suppose, further, that we find independent evidence for A-B. This will necessitate the connection of B and C in order to explain the original sequence A - 0. We may have this argument in any degree of complication. " A " may be analysable into a complex set of conditions ; " B " into an interrelation of many agencies, and so on. That lightning (A) causes thunder (C) is a farniliar but not a simple law. The mutual repulsion of the particles of INTERCONNECTION OF GENERAL TRUTHS 399 air and their subsec[uent collision is the required intermediary (B). The nature of the intervening link may be inferred on the one side by electrical laws from its cause, and on the other by the laws of acoustics from its effect. Inferring it from the effect, it corroborates by an experiment on the grand scale the disruptive effects of the electric discharge (A — B). To take a familiar but more complex case. In breathing, inspiration is followed by expiration, and this by a subsequent inspiration, and so on indefinitely. We can in some degree explain this rhythm. A nerve centre in the medulla is con- nected through motor nerves with the muscles of the ribs, diaphragm, etc. This centre is kept in continued activity by the presence of blood in its normal condition {i.e. not saturated with oxygen). Efferent impulses from the centre cause con- tractions of the muscles mentioned, which enlarge the cavity of the chest, on the one hand by the depression of the dia- phragm (which can be seen from its shape to be an effect of its contraction), and on the other hand by expanding the ribs. This enlargement entails a diminution of pressure in the cavity, which causes air to iiow in from the atmosphere, the oxygen of which diffuses into the blood through the thin walls of the capillaries ; the expansion of the lungs sets up an excitation of the pulmonary nerves, which inhibits the action of the centre ; the chest is then restored to its previous position, .chiefly by virtue of the elasticity of the parts concerned ; and the process begins anew. If, further, the amount of oxygen inhaled is below the normal the blood is less oxidised, acts with more vigour on the centre, and the breathing is quickened till the balance is restored. A similar result happens if the blood is losing its oxygen more rapidly than usual, while in the con- verse cases the opposite effect is found. In this way both the rhythmical character of the process and its adaptation to the circumstances or actions of the organism is intelhgible. Of the details of this account, which of course might be prolonged to several pages, some are more, some are less, clearly made out by direct evidence. But what substantiates them in the main is that together they make up an analysis of respiration and an analysis of which the parts involve one another. Thus, e.g., the increase and decrease in the size of the chest cavity are postu- lated by the inward and outward passage of air, and explained by the movements of the ribs and diaphragm. These movements again are in part directly observed, in part (in the case of the diaphragm) inferred from the visible movements of the abdomen. The muscular movements again imply a nervous mechanism to regulate them, the nature of which we can in part trace by 400 INFERENCE anatomy aud experiment. This mechanism once more must be regulated by the effects of respiration, or the automatic character of the process would be uniatelligible. And here again observation supplies some of the links. The gain of oxygen by the blood in passing through the lungs is matter of observation, and it is explicable by the laws of diffusion ; while lastly, the action of deoxidised blood on the respiratory centre is matter of experiment. Some of these points would be weak enough if they rested only on direct observation. Their strength lies in this, that what is indicated by anatomy or experiment is also postulated by the resulting facts in the way we have tried to indicate. If the thoracic cavity were not enlarged, what should force air in ? if ribs and diaphragm did not move, how should the cavity be enlarged ? how again can this movement take place except by muscular contraction regulated by an automatic centre, and so on ? We conclude, then, that the elementary connections building up a whole already known to be connected are corroborated by the fact that they do build up the whole in question. When your work is complete you can no more suppose a single con- nection altered than you can take a piece out of a Chinese puzzle and leave the whole standing. And it is clear, lastly, that the induction which determines the whole as a whole is independent of those which suggest the character of the elements and their connections. Symbolising, we have A a b c I I d e f g B where A - B are known to be connected, a, b, c are the ele- ments of A, and the simple relations a - d, etc., are inferred or inferable from other cases. 5. The determination of the concomitants. Going back to our first account of the inductive processes, we can readily remind ourselves that uncertainty arose always from the indeterminate character of the action of the concomi- tants. In the method of difference there was no sufficient ground to deny that the concomitants B C might co-operate INTERCONNECTION OF GENERAL TRUTHS 401 with A in producing the effect d. And even when grounds were shown by the method of agreement for denying this, the disproof could not, at least at first, he absolute. But when, from other instances, BEF BGH CKL CMN bef bgh ckl cmn we get positive light on the behaviour of B and C, i.e. ground for determining their effects as such, our certainty with regard to the sequence A — d is materially increased. Conversely, the probability of the sequence A — d itself throws light — nega- tively, at least — on the behaviour of B and C. The negative instance B and b c and the " agreement " instance A E F - d e f combine to show at once that A — d is universal, and that B C as such determines b c only. The result is that we have here a system of mutually determining universal judgments. Each judgment A-d, B-b, C — c has an effect upon the others. If we accept any two of them the third must follow, and the probabilities of each of the three are derived from independent sources. We have inductions determining B — b, G — c inde- pendent of that which determines A — d and supporting it. While conversely, the induction A — d taken alone is evidence f or B C — b c, and taken together with B — b is evidence for C — c. This mutual determination is clearly coextensive with the whole range of reality, so far as we can observe and analyse it. Hence the problem of induction is not that of finding some absolutely fixed points of certainty to begin with by means of which we can judge other things. It is a problem rather of finding a body of judgments not only consistent but mutually supporting one another. As this body grows, and the depend- ence of one judgment on another becomes clearer, the probability of the interdependent members, and therefore of the system as a whole, grows pari passu. The isolated induction is never certain. It is a probable result which, combined with other independent probabilities, approximates step by step to certainty.^ To sum up; we have had five distinct ways in which induc- tions may be so interconnected as to support one another. Beginning at the bottom of the process we find — (L) that since the difficulty of inductive proof consists in disentangling the ^ This differentiates the method from Mill's Method of Residues, in which the effects of B C are supposed definitely known, and the residual effect is attributed to A. My point is that the residual or negative determination is mutual, and that thus the effects of A and of B C become clear pari passu. So far as A's effect is probable, so far also is that of B C, and vice versd. And by taking fresh instances in other contexts we may get converging grounds of probability for both. 26 402 INFERENCE effects of a mass of concomitant facts from one another, any induction determining the effect of any one concomitant determines at the same time the effect of the remainder. The generalisations thus formed are further tested (ii.) by combina- tion with one another. In the simplest case such combinations may be represented as forming a single induction, but the fact that generalisations tested in a given way coincide with one another is a proof of the adequacy of the test employed. In higher cases (iii.) the " combined " laws differ in their working from their elements in such a way that the sources of error which might affect them are quite distinct from those which would affect their elements, and elements and deductions form a set of independent results which support one another. The composition of causes, and the quantitative variation of the cause, are the two main cases falling under this head, (iv.) Particular facts may be inferred by many distinct inferences from other facts with which they are connected by laws which are either certainly or probably universal. And (v.) lastly, both particular facts and the laws connecting them may be postulated by the structure of a known whole in which they are required as elements, and the inference from the structure of the whole may be an independent corroboration of direct inductions on which such facts or laws may also be grounded. Briefly, then, we may say, to combine inductions is to strengthen them. At its lowest, the process is equivalent to welding separate inductions into single inductions of greater extent, and therefore greater strength. At its highest, — since there is no reason to suppose that the same error will affect a result, the same conditions limit a sequence, in different forms, — it amounts to a convergence of independent inductions each with a probabihty of its own, the result being always a higher probability for the connected whole. The convergence applies both to particular facts and general laws, to composite results and to the elementary principles which explain them. It rests in part on the connections and affinities between generalisations, and in part on the better determination of the effect of concomitants which makes each separate induction more certain. We may then restate the process of induction thus. The problem of thought is to make out the network of universal relations constituting reality. In working out this problem it is guided by two main principles. First of all, each fragment of reality with which it starts affords or may afford it certain grounds (on the principles called inductive methods) for judging a universal relation to hold. But secondly, the INTERCONNECTION OF GENERAL TRUTHS 403 judgments so formed are as such of various degrees of strength, and to prove their certainty they must run the gauntlet of one another. Negatively, they must not conflict. Positively, they must support one another. Such consilient or self-supporting results as are obtained thought takes as true. It will illustrate this conception to apply it to the develop- ment of knowledge in time. We have already seen more than once that the theoretical requirements of logic demand precau- tions with regard to the inductive methods, which go far beyond the practice of scientific investigation. The reason of this is that logic has to make abstraction of the surrounding knowledge, which, in fact, qualifies every judgment and every method of forming a judgment in our intellectual world. In any actual, concrete case it is only such and such difficulties that are anticipated, while errors for which logic can see the abstract possibility are rightly put out of account in view of other knowledge on the subject. It is this fact which has tended to undermine the whole theory of induction — for each method at any point seems to postulate something else as known, and we no more come to the primary induction from which knowledge could be said to begin than we reach the horizon or the beginning of motion. But this receding, vanishing elusiveness of the beginnings of induction is explained when we consider that its results develop pari passu. A is not probable except in so far as B is likely ; B depends on the unlikelihood of C, and so on. But we are not bound first to estabUsh C, then B, and then A. The probability of all three emerges simul- taneously from experience as an interdependent result. If we revert to Aristotle's simile, we should think not of a single soldier rallying from the rout around whom others gather, but of a wave of returning courage gradually animating the whole regiment, and bringing them by degrees but simultaneously to a stand. There is no 'rpurov h rfj ^/u^,? xaSoXou in the sense of a fully determinate, fixed, and certain universal judgment standing in isolation and ready to give a hand to the next comer ; but there is always a mass of partly formed, more or less definite, more or less certain, judgments, which gather clearness, connection and strength as a body. And thus we may conceive the inductive process from its elementary beginnings to its ideal completion something after this fashion. Beginning with the tendency to generalise the observed relation as it comes, it finds its results continually corrected by one another. This correction will sometimes amount to an entire overthrow, sometimes to amendment or limitation. Proceeding with its corrected results, it continues 404 INFERENCE the process till it finds some that will hold throughout ex- perience. Meanwhile, rendered reflective by consciousness of mistakes, it traces errors to the neglect of the character of the contents and their concomitants, and for the future it remedies this neglect by the " scientific methods " in which the counter- suggestions of experience are carefully eliminated before any result is taken as established. The results now obtained support one another in two ways. For, first, the exacter Ifnowledge of the effect of the context makes each separate sequence more definite and certain; and secondly, the combina- tion of established sequences gives k priori ground for accepting results established by independent inductions. The resulting system, worked out ideally for all experience, and with all its points of interconnection clear and certain, would be the ideal knowledge ; worked out clearly and definitely in this or that body of truth (such, perhaps, as mathematics and physics)j less coherently and definitely in others (such, perhaps, as physiology), and strongly but indistinctly felt rather than pointed out in the great bulk of our " common-sense," every- day beliefs, it constitutes the knowledge which we actually possess. The result of combined inductions is a body of scientific truth. It is difficult to define science so as to distinguish it from ordinary knowledge. Perhaps it may be said to begin when we mark out a tolerably distinct subject (yhog) for systematic inquiry {ijAMoc), i.e. its beginning is in the intention of the inquirer, l^or is science complete till we are able by long chains of deduction to infer the individual fact without need of verification. But a mass of assertions may be said to constitute a body of determinate scientific truth at the moment when, by the consilience of inductions above described, they come together in such wise that for the future they all stand or fall at once. From this we can at once understand the nature and validity of our confidence in those assertions which we call scientific. The isolated induction we have had to admit, how- ever much it may approximate to certainty, can never, strictly speaking, reach it. But the failure of an isolated induction is no evidence against a connected system. For, first, the former may always be held open to doubt on the ground of opposing evidence from cognate matter, or even of the unknown character of such matter. But ex hypothesi all such evidence is in favour of each member of a connected system. And so f ;ir as the systems remain separate, the permanence of each is an element of strength for all; while so far as all the sciences can be INTERCONNECTION OF GENERAL TRUTHS 405 taken as building up a single system, that system has a unique character to which no analogy applies. In one word, with the connection of inductions we have science and certainty. And secondly, the argument to the possible failure of inference A from the admitted failure of inference B is a kind of argument by analogy, and is strong in proportion as the case A resembles that of B, weak in proportion as they differ. But if the difference is according to experience essential, if, that is, it is uniformly followed by a difierence in the conclusion, there is really no argument at all. Now, the fact of consilience is an essential difference, and so the breakdown of a single induction is not evidence against a connected system. And since each new consilient member makes a difference to the certainty of the result, we cannot argue from the breakdown of a relatively weak nexus of inductions against one which is complex and strong ; and the more complex and strong a body of inductions is, the more whoUy it will be removed from arguments of this kind. The more, then, in any system the several inductions support one another, the more numerous these inductions are, and the stronger each separate member of the system, the more the case is removed from any analogy with minor systems which may have proved deceptive. Genuine scepticism as to inductive science could therefore be motived only by the total disruption of a great mass of belief resting on a consilience of inductions. I cannot but add that, conversely, the disruption of great masses of belief which do not rest on consilient inductions is for the inductive logician the negative instance which goes to consolidate his own theory of the conditions of knowledge. Lastly, the extent of possible error in a well-grounded in- duction must not be exaggerated. Suppose a careful induction, i.e. one that has applied every test suggested by experience, to be reversed. This will mean in effect that it is the strict universality of the relation that is disproved, — the exhaustive enumeration of the conditions. But that the induction should " have nothing in it," that it should not be an approximation to truth, give us no universal holding for a very wide area, or something very near to the totality of conditions, will be scarcely conceivable if our preceding account of induction and its relation to probability be accepted. Thus, e.g., Boyle's law continues to express an approximate truth, though some further condition has to be taken into account which Boyle did not find out. Or again, — to give only one instance of the commonest form of correction of old truth by new discovery, — the common- 406 INFERENCE sense belief that heavy bodies fall fastest is far from being wholly upset by experiments in vacMo. A condition is inserted (namely, that there must be a resisting medium) unnoticed by common sense, and the principle on which the facts rest is accordingly conceived in a modified way. But the original induction contained approximate truth. Our point, then, is that against the claim to be approximately true counter- evidence from failure of this or that induction breaks down. To make these points clear, we may distinguish three ways in which a systematised science may be conceived as modifiable. {a) The real totality of conditions on which its results at any given point depend may not be known. That is, in effect, the conditions pertaining to the human area of investigation, and perhaps certain others with them, have not been elimin- ated. Now, if this is so, no one knows it so well as the student of that science, if he understands his business. And accord- ingly, " modifications " in points of this kind are not really reversals of his results as he will state them at all, but a mere filling up of blanks in his knowledge. In this case, then, modification is always possible ; but, on the other hand, in no way interferes with the certainty already arrived at. The case is nearly parallel with common-sense knowledge, where we are concerned mainly with practical results, and do not care to give an exhaustive account of conditions. Here, again, common sense, so far as it understands itself and its limitations, is not really negated by the discovery of cases in which its results do not hold. It gave what was for its purposes the best working rule, and that was all its business. It is now more clearly defined and limited, and that is all. (b) But now suppose a science to consider itself to have arrived at the true totality of conditions for a given set of results, so at least as to know where alone modification can be found. Is it inconceivable that there should be any mistake here ? May not this or that result, which appears so woven into the system that all must stand and fall together, never- theless turn out capable of a modification which will injure nobody ? Possibly ; but if so, it must be our constructions and analyses which in this case are defective, and which gave this judgment an unreal strength of connection not its own. The isolated act of analysis may be faulty, like the isolated induc- tion. Here again, then, if the meaning is that the single result alone may be modified there is no attack on the body of the system as such. If, however, this possibility is also raised, we must reply that it can be logically grounded only on the complete overthrow of an equally well-established science. INTERCONNECTION OF GENERAL TRUTHS 407 If we can imagine a whole science, such as the science of electricity or of optics, proved to be nothing but a network of illusion, destitute of any sort of validity, we might argue that other sciences were equally false. But, apart from an " instance " of such a kind, what ground could scepticism logically take ? And what holds for the whole system must apply to any members of it connected with the rest, not by an isolated analysis like a single deduction, but in manifold interweavings of correlation. I should say, then, simply that in view of the essential difference between a scientific system and such in- ductions as have been found to err, the suggestion of error in the former, understood as it should be understood, with all the limitations suggested by induction itself, should be simply and categorically rejected. (c) If reasons could be found against this view there would remain a further point. Error, we have found, applies to exact results, not in the case of well-grounded induction to approxi- mate results. If, then, on the ground of the limitations of induction, error were to be imputed to science, it must apply to the exactitude of its results, not to their approximate truth. To deny even approximate truth to the best systematised science would be to put yourself at the furthest possible remove from all reasonable evidence. If I were convinced that accuracy was no more to be found in science than elsewhere, I should still say that in inductive science we had the nearest approxi- mation to reality. We have now reached the point where the requirements of our principle of induction are fulfilled. In the first rough arguments of simple enumeration, reasons for a generalisation could always be met by counter-reasons. "We could always argue from the possibility of a change in concomitants. The next step, therefore, which landed us in scientific induction was to eliminate this possibility. All strong and direct reasons for the relevance of any concomitant could, under favourable circumstances, be met, we found, by such a method. But there remained the bare possibility of failure based on the inadequacy of observation. The strength of this possibility could only rest on experience of failure, and to meet it we had recourse to a further principle — that of combining induction with induction. When such combination is effected, as it would seem to be in some of the physical sciences, counter- considerations are replaced by a consilience of reasons for the same conclusion, and the requirements of our principle are more than fulfilled. CHAPTEE XVII Induction and Hypothesis We have now completed our positive account of induction as a method of obtaining truth with certainty, and upon this method we believe the bulk of well-established scientific knowledge to rest. "We have still to inquire into the character of those methods which with varying, in some cases with very high degrees of probability, establish results which yet, owing to the peculiarity of their subject-matter, cannot be subjected to the whole of the inductive tests with the completeness which we have hitherto demanded. I treat this branch of the subject here, first, because it completes our account of induc- tion ; and, secondly, because it will illustrate by contrast the method of combining inductions which has just been described. 1. To take the second point first. Briefly our method might be described as one which starts with a hypothesis which it continually modifies and strengthens by repeated verification. And this forms a point of contact for our theory — which started from the view of induction which will always be associ- ated with the name of Mill — with the rival account which originated with WheweU and Jevons, and which has gained the authority of Sigwart and, with important limitations, of Mr. Bosanquet. Let us, then, consider this theory in relation to our own. According to Jevons' well-known view, induction is really an inverse deduction,^ and one of questionable legiti- macy. In deduction you know, or take as known, certain universal truths, and applying these you draw your conclusions. In induction, on the contrary, you know your conclusions (i.e. the particular facts), but you do not know the laws or prin- ciples upon which these depend. But you believe (on what general grounds does not matter at present) that there must be some general principles to explain these particulars, and accord- iiigly jo^ invent some. This is your hypothesis. Then you ^■Pply your hypothesis, perhaps combiniag several hypotheses, ' Principles of Science, bk. i. chap. vii. 403 INDUCTION AND HYPOTHESIS 409 perhaps filling up the hlanks which your hypothesis has given you by certaia observable data, and thus get certain conclu- sions.^ These conclusions, lastly, you compare with observed fact, and, if they tally, your hypothesis is a good one, and may be taken as more or less estabUshed. If they do not tally, the hypothesis is at once dethroned and you must make another.2 This procedure is, by the confession of its authors, in a strict logical sense illegitimate. We must just remind ourselves of the reason. Put in the way of formal logic, the reasoning commits the fallacy of " affirming the antecedent on the ground of the consequent," a fallacy which is essentially parallel to that of " simply converting an universal affirmative." Put simply, the argument runs, " If A is true, B will be true. But B is true. Therefore A is true." "If the witness said it," ran the thought in Mr. Justice Stareleigh's mind, " I should have taken it down. But it is in my notes. Therefore he said it." If you take poison you die. But you will die. Therefore you will take poison. If at one time the climate of Europe was Arctic in character, fossil remains of " Arctic " animals would be found. They are found. Therefore the climate of Europe was Arctic. If marriage by capture prevailed in a primitive tribe, some symbols of capture would be likely to survive in its civilised descendants. In civilised Eome the marriage ceremony was a pretence rape. Therefore the primitive Latins captured their wives. The growth of popula- tion tends to lower wages. "Wages are low ia Ireland. There- fore its population has grown. We need not multiply instances. The above will be sufficient to show that this form of argument suits good and bad inferences equally well. This is an objection which is not met by admitting, or rather insisting with Jevons, that induc- tion gives us merely probable truth. We have already argued that probability must have a definite degree, and the stoutest opponent of induction could scarcely deny that some of its generalisations are more probable than others. But the hypothetical or inverse deductive mode of argument entirely fails to explain this difference. Whatever argument you throw into such a form has precisely the same flaw, and as an argu- ment is worthless. It gives neither certainty nor probability : it gives in strict logic nothing at all. The inverse method, taken just as it stands, does not, I venture to think, distinguish between the plausibility of rhetoric and the probability of logic. The hypothetical form of statement is one which the mind ^ Op. dt. bk. ii. chap. xi. ^ Op. cit. bk. iv. chap, xxiii. 410 INFERENCE easily follows, and is therefore plausible. But the precise business of good reasoning is to get rid of plausibilities, or at least to get beneath them and analyse them. If it is replied that this is taking a very formal view, that after all the form of an argument need not concern us, and that materially sound reasoning is just as sound whatever way you put it, we shall rejoin that this position may quite fairly be held by the_ man of science to whom the particular truth, and not its ultimate epistemological grounds, is the essential thing ; but if this is also to be the attitude of the logician, why have a logic at all ? Logic, according to the view which we have contended for all along, like any other scientific inquiry, has to explain the facts. What are the facts of logic ? Certain judgments and inferences. In this case we are concerned with inferences. These inferences are correct or incorrect, or, on the very minimum admission, at least more or less probable. Then the business of logic is to explain this more or less of probability. To fail in that is simply a confession of inadequacy. It will be replied that Jevons does not leave the inverse theory in the naked form in which we have stated it, but that he infers the probability of the suggested cause in accordance with the theory of chances. Now an argument of this kind is quite possible, and is, in fact, frequently used, as we shall presently see, but as Jevons puts it, i.e. in the form in which the inverse method requires it, it is unsound. Jevons tells us, that " the most probable cause of an event which has happened is that which would most probably lead to the event supposing the cause to exist ; but all other possible causes are also to be taken into account, with probabilities proportional to the probability that the event would have happened if the cause existed." ^ That this statement represents the true probabihties of the argument from effect to cause, we must directly deny. It leads at once to manifest absurdities. An acquaintance is dead, and I know nothing of the cause of his death. If he was shot through the heart he would certainly have died. Am I therefore to conclude that he was murdered ? If he had typhoid fever he might or might not have died. Can we on this ground compare the probability of his being murdered with that of his dying from typhoid fever. Suppose I still know notliing of the cause of his death, but am aware that he had been in the centre of cholera infection. Most people would think it not improbable that he died of cholera. But on Jevons' principle it is much more likely that he was murdered, forcholera is not always fatal. We need not multiply instances. It is clear that Jevons' ' Princvples, vol. i. p. 279. INDUCTION AND HYPOTHESIS 411 principle only takes one side of the matter into account. You must not only consider the probability that a certain antecedent would, if it existed, produce this result, but must also consider the probability that this antecedent does or did eosist as compared with alternative probabilities. In fact, Jevons, like a good reasoiier, always does consider both points in his illustrations. Thus in explaining KirchofTs proof of the presence of iron in the sun, we have the two alternatives before us of a casual coincidence of sixty hues in two spectra, and on the other hand of an " explanation " of this coincidence by the presence of iron in the sun. Now, either a coincidence (between the spectral properties of some other substance with iron) or the presence of iron would equally explain the result, i.e. the result would be necessary in either case, and there is no question of the degree of probability with which the effect might be inferred from the hypothetical cause. The improbability attaches really to the suggestion that the "other" substance exists, i.e. that there should be so remarkable a coincidence without fundamental community of nature.^ Jevons' principle enters into account in certain complex cases of which he gives instances, and which we may explain in this very simple way. Suppose an event a for which we require the cause. Two antecedents are suggested as possible, A and B. There is nothing to show that A is more likely to happen than B. They are, as far as our knowledge goes, equally frequent. But A is the true ground of a ; i.e. given A we get a universally, while B is not always followed by a. This will mean that if we assume B we shall also have to assume some other conditions, positive or negative, i.e. we must assume a coincidence of B with something else. But if B as such is not commoner than A, B in such surroundings will be less common than A. Hence there is a reason, weak or strong as the case may be, for preferring A.^ Attending carefully to our reasoning when we infer from ^ I do not here inquire whether this is the full logic of the argument. See above, Chap. XL p. 312, note. ^ We may perhaps so eztend this account as to bring it into relation to every case, at which point Jevons' principle, slightly reconstructed, will become identical with ours. If A and B are in themselves equally likely, but assuming A we must also assume C, while assuming B we must suppose D, then the probabilities of A and B will be as the probabilities of C and D. Thus assuming iron in the sun (A) we explain the solar spectrum (a), with no further assumption but that of the uniform nature of iron (C), which may be regarded as certain, i.e. as giving the limiting case where there is no really fresh "assump- tion " at all. On the contrary, assuming another substance (B), we must assume a coincidence in spectral characters (D), the odds against which are a trillion to one. The argument here may be put in Jevons' form, because we begin by supposing A and B equally probable. But if B were much more 412 INFERENCE an effect a cause which we cannot directly observe, we must admit that the logical starting-point is not, what Jevons would have it, a supposed cause, but the effect itself, along with what- ever we know of its cause or causes, their probability or fre- quency, from parallel cases. Doubtless the cause suggested must explain the effect ; that is a preliminary condition. But more is required before proof even begins: the effect must probably or certainly imply the cause. And as is the strength of this implication, so is the probability that the cause suggested is the true one. When the Cornish peasant attributes the moaning and howling of a stormy night ou the Bodmin moors to the giant Tregeagle, the unjust steward who is con- demned to empty Dozmare Pool with a limpet shell, it may be quite true that if Tregeagle existed the noise would be explained. A giant who could stride from Castle Andinas to St. Agnes Beacon, and from St. Agnes Beacon to Cam Brea, might well fill all Cornwall with his lamentations. But we who have never met a giant like Tregeagle, but have often heard the wind howl, will probably prefer a more prosaic explanation. "We shall consider presently the logic of the argument from effect to cause. For the present we wish to point out, (1) that even this argument is not logically an " inverse " method, but an inference from known facts to a suggested ground. And (2) we must insist that it is far from being the normal type of inductive inference — so far that it cannot exist at all without presupposing inductive results of another kind. For how could I argue that a suggested cause will explain a given effect unless I already know the causal relation used in this " explanation." How could Newton suggest that gravity would explain the motions of the earth if he were not already familiar with its laws as affecting bodies on the earth's surface ? The cause A suggested to explain the effect B may be simple or complex. If simple, it must resemble simple causes the effects of which are already known. If complex, it must be a construction of such causes. But how are such causes known ? How do we learn the effects of inertia, gravity, friction, or any other elementary agent? How do we get the results of artificial selection from which the explanation of the development of plants and animals by natural selection takes its start ? The inverse method works with known causal laws. It may con- struct elementary laws into a complex whole, and so " prove " probable than A we should have to measure off its strength against the weakness of D. The result in any case really is that we have to be guided by the prob- ability that the whole A C exists, as against the probability that B D exists. Jevons' view as formulated by him confines itself to one part of this whole. INDUCTION AND HYPOTHESIS 413 a derivative law, but to be even plausible it must have its elementary laws to work with. In fact, deduction, and hypo- thesis so far as it uses deduction, require at least certain elementary universals to form their constructions. Without these they " will not march." But these elementary laws must come from induction. Hence the " inverse method " can only work if a different method has gone before it.^ Thus even admitting the merely probable character of induction, we should have to reject the inverse method as inadeqate ; since the result of such a method is neither prob- able nor certain, but merely plausible, i.e. for logic it is nil. But we cannot admit the postulate. If our best established ^ This point seems to me the main weakness in Mr. Bosanquet's otherwise useful account of induction. " Inductive proof," he tells us {Logic, vol. ii. chap. V. p. 177), "rests, like all inference, on systematic and necessary connection of content. The obseiTations do not give us the connection, but we judge the connection on the basis of the system demanded by the observations, and this systematic or reasoned judgment is the essence of proof." I confess this sentence puzzles me. If it means that observations do not give us the system of themselves, i.e. without analysis, comparison and other acts of thought, of course I agree. But it seems to mean more. It suggests that the observations are not the facts which prove the system, still less do they suggest the system ; but we have, as it were, a system, or perhaps two or three systems on hand, and we try these until we find one that fits. This we retain, while the others (I imagine) we dispose of at a reduction. I hope I am wrong, but all through Mr. Bosanquet's great work I am haunted by a system which is always operating in a powerful and effective manner, while its origin and validity are \vrapped in what is to me total obscurity. I am quite at one with Mr. Bosanquet in thinking — or, to be more accurate, I have learnt mainly from him to think — that the work of thought is to form the real world into a connected system. But I suggest that if we are to have a fabric we must have the thread to weave, and the tools to weave with. On my view, the thread is the world of sense, and the tools the activity of thought ; but what Mr. Bosanquet's thread is I cannot make out, and it is just in the theory of induction that my difficulties come to a head. (See, however, below, p. 419, note.) It is noteworthy that Jevons, in his chapter on Hypothesis {op. cit. bk. iv. chap, xxiii. ) fully recognises that the modus operandi of the cause suggested must be known aliunde. "If, in order to explain certain facts, a, a', a", etc., we invent a cause A, then we must in some degree appeal to experience as to the mode in which A will act. As the objects and laws of nature are certainly not known to the mind intuitively, we must point out some other cause B which supplies the requisite notions, and all we do is to invent a fourth term to an analogy. As B is to its effects b, b', b", etc., so is A to its effects a, a', a", etc. " This recognises our point. But Jevons does not seem to have considered its bearing on his general theory. The attempt to prove a simple law by the inverse method could only resolve itself into something of this kind. " If all A is B, this A will be B ; but this A is B, therefore all A is B." If matter has the property of gravitation, the matter which we see will gravitate. It does so : therefore gravity is an universal property of matter. But this is simply a longwinded and tautologous way of saying, "If some A is B, all A is B. " In fact, at this point the inverse method reveals itself definitely as a simple inference from "some" to "all." And that is at bottom its real character. It wiU be understood that I attack Jevons' view only as a final analysis of induction, and am far from denying it considerable value of its own. 414 INFERENCE inductive sciences are not to be regarded as certain in their general framework, really the only conclusions I can draw is that the word certainty must have changed its meaning, and refer to some supernatural state of mind of which we have no experience. If the general principles of physics are not in their main purport established truths, I cannot consider that we have any knowledge of what truth is. Of them we may say with Aristotle — o SiaXOan rabrriv rriv viern (i\i -rravii 'Tnararipa. IpiT. The truth is, that the logician ought to take this admitted certainty as a fact to be explained, and if his theories do not explaia it so much the worse for the theories. Scientific fact and certainty must settle itself, and — at least until all logical reasoning rests on a far more certain and generally admitted basis — must give the law to the logician, and not conversely. Provisionally, at any rate, if not ultimately and always, the logician has to learn what is good evidence and what is bad from those who are practically conversant with the use of evi- dence itself. So far as these doctors disagree, logic, strictly, has no facts to go upon. So far as they are at one as to the facts, logic has so many data, which it is its business to explain. If prolonged investigation shows some of these data to demand explanations incompatible with the existence of others, it may be that some portion of the data themselves must be revised. But in the present state of logical inquiry it is far more likely that the explanation should be wrong than the data. But now, how does our view as explained in the last chapter differ from that which we reject? We, too, begin with hypotheses, proceed with corroboration, and conclude to cer- tainty. How can this be right if Jevons' method is wrong ? The difference is simple. (1) Jevons' hypotheses are, to begin with, assumed. They are suggested to explain the facts, not necessitated by the facts. Our hypotheses, on the other hand, are inductions from the facts in their most elementary stage, arrived at by comparing, analysing and generalising the facts themselves. (2) Jevons' hypotheses are held good, because the conclusions deduced from them conform to fact ; this is as much as to say that they are probably true because not contra- dicted. Ours, on the other hand, are substantiated, because other inductions, independently arrived at, and also probable, equally necessitate them. That is to say, they are confirmed as true, not merely because they are not contradicted by other facts, but as actually supported by other judgments. Not mere consistency but positive consilience of results is our test. Our inductions are not at first certain. But they give partial or INDUCTION AND HYPOTHESIS 415 probable reasons for the theories. Corroboration by further inductions from fresh facts gives additional reasons, more prob- ability; until by the summation of reasons probability passes into certainty. Jevons begins with assumption and ends with plausibility. We seek to make no assumption throughout, but begin with probabilities, which we gradually piece together. The assumption would be on the side of those who should dispute inductive results without ground in observation. I conclude that a hypothesis which is merely assumed can never be substantiated by explaining the facts. Hypothesis which is not assumption, but is grounded on a partial reason, can be substantiated by the production of further reasons. Incipient inductions are the partial reasons, further inductions are further reasons, and the concatenation of the whole is the substantiation of the joint result. 2. Much that passes on a surface view for the formation of hypothesis to explain facts belongs in effect to a very important element in the procedure of science on which it would be easy to enlarge, but which we must here treat in a scanty notice. It has been seen from our account that inductive results, to be established, must be brought together ; and we shall see sub- sequently that the same process is necessary in order to under- stand or explain them. Hence the piecing together of results, i.e. the building up of conceptions, goes on in every stage of scientific discovery. And at no stage in science, except that of its final perfection, can every step in this process be completely assured. But the piecing together is an imperative necessity. There must at least be some way in which it can be " conceived," thought of as possible. Otherwise the different results will conflict. Hence the construction of conceptions tends to out- run established results. The points of certainty are eked out with more or less probable extensions of inference, by the argu- ment from continuity, by analogy, and, lastly, by mere supposi- tion. Hence the line between the true hypothesis — the sup- posed content from which, if it existed, the actual result would follow — and the probable truth for which there is some evidence tends to fluctuate ; while the probable conception again passes only by slow gradations into the certain. And thiis in the total conception of the way in which a mass of data are to be inter- preted there is a complexity of elements of very different logical value, and putting the value of the whole for safety's sake at its lowest, we spoak of it as at least a hypothesis which will, if true, explain the facts. In reality much of it will be far above the hypothesis in logical value — it will be, to use Lotze's ex- pression, a postulate. This building up of conceptions is un- doubtedly one main work of science, but to speak of it as 416 INFERENCE essentially the formation of hypotheses to explain results is to distort its character. Two brief illustrations must suffice. We may determine the path of a motor impulse almost with certainty from the Rolandic region through the corpora striata and the crura cerebri ; we can assure ourselves that it crosses at the foot of the anterior pyramids, and descends the cord by the lateral column of the opposite side. "We can see it, mentally, issuing through the anterior root and descending the sciatic until it reaches the muscle of the lower leg, which it is its business to set in motion. Now no whit of this is matter of direct observation, but all of it consists of a piecing together of a mass of inductive results. If we wish to go further into detail in determining the path, — to consider, for instance, whether this or that ganghon cell has a hand in it, or whether the impulse is conveyed directly by the fibres of the white matter, — we must piece out our information by probable reasoning and analogy. But up to a certain point we can elaborate a conception which does little more than em- body in a single whole our ascertained results, at most piecing them together by the conception of continuity. Here, then, we have the construction of a conception from a mass of data. The conception is not a supposal, not a hypothesis ; it is a conclusion. Contrast this case. The practice of exogamy is found in connection with totemism, and with other indications of a state of society in which descent is reckoned through the mother only. We know that marriage by capture is very common among primitive peoples, and the same is true of female infanticide. If we suppose, in the case of every tribe practising exogamy, that female infanticide was at one time so common as greatly to reduce the number of women bred up in the tribe, we can imagine marriage by capture from another tribe becoming so universal a custom as to acquire a traditional sanction, and to be the only form of marriage recognised as allowable. The women so captured would have different totems, and their children would inherit these totems (not the father's). But this totem being the mark of the foreign tribe would sanction marriage, and hence we get the remarkable system of exogamy under which you may marry anybody except those of the same totem. Now here we have a result, exogamy, explained by supposing an anterior state. For this anterior state we have no direct evidence, and the explanation is therefore conjectural. So far as it has probability, that depends on the analogical reasoning (the value of which it is not my business to determine) which suggests the practice of female infanticide on the scale required. INDUCTION AND HYPOTHESIS 417 So far as it is " mere " hypothesis, it is not a conclusion but a supposal. 3. The tendency to identifyinduction with hypothesis gathers strength from the particular form of inductive reasoning which argues, not from cause to effect, but from effect to cause. For here the cause is identified with the true logical ground and the effect with the consequent. Thus when the effect is given and we wish to argue to the cause, the process reduces itself to the inverse method. All we can really say is, " If A existed B would come about, but here is B ; well, then, assume A to have existed, and no difficulty arises." B is explained, and no further explanation is required. But this, as we have seen, is not proof ; it is not even argument ; it is merely a way of obtaining iatel- lectual comfort. How then do we argue from effect to cause ? — By the same reasoning which leads us from cause to effect. If and so far as the effect is a true logical ground which will take us to the cause as consequent, the inference holds ; and if not, not. We may exhibit the argument in several distinct cases. (a) If an effect a is known to have several distinct causes A, B, C, its existence as such is obviously no ground for inferring A rather than B or C. But if A is the only known cause of a, the case is different. The inference a- A is then a generalisation precisely like A - a, open to the same doubt and susceptible of the same tests. If a is not found unless A has gone before (negative instance), and if a is found preceded by A (positive instance) in very diverse contexts (" agreement" instances), it be- comes probable that the connection is not due to any extrinsic circumstances, but is universal In short,if no concomitant of a can be pointed out which is relevant to the mode of its causa- tion, we must infer that it will have the same cause in every case. The generalisation a-A may be very strong. Thus no in- stance, in all the multiplicity of cases and contexts in which observation has been made, has ever yet succeeded in detecting any cause for the existence of an organic being except the previous existence of some other organic being. Hence what- ever may be our views on the absolute universality of the re- lation, or on our right to apply it in remote epochs to different physical conditions, no one would agree with Topsy that she " growed,"nor, generally, could we doubt that if flora and fauna are discovered on an island they or their ancestors must have got there from somewhere. There are no autochthones. Here, then, we have the simplest case of argument from effect to cause, which is simply the application of a wide generalisation under the joint method. 27 418 INFERENCE (6) The case becomes a degree more complex when the effect to be explained is a whole of which the elements are known to have several causes, but of which as a whole nothing is known directly. Thus the effect C to be explained may be analysed into the elements a 13. And a may have causes ABC, and/3, causes ODE. It is clear that assuming C we can " explain " both a and /3, and what probability this alone gives us in favour of C we shall consider immediately. But if, further, we can show that A and B would have consequences incompatible with /S, while D and E have consequences incompatible with a, we have proved to be the true cause.^ This is of course the ordinary case of proving a hypothesis by means of excluding its rivals, and is only one form of a process which we have seen at work throughout inductive inference. The phrase, indeed, as used by Mill,^ has given rise to a not unnatural misunderstanding. It has suggested that we must exhaust our imagination in endeavouring to invent hypothetical explanations of a given fact X, and after refuting all but one, then, and then only, might we say that that one is the true explanation. But this obviously would lead on to infinity. You would never be theoretically certain that the wit of man had not the capacity for imagining some further theory. And clearly there is no reference in a logical proof to what a man can or can not imagine. The question is. What do the facts themselves render certain or probable ? And here we come to the true meaning of the requirement. As long as any data to be explained, either of themselves or in relation to the re- mainder of our experience, suggest alternative principles, so long neither of these principles can be regarded as certain. But the gradual consoKdation (by fresh discoveries, or analysis, or what not) of the one principle, will itself detract irom the probability of the other; and when, though only when, every such alternative principle has been disproved, the remaining principle is assured. For any other hypothesis, though perhaps imaginable, would ex hypothesi have no evidence to support it in the facts themselves, i.e. it would be an unmotived possibility. At every stage in induction we are discarding possibilities of this kind, the truth in effect being, in all rigid inductive argument, that what tends to prove a tends to dis- prove anythmg other than a. Our inductive results, then, 1 That is to say, assuming the original inductions which connect a with either A, B, or C, and (3 with either C, D, or E. The logic of these induc- tions is identical with that of the first case, except that the conclusion is disjunctive. ' Logic, bk. iii. chap. xiv. INDUCTION AND HYPOTHESIS 419 must not only explain the facts, but must be the only explana- tion compatible with the facts.^ So far of cases where either from the beginning or in the result only one cause is suggested by inference from the facts. To complete our account, we must notice the probable arguments which arise where many causes are possible. (c) If a is produced indifferently by A, B, C, and all I know about a certain case is that it is qualified by the presence of a, then I have no ground for preferring A, B or C as the cause in that case. Death is caused by hundreds of things ; and if I find a man dead, I have not the shadow of a right to conclude that he was murdered. But now suppose that our experience is carefully registered and analysed, and that in this experience a. has been caused by A in the ratio of 20 times, by B 10, and by C once ; then, if I see a, I have some reason for presuming ^ It is a little diflficult to make sure of the position of those ■writers who have defended what I may call the "hypothetical" view of induction. Whewell, who is often regarded as one of its strongest exponents, seems partly aware of its logical weakness, and makes the not unreasonable suggestion tbat consilience of very diverse results should be taken as true, and this on the ground that you could not, in the history of science, find an i istance of such a consilience turning out false [Philosophy of Discovery, vol. ii. p. 60 ft'. ). This, as far as it goes, Ls a way of saying that experience gives us no counter suggestion, and provides at least a via inedia between his view and our own. Mr. Bosanquet's account of induction I have already alluded to. He expressly ranges himself on the side of Whewell, Jevons, and Sigwart, but for which I should have regarded him as an ally rather than as an enemy. His account of perceptive analysis (vol. ii. chap. iv. ) corresponds to the forms of compavisou, etc., required by the experimental methods ; and in the part played by the theory of chance and the enumeration of instances, I find myself in close agreement with him. Again (chap, v, passim, see, e.g. pp. 164, 166), he lays down that the data must be in effect so "extended "as to "include" the hypothesis. I cannot, there- fore, think that on the whole there can be any substantial diflerence between his view and that of the text. Sigwart's view (as Mr. Bosanquet points out) appears to fluctuate. He never, so far as I can discover, clearly states whether induction does or does not prove anything. In general, he adopts the " hypothetical " view, agi'eeing (as he explicitly states) with Jevons. But he appeals sometimes to coincidence of quantitative variation, sometimes to com- plex correspondence of deduced result with fact, and sometimes again to principles which are in effect those of tbe joint method or its elements. Since I wrote the above, Mr. Bosanqiiet's Essentials of Logic has appeared. This masterly sketch throws (for me at least) considerable light on some of the most difficult points in the writer's views, but at the same time appears to me to render the final inadequacy of his theory of science fatally apparent. It is now clear to me (1) that Mr. Bosanquet intends ns to find "the system " somehow in the facts which we know (p. 140), but this position collides hope- lessly with (2) the denial of any certain generalisation except that "by determination," i.e. by tautology. If we cannot generalise observed results we can have no knowledge outside the memory series. To give up the attempt to explain generalisation is to evade the chief crux of logic. And as to "the system," generalisation is one of the main strands that run through it, and net its parts together. "Without generalising, how can we use the facts that we know as evidence for the character of those that we do not know, i.e. how can we form from the part a system which shall comprehend the whole ? 420 INFERENCE that A has gone before, and very strong ground for iDelieving that either A or B was its cause. A child tells me that he has seen a man seven feet high. The statement is a fact for which there are two possible explanations. The first is that it is the truth. The second is that the child exaggerated. Now there are not many men seven feet high, but children often exaggerate. Most of us therefore would prefer the second explanation. ((T) We proceed to a more special case, which may be called the explanatory method ^ proper. This depends not on a direct generalisation from efiect to cause, but on a construction of generalised relations, and is the argument which falls most naturally into hypothetical form. Suppose, as before, that we have two efl'ects a, and jS of each of which we know the causes exhaustively. Let the causes of a be M N 0, and those of /3, P Q. Then 0, and only 0, produces both a and |3. Kow let us observe both a and jS together. The obvious conclusion is that O is their cause (" will explain both "), but this is going a little too fast. A combination of M and P would also explain both, so again would N and Q, and so on. Supposing each " cause " M N P Q to be equally probable, i.e. equally frequent, a combination of any two of them, as M P, will be much less frequent than the occurrence of any one, M or P.^ But there are four combinations, M P, M Q, IST P, N Q, which will give a j3, and each of these has to be reckoned as a counter possibility to 0. Still, if the probability of each is very low, that of will exceed the combined probabilities of them all. In any case, is more probable than any other single ex- planation. And we may say generally that if the component causes be equally probable, the simplest explanation which will explain the total effect is more probable than any explanation which is more complex; and the greater the complexity of the alternative explanations, the more probable ' A term whioli I derived from Professor Minto {Logic, bk. ii. chap. vii. ). The dififerenoe between it and the method examined above is that it does not decisively eliminate rival possibilities, but rests on the theory of chance. ° How much less frequent we cannot say precisely. We must not assume that M win coincide with P as often as not. There is no reason assigned why M should coincide with P more often than with any other fact, X, Y, or Z. Unless, then, P is itself very common, the number of combinations M P should be very small as compared with the occurrence of M. It is tempting but illegitimate to argue that given a the chance of M is one-third, and given j3 the chance of P is one-third, and that, accordingly, given o and p the chance of M P is one-ninth. This ignores the question whether there are independent prob- abilities affecting the combination of M and P. These probabilities (seeing that a and j3 may be caused in other ways) are found in the chance of M coinciding with P, a chance which must be measured by the frequencies of the two elements. INDUCTION AND HYPOTHESIS 421 the simple explanation. We assume, of course, that no reason is known for taking one of the causes M N P Q to be more frequent than any other. So far as anything is known which leads us to treat O as intrinsically improbable, the argument must be proportionally modified. Lastly, we have so far assumed exhaustive knowledge of the list of causes of a and j8. But this can only be arrived at with more or less of probability, in accordance with the argument of the preceding section. Except therefore as presupposing that argument our present considerations have no locus standi. It results then that when we have only a simple combination a/3, in which there are but two separable elements, the argument to a common cause will not be strong unless the experience bearing on the subject is of a very special kind. If, however, we take in fresh elements, if, that is, the complexity of the effect increases, the argument becomes stronger. If we have 4 elements a ^ y S, and even if, assuming that we know nothing whatever about their collocation, we take the chance of each at J, the probability of the whole collocation will be (J)*=T'g. The actual prob- ability, as based on observation, may be very much less. The probability of such a collocation of separate causes will be proportional.^ Hence if one cause is known which will " ex- plain" the whole, its probability as against a quadruple collocation is as ^ to -j^, i.e. 8 to 1 ; whUe, if we suppose a possibility of a collocation of two causes explaining the 4 effects, this chance would be more probable than the quadruple collocation though less probable than the single cause. We thus get an explanation of the rule that the hypothesis is more probable in proportion as it is simple and as the facts it explains are complex. Of course, so far as we have definite information on the frequency of any of the alternative causes, our result wUl be so far modified. («) Lastly, additional characteristics, or the precise definition of the effect, may put certain causes out of court altogether. It may be that a is caused by M, and /3 by P, when MP would give a/S. But suppose M also gives y, or P, &, and that either y or 5 are absent in this instance, it is clear that the suggestion of MP must be rejected. Thus the comparatively simple, undefined, effect may have any one of a great number of causes, while further attention and analysis, or additional information, ' This will hold whether a (3 7 and 5 have each one cause only or many ; for given their frequency, the frequency of their causes as a body is fixed. If x has a frequency of one-twentieth, so have all its causes taken together. If it has one cause, that cause has a, frequency of one-twentieth If two, each has, say, one-fortieth, and so on. 422 INFERENCE may so qualify it as to rule these causes one by one out of court. Another common result of more precise knowledge is to necessitate the suggestion of further complexities, each of which, without absolutely entailing the rejection of the hypothesis, makes it upon our principle more and more improbable. AH "circumstantial evidence" rests upon the foregoing suppositions. A man is found dead with his throat cut. A knife is found in a ditch close by. There are footprints in the mud. X was known to be in the neighbourhood on the day ; evidence is given that he purchased the knife a week before ; his boots fit the footprints. All these facts might be due to a collocation of separate causes, but all are explicable by a single cause, namely, that X planned and carried out the murder. The single assumption is so much more probable than the multiple combination of circumstances that it is likely to go hard with X, and his business is to produce some fact incompatible with the above explanation. Failing this, one or two more such combinations of circumstances and our conviction of the strength of the hypothetical argument will he evinced in a very practical manner. We may sum up the whole argument in the positions, (a) that other things equal, the simplest collocation is more frequent than the more complex ; and (S) that the only other thing that can be unequal is de facto observation of the frequency of a suggested cause. From these positions it follows that when the effects are many and separable, but all explicable by a single cause, that cause will be more probable than any com- bination of separate causes, in proportion to its own simplicity and their multiplicity ; while, further, this probability is heightened or diminished according to the results given by observation as to the comparative frequency of the different causes compared. It will be seen that our statement of the hypothetical argument justifies an earlier remark, that this method assumes pre-existing knowledge of causal relations. For until such relations be known for the single elements, however likely it be that a, ^ y h should have a single cause, that is no evidence whatever that any fact A is this cause. That A is such a cause can only be shown by ordinary induction for the whole complex a B y d, or for each part of it separately. In either case the foundation of the process is direct induction. On this ground alone the theory which identifies the hypothetical method with induction stands condemned. The truth is that this method is a complex result of the theory of probabilities INDUCTION AND HYPOTHESIS 423 as applied to a subject-matter in which many simple inductions are already known with a view to explaining a complex case — whether an individual fact or a species — for v,hich, from what- ever cause, direct observation aud elimination are impossible. It is hard to see how we could possibly imagine a cause which would " explain " an effect unless we already knew that that sort of cause explained that sort of efiect, i.e. in cognate cases, or in cases composed at least in part of similar elements. Explanatory causes are nut revealed by intuition, but learnt by experience. And only such causes as resemble those experienced can be used as explanatory of new effects. In fact, induction gives us probable inferences from cause to effect, and with less ease (since experiment is impossible and we rest on observation) from effect to cause. In complex cases of special interest we utilise tliis basis of knowledge to construct ex- planations to which the facts point as being more or less probably the explanations available. The "explanatory" method is thus not induction proper, but a special application of inductive results. CHAPTEE XVIII Constructive Generalisation We have seen in Chap. YI. that what appears at first sight as inference by construction is a genus containing two species. The first consists of syllogism, in which the premisses give conditions combined into a result. The second combines parts into a whole, or unites relations to form a resultant. These last appeared analogous to ordinary perceptual construction, but with this primd facie difference, that they were or could be stated as general truths. This form of construction appeared in fact as a generahsation from experience, and a generalisation of a peculiar type. Our business in the matter is twofold; first, to get at the generalisations involved, and secondly, to explain and justify them. 1. We have already (Chap. VI.) noticed some cases of this kind of inference. We may now distinguish its two main types and bring them provisionally under appropriate axioms. (a) The first type is that of arithmetical addition or sub- traction 3 + 5 = 8, two pints one quart. In these cases we are given certain elements, and assert that these elements form a certain whole. Both the elements and the whole must be such as to be known otherwise than in relation to each other, or we get into tautology. Thus, if 8 only meant 5 + 3 the statement 5+3 = 8 would be an idle play on words. But 8 also means 4 + 4, 10 - 2, 4 X 2, and I will venture to say that it also and primarily means 8. That is, it is a name for a certain whole qualified to our apprehension, or to our construction of appre- hensions in a definite way, which distinguishes it from all other wholes, and is in fact the basis of all the analyses and relations mentioned above.^ But if 8 does not merely mean ^ The qualitative character of a nninber is well illustrated by the case of children and primitive men, who can discriminate numerically different wholes which they cannot count. This means that the unanalysed qualitative character of the wholes is different for them, whence each totality must be recognised by its character as a totality. This is how a savage who cannot count much beyond ten can tell whether any cattle in a herd of 400 or 500 are missing (Cantor, Oesch. der Mathematik, Introd. p. 4). 424 CONSTRUCTIVE GENERALISATION 425 5+3 over again, what is the nature and validity of the judg- ment ? In the first place, it is a generalisation, being stated not of this or that 5+3, but of 5+3 as such. Secondly, it may be taken as resting on observation ; for siace we know observa- tion to be a basis for generalisation, and since we know the relation in question to be observable, we have no right to assume the contrary, seeing that the simpler hypothesis which rests all generalisation on a single basis iBprimd facie capable of explaining the facts. But it has often been urged that there is this peculiarity in generalisations of this kind, that they become obvious upon the first observation. Well, assume it to be so. What then will be the axiom involved? This, that if certain facts taken together constitute a certain whole, pre- cisely similar facts will together constitute a precisely similar whole. 5 and 3, to whatever objects applied, are in themselves precisely similar. So is 8. The generaUsation in question, therefore, follows immediately from the axiom. The axiom, it must be explained, must be taken very strictly or it will give false results. That is to say, the facts first taken must by themselves, and of themselves, truly build up or form the whole. The whole must consist of the parts, neither more nor less. The formation of the ideas of such a whole and parts may involve a high degree of abstraction, which is indeed the case with all additions of pure numbers, and it is only when the abstraction is completely and con- sistently carried out that the result is true. Two bodies of ten men each are equal to one of twenty in point of number, but one blast of Eoderick's bugle-horn were worth a thousand men. That is, to avoid error we must know precisely what we sum, and we must know precisely what our whole is. The whole must not even be a physical or psychological effect of the elements, for the effect in this case will mean an affection of something else, and that affection may be partly due to some further circum- stance. Thus it would at first seem fair to generalise an aesthetic effect. If two colours make a horrible combination, surely that combination is simply the total of the two in the relation of juxtaposition ? Not necessarily, for neighbouring colours, intensity of light, and so on, may contribute to our view of the total, which is in reality a reaction of feeling on the stimulus here produced by the colours. We must restrict ourselves, then, to the mere summation of parts if we are to get a true whole which is determined by, and itself determines, the parts. On the other hand, we may or may not take account of the relations of the parts, and according to our attitude adopted on this point the character of our construction, and 426 INFERENCE therefore of our whole, will be materially modified. In pure counting we take no account of the relation of the units, except such relationship as is involved in their all belonging to some kind of unity natural or arbitrary. On the other hand, in analysing any geometrical figm'e our attention to the relations involved must keep pace step by step with the analysis of parts. Two right - angled isosceles triangles form a square, but only in one special relation, namely, where they have the hypotenuse common. Our axiom, then, states that the relation of whole to parts is uniform, and that we may accordingly generalise any single case of such a relation, pro- vided that our analytic observation has determined accurately that the given whole is formed of the given parts, that the relations of the parts do or do not enter into the composition of the whole, and that it is understood that the relation of whole to parts is one detected in the given ^ by analytic attention itself, and is not any effect beyond the given elements. But these conditions are to be secured by ade- quate abstraction, i.e. by perfected analysis, and accordingly it is on that perfection of analysis, which enables various elements of the given to be considered apart from their context, that the sciences of pure quantity depend. (6) A second class of constructive generalisations are dis- tinguished by dealing with a nexus of relations. We have already, in Chapter VI., given instances of these, and we have only here to suggest an axiom which, without being inclusive of all the cases in point (as we shall see presently), will sufficiently exemplify the mode of reducing such inferences to rule. Amplifying the diagram of Chapter VI., we are given three points ABC, such that B and C both stand to A in a definite observable relation, and if the relation B C be observed, then this relation may be regarded as the resultant of the other two, and may be generalised so that if we have B^ and C^ (precisely similar terms to B and C) stand- ^ By "the given" it will be recollected that I intend not only the content of any single act of apprehension, but also a content formed by construction of such contents. "Within either content analysis may directly observe the relation of whole and parts. CONSTRUCTIVE GENERALISATION 427 ing in relations to A^ precisely similar to those occupied respectively by B and C to A, the resultant relation Bj C^ will be precisely similar to the resultant B C. Here, as we before pointed out, the resultant is not a simple construction of ABC. That construction, the true whole formed by the arithmetic summation of the data, is accurately represented in the diagram by the complete line BAG. In fact, the line or relation B C is a relation discovered by analysis in the whole BAG formed by the given elements. Thus before, we had an inference from parts to whole; here we go a step further and infer to the new feature contained in the whole as constituted by the given parts. Of this type are all generalisa- tions of that rudimentary but often necessary Mnd of geo- metrical reasoning which infers from a plan. So at bottom are all generalisations about degree and proportion. That degrees form a scale we learn, I take it, by observation ; and by the same observation we learn the meaning of intermediate steps. At the same time we rigidly generalise every fact observed. Thus, that 6 feet being more than 5 feet is also more than 4 is not a purely independent generalisation, but having once apprehended the relations of greater, middle and less, together with the resultant relation of the extremes, we apply this knowledge as a generalisation to all quantities similar in the points compared, i.e. similar in admitting of direct quantitative comparison and of presenting the above character of graduation. That being granted, the relation of 6, 5 and 4 being observed, its resultant is a deduction from the major premiss laying down the character of such degrees. Every method of relating contents to one another by comparing them with an intermediary thus learnt once is learnt once for all. Wherever such a relationship is ultimate, i.e. does not rest on calculation by the putting together of stiU. simpler relations, its basis is immediate generalisation from an observed case.^ ^ M. Georges Mouret (in a discussion suggested by an article of the present writer, Miiul, Jan. 1892) di-aws a useful distinction between a "resultant relation," whicli is in effect a mere definition, and one whicb states a law. Thus, defining equality of forces, as he does (see his able articles " Sm- I'Egalite Mathematique, " Mevue Philoaophique, vol. xxxii. esp. pp. 136 ff. ), in terms of equilibrium with a third force, he is quite right in saying that to conclude from the equilibrium A - B and B - C to the equality A - C "is not to express a new fact, . . . but to repeat a definition." I agree. This is my case (explained above. Chap. VI.), when we construct a whole, but without inferring any further resultant relation between any of its parts other than is involved in their coming to form a whole. Equality (if we take M. Mouret's definition) is not inferred from the double equilibrium, but is the fact of this double equilibrium. Here, then, our axiom of construction does not apply. Other cases, says M. Mouret {MiTid, loc. cit. p. 103), are those of tme ' ' laws " of coexistence, and are based on 428 INFERENCE 2. We will not at this point attempt to exhaust the axioms of that character which are tacitly employed in the various parts of mathematics and other sciences. We shall have to return to the subject later in the chapter, and meanwhile the two axioms taken wOl sufficiently exemplify the class. Our problem now will present itself thus. Granting the existence and truth of axioms of this class, the immediate necessity of mathematical and other truths explains itself. For these axioms are such as to give a certain generalisation on being appUed to a single observed case. If then they are taken for granted, the primary truths of mathematics fall into a deriva- tive place as generaUsations from a single instance by means of these axioms which in themselves are essentially principles of generalisation. If this is so, then the grand problem of the affinity between mathematical and other reasoning resolves itself into the question. How are these axioms connected with the general principles of reasoning ? Starting from the induc- tive principles which we have assumed all along, can we connect them with our axioms of construction in such a way that the latter follow from them either directly or by their induction. This is also possible. But there is a third and important class of oases Tvhere a resultant relation is asserted as coming about when certain elements are combined, which relation is not a mere expression for the fact that the elements are combined, but is neyertheless generalised with confidence, as it would appear, from a single case. My axiom is intended to cover these instances. One further point must be mentioned. I have tried to make clear that two relations can only be so constructed as to form a third on the basis of an observed case in which they do so form it. You cannot (except perhaps in a few cases to be explained lower down) construct relations without direct empirical knowledge of the whole that they form. Hence I do not think M. Mouret's axiom of symmetry {Sevue Philosophique, vol. xsxii. p. 286, etc.) applicable except on the basis of experience (see Mr. F. C. Eussell's criticisms, Moniat, April 1894, p. 462). You cannot say generally that if there are relations of like kind between A B and B C, that there will be a similar relation between A and C. You can only say so when experience shows it you in a given case. If you find A - B, B - C actually giving you the relation A - C, then you can generalise it. If not, not. You cannot even say that if A and C are both related to B they must be in some definite relation to one another — other than that in which they already stand as being thought of together (see Bradley, Logic, bk. ii. pt. i. chap. ii. — "A runs faster than B, and B keeps a dog" — what relation is there between A and the dog ?). Hence my axiom is modelled on that originally suggested by George Eliot — "Things that have a constant relation to the same thing have a constant relation to each other," and not on Mr. Herbert Spencer's amendment of the same {Pritieiples of Psychology, pp. 107, 108, note). My argument, in fact, does nothing but define and apply George Eliot's axiom. Any such axiom is of course merely implicit in ordinary thought. Mr. Bradley is fully justified in denying the use of an explicit major in construction. But it remains that an observed parallel is the ultimate logical basis of the con- struction before us, and that in making constructions analogous to such as we have found we commit ourselves to a general principle. CONSTRUCTIVE GENERALISATION 429 application to experience ? In either case the guarantee of mathematical truth will be in the last resort the same as that of all truth whatever. The obvious way to explain these axioms — the intui- tionist way is no attempt at explanation, but a mere reitera- tion of the fact of subjective certainty — is to treat them with Mill as generalisations from experience. But in carrying out this idea, Mill made an unfortunate " strategical " blimder. Having suggested that necessity is hypothetical in character, a suggestion on which aU fruitful thought has subsequently pro- ceeded, he unfortunately deserted this point of view and endeavoured to explain it as a kind of psychological fiction arising from multiplicity of observations. Against this, thinkers like Professor James retort with crushing effect, that if you take simple observations as they stand they are far from giving you the multiphcity of instances required. Two and two do not always make four in the physical world, e.g., in one of Professor James instances, add two drops to two drops physically, and the whole makes one large drop. Two straight lines do seem to enclose a space. Apparent circles have unequal radii ; and if irxiov ij/Mgi> cravro's is obvious metaphor, it is at least doubtful whether direct physical experience would make us confident that the straight line is the shortest possible between any two points. The rejoinder of the sensationahst to these objections is, that you do not in mathematics mean the same thiiig by straight, equal, circular as you do in the crude observations of daily life. But this answer is fatal to sensa- tionalism, because it admits that the truths ia question are due, not to the accumulation or interaction of the observed facts as they are in their concreteness, but to the abstractions and universal relations of abstractions which are picked out of the concrete by construction and analysis. The truth is, that the bricks of which mathematics are built are not sensations or facts of apprehension in their concrete form, but certain elements in these facts detected and fastened on to by analytic attention. Along with this goes one other of Mill's points, the effect of multitudinous experience. The many experiences are not there, and if they were they would not give the logical cer- tainty required. Clearly, if we are to explain the axioms as generalised from experience at all, by far our best move is to play the scientific methods. And no one could deny that the axioms regarded as generalisations conform quite strictly to the scientific canons of difference and agreement. Things equal to the same thing are equal to one another in omnimoda 430 INFERENCE materia (agreement) ; and if you disturb the equality of either to the intermediate, you disturb its relation to the other extreme (difference). But though the inductive view cannot be disproved, inas- much as axioms, being good generaUsations, will obviously pass all the tests of sound inductive results, there are reasons in the general character of these truths which incline us to look else- where for their real explanation. There is a neatness and unconditionalness about our mathematical reasoning, and above all a finality in its certainty, which we cannot help contrasting with the lingeringly hypothetical character of induction, which always seems to keep an eye open to the odd chance of error. I propose, therefore, to substitute a different explanation, which is I think more complete and certainly to my own mind more convincing. Granting their immediacy and necessity, both the axioms mentioned, and others of the same kind, may be explained as following directly from the axioms of induction together with a postulate of the judgment. All judgments, whether resting on explicit inference or not, wish to assert truth, and the method by which a judgment is formed should therefore be a sound method, i.e. a method by which, granting its premisses true, only true results can be obtained. Hence, however we analyse such a method, whether it resolves itself into any form of inference or exhibits any other general principle whatever, that principle must be a true one. This may be said to be a postulate of the judgment, i.e. by forming and adhering to a judgment we postulate the validity of the method by which we have formed it. The truth of our judgment, again, stands or falls with the validity of its method ; and if, finally, there is some particular method upon which all judgments rest, upou which judgment as such rests, the validity of that method is implied by every judgment which we make, i.e. by the whole body and structure of our knowledge. Now, judgment, we have seen, involves construction and analysis. It puts different apprehended contents together ; it fuses apprehended with remembered contents ; it combines contents originally given in separation and capable of beino recalled separately in memory. Similarly, it directs its atten- tion analytically, now to one part of a given content, now to another, now to a relation, now to an attribute. Confining our attention to the points that immediately concern us, itthus asserts (i.) wholes of which the elements are or have been given. The simple judgment " It lasted two hours " involves the sum- ming up of the content of a very long continued apprehension, CONSTRUCTIVE GENERALISATION 431 or of distinct and successive acts of apprehensions in a single assertion. The whole has never been given as a whole to ap- prehension, though its parts have been all apprehended whether continuously or ia succession. But the judgment takes the parts and forms them into a whole, i.e. it makes the parts a basis for the assertion of the whole. And in this the axiom " Same parts same whole " is imphed. If, as a fact, the whole was not entirely determined by its parts, a judgment which asserted a whole immediately on the basis of its parts and without any further consideration would be liable to error. Accordingly, the very existence of the constructive judgment postulates the relation of whole to parts according to which they mutually determine one another. And (ii.) the judgment asserts relations which have not been given, between terms which have been given separately. " A is like B," when A is a present, B a remembered, content, — is a simple instance of this. The relation of likeness has never been given in the way in which the hkeness of two i's or two e's is given to me on this page. Here again, then, we postulate that the relation is fixed by the terms. If, when the terms were once clear, the relation might yet vary, there would be no safety in any comparison that should go beyond simultaneously presented data. Now, if we treat the relation as a fact discovered by analysis of a whole which in fact contains both terms and relation, we may go on to put the principle thus — that similar wholes can be analysed into similar elements. Just as before we saw that the constructive judgment implies that the parts determine the whole, so here we see that the relative judgment postulates no more than that the whole determines the parts. The relative judgment, in fact, first builds up a whole (two ideas, two remembered contents, or one idea and a present content, as the case may be) and breaks up this whole into the two terms and their relation. But that this shall be true, both our axioms of the determining of whole by parts and of relation by terms (or, if we now prefer it, of relation and terms by the whole which they constitute) must hold good. Our axioms, then, are postulates of judgment. Observe the result. By the axioms of induction, what is true of A as such is true of it universally ; or what can be affirmed of A without further consideration, without regard to any further fact, can be affirmed of it universally. The postulate of the judgment is that we can assert a whole on the basis of its parts, and the parts on the basis of their whole without considering any further fact; that is, 432 INFERENCE we can affirm the one term of the other as such, that is universally. Now, in any case, let a relation of parts to whole be observed, whether by immediate apprehension or by the help of construction and analysis. It must follow that the given relation must be generalised. Hence every addition, every analysis of a whole into terms and their relation, once per- formed, holds good forever for those parts, for that whole. I do not seriously require to add up 2 and 2 and make them 4 in different contexts and under different conditions in order to assure myself that no casual concomitant interferes with the result. I do require to add them once, but that done I generalise the result by means of my knowledge of the nature of the relation before me. I no longer need to place 2 sets of 2 objects before my eyes, nor 2 ideal 2's before my mind. The symbol-figures 2 and 2 taken to stand for such ideals give me 4 by inference. All actual calculation, then, whether in pure or spatial quantity, going on, as it does, vnthout the necessity of repeated observation, involves the application to fresh cases of generalisations originally derived from single observed cases. Give me two quantities to add. I may per- form this by counting, i.e. actual construction of apprehensions of these numbers. Then my act is original and independent. Or I may bring these numbers, either directly and as wholes, or indirectly and part by part, under generalised constructions already made. In the more complex case, when I take part by part,i the synthesis of the parts is again a further applica- tion of yet another construction. These constructions and their applications in ever-growing complexity constitute the work of mathematics. 3. It was generally admitted by the defenders of the " inductive view " of mathematics that its inductions were few, simple, and easy, and that the main business of the science was to combine the general principles once obtained into fresh deductive results. And it might be thought that our present argument would go to confirm that view. But two limitations seem necessary. First, much so-called deduction in mathe- matics consists really of a repeated and special act of construction, which must be noted in some special case, whether on paper or in the mind's eye, and tacitly generalised for every case of the class. Thus, in Euclid, I. 5, we produce the two sides A B, A C in accordance with the postulate that any straight line can be indefinitely produced. "We take the points D and E, such that D B = C E in accord- ^ As, e.g., in the addition of all double iignres. , CONSTRUCTIVE GENERALISATION -433 ance with a previous problem. But that, by joining C D and B E, we shall get two triangles, that these triangles will have the angle A common, and that their sides A B, A E, A C, A D will be made up of the two equal sides of the original triangle and the equal added lines B D, C E, could surely be clear only by a special analytic or constructive act. I must " see " that it is so, by either physically or mentally making it so; and I must be clear, further, that this result depends on no special feature iu the triangle ABC, but merely on the fact that it is a triangle and has equal sides. Every such construction seems an original and independent mental process, not to be identified with the application of a general truth already known to a fresh case. And so geometry will appear as not a mere set of deductions from a few principles, but equally as a network of constructions without which these principles could not be applied to such a complex variety of data. Now, secondly, these and even simpler constructive generahsations are not without . difficulties of their own — were it otherwise, mathematics would be all plain sailing to every dullard. They involve a certain combination of con- struction with analysis which may be by no means easy to carry out with success. When a construction merely combines certain apprehended contents as they are given, there is scarcely room for error as to the whole formed by them. The case is the same where analysis breaks up a given whole into parts. Now, the generalisation in these cases holds simply for contents precisely similar in every point to those originally taken. But in the ordinary constructive generalisation, a good deal of diversity is allowed, and is held to be immaterial. Thus arithmetical generahsations fasten on the mere quan- tity of objects, and claim to take that aspect of things and generahse its relations on its own account. Here each quan- tity at least is definite ; but in algebra we go a stage further in abstraction, and form calculations regarding quantities as such. So, again, the generalisation, that if equals are added to equals the wholes are equal, may be founded on per- ception; but any perception of equality must involve con- crete quantities of concrete things of which the equality is only one aspect. In all these cases analysis marks out for itself certain aspects of the given ; and it is, again, analysis of the given total which determines what those given parts amount to when summed. In 6+4=10 each term is (relatively to any given facts, small concrete objects or strokes of a pen) an abstraction 28 434 INFERENCE obtained by analysis. Tbis is equally true of the whole 10 and of the parts 6 and 4. Now, the judgment says that the one side of the equation is a construction of the elements con- tained in the other, and accordingly it generalises this equation. Hence the truth of the equation depends on the correctness of the analysis. And this correctness involves that in the simimation those ideas referred to in the judgment, and only those ideas, are before the mind. If any other part of the given content creeps into the formation of the whole, the generalisation will be wrecked. The same result will happen if one of the terms has in the given case a special character which is ignored in stating the generalisation. In that case the whole, in the form of it here given, may correspond to the parts, but not in its other forms, and we get the fallacy a dicto secundum quid ad dictum simpliciter. This fallacy, no doubt, more often attends the verbal expression, the proposi- tion, than the judgment as an actual thought; but the proposition modifies the judgment, and transfers its fallacy from the spoken to the thought content. 4. The difficulties of construction based on abstraction give a certain place in the formulation of axioms to a regular eliminative induction, though rather, perhaps, by way of verification than as the sole and sufficient foundation of the axiom. Is it doubted whether a given combination of ideas is correctly formed ? Then the fallacy may be in the sub- reption of part ,of the concrete setting of the ideas. In that case try the same idea in a different context — just as in the method of agreement. Again, was it a special form of idea A which broke up into the parts B - C ? If so, a different form of A will not reveal such an analysis. The old axiom famous in controversy, that " Two straight lines cannot enclose a space," appears to me a generalisation of this kind. If I take any two drawn lines P and Q — they clearly meet in one point only and then diverge, and any other pair of lines, 0' P' Q', precisely similar to these, will not only diverge but wiU diverge at the same angle and at the same rate, i.e. imaginary base lines P Q, P' Q' drawn at the same distance along each line ^ from and 0' respectively would be of the same length. But that two straight lines cannot enclose a space is a proposition of a more abstract character. It involves the analysis of a given content such as that drawn above, and implies that we select the more general contents, one straight line, another straight line, and (relation between CONSTRUCTIVE GENERALISATION 435 them) divergence from a common point.^ This analysis takes us into the region of ideas, and if we can so fix these ideal contents as to he able to form in our minds a construction of them with the definite relation resulting, then we can have true abstract construction, and can generahse accordingly. Hence it is true to urge agaiast the sensationalist theory that mathe- matical (and other) constructive generalisations are not, or at least are not always, made directly from sense-perceptions. But seeing that the ideas used are themselves derived from sense, the constructions of them are mediately so derived also. Nor have the ideas or our constructions of them any validity unless they will stand the test of appKcation to sense. But the ideas are intermediaries, and intermediaries which do not merely pass on results, but which form the basis for further constructive and analytic action. Hence it is true that in abstract con- structions ideas form our immediate data, and hence, also, certainty of appKcation may be increased by a true inductive {i.e. eliminative) verification.^ We conclude that the con- crete wholes of apprehended contents may be generalised immediately, while, as to abstract constructions, two processes may be employed. In many cases construction may depend purely on perceptive analysis. Just as (according to our contention) we perceive the abstract attributes of things, so we perceive directly the summation and division of such attributes. That 7 is composed of 4 + 3 is then just as direct a perception as that of 7, 4 and 3 themselves. Attention is concentrated on the purely quantitative aspect in the mere judgment "There are seven," and in the equation 7 = 4 + 3 it is similarly directed to the specification of the parts of that aspect. Then the analysis once performed holds good univer- sally. But in other cases that analysis may be helped out by a true eHminative induction. The starting-point in this induction is that the elements of the construction must be within the given concrete whole. But the doubt is whether some other elements of this whole have not crept into that construction which we have taken to depend on such and such elements, and on them only. Thus in combining two conceptions I ^ This by itself would give us the axiom that two straight lines can meet in one point only. The case of parallels has to be included before we make the wider generalisation. Does not the rejection of these and Euclid's twelfth axiom, as neither self-evident nor deducible from any other axiom, rather ignore the possibilities of inductive proof ? ^ Ideas, it will be remembered, have contents drawn from given reality, and bear reference to that reality. An "ideal experiment," then, a construction of ideal elements, is logically a construction of real elements, and to generalise such a construction is ultimately to draw an inference from the behaviour of given wholes. 436 INFERENCE may be unconsciously influenced by the " image," the concrete setting in which the conceptions are present to me. If, then, by applying my conceptions to varying matter, I eliminate aU the elements discovered in the concrete given whole except those of which my construction takes account, I remove this doubt. And observe that induction of this kind is for its purpose final, since it has merely a definite, given number of possibly interfering concomitants to reject. Such induction, then, may in many cases help out perceptive analysis. It may be added that an axiom resting on this kind of induction may have two possible meanings. If we have examined A^, At, A^, and found them all to be B, and thence generalise A B, we may mean by A only cases exactly similar to those examined. Then A B is a summary of generaUsations each perfectly certain. But A may be such as to admit of further species A^, Ag unknown to us ; and if we intend our axiom to include such possible cases, it will be safe only so far as the analytic ehmination in the instances given has been complete, i.e. as B is known by them to be constituted by A and A alone. There is an element of ambiguity and uncer- tainty here which should not be overlooked in the use of axioms.^ ^ From the theory of the text we should naturally infer that mathematics in their primitive stages would have a quasi-inductive character. That is to say, that (1) they would tend to deal with concrete ohjects, or classes of such objects ; that (2) their results would have the aspect of independent generalisa- tions, rules of thumb, and so on ; and that (3) they would be encumbered with difficulties in rising from these iirst generalisations to higher, more compre- hensive, and more abstract principles. All these points seem to be borne out by the little that is known, or probably inferred, as to the early history of arithmetic and geometry. As to (1), the familiar facts of counting by fingers, or other concrete objects, is a sufficient illustration (seeTylor, Primitive Culture, vol. i. chap. vii.). The relation of geometry to land-surveying is equally familiar (Cantor, p. 53, who refers to Herodotus, ii. 109, etc.). Traces of (2) appear, even in arithmetic where one would be least sanguine of finding them, in the papyrus of Ahmes, a book of arithmetical rules of the time of the Hyksos. "The first part" of this treatise "deals with the reduction of fractions of the type 2/ (2n 4- 1) to a sum of fractions whose numerators are each unity" (Ball, Short History of Mathematics, p. 4). With this object, Ahmes gives a number of rules dealing with quite similar problems, but witJiout reducing them to any single rule (Cantor, op. eit. p. 21). The solitary exception is the rule for finding the value of g of another fraction, but even here the list of instances given presents exceptions wliich lead Cantor to con- clude that the only possible explanation of the tables is a gradual origin with no comprehensive unity of thought (p. 27). In geometry we have fuller evidence, though the comparative absence of information as to the proofs used by early geometers must make us careful iu resting much upon it. Three things, however, seem clear. The Egyptian geometers worked on concrete problems mainly with numerical data (Ball, p. 8 ; Cantor, p. 56). The turning- point in geometry came when Thales and the early Pythagoreans began to generalise their results. And this "generalisation" proceeded only piecemeal CONSTRUCTIVE GENERALISATION 437 5. So far for our general theory. We have only now to remind ourselves that we have carried it on by the help of two axioms for which we did not claim a comprehensive character, but which we took as illustrative. From these axioms many seemingly axiomatic truths may doubtless be derived, but some I think are better explained as directly due to the postulate which we have seen reason to place at the basis of the whole matter. One illustration of this wiU be sufficient, and I will take the famous axiom of measure (things equal to the same thing are equal to each other) for the purpose. It is a postulate of the judgment that likeness (like other relations) depends on the terms related. Between Aj and Aj I observe perfect likeness. That relation, then, is due to nothing but the directly observed character of the two terms them- selves. I have now A3, which I cannot compare directly with Ai, but which is given exactly like Aj. Whatever follows from the character of Aj follows accordingly from that of A3. But A2 and A^ exhibited precise resemblance, therefore A3 and Aj must have the same precise resemblance. Equality is simply a case of precise resemblance in the particular point of quantity. Whence the axiom, which is in fact a particular and by slow degrees. It seems clear that Euclid, i. 32, was first proved for separate classes of triangles, and then generalised for triangles as such. (This important point rests on a statement of Geminus given by Cantor, p. 120 ; and we may add, that it is borne out by the constant choice of this property by Aristotle as illustrating the true method of . eit. chap. v.). The moving body "is" not in two places at once, nor "is" it in one at once, it "is" not in any place at all in the sense which the paradox wants us to imply, i.e. it is not resting in any one place. Its motion is not a synthesis of two rests with a jump between, but is a state of the body which we can only define by contrasting it with rest. It is moving through space during time. Shorten the time and you reduce the space. Annihilate the time and you bring the space to zero. But just at this point you have left reality altogether and fallen into abstraction. You make an unreal premiss and are surprised at reaching an unreal conclusion. You do away with time and are surprised to find motion cease as well. So is it with change. The change is real in time, and in any different moment presents a plurality of characters. Crystallise these characters, i.e. suspend the conditions maintaining the change, and we have two statical points, A and B, sis the first and last stages of the process. But A and B with a jump do not make up the Erocess. It is a continuous alteration of A into B, which as before is less and iss the shorter time you take, and in an abstract section of time is an abstract section of a changing fact. In fact, there is no difference as to reality between change and persistence. The permanent A is neither more nor less real in any point of time than the changing A - B. Both as real fill time, and they differ only in that one fills time as a segment of an identity, the other as a change. 456 INFERENCE implicitly by Fichte, that the sense datum on the one hand, and this nexus of relations on the other, were, in fact, abstract expressions of two sides of the same concrete whole, the effect was not to rehabilitate the given, but to extend further and further the scope of the mind's activity, so that not the order of things only but their whole existence was assigned to the creative understanding. But now the question arises, what warrant have we for thus attenuating the character of sensation ? Do we know of any sensations that do not contain duration as an element ? Have we any experience of " coloured or tangible points " themselves spaceless, which either laws of association or a timeless ego could build up into a world of space ? Lastly, in this chapter I ask whether the causal relation itself may not be in an elementary way given? Not, indeed, that mere observation could distinguish the universal from the con- tingent, but that it may suggest universality. It may present us with the pieces of our fabric in a form in which they are already fitted to take their places in the whole. In the final analysis we may probably find that in building up the system of knowledge not all the construction is done by thought, but bricks, and mortar too, are supplied by sense in a shape which goes to determine the construction. (b) At an earlier stage in this chapter we have insisted that not only can some things be explained, but that in the last analysis everything, every part of the great whole of being, must be explicable. And we have seen that on this postulate inferences might be founded leading to the rejection of this or that sequence as inexplicable in view of other sequences taken as established. The present discussion might suggest a still shorter and more certain method of forming inductions, one which would dispense with many of the doubtings and balancings of probabilities which we have been compelled to admit into our account of generalisation. Assuming the present account of explanation, it might be said that here we have a test of causal connections. For every fact must have an antecedent which will explain it in our sense ; and conversely, no antecedent whose action cannot be " explained " can be admitted as relevant. It is clear that this conclusion would take us very far from the true spirit of inductive science, which has owed much of its success to the determination not to reject that which it does not yet understand. Put in terms of theory, the reply comes to this, that the effect of any fact M may not be understood, either because our analysis is imperfect or for the more simple reason that the factors X or Y, working with M, are not EXPLANATION 457 observed. The inference from the inexplicable, then, could only be applied if we had a complete knowledge and understand- ing of reality, in which case we should not want it. The utmost we can say would seem to amount to this. Supposing all methods of explanation known, and supposing a sequence A - a to be explained, that sequence will be necessarily universal, for a modification of it will involve the overthrow of some principles of continuity or construction. But supposing the principle of continuity itself to be applicable only on certain conditions, we must know those conditions before we can ground an inference on an explanation. We shall see in a following chapter that there are certain conditions upon which, and upon which alone, we can be sure that a content will persist. Only if these conditions are taken into account, only, %ye may add, so far as they can be laid down and made sure of, can we apply the inference from continuity with any certainty. With these limitations, the result of which will be clearer later on, the argument from explanation is a method which may be combined with those of elimination as an independent source of probability. We cannot say offhand, " This is intelligible, therefore it is true." We may say, " In accordance with such principles of sequence as are known to us this should follow ; there is therefore no real ground for doubting that it will happen ; it has therefore a degree of probability approximating indefinitely to certainty." (c) Our account of the causal nexus will not be complete without some attempt to discuss a question left over from an earher chapter. Are we to recognise plurality of causes ? Is uniformity in causation all one way, or is there also a principle by which we can go from effect to cause ? Hitherto we have recognised plurality of causes. The axiom of reason- ing merely stated that there must be a cause, but not that the same consequent must always have the same cause. And when in dealing with the explanatory method we spoke of inferences to the cause from the effect, we based our procedure on no arbitrary assumption contrary to the plurality of causa- tion, but merely on observed uniformity of causation as given us by simple enumeration and the method of agreement. We have now, however, to ask whether in the last analysis plurality of causes is a possibility, and, if so, how we are to understand the principle ? At first sight the doctrine of the plurality of causes appears as the innocent expression of obvious facts. All roads lead to Eome. Human ends can be compassed by most diverse means ; and natural events are produced by the most heterogeneous causes. 458 INFERENCE You may die of cholera or consumption, of prussic acid or a broken heart. So far we get on a first view of the subject in which by the cause we mean the concrete sensible antecedent, or so much of it as strikes our attention as interesting or important. But as against this view, to begin with, it is possible even in cases of the greatest apparent difficulty to resolve plur- ality into an underlying unity. The alleged plurality of cau- sation, in fact, is for the most part the result of a very partial view. Some part of a totality has very different causes perhaps, but a closer inspection would show that where the cause differs, there also the totality of the effect differs; while, conversely, in all the different causes there may be some element of identity. Thus a. is apparently due to two very different causes X and Y, but analysis resolves X and Y respectively into ABC and A D E, while further comparison shows that the first a was part of the whole a, B y, and the second X part of the quite different total a 1 1. We get, then, X Y not the crude , with no reason for the difference, but a a ABC ADE I I a, j3 y a d e in which we notice three things : (1) The causes qud different have different effects (a /3 7, a 5 s) ; (2) qua similar they have similar effects (A - a) ; (3) not only has a, if you take it in the abstract and its antecedent in the concrete, two different causes, but A if you take it in the same way has two different effects. The suggestion results, that in the last analysis causes qua identical, and only qua identical, have identical effects; that plurahty of causes is an idea that comes from a partial analysis which makes us take the effect more abstractly than the cause, and that by a similar process we could get equally well to plurality of effects. But our principle should be, same cause, same effect ; different cause, different effect. This resolution of differences may be carried a great deal further when we remember that likeness may be not only simple or direct, but constructive. Two constructions are similar, however different their elements may be, if their result- ants are alike. Thus a system of forces P Q E may be dissimilar in number and separate quantity and direction to a system S T, but their resultant may be the same. And this does not only mean that their effect (the perceived motion) is the same. If this were all there would be undoubted plurality of causes. It means that their resultant pressure as a, felt fact (if the forces are acting on a portion of our bodies), or as inferred from a felt EXPLANATION 459 fact (if otherwise), is alike in the two cases, and this is the explanation of the similar effect. The distinction between the apparent plurality and under- lying unity of the cause coincides partially with that expressed by Bacon in the distinction between the cavsa physica and the forma vera. The former was Jiuxa, nihil aliud quam formam deferens in aliquihus, the object of sense differing according to the matter, while the most widely different causae johysicae coeunt in formam, which naturam unit in rehus dissimillimis, which produces the effect in omnimoda materia et subjecto susceptilili. Thus in Bacon's own instance the causae physicae of heat are many and various. Friction, combustion, pressure, the liquefaction of a gas, the solidification of a liquid — what have they in common ? Precisely this, the transforma- tion of some other form of energy into vibratory motion. This common characteristic makes all bodies undergoing any one of these processes " hot," if we are to regard heat as a quality of the bodies ; or a stimulus producing increment of heat in a normal nervous condition, if we are to regard heat as a modifi- cation of our feeling. All these causes have a common point which gives them a common effect. All have individual differ- ences which give them otherwise different effects — what else is there in common between the effects of friction and of freez- ing ? As identical their effect is identical; as different, different. But now if we grant that this is so in some cases, — that plurality has been resolved into unity in many instances, especially in mechanics and all sciences immediately depending thereon, and that by analogy it may be expected that the same process may go further in other cases also, — can all this be ground for the extreme conclusion that all plurality must be similarly resolved ? This conclusion may perhaps be true, but I do not think it can be inferred from the principles of generalisation hitherto assumed, and if these principles are adequate to the explanation of inductive reasoning we shall go beyond our book if we lay down any further assumption as axiomatic. We must confine ourselves, therefore, to setting forth the results which can be arrived at from our assumptions as already made. These appear to be two. (a) Different causes have different effects ; and any effect is either a whole or part of a whole which has always the same cause. The argument here is from what we may call inverse uni- formity. A. causes B. Then B is caused by A. But if B is caused by A in certain instances, it will be so always unless there is a reason for the difference. Now if, not B, but B C is 460 INFERENCE the total effect of A, and if, in a fresh case, we have not B C but BD, there is a very obvious reason for a difference in the cause. A cannot be the cause of B in both instances. Con- versely, if B is the effect, and the whole of the effect of A, it would seem that A must also be its only cause. For consider the relation A - B, and ask what determines it. Nothing out- side of A and B, for A is the whole and sole ground of B. But A and B are each essential to the other; for A is the ground of B, and if B were other than it is, it must have some other ground. Hence B stands in a relation of sequence to which no fact other than A and B themselves is essential. But such relations are universal. It follows that the total effect of any cause always presupposes that cause and no other. Whence, conversely, two different causes cannot have wholly similar effects. When the causes differ, certain concomitant elements of the effect must differ also. (/3) An effect may have as many different causes as there are ways of constituting it by construction of elements: or different causes of a given effect are composed of elements, the results of which form by construction similar wholes. Consider any elementary cause a, understanding by the term elementary that the content does not admit of the working of two processes on one another, but is a single and simple self-determining content. The " result " of such a cause will, as we have seen, be simply the persistence of the content — a persistence which may or may not involve changes in relation to other contents. That is, the consequent of a will be a ; and similarly, the consequent of b will be b — a different effect for every difference in the cause. With strictly elementary causes there is no question of many causes producing the same effect. But when elementary causes combine with one another, a different result follows. It is true that if A and B, C and D work together, the total results a. ^,y h must be different, but they may also in certain points be alike. The effect for which we are seeking a cause may be a whole or a certain character- istic of a whole, which may be constituted by very different elements. No doubt, since these elements must in every case " come to the same thing," there must be certain fixed relations between the different ways of constituting the whole. But still, by combining what are in themselves, and therefore in their antecedents, very different elements, we get totalities which are in some respects alike. I can form a square by putting together two triangles or two oblongs. And as far as a fact may be so differently constituted, so far may its antecedents differ among themselves. EXPLANATION 461 As between the different modes of constructively constitut- ing the whole, there is always ex vi termini a certain construc- tive similarity. Its different elements have just this common character, that they form this particular totality ; and this is, as we have all along held, a character attaching to the elements themselves taken together. In certain cases we may attribute a similarity of this kind to the different antecedents of a residt. Thus in mechanics we think of the resultant force as the true antecedent of the motion, and we think of that force as the point of similarity in all systems of forces that will produce just that motion. But as a point of similarity it is of course obtained by elaborate construction and analysis. In other instances there seems no point of similarity to be assigned as attaching to the different antecedents as such. They terminate in the same point, and that is all that we can say. Taking the instance already used, and pushing it back a step further, what common character can we find in all the forces which, acting on one another, produce ultimately a system with a given resultant at a given point ? They have not themselves a fixed resultant, but they produce changes, concentrations, and dissipations of energy that result in one or other of the systems with the resultant required. There seems no point, therefore, in assigning them any common character beyond the bare fact from which we started, that they have a common result. Our conclusion, then, is that plurality of causes depends on plurality of constructions. It is, of course, impossible to verify this result in detail. It could only be tested by an appeal to facts of observation, if we were in possession of a complete explanation of all effects ih the world. But it is at least the most probable result suggested by what we can understand of the ultimate nature of the causal relation. Antecedents do not cause consequents anyhow. There is, un- doubtedly, some definite principle determining all causal relations, but that principle may not entail strict uniformity of character in the cause, but only such limitation as is in- volved in the principles of construction whereby the effect is constituted. One last point should be noticed. On our principle, com- paring different causes, we expect to find the differences compensating one another. If I modify a system of forces in a certain manner I must introduce a corresponding change of a different (in this case of an opposite) kind in order to maintain the same resultant. And on the view of this section some such "compensation," however difficult it may be to phrase it with an universally suitable name, or to assign it in 462 INFERENCE every particular case, must be imagined as always occurring where causes are many. Then, on the one hand, the occurrence of many causes of an effect is always " casual " in character, depending, so to put it, on the meeting of just the appropriate differences. On the other hand, a principle which we have already used in considering the joint method follows as a deduction. If different elementary causes a and b act on the same element c, the total results ay, (By cannot as totalities be alike. They must be constituted of elements of which some are like and others unlike, and likes added to unlikes will make unlikes. There may, of course, be an element of identity 7 due to the common antecedent c, but the wholes in their character as wholes will differ.^ Broadly, if wholes are to be alike, but differ in one constitutive part, they must differ in a compensating manner in the other part as well.^ 5. The element of variability. Connected with the question of plurality of causes is a point of some interest bearing on the possibility of a complete explanation, or to use a more general term, systematisation of existing facts. In any complete system based on the idea of the universal it should be possible either to generalise any given relation or assign reasons, which must again be general in their character, differentiating this relation from any other which contains a similar term. In this way the variable is usually held to be explained by the uniform. Everything is in accord- ance with law, only the laws are entangled together and so give apparently irregular results. But the question arises, how far this reduction to uniformity can be carried. Clearly,' starting from certain points, — taking this or that collocation of causes as given, — we may be able to show that everything else follows uniformly without break or exception to any universal truth. But why should we start from one point rather than another ? and if we can assign no reason for such procedure, can we take the further step which would seem necessary to a complete systematisation of reality, and assure ourselves that at whatever point we start, whatever relations we consider, law will reign supreme, and there will be foimd for each relation an universal ground ? ' It is possible that there may be elements in a and c forming some abstract character of the whole 07, which agrees with n, similarly formed character of /S7. But this, again, will be a mere "chance." ^ The above discussion, of course, owes much to Mr. Bosanquet's analysis of cause and ground {Logic, bk. i. chap. vi. pp. 264 ff.). But I cannot feel as con- fident as he does of the ultimate identity of the ground in any fruitful sense. But the matter, at least, requires more discussion than is allowed it by Mill (Logic, iii. x. 1) and Schopenhauer [Sufficient Reason, § 48), who simply state the plurality doctrine nakedly and leave it unaccounted for. EXPLANATION 463 This result would follow most easily if we carried the doctrine of the preceding section a step further, and threw over the plurality of causes altogether. We could then generalise each causal sequence in the fullest sense. Let us see what would result. If every sequence is really " convertihle,'' so that when we can argue from A to B, A being the total and the sole ante- cedent, we can also proceed from B to A ; this will hold of all sequences alike, and of all facts whether they are universal wholes or casual conjunctions. Now, let any conjunction M - N he considered. It must have an antecedent L, such that we can argue L .•. M-N, or M-N .■. L. Now there are two possi- bilities. Either L is the universal of A and B taken separately, or it is not. If it is not, we have plurality of causes. M in some other context is produced by X and N by 1. But if we reject plurality of causes, this is impossible as a statement of the final analysis. Hence M and N can only have the ante- cedent L. But L is universal to M-N, .•. the conjunction M - N is invariable. But not all conjunctions are invariable. How are we to explain this ? Put the case again, beginning from the assumption that M-N is a variable conjunction — say, fine weather and a picnic. What is M's antecedent ? — say X. Then X - N cannot possibly be universal, or we shall have M — X - N and .'.M-N universal, which ex hypothesi is not the case. What, then, can N's universal be ? Say 1, and X + 1 may constitute the whole L. But — and this is the important point — the conjunction X-1 must itself be variable. Tor if it is imiversal we have M - X - 1 - N all universal, whence M-N would be universal too. Thus, if fine weather (M) followed always on given meteorological conditions (X), which also infaUibly and alone produced a certain temper of sociability and excitement (1) leading us to arrange the particular somewhat questionable form of entertainment mentioned (N), our picnics would always fall happily on fine days. It results that if L be the cause of M - N, L itself must be composed of elements not universally conjoined. The antecedent of a variable relation must itself be variable. This, I take it, will hold indefinitely. The same argument can be repeated for 1 and X, and for their antecedents in turn. Hence, admitting the de facto variability of nature, we must postulate a variable element running right through it, and never resolved into uniform sequence from any conditions whatever. We can no longer explain variety as aU issuing by uniform laws from necessarily determined conditions. Each variable relation must indeed have conditions, and from these 464 INFERENCE it must follow uniformly, but, as it would appear, as a con- sequence of the same principles a corresponding element of the variable must crop up again always and everywhere in the grouping of these conditions themselves. The " casual " con- junction, like every other fact, has antecedents which it follows uniformly, but in these antecedents there is the same variability. " Chance " is a fact and not a fiction. It is no mere expression for our ignorance, nor is it the name of some mysterious agency. It is a word which expresses, perhaps not very happily, the fact that the natural order exhibits variety no less than uniformity. If this conclusion seems paradoxical, I would ask whether any good ground in experience can be alleged against it. "Whenever we have any concrete phenomena to explain we proceed, no doubt, through laws which are abstract and general, but these laws do not hang suspended in intellectual air, nor are they derived from a first principle of existence. They show how certain other concrete beings might have produced these now present ; and if we are " satisfied " with the explana- tion, it is because we already take the alleged antecedents as known, or as probable, or as accordant with general knowledge. Thus, if we try to explain the presence of flora and fauna on a certain island, we are satisfied if they are such as could easily get there by air or water from a neighbouring continent ; or if this hypothesis is inadequate, and geology tells us that the island was once a peninsula, it is easy to suggest that the fauna once walked there. But why these particular species ? Why these genera ? Why this order and not that ? Why is this island richer in this respect than its neighbour and poorer in another ? For the most part we shrug our shoulders at such questions, and answer. Who can tell ? ISTo doubt some explanation might often be given, in the situation or character of the islands, or in the earlier distribution of animals on the mainland, in the habits of seed-carrying birds, or what not. Not only are there more things in heaven and earth than are dreamt of in our philosophy, but there is a philosophy for more things in heaven and earth than our philosophy itself yet dreams. Still, to what, after all, are we constantly driven back ? To the actual, factual, then-and-there collocation. It is so because it was so, and that is why it will be so. We are content if we wipe away the improbable, if we resolve the strange and unique into the well-known or even the average ; but we cannot undo the individuality of existence. The world does not become less concrete by being explained. Nor can we get rid of our dif&culty by reintroducing the plurality EXPLANATION 465 doctrine. Assume for a moment that M has two separate and distinct causes L and K, that L gives us M - N", whUe K gives M-0. Why, I shall ask, has this particular M the ante- cedent K ? Because it has N for its concomitant. Why has it N ? For whatever reason the economy of things may please, but not ex hypothesi a reason that makes M — N universal. Or, it may be replied, you have no business to ask the why of a sequence K — M. K is the reason of M, and that is enough. But this is a one-sided view. Looked at in the direction K - M, we have an universal sequence, and all is satisfactory ; but looked at the other way, it seems a pure " chance " — much purer if you reject the unity of causation — whether any given M shall have K or L for its cause. It is a one-sided necessity. We may put the matter more clearly by reverting to the doctrine of causation to which we were finally led in the pre- ceding section. Grant that M has two "causes," L and K. This means that each of these three expressions is a synthesis of parts, and the concomitance of these parts must be regarded as casual in character. For if the one brought the other into being, we should have the part as such constituting the whole. Our dilemma, then, is clear. So far as we have plurality we have variation in the conjunctions forming the cause. So far as we have uniformity of causation we must have variable conjunctions as between different causes. In either case variety in the effect postulates antecedent variety, and this ad infinitum. On the whole, then, there is reason to suggest — at least as a possibility that must be faced in constructing in idea the fabric of knowledge — that the variable element in nature is not to be resolved into a complex effect of interwoven uni- formities: that uniformity is not in everything, though it interpenetrates everything. One point remains to be noted. We naturally think of uniform necessity as existing between the facts of temporal sequence, while variability, if we admit it, has its root and ground in the coexistent. If you fiigure to yourself straight lines drawn across this page from top to bottom, and other Lines crossing these at right angles, and if you think of the whole page as the stream of time advancing from the top downwards, while everything in the same horizontal line is contemporaneous, then if we are told to distinguish necessary sequence and casual conjunction, we should naturally think of each vertical line as forming a chain or (as we prefer it) stream of necessary sequence, while the casual collocations are the 3° 466 INFERENCE relations of any of its points, or of the line as a whole, to its contemporaries ; or, if we figure it thus AMY B N X COT D P Z we suppose each sequence A B C D, etc., to be necessary, while B N, Y, DP may well enough be casual collocations. Of course, however, if B N is casual so also is N C, though they form a temporal sequence ; but we should " accoimt " for this by referring C to B, while we leave the casual character of B N untouched. In other words, we assume that any fact which can be taken as an event in time has its ground in a previous event in time. This assumption is not free from difficulties, for our original position in the matter was merely that any fact must have some ground, i.e. that there must be some other reality to which it is related universally. Again, in actual reasoning we use as logical grounds things that certainly cannot be temporal causes. And though in Chap. VIII. we saw reason to maintain that the ground or consequent of an event in time must be continuous with its correlate, this was not enough to justify our position ; for why should not 0, which is later in time, be the true ground of B rather than A, which is earlier ? B would then have a logical ground, but not a tem- poral cause. The solution of this problem, which we left imtouched in Chap. VIII., seems to depend on the principle of continuity. Just as you can start from any fact in time A, and argue for- ward to its continuance, except in so far as it is modified by concomitants, so you can start from C and argue backwards to the previous existence either of C itself or of something that became C. Now, suppose per impossibile that in the succession B - C, B is dependent on C alone. Then tracing C backwards, it passes into B as its (logical) consequent. But wherever we take this regress, it is either a process or a persistence; we have either a change from C to B or a persistence of B, or in B itself a change to something anterior, as A.^ Of course, A may be replaced by E, if B is accompanied, say, by D, which is such that B D pass back into E as their temporal antecedent. But this is only an instance of difference of cause with differ- ence of total effect, and B will still have its share in determin- ing what E has been. It follows that the causal process cannot begin at any point, and that there must be similarities and 1 That B cannot be a process ending in zero is argued lower down, Pt. III. Chap. IV. EXPLANATION 467 differences in the temporal antecedents at any moment corre- sponding point for point with those in the consequent. The temporal antecedent is not the ground par excellence, but it is a correlate necessarily implied, and necessarily implying what follows, and therefore a ground from which we can logically argue. 6. Explanation, Classification, and Description. Before asking whether in explanation we have the ultimate and highest ideal of science, we must compare it with its possible rivals in the other "systematic forms" into which advancing knowledge ranges the facts of the universe. The principal of these is known as Classification with its correlative Definition, or, as I prefer to call it, Description.^ We there- fore must inquire what classification does, and how it is related to explanation. All these scientific operations — and we may add inference and even the judgment to the number — grow out of a common matrix, and depend upon a single comprehensive principle. The principle is that of the relation of the general to the par- ticular; the common ground of all intellectual operations is that they deal with and exhibit this relation, while the special character of each depends upon the particular side of the relation that they take up, or the particular attitude of the individual mind, with its hitherto ascertained quantum of knowledge, to the whole of the facts. Thus the group of relations A-B A. - B» A;3 - B^ where A, — B„, A^ - B^g fall under A — B as specific cases, pre- sents opportunities for all these modes of operation. I may first, by induction, infer A — B from A„ - B„, and from A — B, by deduction, infer A^ — B^g. This I shall do if A, - B„ are first observed, and subsequently Ag. I may, second, classify A. - B„, A3 — B^ as species under the genus A — B ; or, again, describe either member as the relation A — B differentiated by the quality a or the quality /3. Or lastly, I may be said to explain either of the special relations by reference to the generic. The cases of inference on the one side are distinguished from those of description, classification, and explanation on the other, ' Definition is in effect conventional description. It is a selection of certain attributes from a group for assignment with a view to a special purpose {e.g. distinction from other species), and in accordance with certain conventionally- understood rules. 468 INFERENCE not by the facts dealt with, but by their relation to the exist- ing store of knowledge. In the latter case we presume all three relations to be known. In the case of inference, by means of the one relation we come to know the other. Infer- ence, then, is not itself a systematic form of knowledge, but a method of forming judgments depending on the same prin- ciples and relations of facts as those which generate the said forms. Coming now to these forms, we see that they agree in sub- suming particulars under a general. As to their difference, we have already discussed the character of explanation at consider- able length, and it remains to set out that of classification and description in more detail. Frimd facie we may distinguish two main forms of classification, which, for reasons which will be clear as we proceed, we may distinguish as disjunctive and subsumptive. (a) Disjunctive classification proceeds by added deter- minants without seeking in them any common character. It has no guiding principle, except that of enumerating exhaust- ively (or sufficiently for the purpose) all possible cases in which the generic content with which it starts may be found. Thus A is found in the cases AB and AC ; again, AB may be ABD or ABE, while AC may similarly be ACD or ACE. Then we have A Figure I 1 AB AC Eegular Irregular I ABD ABE ACE ACD | I I I I 3 sided 4 sided etc. 3 sided etc. = equilateral = square = scalene triangle The value of such an exposition is usually relative to its special purpose. Speaking generally, it amounts to a complete and systematic exhibition of the affinities of a certain set of con- tents. The various differentia found to determine a general characteristic of reaUty are enumerated ; or (better), starting from the more concrete contents we find the various points in which groups of them resemble or differ, and this in a complex way, since we point out at once the resemblances and the differences. A classification is, in short, a construction of com- parative judgments. A description is in form nothing more than an ordinary analytic judgment, but it may in form and even in matter be determined by relation to some classification. EXPLANATION 469 And while this form of classification rests on the judgment, and that alone, in description there is potential inference, seeing that by the principles of construction the same elements must always give the same whole. This generahsation, however, should not he regarded as the aim of description proper, unless it is exphcitly laid down as such. (jS) Suhsumptive classification is a name which may con- veniently be given to all systems which seek to proceed on a single principle. Here our actual procedure may be of two kinds. We may be struck by some particular distinction be- tween things, some characteristic differentiation, and we may try to fit this differentiation on to successive classes. The differentia itself may perhaps be modified, but its modifications also must exhibit some principle. Thus certain affinities and distinctions of sexual character are fastened upon by the Linnaean system, and are carried out right through the vege- table kingdom. In this case we begin with the principle and fit the facts into it. Or, secondly, we may begin by arranging the facts in accordance with some principle not understood by ourselves, and may then, when the arrangement is far advanced or even complete, come by comparison and analysis to discover the principle of arrangement. This was the history of the " natural system " of classifying plants and animals. Darwin has shown^ (and I imagine that this result holds good inde- pendently of the evolution hypothesis) that naturalists, almost (or entirely) without knowing it, in forming the natural system, have been employing the principle of inheritance, ie. have been arranging orders, genera, and species by affinities of the kind ivMch inheritance would produce. This affinity was, tUl Darwin, unanalysed. It was effective, it was felt. But it was not understood. It was effective in determiuing the classification, but was not known to be so. Darwin's analysis altered this. Here, then, we have a principle first used and then declared; as, before, we had it first declared and then used. In either case, however, classifications of the kind now before us are distinct from the former sort, in that they attempt to follow a single principle or system of principles. They are thus also in a way inferential in character ; for given one part of the classification effected, the further orders and families and genera fall one by one into their places by a sort of necessity. If we are to carry out our principles, they must have the place assigned to them and no other. Conversely, the attempt to carry out the principle is itself a kind of experiment, like an 1 Origin of Species, chap. xiv. p. 369, etc. (6tli ed.). 470 INFERENCE incomplete deductive inference that needs verification. For our method of classification may now be said to be " correct " or " incorrect " as a whole or in any part. -If we want to arrange a given whole, and begin with a principle which clearly fails to give us all the distinctions required, that principle is " inade- quate," and so far false — not the principle required. The disjunctive classification, on the other hand, could scarcely be incorrect, unless memory or words actually misrepresented the given facts of similarity or difference. Subsumptive classification is thus transitional in character. It is no mere combination of comparisons, but expresses some systematic interconnection of facts which may, if such be the purpose of its framers, give us deep insight into their character. Thus from classification in such a science as biology to explana- tion is but a step. But there is a step nevertheless. As long as we retain the purely classifactory point of view, we note de facto resemblances and differences ; but no reason is assigned for these. Explanation assigns the reason. It shows not merely how the generic content has become modified in the species, but why it is so modified, — what has modified it. That is, it assigns the ground of that which classification only describes. Let us first exhibit the difference schematically. In classifi- cation we have aA j8A = X =Y yX 8X lY ?Y = Z =Y =U =T Here, if we take the Greek letters as bearing some definite relation to each other, we have a subsumptive classification. What is effected by it? Each point of difference — between X and Y, between Z,Y,U and T — is analysed, and the differences themselves have their respective affinities. But no reason is assigned why A should be affected by the differences a and ^ ; nor, again, why those A's which are already differentiated as X should have the further qualities 7 and 8, while those which form the group Y are further distinguished by i and ^. In all these points we are simply analysing and recounting facts which we take as they are given. Now, if we were explaining we might (for instance) take the content Z and show how it followed from the combined antecedent 7 and X. Here, so far as we assume the antecedents y and X, we are taking things just EXPLANATION 471 as they are, precisely as in classifying. But when, given the antecedents, we go on to analyse them, and show how, part by part, — in accordance, if you like, with the law of continuity, or, if we are to speak more generally, in accordance with laws already known as operating in other sequences, — each is responsible for its part of the effect, then we have explained, first, the effect itself, and, secondly, the law. Thus our scheme of explanation is rather A-B B-A-C I I I X XT This for the particulars X or Y. For the explanation of laws we require A- f «-7l _-R Thus the whole arrangement of explanation is really different. If in a way we are classifying laws, we are not attempting to bring them all under one genus, but to reduce them to a series or system of elements which shall ia turn be mutually connected. A multiplicity or system, not a single generic concept, must stand at the head of our explanatory table. The truth is, that classification, however deep it goes, does not get beyond the analysis of general attributes. It does not treat the universal laws as such, whereas it is precisely with the universal that explanation deals. The ideal of classification is to exhibit the whole network of resemblances and differences in a mass of general attributes ; and natural classification further shows how a certain constant type of difi'erence runs through the whole. But it nowhere states on what conditions those differences arise. It does not enter into their antecedents. It does not deal with them as sequences. This is the business of explanation, which in its crudest form takes the laws of sequence and treats them like classification, bringing them always under higher universals, but which soon learns that here too the classifying work is superficial and preparatory, and that only in the connected system of universals can you find ground for difference as well as resemblance. The classificatory ideal could only amount to explanation if the universal, and that the abstract universal, contained in itself the ground of its differences. But this is impossible ; for though a content A might determine itself in the direction a A to form X, it is absurd to assign to the very same 472 INFERENCE content, apart from all foreign reasons, a self-determination' in the quite different direction /3A to form T. If contents were self-determining only, we should have no hierarchy of universals. The illusion of the universal determining its own differences is fostered by the present state of biology, in which classifica- tion has played an important part as leading to explanation, That this should happen is no matter for surprise. If you find a single differentia, or a set of differentiae united on some single principle running through a complex set of facts, you are already on the traces of the cause of that differentia. What will cause that differentia in one case will cause it in others. And thus, when a peculiar synthesis of relations of resemblance and difference is already attributed in certain cases to inheritance, and when a corresponding synthesis is found to unite all members of the organic world, it is an easy step, comparatively speaking, to extend the area of the cause also, and infer that the actual species of the organic world are related by and owe their present existence and character to inheritance. At this point classification passes into explana- tion — not explanation of the laws of action of inheritance (that is still to seek), but explanation of this vast system of concrete fact which we call the organic world. And in this explanatory system certain organisms, protozoa, take the place at the head occupied in a classification proper by the abstract notion organism. But this change marks the transition from the one operation to the other, and should not lead to a confusion between the two. The protozoon is not an abstraction like " organism," pervading the whole field of facts ranged beneath it ; it is a definite concrete creature living under conditions of its own. You cannot call a horse or a man a protozoon as you can call them organism, a vertebrate, a mammal. Precisely, when we come to the antecedent (real or alleged) of our mass of facts, then we part from the idea of the genus or generic character that merely pervades them. Nor even so is the protozoon itself, and as such, responsible for the variety of creation; but the differences thereof are on any evolution hypothesis due either to the response of its descendants to difference of environment, or to the intermingling of different protozoic, and subsequently metazoic, individuals. To talk, therefore, of an amoeba as an organism in the abstract is a logical mistake; to suppose that such an abstract organism develops itself independently into the variety of the animal and vegetable kingdom is an error at once in logic and in biology. EXPLANATION 473 On the one hand, then, the processes of classifying and explaining remain distinct. At the same time the present discussion will have given us some insight into the logical value of the distinction between natural and artificial systems of classifyiag. Both these systems rest on a single principle or connected set of principles. That is to say, they endeavour to arrange all their facts on a single method. Both therefore are subsumptive. But the most consistent and complete applica- tion of a single principle may take us very far from any arrangement that we should call " natural." A. dictionary, for instance, supplies us with an example of an arrangement of words superior for its own purposes to any other, and superior just in this, that it carries out an extremely simple plan of arrangement over all the tens of thoiisands of words which form a language. But "natural," ia the sense that by its arrangement it throws any light on the structure, origin, or use of language, it is not. If, on the other hand, we can find a principle (or connected set of principles) of differentiation which can be thought of as an actual form of change which the objects in view may undergo, then that principle would explain the genesis of the variety of these objects from a generic type. And from the classification to the actual explanation there is here only the step — though it is a great step — of verifying the principle of differentiation as an actually operating law of change. A subsumptive classification, then, becomes " natural " when the principle which it employs is that on which the genesis of the forma actually depends; otherwise it is " artificial." Briefly to sum up. In classifying we deal with general attributes and their relations ; in explaining, with universal laws and their relations. Thus in classifying we describe what is ; in explaining, what must be, and why it must be : in classi- fying, we do not look for antecedents ; in explaining, we so analyse the antecedent as to show ground for the consequent : in classifying, our ideal is to bring our contents under a summum genus by some fixed principles of differentiation ; in explaining, it is to resolve complex laws into elements which are themselves connected. But though classifying and explain- ing may never be the same, the first is the true step to the second, in that in laying down resemblance it presumes identity of causation, and in pointing out differences it sets the problem of discovering reasons why; while lastly, in identifying differences it indicates the solution which would cover in one explanation its total field of facts. To conclude. The ideal of knowledge, as we understand it. 474 INFERENCE is to reduce the mass of facts with which it deals to an orderly and intelligible system. In this system every element, whether a particular fact or a general law, would be " explaiaed " by its relation to the system as a whole ; the whole itself would not be explained as depending on anything outside itself, but would be intelligible as a system of related elements. The " explanation " on which such a system would rest is not to be identified with any kind of classification, but is a distinct method of systematisation : in detail, the particular fact is " explaiaed " by reference to the ground from which it flows ia accordance with a uniform law ; derivative laws are explained by analysis into their elements, and elementary laws by correlation, through their resemblances and differences, with one another. The ideal of explanation in this direction is to reduce all simple laws to a form in which they follow directly from the principles of reasoning and of construction. So far we have found no difficulty in forming an ideal of the totality of knowledge, however remote that ideal may be from any chance of realisation. But another point gave us greater difficulty. A necessary preliminary to explanation is the reduction of all particular facts to universal laws, and here we found a theoretical obstacle in the element of variability. It is clear that if the ideal of explanation is to be realised, this difficulty must be dealt with. How far in dealing with it we are forced to modify our ideal, and to what conception of knowledge as a totality we are finally led, are questions which must be taken up again at a later stage. CHAPTEE XX SUMMAEY OF THE ThEOKY OF INEEKENCE We have now to bring together the main lines of argument in the preceding chapters, and to indicate the broad conclusions as to the nature, results, and postulates of inference which emerge therefrom. Broadly, we may say that the function of thought in inference is to connect the given, with the result of extending its knowledge over the wider reality which is not given. In the act of inference thought takes the actual relation as also a necessary relation, and as a fragment of a system of necessary relations. In this function thought has no system ready made, no criterion of necessity lying at hand to apply. It learns the concrete character of the system from the facts themselves, and hence by slow and laborious degrees with constant mistakes. Its only postulate is that there is a system ; there are relations which are necessary. What the system is it must find out from the facts themselves. Thought, then, in the act of inference, imputes connection or necessary relation to given facts. What now is the nature and meaning of this connection, and by what are we guided in applying it ? To this question objection may be taken. We must first ask, it may be said, whether there is any guiding principle at all before we determine what the principle is. It may be that thought is guided, as it were, by an instinct of its own which is incapable of analysis, or, if the notion of instinct be rejected as proving too much and explaining too little, it may be that thought has many methods of dealing with the infinitely various facts of experience ; that no single principle, nor any assignable set of principles, would be applicable to them all. In short, it may be said, we work with methods that defy, perhaps rise above, analysis. We must be content to point out the fact that as reasoners we do connect and systematise, we do attribute necessity, but we must not expect to find any clear and absolutely certain criteria by which these operations are carried on. 476 476 INFERENCE This negative account of the matter may or may not be true. But it can be proved only by showing the actual failure of all attempts at systematising the operations of the miad in inference. What is certain is that the analyses of logic are at their best an inadequate attempt to render articulately, and, from the nature of the case, in abstract terms, that which thought executes unconsciously and in the concrete. The utmost, therefore, which can be hoped of any analysis like the preceding is that it may form a ground - plan on which subsequent reflection, by adding this and subtracting that, may approximate to a true reconstruction of the inferential process. We have attempted, then, to correlate the operations of inference by exhibiting them as based on a connected series of principles. Starting from the characteristic endeavour of inference, to extend our knowledge from the given to what is beyond, we found that a single type of consideration is appealed to when we argue, whether with certainty or probability, viz. parallel experience, and that if the argument is to be held sound and certain this experience must be, so far as we know, uniform, unbroken by an exception. We next saw that argu- ments of this kind could be applied in opposite ways, since it was always possible for the concomitants of any given relation to " make a difference." But we inferred that if the concomi- tants were taken into account, and no ground for a difference was to be found in them, the conclusion must be taken as certain. And here was a broad justification for ordinary common-sense inferences from uncontradicted experience, on which our or- dinary everyday certainty may be taken to depend. And such certainty, we have since found, is only not justified in theory because of the complexity of the factors which may in the end modify a uniformity that has been long maintained, while it does in the main meet with practical success owing to the width of the experience which, for reasons shown, in some degree compensates for incompleteness of observation and analysis. From this principle of inference, which appeared at first as a mere guide for our own judgments, we were driven to infer a general principle of connection between the elements of reality themselves. For our principle would, under certain circum- stances, have proved false unless we assumed that every change in the order of events had its ground in other facts ultimately discoverable by us. From this we could infer the simple statement that every fact has its universal ground. And here we reached a point whence, as we may now make clear, we might equally well have started in order to deduce the positions previously taken up. For assuming that every fact has its ground. SUMMARY OF THE THEORY OF INFERENCE 477 it would be clear that any given relation would be universal unless there were some change in the concomitants as a ground for the difference. From this, again, it would result that the only consideration used in inference would be the points of likeness and difference to parallel cases. For it must be a point of likeness in the antecedent which should determine likeness in the consequent, and a point of difference which should be a motive to the denial of that result ; so that, if we admit the axiom as expressing what it is reasonable to take into account in generalising, we must admit these to be the considerations, and the only considerations, by which we are guided. At this point, then, the series of principles so far formulated, though each in itself a distinct point, has come full circle. We can start at either end and deduce the remainder. If either the first or last is true, then all are true. This is important, because we do not claim self-evidence for any one of them. We " assume " them because they seem to express the action of thought in different phases or at different points. And if the analysis is correct, and we are able to connect these principles as above, we may claim at the same time to have interconnected the various modes in which thought operates. Dealing next with ths manner in which these principles are applied in inference, we argued that certain further positions must be deduced to bring principles and facts into relation. The chief of these were — (1) that the same ground has as such always the same consequent, however much this may be disguised by the concomitant operation of other factors ; (2) that, so far as we are considering events in time and space, we must assume ground and consequent, or, as we should here call them, cause and effect, to be continuous ; while (3) in the last chapter we have seen that every event must have an universal correlate among its temporal antecedents, i.e. a cause in the usual sense. These positions, we argued, followed from the axioms originally assumed. Applying our principles next to the foundation of probable reasoning, we argued that since it is better to be nearly right than always wrong, it is well to know what will happen most often if you cannot know what will happen always, and that on such knowledge, if attainable, a probable conclusion could be logically founded. Applying our reasoning, then, to the facts of frequency, we found that these too must have their ground, and that ultimately this must be looked for in the degree of connection between the conjoined phenomena. Whence arose a converse argument from given frequency of conjunction to degree of connection. 478 INFERENCE Lastly, we urged that if in our experience we could find no argument certain or probable with even the lowest degree of probability for a suggestion, that suggestion must be taken as logically worthless and without effect; while, so far as it should suggest a difference in the order of reality as inferred from observation, it must even be directly denied, since the result of induction is exclusive of difference in the sequences of facts, just in proportion as it affirms uniformity. From these results we formed a general conception of the way in which general- isations are estabhshed. That which depends on uniform experience is probable in proportion to the weakness of the considerations that can be urged against it, and when these considerations fall to zero must be taken as logically certain. Applying this conception, we considered first the methods of observing sequences without regard to their concomitants, and we saw that from them some kind of connection could be inferred, but that there was no means of telling whether that connection were direct and so strictly universal, or indirect and so dependent on other conditions. For practical purpose such in- ferences could be applied, in circumstances not notably different from those from which the premisses were derived, with a proba- bility proportionate to the number and extent of these premisses. We passed from them to inferences from the nature of the con- tent and its concomitants, and argued, first, that the mere existence of an unchanging content gave ground for expecting its continuance ; secondly, that when a single change in the tem- poral antecedents is followed by a change in the consequent there is a very high probability that the first is a part of the cause of the second ; while, thirdly, if we find a similar sequence of changes in totally difi'erent surroundings, it is highly probable that the first fact contains the whole ground of the second. The results so far gave us a high probability for the required generalisations. This was increased when we found results independently arrived at corroborating one another by forming a nexus of interdependent judgments. We urged that there is no motive in experience for suggesting such a concatenation of chances as would cause fundamental error in such a case, and that accordingly a systematised body of inductive results must be taken as certain. We passed next to the consideration of a special class of generalisations embodied conspicuously in mathematical sciences, and more sporadically (if we may use the expression) in other maxims and modes of thought. We found that these results could be reached in any concrete case by an act of analysis and construction, and the problem reduced itself to SUMMARY OF THE THEORY OF INFERENCE 479 the question why the results of these acts could be generalised without the processes of elimination necessary in other cases. "We found here a distinct postulate of thought in addition to those employed already in inference — the postulate that the processes on which the judgment rests is valid. This process iavolves that the data used in construction and analysis should be in themselves a sufficient ground for the results based on them. And from this it followed at once by our axioms that the results so reached can be generalised without more ado. We turned finally to the question whether the inductive process led to anything like an " understanding " of nature as distinct from the " calculation " of its course. We found that explanation involved a resolution of laws of sequence into simpler elements, determining the wholes by principles of con- struction, and interrelated with one another by laws of varia- tion. We saw reason also to suggest an ultimate type to which explanation might reduce these primitive laws, that, namely, of continuity of content. In this form of sequence we urged that the content by its own nature contained a ground for its result, and that this relation is that which we strictly mean by one that is in itself and of itself iutelligible. We thus found an ideal for what we called " mechanical " explanation, leaving it an open question whether other ideals of explanation might not be justifiable. Our theory, it will be observed, has two main features. On the one hand a number of principles are postulated as necessary to the work of thought ; on the other an attempt is made to connect all these principles so as to reduce them in effect to a single assumption with which the whole work of thought will stand or fall. Such a theory is clearly liable to error in either point. For, first, it may form an incorrect con- ception of some or all the several postulates involved in the various methods which thought uses. It may assume some that are not necessary, or leave out of account some that are essential. And, secondly, it may err in its method of con- necting the positions assumed. The connections may be illusory or incorrect. To a theory, then, which does not claim self- evidence for its assumptions, nor the accuracy of omniscience for its deductions, a word should be added as to the grounds on which it rests and on which it must be modified, if modi- fication should prove necessary. The position, then, of the preceding chapters has been that the validity of an axiom depends on the fact that it is logically implied by some activity of thought the results of which are not contradicted by experience; that is to say, that if the 480 INFERENCE axiom be true, that actmty will give good results, and if not, not. Granting, then, as the result of a first analysis of scientific operations that we have such a method as, for example, the method of difference, the canon of that method acquires a claim to be axiomatic. That this claim is not final we shall see at a later stage, but we take it as final for our present purposes. That is, as logicians assuming the validity of thought in general, we have only to find a principle on which some operation of thinking rests, and we are bound, if the results of such opera- tions are not contradicted by experience, to take that principle as for our purposes good. In this way, then, we obtain one by one the series of principles above explained, the law of the ground, the law of chances, the principle of continuity, and so forth. Apart, then, altogether from this interconnection, these principles claim a certain validity of their own, and they would stand on that ground if every argument by which we have sought to connect them were destroyed. Again, any law directly deducible from these principles must be held true although not directly implied in the work of thought. While, conversely, any law claiming to be axiomatic and appearing self-evident, which cannot be shown to be implied by reasoning, loses all claim on our assent. We saw some reason to think that this was the case with the doctrine of the unity of causation in its extreme form. It becomes, therefore, a matter of great im- portance to make sure what assumptions, what minimum of assumptions, will explain the work of thought. By " explaining " I mean here, stating precisely what' must hold true if the results of thought are to hold good. If we possess accurate knowledge on this point we shall have to discard any other principle, however plausible, as non-axiomatic in character. Our aim, then, has been to examine the broad fact that reason works by connecting and systematising ; to analyse the method by which these connections are formed ; and by reducing them to common principles to connect these methods themselves. The logical basis of this whole process is not the first principle to which we lead up, but the actual work of thought from which we start and to which we return. Our postulate throughout is that thought is valid ; and that postulate would remain if our analysis of the detailed character of the principles of reasoning were riddled with disproof from beginning to end. But this postulate is for the present an assumption which must not be left unchallenged. The problem of its grounds and justification is the final question for the theory of knowledge on which we have now to enter. PART III KNOWLEDGE 31 CHAPTEE I Validity We have now given what account we could of the structure of knowledge in its higher and lower forms. We have shown that it rests upon a certain limited numher of presuppositions, some of which, called collectively the inductive principles, have been stated as universal truths holding of reality at large, while others, such as memory or construction, may be looked on as powers or faculties of the mind which forms and possesses knowledge, and are for our inquiry ultimate facts, since any attempt to explain their origin or character postulates at the outset their general trustworthiness. In the progress of our inquiry we have had at several points to distinguish between truth and falsity, and between valid or invalid methods of forming assertions. And we have so far assumed, without hesitation or self-criticism, that every assertion which issues from one or several of these presuppositions, and from no others, is valid, and is to be taken as true. But now that our survey is complete, a deeper question naturally suggests itself. Having admitted the possibility of error, it may be asked. Why, after all, should we take these half-dozen methods (as we may call them generically) of forming our assertions as especially valid ? We . have used them, one and all, for testing various judgments ; but what shall test them ? Or have they an inherent right to stand untested ? If we are not to leave this question un- answered, we must get some notion of what validity means, and what sort of test can be assigned for it compatibly with the limits of the human iutellect. There are here two questions, and we will begin with the first. We will try to show first what validity means, and then consider the tests or guarantees of the validity of our know- ledge which have actually been proposed by various schools of thought. 1. The notion of validity may be regarded as a generic concept, including one that is more specific and more easily recognisable, 483 484 KNOWLEDGE and from which we will therefore begin. The notion of truth and falsity has underlain the whole of our previous discussion ; and though we cannot do much in the way of analysing this notion, we may say a word or two as to its genesis. The idea of truth and its opposite appears to be the result of a compara- tive judgment, just like other ideas. I have in my mind a formed judgment that A is B. I observe A, and find that it is B. Then, if I happen to form a construction of the judgment already present and the apprehended relation now presented, I find a particular relation between them which I express by the word " correspondence " ; and when judgment and the given correspond, the judgment is said to be true. This relation of correspondence is not precisely one of similarity or identity, and much confusion has been caused by expressly or impUcitly treating it as such. For the judgment is a mental event, and the content apprehended not necessarily such, so that they may not be in pari materia ; while, if we abstract the judgment from its content and regard the content as similar to the given, we are again open to the objection that the given (seeing that the judg- ment is true) is precisely the very thing which it asserts — is not therefore similar, but identical, with the content of the judgment. One assertion, then, is true according to another if the con- tent which they assert is identical. Now, antecedently to the supposed comparison, the judg- ment A-B is a psychical fact having a certain degree of psychical force. That is to say, it is held with greater or less tenacity, with absolute conviction, with certainty, with " toler- able " sureness, with strong belief, with some hesitation, as the more likely of two alternatives, and so on. There is, as we have already argued, every degree of " force " in an assertion, from absolute conviction down to the merest suggestion. In ease of a correspondence with the given, a judgment is con- firmed, and — whatever its strength previously — it rises for a moment to the maximum of certainty, from which it only descends very slowly as it becomes memory and fades into the distance of the past. We might represent its fluctuations of strength somehow thus 01 VALIDITY 485 where 0^ is the zero of belief, F is the period before apprehen- sion, A marks the beginning of apprehension, Aj its completion, P the short time of primary memory (transitional in character between apprehension and memory), and M the period in which it has settled into the groove of memory, and takes its place among other memory-judgments. The line from A to A j is not drawn perpendicularly, since both apprehension and the judgment of correspondence must, as psychological facts, occupy a short time, however much time may (be irrelevant to the content of the latter. If, in another case, apprehension contra- dicts the judgment, the upper line would sink after the point A to the level of the lower ; the strength of the antecedent judg- ment would fall to zero. 2. The notion of truth and falsity therefore supposes a special mental power (already alluded to in dealing with inference) of criticising and " correcting " our own judgments. The criticism, indeed, we have seen to follow from the ordinary methods of construction and comparison. But the correction is a further peculiarity which means in essentials this — that the intrinsic force of any judgment, its command over our minds, can be modified, raised, or lowered, as the case may be. So far we have only considered extreme cases of such modification, the definite and complete reversal or confirmation of a judgment by the given content which is fact. But just as we compare judgment with apprehension, so we may compare judgment with judgment. On one set of grounds I may assert A - B, while a different set of considerations leads me to deny it. Here, then, is a conflict of judgments in which more than one alternative is possible. One judgment may amount to con- viction ; it may be so strong as to be indistinguishable in its force from the certainty of apprehension, while the other is weak. In that case the result is scarcely different from that already described. This is the simplest case; but starting from it we may have any degree of relative certainty in either or both of our judgments ; and if, for purposes of illustration, we assume this felt certainty to operate fully, and to be the sole psychical force acting, then in accordance with this ratio will be the resulting attitude of mind. Thus, if the affirmative judgment has the force m and the negative n, the result will be a judgment m minus n, — affirming if m is greater than n, denying if n is greater than m, and resulting in pure doubt if the two forces are equal. The modification of a judgment's force, or value, is then dependent on other judgments with which it is brought into contact, that is to say, which make an assertion about the same content. Now, apart from the question of 486 KNOWLEDGE precise measure, here we have at least a general conception of validity. Every judgment as such has its own degree of force or value. Its validity is simply its corrected value. This correction, we have seen, may be made by a comparison with an act of apprehension or with another judgment. It may, as we shall afterwards see more fully, be final and complete, or temporary and partial ; but, in any case, it is a value deliber- ately assigned to the judgment by the reflecting consciousness, not determined wholly, though in part it may be, by the original value of the judgment itself. Such is the general notion and such the postulates of validity, and the important philosophical q^uestion with regard to it is whether there is any final validity, any ultimate value, attaching to a judgment that can need no further correction : and, if so, what is its standard, and how is it known ? 3. We shall deal presently with suggested answers to this ultimate question. But we must notice first a special applica- tion of the conception of validity which leads to some of the most peculiar difficulties of the question. I mean the applica- tion of the idea to the methods whereby a judgment is formed. For the purposes of this chapter the term method may be used in an extended sense, as embracing any or all of the conditions on which a judgment rests. Thus we may speak not only of inductive or deductive methods, but of the method of memory, of construction, of analysis, or of the union of several or all of these. Now, as to the idea of a valid method there is no very great difficulty. A method is valid which gives valid results, and only valid results. I " trust " my memory because it has never deceived me; or I trust it in such and such particulars, for such and such a period, when its contents are of such a degree of clearness, — because for those particulars, for that period, with that clearness, it never deceives me. In short, given that I can compare the resulting judgment with the facts, and that I can also be aware , (by immediate introspection or by a synthesis of memories) of the steps by which I arrived at that judgment, I infer that those steps led me to truth. In a parallel way, other mental operations are convicted of resulting in error. Hence the first are accepted as sound or valid methods, and the second dismissed as invalid and misleading. Now, as an account of what is or has been, this is all very well. But especially with regard to our methods of ascertain- ing truth we wish to extend our inference to the future and the unknown. Suppose, then, I see that a method has led me VALIDITY 487 to true results, how am I further to be sure that it always will do so ? If, on the ground that it has been valid, I extend its value prospectively, that is an inference, a generalisation ; and how is that generalisation in turn to be guaranteed ? We move here in a circle. Had I already attained the totality of know- ledge, if I knew " whatever there is to know," and knew that I knew it, 1 should be able ds posteriori to dissect out all the methods which had led me to knowledge, to distinguish them from those which had been paths of error, to name the first valid and the second invalid, and that with no limitation to any particular sphere or period of experience. But it is just because we are not as gods, knowing the whole of things, that the question of validity arises. And it is by means of the methods that we have that we hope to attain more knowledge or test the knowledge we possess. Hence the circle : our methods create and test our knowledge, while it is only attained knowledge that can test them. From this circle what escape can there be ? Is there, after all, any final and genuine test of truth, or is vahdity a purely relative term, denoting at best the de facto action of one judgment on another without expressing any result which we "must" or, as "reasonable" beings, " ought " to accept ? This is the deepest question of philosophy. Let us consider briefly the general character of the answers returned to it by different schools of philosophy. 4. (a) Scepticism occupies two rather different attitudes to the present question, according to the general state of the sceptic's mind. Thus we may have on this point a purely philosophic scepticism, which amounts in fact to the theory of not having a theory. There is and can be no rational or scientific answer to this question. There are some beliefs which we accept and others which we are comparatively ready to reject. When beliefs clash, one normally extirpates the other, or perhaps we are left in doubt. That is as the case may be. The whole question is one of pure fact. There is no right or wrong in beliefs. If these names are used at all, they can only have meaning as applied ex post facto to the beliefs which we finally accept. All this may be compatible with a practical acceptance of felt certainty — indeed, it tends to that attitude. What is felt to be certain, is certain, is true, is reasonable ; for what meaning else can we attach to those words ? Hence philosophic scepticism may be robustly practical in hfe, and must be distinguished from what we may call practical scepticism, which is also a not unknown phenomenon. The practical sceptic is only in partial agreement with the philosophic ; for though he denies the possibility, or at any rate 488 KNOWLEDGE the actual knowledge, of any standard of the true and reason- able, he still seems to admit that the words have meaning, that the de jti,re. is not a mere case of the de facto ; for he refuses to admit any actual certainty, and is determined not to do so unless or until the required standard of rational certainty is found. Hence so far as he is logical he is a practical sceptic, — his doubts affect his working beliefs and actions. He is, iu a way, the opposite of his brother doubter who takes things for granted because he disputes the possi- biUty of a theoretic justification ; for this man demands such justification, and because it is not forthcoming refuses to take things as they come. Any positive theory of validity must meet the objections of both these doubters. It must show — (1) that a definite meaning can be attached to the words " valid," " reasonable," " right," or whatever other word we may use to express that a belief should be something as agaiast merely saying that it is ; and (2) that intelligible grounds or principles can be laid down to guide us in applying those terms to our actual judgments. Scepticism in both its forms is answered if, and only if, these requirements are fulfilled. We have now to examine three lines of thought which seek to fulfil them. (h) Intuitionism has a royal way of cutting this, and indeed most other knots ; for it has but to appeal to a per- ceived necessity, to a clear idea, to the inconceivability of the opposite, all of which may be known by simply attending to our own judgment, and its task is done. It is an easy theory, but unfortunately it is not true, and if it were would not explain anything. We have already said something of necessary connection, of clearness of ideas, and even of the inconceivability of the opposite, but precisely what we want explained is how far and why we can rely upon them. Granting this or that to be the principle of reasoning, why has it validity ? To appeal to the fact that we feel its force, that we cannot help thinking it so, is merely to repeat the fact. The question is, should we think it ; and if so, why ? To this intuitionism answers, we must think it because we must. This answer can indeed escape from tautology at the cost of being untrue. It may be rejoined that my last statement is unfair. Intuitionism really says we ought to think it because we must, i.e. felt necessity is the real guarantee of truth and standard of rational belief. Very good, if it were so ; but it is not so. The inconceivable has before now turned out true, and the apparently irrefragable method of proof has played us VALIDITY 489 false.^ Subjective certainty, as such, if that is the test to which intuitionism would have us resort, is a bruised reed. But the intuitionist has another reply. There are various subjectively certain methods of beliefs, but many of these may be due to some accidents of experience or idiosyncrasy. There are, however, in addition, certain genuine ic priori judgments of which the average man, who is not a philosopher, may be quite unconscious, but which, nevertheless, are actually im- plied by every experience which he registers, every thought which he conceives. If his mind did not possess these principles from the beginning, at least as methods of arranging its data, no knowledge would be possible. Hence the very existence of knowledge logically implies these truths, and truths they must accordingly be. Here we begin to touch solid ground, but at the same time we begin to leave intuitionism ; for though the appeal is to principles resting on the mind's own nature, the proof that such principles exist and are valid is no longer grounded on the simple feeling of assurance. For, to begin with, what is truly a priori has to be dissected out from the web of opinion and appearance by an a posteriori analysis ; and, secondly, as a matter of history the founder of this mode of thinking rested the trustworthiness of the pure principles of the under- standing on a quite different ground. The famous deduction of the categories argues in effect that every object of experience must conform to those rules and principles which the under- standing lays down k priori, because they could not be objects of experience if they failed to do so. What is an object ? not a mass of unrelated sense-data, but something which is presented to me (or represented by me) as constituting some definite whole with parts and relations and so forth. The very least I can know of a thing will yet involve it in some relations, if only of distinction (involving it in temporal or spatial relations). But this means that to know a thing I must hold it together ' It would be out of place to rehearse Mill's argument against Whewell. Apart from Mill's own unfortunate psychological theory of necessity, the destnictive side of his work has been done once for all. One criticism, how- ever, is sometimes made, and should be noticed here. It is said that the really inconceivable has never turned out true. Thus the Antipodes, for instance, were not really inconceivable at any time if only you conceived them in the right way. Grant this if you please, it stiU destroys inconceivabOity of the opposite as a test of truth. For (a) if I do not really know what I can or could conceive, how can I say what is inconceivable and what not ! While, if (6) you insist that I do know my own powers of conception, and that the incapacity to conceive the Antipodes was for our forefathers what the inability to conceive spherical space is to the average man to-day, a real thing only dependent on the limita- tions of experience, then yet again inconceivability becomes a relative and variable matter, and therefore utterly useless as a standard of objective truth. 490 KNOWLEDGE with, some "S ter data in one act of consciousness. I must make a synthesis whicli forms different objects into one. This is the action of the synthetic unity of consciousness. But now I can only make synthesis upon certain definite principles, or (if you prefer it) by means of certain definite conceptions; these are the various conceptions -which each several form of judgment is found to imply. Hence an object which should not fall under one of these categories would not be capable of entering into any intellectual synthesis at all. It would be unknowable ; or conversely, that an object may be known, certain conditions are prescribed which it must fulfil. The understanding itself conditions experience ; it does not learn its primitive conceptions from objects, but imposes them on objects as conditions of their becoming parts of its world. And hence the universality of the categories in experience is clear ; for that could not be a part of, or element in, experience to which they should not apply. Thus the truly a priori is universally valid. (c) Eelativism and Idealism. But it was impossible to stop here, for the position is ambiguous. Does it mean that there is, after all, a kind of unformed material of experience upon which the synthesising intellect acts, which it groups under its primitive categories ; or does it mean that the mind really forms or constitutes the order of which it is aware in knowledge 1 The first alternative, adopted after some vacillation and ambiguity by the originator of the whole conception, leads to great difficulties. Por, after all, it would seem, an essential element in reality is given to thought to make the best of. This element, in order to become part of our knowledge,must submit to the conditions of synthesis, that is, to the categories. And only so far as it submits can we know anything about it. But this proves nothing of reality as a whole. For suppose any reality to be of such a character that the categories are inapplicable to it, it will simply stand outside our world of experience, a background always possible yet never capable of certain affirmation or denial. By consistently regarding the understanding as a synthetic activity, and admitting that it must synthesise something, Kant was driven to the conception of this back- ground of reality, and the consequent limitation of knowledge to the field of our own representations as constituted and determined by the categories. But now it is clear that we have not gained much. For anyone having got to some notion of the fundamental activities of the mind could surely say that they are applicable and valid in their own sphere, that is, so VALIDITY 491 far as they apply. The question really is, How far do they apply ? and here, if Kant's answer is not tautological, it is only hecause he confines knowledge rigidly to a world of phenomena or representations, with the consciousness all the time that there may be another world that must remain for ever unknown. This is a heavy price to pay for the necessity of the categories within the world of experience. It would be surely better to feel that if our views and modes of thought are of limited vahdity, a wider experience can correct and supplement them. Nor, lastly, is it seriously a possible view even as it stands. Tor if the material of experience be genuinely regarded as a con- ditioning element, and if nothing can be known as to the applicability of our conceptions thereto, it cannot logically be maintained that the regularity of our own world of experience is not threatened thereby. If we are to conceive a world of things in themselves as even possible, and if we are to think of them as supplying the material of sensation (and this was in the end Kant's view), then the order — at least in some respects — of experienced sensation must, if only ia the most partial way, depend on the character of these things. Now, so far as our experience has hitherto gone at any time, the material supplied thereby may have been such as our conceptions could unify and harmonise ; but that it will always be so is a sheer inference, primarily, no doubt, about our experience, but secondarily concerning those things in themselves concerning which we can ex hypothesi make no inference at all. To this alternative Kant was led (as we have seen) by considering what was implied in the idea of synthesis. There must be something to synthesise: this something was the manifold of sensation ; and its origin was ultimately the thing in itself. When this led to manifold difficulties, and even contradictions, another alternative coquetted with by Kant himself was adopted. This was to deny the existence of any material on which the mind should work. The mind is no longer, from Tichte onwards, to work on a material ; it is to work out a material. We have already learnt from Kant that the understanding makes nature, but we have to apply this principle in a more thoroughgoing way. The alleged sense- datum on which intelligence acts is found to be a mere abstrac- tion apart from the relations which the Kantian admits to be the work of intelligence. No line can be drawn between the a priori and the h, posteriori ; and as a result, not a part only, but the whole of nature is the product of intelligence. Merely as a theory of validity much might be said for this view. There would, indeed, stUl be difficulties. For example, 492 KNOWLEDGE granting that mind is all things, or that all things constitute the full concrete realisation of mind, we may still ask, Does mind at any stage know itself fully? There seems every reason to deny this and none to assert it, since the very existence of philosophical controversy shows the difficulty men have in analysing their own conceptions. And, in- deed, the most influential, and perhaps the most philosophic, system of idealism aimed specially at exhibiting mental development as a " dialectic " in which the lower point of view is continually, and in virtue of its limitations and consequent contradictions, being merged in a higher. But what we want to know is the degree of truth in our own point of view, in the body of scientific opinion which we take for truth, and in the principles on which that science rests. Our question is not whether these opinions are a phase of mental development, which, indeed, is intrinsically obvious, but whether as they stand they are in whole or part final. The universal consciousness or the self-conscious idea may know all this, but since we are not the universal consciousness we know no more than before. But supposing difficulties of this kind, which may be admitted to be of minor importance, to be surmounted, the graver question would remain, whether idealism is consistent with the facts of our experience and the principles of our intelligence. After all, even idealism requires some proof. We cannot begin, continue, and end in assumption ; and the question is, whether some of the essential assumptions of this system do not break down when tested by the facts. I may illustrate this by a brief reference to two main lines of argument on which different forms of what we may broadly call idealistic theory have rested. One of these is the alleged dependence of sensation on thought. We have already dis- cussed this in Pt. I. Chap. I., and seen reasons for rejecting the idealist doctrine. We will here only add this remark, which seems in some degree to give the ground of error. Kant held to the d, priori character of the forms of sense and the concepts of the understanding on two essential grounds. The first was the inadequacy of sense-data as conceived by Hume him- self to furnish these conceptions. The second was the necessity and universality of mathematical and (generally) axiomatic truth as opposed to empirical truth. Both these grounds are abandoned by the idealist. The first because it is admitted and insisted (quite rightly) that the spaceless, time- less, relationless sense-datum is a figment : it is an abstrac- tion from the concrete whole of which we have actual ex- VALIDITY 493 perience, which has duration, which stands in uniform relations and so forth. The second, because according to the truer con- ception of sense experience, all truth when fully understood is necessary. There is no longer a distinction of empirical and a priori, for aU is a priori, though not all is completely worked out and elaborated. But in both these developments of Kant the idealists have cut the ground from beneath Kant's feet and their own. If the "given" element and the "work of the mind" in the contents of observation are indistinguishable, it is as easy to contend that all is "given" as that all is formed by the under- standing; and if (as empiricists have always contended) the distinction of a priori and empirical truth is relative and contingent, we can as easily infer that none is & priori as that all is so. In short, Kant reintroduced the work of the mind to cover certain deficiencies in observation and explain certain distinctions in knowledge. Idealism denies both the de- ficiencies and the distinctions, and therefrom infers, not that the work of the mind is nil, but that it is all A curious inference ; the real fact, as it appears, being that ideahsm has extended Kant's conceptions while annulling his reasons. Another line of thought leading to a more ambitious form of idealistic doctrine ran roughly as follows : — Any one of the ordinary conceptions which we take as true will turn out, if we seriously examine it, to be an inadequate expression of reality. It is more than this ; it is, if asserted without qualification, a sheer self-contradiction — so much so that in endeavouring to assert it we find ourselves asserting just its opposite. Being, taken bare and naked as mere being, turns out to be nothing at all, mere Nothing. But Nothing, again, cannot stand investigation. We are forced on further to a fresh conception which wiU include both these illusory notions. But our new hope turns out deceptive. The definite being (for example) which we have now reached is equally, when we try to grasp it, a bruised reed, and we are forced on again and again. So the process repeats itself, as it might at first seem, without end or hope. But this is not altogether so. Each conception that we took up contained some element of truth ; for to contradict it was as wrong as to assert it with- out qualification, and the right way onward was always to find a new conception which should contain the old along with its opposite, only as merged in a higher whole. And this gives us hope of an ultimate conception which shall contain within itself all possible elements, each in its proper place, with its 494 KNOWLEDGE own amount of truth, and this absolute idea would be the whole and the true. With regard to this conception there are two questions to ask. First of all, is it, so far as it goes, correct ? Secondly, would it, if correct, give us a criterion of validity ? The first point is a question in part of detail in part of method. The principle of the method we have already dealt with.^ As to the detail the question is this : Do our partial and limited conceptions contradict themselves after this fashion, and force us on to a whole in which they are merged, and which can alone be the real ? We have tried to show — in the case, e.g., of immediate consciousness, of space and time, of the relation of sub- ject and attribute, and we shall try to show later of substance, cause, and self — that this is not so, that these conceptions properly understood have an intelligible and self-consistent meaning, and that the inconsistency lies always in a false way of representing them. And in general we may add, that falsity consists in an alternative exaggeration, first of this side of the conception and then of that. If we dress, for instance, the unity of the thing so as to make it the whole character of the thing, its plurality disappears ; and then the unity in turn contradicts itself because it is twisted into a featureless abstraction. Then accentuate the plurality in the same way and unity can nowhere be found. In short, conceive unity and plurality as they are not, and you can easily show them to be unreal. Conceive them as they are given, and you no longer find them irreconcilable. In a sense, it might be said, this is Hegel's own aim. No thinker, so far as I am aware, before him gave so clear an emphasis to the statement that "the truth is the whole," nor waged so vigorous a warfare against the mass of abstractions that constantly threaten to suck the life-blood of philosophy. So far as Hegel's work went to exhibit the inherent weakness of abstraction and to force the overdone abstraction to submerge itself in the truer life of the concrete, his achievement cannot be too highly rated. But here all seems to depend on the correct or incorrect formation of the concept, and on its reference with or without due Kmitations to reality ; and it has been a principal aim of the preceding chapters to argue that the conceptions of science and common sense can be correctly formed and legitimately applied, and that not as mere elements of uncertain value merged in a higher concept, but as actual expressions each of some part of the truth. The result, then, would be that we are not forced on by any I Above, Pt. II. Chap. II. VALIDITY 495 dialectical movement to a supreme thought which includes all reality. Nor are we bound to know everything before we can begin to know anything. An ideal this thought doubtless is, and as such legitimate ; but as an ideal it can have no bearing on our present question — how we are to find anything which will give us confidence in the validity of our beliefs. We can- not be the supreme thought, nor therefore, if we imagine it, can we know that we have framed it rightly merely because it is the supreme thought that we have imagined. To make the absolute idea in this way its own evidence would be to revive the ontologieal proof. This will be clearer if we consider the one claim on our allegiance which the supposed all-inclusive conception may make. Other conceptions, it may be said, contradict themselves. This alone is self-consistent, and therefore true. This brings us to the question of the principle of contradiction as the test of truth.^ Now, that this principle is a negative test no one I imagine denies. What is real cannot contradict itself, whatever else it may do. And we need not combat the view that this statement attributes some positive quahty, however meagre, to the real. What we must entirely deny is, the power of going beyond this meagre qualification on the strength merely of the principle before us. We may put our objection in two ways. A certain suggestion ^ does not contradict itself. It is therefore true. But there might be a hundred other suggestions which I might make and which would all alike be self-consistent, though any one of them might be incompatible with the first. Mere self-consistency is not proof. It is simply the first con- dition which a suggestion must satisfy before it is worth while to consider whether proof exists. The application of the principle, in fact, becomes plausible only when there is an apparent restriction of our choice to two alternatives {e.g. unity or plurality in Mr. Bradley's argument). Then, if one of these involves a contradiction, and if the restric- tion is real, the result follows. But both of these points must be known ah extra. That reality must be one or many is a disjunction inferred from the alternatives with which ordinary phenomena present us, and it might be questioned whether the inference is legitimate ; it might be suggested that the whole would not have any attribute applied to it derived from a part, 1 AssuggestedbyMr. Bradley, ^;5pear(z?ic« a7iiiJea7%,bk.ii. chaps, xiii.andxiv. " Mr. Bradley speaks, not of suggestions or assertions, but of reality as being self-consistent. But it must come to the same thing. The reality as conceived by you or me is what is in question. Is that or is it not self-consistent ? My point is, that reality might be conceived Tvithout contradiction in more ways than one. 496 KNOWLEDGE so that reality as a whole would be neither one nor many in the same sense in which the partial facts of our experience are one or many. I am not contending that this is so, I am merely instancing the kind of material considerations to be met before the principle of contradiction will " march " at all as a test of truth. Still more strongly I should insist that the question whether unity or plurality is self-contradictory is one that can only be settled by quite other methods than a bare appeal to this principle. To put the matter broadly, we may say that while the prin- ciple of contradiction is an undoubted axiom, the question, what assertions contradict one another, i.e. what facts are incompat- ible with one another, can only be answered by a study of reality. This much only can we say on the strength of the bare prin- ciple — that the same proposition cannot both be true and not true, if the terms same and true be taken strictly. "When from the direct assertion and denial of one and the same judgment we go on to deal with different judgments or with different qualities of reality, the bare principle of contradiction gives us no light whatever. It is a remark (I think) of Lotze, that only experience shows us what qualities can and what cannot be attributed to a body at the same place and time. "We can think of a body as at once white and soft, because we have seen and felt snow. "We cannot think of it as at once white and blue without the white and blue being both modified into bluish white, because that is the form of union of those qualities which in fact we find in the real world. So, again, the union of the one and the many which Mr. Bradley finds self- contra- dictory appears to me valid, simply as expressing the nature of the real as I find it. And here the opposition of our criteria comes to a head. For Mr. Bradley would say that such a union, being self-contradictory, proves that in which it is found to be mere appearance ; while I should reply that the union in question, being found in reality, is not self-contradictory. It may be urged, lastly, that the principle of contradiction is an ultimate test. Tor the false must show its falseness some- where. If the untrue never were betrayed, how could we ever distinguish truth and falsehood ? I will grant this, but I must ask one question — Where will the false reveal itself ? In the long run. "Well, but how long is the run to be ? And if you cannot tell me this, will you justify our confidence in our own knowledge ? Our knowledge, you say, does not contradict itself ; and if false it would do so. Yes, we may answer ; and perhaps it will do so yet. If, finally, you reply that our knowledge is great and comprehensive enough to obviate this fear, we may rejoin VALIDITY 497 that this is just our question. It is the point on which we wish to assure ourselves. From the whole line of thought now touched upon we have learnt one great result. In some way or other the whole body of our thought is its own test. If you could get knowledge, or let us say, thought, complete enough you would get it true. The ultimate test is not a principle standing above belief, it is within the system of beliefs itself. Just as the concrete is more real than the abstract, so the whole is more certain than the part. But after our quarrel with the method of idealism we shall have to reach this result by a way of our own, leaving the question of method to be settled point by point as it has already been raised in more than one chapter. Meanwhile we have to consider other possible theories on our present subject. (d) Empiricism. In the hands of certain writers the vaHdity of knowledge has been rested upon actual experience. Thus Mill examines the grounds of our behef, not indeed in knowledge as a whole, but in the principle of uniformity which we have agreed with him to be the fundamental principle of inference. Now that Mill's argument cannot stand as he states it, is clear enough, and is I imagine agreed. It is a manifest circle. Uniformity is observed de facto in a vast number of cases. Therefore it will be found in all others. Therefore ? — why, on what principle ? Why should we extend our observations so as to infer from them the future and the rmknown ? On the principle that the unknown will resemble the known, that is, on the principle of uniformity, loosely stated. In other words, this principle can- not possibly be " proved " without assuming it ; and for this there is reason good. For it is the axiom of reasoning, and whatever be the axiom of reasoning is precisely that which we assume when we reason, and is therefore unprovable in the ordinary sense of the word. This is fatal to MUl's argument as it stands ; but whether there may not be something more solid in the matter of Mill's argument is another question, not so easily dismissed, to which we shall presently revert. Analogous to Mill's argument, but, if put crudely, even less satisfactory, is a more recent view which makes success the test of truth. Evolution must have its say everywhere, and so we get a theory of the survival of the fittest opinion. But like bad men, untrue opinions may survive long enough, and may often overcome those which are really better grounded. If you dispute this, you must mean by the survivors those which survive in the long run ; and if your argument is to have any weight, the long run must be so very long that I do not know 498 KNOWLEDGE where it will stop. To put it differently, will the opiaion that has succeeded in the past succeed also in the future ? If you say yes, that is an inference ; and on what is the inference grounded ? — on experience of de facto success. Then why, pray, infer from past to future ? — on the ground of uniformity. Then we are back in Mill's circle, from which we might as well have started. With all the difficulties that beset both Kant's theory and Mill's, and Hegel's and Mr. Bradley's, they give us a clue which is worth following up. To do so effectively we must return to our conception of validity as a starting-point. From it we shall try to develop a conception of a reasonable criterion of truth, and we shall then ask finally what claim this has on our acceptance and what light it throws on our de facto beliefs. CHAPTEE II The Validity of Knowledge 1. The criterion of validity is to be arrived at, according to our view, from an analysis of the idea of validity itself and its implications. What these are we have already seen in a general way, and it only remains to show how this conception of validity indicates of itself the nature of the criterion. Validity, then, as we have seen, is assigned to a judgment on the ground of some other judgment. The isolated judgment qua isolated may possess a certain force, a felt certainty, but cannot be said to be valid or invalid. Its validity is tested by comparison with some other judgment with which it is in some way connected. But in this it is not implied that the second judgment is of itself necessarily and intrinsically valid. Indeed, such a requirement would itself contradict the notion of validity as just analysed. According to that analysis we cannot anywhere find an isolated judgment of final and intrinsic validity, for ths very reason that intrinsic validity as applied to a single judgment is a contradiction. But where, then, can a test — I do not yet say the ultimate test, but any test — be found ? From judgment A I appeal to B, and from B to C, and so on ; but if C is not valid, why should B be so, and if B is not valid, why A ? In short, li validity cannot be found in any one judgment, where is it ? We answer, where the conception of validity would have it be, namely, in the consilient judgments themselves, as forming a consilient system. A is judged valid in view of B, B in view of C, C in view of A. Then the three judgments A, B, and mutually support one another, and this mutual support constitutes their validity. Two mutually supporting or consilient judgments constitute the minimum requirements of validity. If A is such as of itself to lead to B, while B also leads to A, the two judgments A and B are, so far as we confine our view to them, valid. Validity, in short, is to be measured by consilience. But this validity is only relative. To a consilient or 499 500 KNOWLEDGE coherent system A B may enter a third judgment C which is dissident. That is, from C alone we should be led to negate A or B. Assuming for a moment that such dissidence has been overcome (we shall inquire presently in what way that is possible), and that we now have a coherent system again, there would still remain the possibility of any judgment based on some further fact not taken into account turning up to destroy our system. This possibility could only be put out of the way permanently and absolutely if our system took into account every existing or possible fact. The completed system of consilient judgments, then, would possess absolute validity, for there could no longer be any possible judgment to disturb it. This ideal is, of course, unattainable, but meanwhile the highest possible validity would attach to the completely coherent system of all judgments actually existing for us, and taking into account all facts actually known to us. Of our actual knowledge, it has to be asked how far it attains this validity. Or more generally, since validity depends on consilience, and is to be mea- sured by the number of consilient judgments, we may aslc what degree of validity does our knowledge or any portion of it attain ? 2. This question necessarily arises in view of the actual occurrence of dissident judgments. How are these to be dealt with, and how do they modify our criteria of vahdity ? As consilience is the ground of validity, so dissidence is the ground of invalidity. If two judgments A and B oppose one another they cannot both be valid, and if there is no further consideration bearing upon the matter mere doubt or suspense of judgment is the logical result. The result of dissidence is in this respect different from that of consilience, that it leaves us, not with a single necessary result, but with the possibility of two or three results ; for when A contradicts B, if we make no assumption as to the validity of one judgment rather than the other, either A or B, or both, may be false. The mere dissidence of the two leaves us with three alternatives, and no ground for choosing one rather than the other. But now, suppose a third judgment confirming B, and here we have a motive for adopting one alternative. On the ground of C, B is true and A false. If we grant every judgment to be a ground for the validity or invalidity of any other judgment with which it is brought into relation, this result must foUow. But another result follows at the same time, namely, that the dissident judgment remains a ground for disputing the result arrived at, and hence we get the conception of degree of validity. The combination B C regarded alone would be completely valid. The judgment A is a reason for disputing THE VALIDITY OF KNOWLEDGE 501 that validity, and though it remains reasonable and necessary to " prefer " B C to A, this preference cannot, with a view to the three judgments alone, be taken as final. Any further judgment D may support either side. If it coalesces with A we have an equally valid system A D disputing B C, and we are reduced again to doubt. If it joins B we have an increased reason for the whole B C D as against A. The degree of the validity of a system, then, is as the ratio of the consilient judgments to the dissident. To this we are led by retaining the primitive idea of vahdity as something to which each judgment of a connected system contributes, whether its tendency be to the negative or positive side. But now, however numerous and ramified our system of corroborative judgments, a single Athanasius contra mundum will always cause disco atent. We could never at this rate arrive at a validity which, even if we confine our considerations to the judgments concerned, would be complete. We should never be able to say that, so far as our own minds can reach and can determine the matter, we have valid knowledge. On the contrary, this validity would be always partial and problematic; however high in degree, it still would not be " validity" without drawback or qualification. We seek, then, always, as reasonable people, to come to terms in some way with the dissentient. This can be efi'ected in one way only. I have three judgments a, B, C, of which B and C support each other against a. Now a fourth judgment d presents itself such that, combined with a, it gives the whole judgment A, which will now cohere with B and C. Then the total system, a 5 B C or A B C, is completely coherent internally, and therefore, so far as it goes, completely valid. The most familiar instance of this is a " psychological explanation " of a judgment. If a is a given belief, and d reveals to me how such a belief woiild arise from a fact A, then the combination of a and d itself leads me to assert A, which is further confirmed by B and C. So far, then, as an assertion may be modified without being destroyed by being taken up as an element in a new whole, we may turn apparently inconsistent judgments into actual supports of our system, and in this way we are in fact con- tinually getting rid of discrepancies by " explaining " them away. Hence a discrepancy is not necessarily permanent, and the problem of attaining to undisputed validity is that of thus absorbing every discrepancy into a whole, which will consist with and even lend support to the remainder of our knowledge. 3. Hitherto we have assumed the possibility of connecting judgments ; but to complete our account, we have now to ask 502 KNOWLEDGE how these connections are effected. We may, indeed, have judgments which directly assert or deny the same content, but normally this convergence of two or more mental opera- tions on one and the same point is the work of what we call inference ; that is to say, a felt connection represented in our speech by such words as " therefore," " because," and the like. Now we have represented judgments as valid when connected ; but when the connection itself is seen to be a mental operation distinct from the assertion of either judgment as such, the question will at once arise as to its validity. This question must be treated on the same lines as those already followed. Let us illustrate it first by showing how methods of connection may be dismissed as invalid. Suppose, for example, I have formed a highly valid body of judgments M, and another of equal cogency N, and that by the method P I am led to question M on the ground of N. Then, assuming P, I find M and N to conflict. But why should I assume P ? P is itself a method of connecting ; but with what judgment is it itself con- nected ? If I can find none for it, I must, on the principles already laid down, dismiss P as invalid, though as requiring subsequent explanation if my whole system is to be harmonious. But now suppose P (which can be analysed into and regarded as equivalent to the judgment, if M then no N) can be connected with some similar judgment Q, which I have already made, such as, if K then L. Then P has a certain guarantee, the system P Q has a validity of its own ; and if a sufficiently ex- tended system of connection-judgments thus cohere, they may suffice to validate P as against the bodies of judgment M and N. This, of course, is a question of degree to be settled on the principles above determined. What requires our attention is, that the methods of connection form, or may form, a system among one another. To form this connection is precisely the work that logic can itself contribute to the theory of knowledge. Let us see how the work is carried out. Taking, first, inference, let us go back to the simplest primd facie form of explicit inference, the argument " from minor to conclusion." This is A : it is B. This inference we have taken as implying a certain principle, but we have now to inquire into this implication a little more closely. The inferential process, it will be observed, is not itself a judgment. You might call it a connecting of two judgments, or you might call it an element expressed by the word " therefore " or " because " in the whole judgment. This is B, because it is A. But a single explicit judgment it is not as it at present stands. And it is just this that creates our difficulty. THE VALIDITY OF KNOWLEDGE 503 In detail, the act of inference may appear in two stages. In its lowest, least reflective form it is a process ia which one assertion in fact determines another, acts as a considera- tion leading the mind to that other. In a higher stage, where such a word as " therefore " comes in, the mind is so far aware of its own process as to recognise a certain relation between the two contents, which it may express by saying that they are connected, or that one is the condition of the other. But whether recognised or not, what analysis has to say is that the first content operates on the mind as a condition leading it to assert the second. Further, if the inference is justified this operation must as such give a true result ; the first con- tent must be a just or sufficient ground for asserting the second. But what is the consideration taken into account ? It is, as careful attention to our own thought tells us, the content A. We deal with this A, but it is not the fact that it is here and now, but the fact that it is A, which makes us proceed to the assertion, it is B. This is B because it is A, not iDecause it is this. The content, then, or rather the character of the content, not the relations which constitute its individu- ality, is the ground of argument. That is, according to our analysis the act of inference makes in effect the distinction between A as a purely individual fact and A as a characteristic of the real world. A as existing in reality, not A as here present, is its ground. The process of inference, in fact, takes A as such as the basis from which it draws its conclusion. And the process claims certainty as a process. But now, suppose there be any- where an A which is not B, it is clear that the result would be doubtful For A is taken without any further consideration as a condition from which B follows as consequence, and there is therefore nothing to show that this is not the parti- cular case in which the relation A — B fails. If, therefore, we take the inference from A as such to B for a certainly valid process, we must deny that any A can fail to have B in rela- tion to it. That is, the inference implies that all A is B. This in the last analysis seems to be the logic whereby the infer- ence from minor to conclusion postulates the major. The validity of the inference from minor to conclusion, then, postulates the truth of the major premiss. It follows that now, if we deny the inference in any one case we deny it in any other, and if we affirm it once we af&rm it universally. The set of inferences under that major stand and fall together. They are connected by the implied judgment discovered in each one by analysis. That implied judgment is, that A taken o 504 KNOWLEDGE by itself is a sufficient ground for the assertion of B. Formed into a major premiss, this is applied syllogistically to any fresh case, and so connects each case with every other. Now, any ordinary judgment that figures as a minor pre- miss from which conclusions are drawn rests no doubt upon antecedent experience, without which there would be no tend- ency on the part of thought to draw the conclusion from it at all. But, according to the view urged in preceding chapters, there are certain premisses upon which thought sets to work without any antecedent experience to go upon. I mean those uniformly observed relations which, in the absence of what are in fact conflicting uniformities, thought will tend to generalise. Here again we have an inference in which — to reduce it to its simplest terms — the observed relation a^ - bj is taken as ground for the generalisation a — b. Now, applying our previous analysis, it is clear that if we claim to make this generalisation in the absence of other considerations deter- mining the relations of a and b, the ground used is not the specific character of a and b themselves, but the fact of their uniform conjunction. And by our previous reasoning this fact must now become as such a basis for generalisation, and that is again an universal basis for generalisation. This means that all our generalisations — all our inferences from one con- tent to another — will stand or fall with this principle, and therefore will stand or fall together. None can be valid unless the principle holds ; all must be valid if the principle holds. The truth of one, then, implies and is implied by the truth of all the rest. Our analysis, then, claims to have connected all those ways of forming inferences — even we may say all the individual tendencies to form inferences — which, as tested by experience, give good results. The methods of inference, then, are valid as forming a connected system. Observe now the nature of the connection. "We analyse a given inference. We find that if it is warranted a certain con- sideration must be adequate to such and such a result. We for- mulate this relation in a principle. This principle, being applied syllogistically to any other case, necessitates the inference in that case.^ Or we could equally reason from the second case back to the first, and so from any one of the generalisations carried out on these lines to all the rest, and from all the rest 1 We see here the element of truth in the theory which would base inductive argument on syllogism. It is, however, a very one-sided truth, since the major of the syllogism in question is itself derived from the impulse to gener- alise, which is the basal fact of induction. Here, as elsewhere, the principle is not the iipx,« from which validity flows, but that expression of coherence between truths which assures us that validity is within them. THE VALIDITY OF KNOWLEDGE 505 to any one. That is, they are connected first by an analytic judgment giving their principle ; secondly, by a syllogism apply- that principle. The " methods " of generalisation, then, are con- nected by the remaining " methods " of construction or analysis. Conversely, construction, analysis, and memory are inter- connected by generalisation. Not, of course, by expKcitly formulated generalisations, to apply which would involve con- struction and analysis, but by the impulse to generalise which precedes explicit formulation. I mean, that as we construct and get truth in one case, so we expect to do in another, and the methods of analysis or construction in parallel cases sub- stantiate one another. Thus all the methods of dealing with the given, and making it the basis of a further truth, are connected with one another in a completed circle. One point only might seem to stand out. I mean, the very use of one fact as the condition of another. That usage is employed in our analysis of generalisation, and is implied in any of the applications of syllogism. How, then, can it be tested ? We can only answer that the notion of a condition is the basis of the conception of validity itself. That is valid which is interconnected ; and to ask, therefore, why a connec- tion should be admitted at all is to ask for a reason for the ground of all validity. Now, for the principles by which validity is tested, we cannot give any reasons of which, the, validity is already assured. To expect such reasons would be a self-contradictory demand. Whether in any other way we can support our conception is a question to which we shall recur at the end of this chapter. If, however, we are asked proof of the validity, not of the notion of system in general, but of any given method of con- nection, such as the axioms of reasoning, we may claim to have some answer ready. It is not self-evidence, nor a generalisa- tion from experience, nor yet the fact that it is a method by which thought works, which establishes a principle. It is the in- terconnection of a mass of methods of thought which establishes them all, and our axioms claim to be valid precisely as formu- lating this interconnection. They are the generalisation of all such methods of generalisations as are undisputed by the facts ; and if they in turn are to be modified, it must be by the produc- tion of some facts, or body of judgments, the coherence of which can be explained by means of their modified form, and which is at the same time inconsistent with them as they at present stand.^ ^ A grounded, as distinct from an unmotived and unreasonable, doubt of the postulates of thought would arise if two incompatible systems of belief should aiise and acquire nearly equal strength. In this case the reasonable 506 KNOWLEDGE An ideal system of knowledge, then, would present itself as a coherent organisation of judgments supporting one another in virtue of certain methods of connection, the methods in their turn being supported by one another, and being con- sistent with the judgments which they connect; those methods and judgments which, in the formation of the system, appeared from time to time to antagonise the rest having been formed by combination with further judgments into resultant judg- ments which take their place in the system. Supposing such a system to include every possible judgment, it would be abso- lutely valid. There woidd be no sense in questioning its validity, as there would be no further judgment to which appeal could be made. Supposing, again, the actual body of judgments existing for us at any given time to form such a system, it would be for us the most valid truth attainable, and would be the test of any new judgment. The system as now described is the test.^ 4. We may deal here with a certain ultimate doubt of induc- tive science of which hitherto we have said nothing. The valid method, -as we now see, must, as the first negative condition of its validity, never give a false result, never — ought we to add ? — be capable of giving a false result. Now, in our theory of induction we have tried all along to guard ourselves from this contingency by a deference to the possibilities of error suggested by a wider experience. But is there not here an attitude would be to expect and endeavour to effect a reconciliation. Such reconciliation might be brought about either by the modification of some of the results of either of both systems, or by that of the principles on which they are based. And until it should be effected, each system could only be adopted provisionally, and as an adumbration of tbe truth. In no case could one principle or one system be preferred to another, except on the ground that it actually effected a fuller harmony. On the theory of validity, any postulate of thought may be called upon to justify itself, and thus any reasonable or grounded suspicion can obtain a fair hearing. '■ Our theory, it will be seen, tends to separate questions of validity from those of origin. The validity of reason must be tested by its own internal coherence, and by no other method. Granting reason valid, however, we must not make off-hand inferences as to its historic development. Mr. Balfour {Foundations of Belief , pt. iv. chap, v.) urges that to derive the premisses of reason from the "collision of atoms" would destroy all its authority, because atoms have "no prejudices in favour of truth." But surely if this theory, instead of being intrinsically nonsense, were demonstrated fact, it would prove, not that proof itself is non-existent, but that atoms, whether "prejudiced" or not, have at least the power of generating rational beings. As to the exist- ence of human reason postulating a divine reason as its source, this is merely the ''like-cause-like-effect" theory iu its crudest form. In fact, the historical origin of reasonable beings is a question of genesis, and one of extreme, perhaps insuperable, difficulty, not to be settled by these off-hand assumptions. On the whole question we may add, that the origin of a belief is a fair test of its validity if, and only if, no positive proof or disproof can be found. THE VALIDITY OF KNOWLEDGE 507 element of relativity which could not be escaped except by a mind that knew the whole of things, and knew that it knew the whole ? If this is so, is our knowledge reaUy valid after all, or is it only something possessing force for our miads as we are constituted ? "We may put the case thus. Suppose, if we can conceive the supposition, a mind hmited in its knowledge to a single experience and applying to that experience those methods of induction which we have assumed as sound. It fastens on a conjunction which we (suppose) with our wider experience, see to be determined by accompanying facts. But knowing nothing of these facts, it generalises the conjunction. This is clearly on our principles a logical step, and as clearly it will lead to false results. If this is so, what becomes of our certainty ? and why may not a greater mind than ours in contact with a wider reality see that we in our turn are making just the same mistake ? It is no answer to say that we are already aware of the possibiKty, and are constantly on our guard against the assump- tion, of a complete knowledge of conditions as a " most dangerous downfall " to science ; or that, accordingly, all cautious science guards its statements so as to cover the possibility of a differ- ence of conditions. For the question is one of the ultimate limitations of belief and its grounds, and as to whether, when we have taken all the precautions which experience suggests, we have yet exhausted the possibilities of that which is wider than experience — reality. To this we can only reply that it is by such elements of reality as are given to us that we must judge such further elements as are not given, and these possi- bilities, their weight and value, among the rest. But how then are we to meet the present problem ? There are two possible answers. (1) We may say that a conclusion drawn, on our principles, from an inadequate experience is logical though not correct. The considerations, then, which we have held to form the groundwork of science would be intrinsically valid as logical methods, but will give us truth only if their premisses are adequate. How, then, can this adequacy be as- certained ? It can only be affirmed on the ground of con- silience as between different results, or denied on that of inconsistency, and thus so far as we find consilience we must accept the result. But is not the mere fact that inconsistency, and therefore error, exists in certain cases an argument that it may be found by a wider experience elsewhere ? Yes, if the facts in that elsewhere are parallel; but, once more, when the connections are so manifold and intricate that results so formed 508 KNOWLEDGE have never been destroyed, the counter argument from the parallel ceases, and those results are certain in proportion to their systematic connectedness. Nor can we deny that in their highest stages they reach real or complete certainty ; for taking them as merely probable, some of them should within our experience break down, — and if we can find a class of a given stage of systematic interconnection clear above that in which failures have been found, the certainty which on our methods we attribute to its members is justified, on our principle of validity, by repeated tests. Just as at a lower stage the attribution of probability would be valid, so here is the attribution of certainty. But if this answer is to stand, the word " certainty " must be understood in a special, though perhaps not wholly unjustifiable, sense. For by the original suppositions of induction, which it has been our business throughout to justify, observed uniformity and observed difference were not only considerations on which we could generalise, but the only considerations upon which we could either form or deny an assertion. And conceiving logical certainty as that which is based on a totality of considerations, we laid down, that that must be certain which is grounded on one of these considerations and is at the same time impervious to the attacks of the other. It would follow that when, as in the case suggested, we conclude from an inadequate basis in ex- perience, we have a logical, and therefore I suppose a justified, certainty, which turns out to be false. And if, further, we compare that hypothetical certainty with the certainty claimed by our actual sciences, we must admit that they stand on the same theoretical basis. Here in our experience is a uniformity. Experience does not afford any ground for supposing an excep- tion to it ; and that, as we argued before, is as much as to say that experience rejects, negates, any exception to it. True, but this is, after all, the work of our experience, which may be as meagre in comparison with the plenitude of reality as the supposed experience was in comparison with ours. If, then, we deduce, you are to continue in the position that induction gives certainty, you must mean by certainty an atti- tude of mind such as we discussed in Pt. II. Chap. X. — an attitude which is simply the extreme case of belief where no further attention is paid to the possibility of an alternative. Such a certainty will, in the terms of our definition in that place, be logically justified if it lead you right in the long run. If, on the whole, you come nearer to truth by maintaining that atti- tude of mind under certain conditions, then it is justified under those conditions. And if we now mean by a logical principle THE VALIDITY OF KNOWLEDGE 509 one which leads us to truth, not always, but most closely in the long run, then we may perhaps say that our principles are in any case logical. For, we may contend, even if in this or that case they may lead to error when freedom from all principles would have left us in doubt, yet the way to truth is through error rather than stagnation. It is better in the long run to be guided by the evidence as far as we have got it than to sit down with our hands before us because half a loaf is worse than no bread. The over-hasty conclusion will, if we are faithful to our principles, constantly correct itself, and so we shall always be coming nearer to truth. On this view we should always be justified in holding to our systematised knowledge, even in holding it with certainty as that word is now deKned. But the real certainty would be, that we are on the right road, not that we have arrived at our promised land. The tendency of knowledge is right. Science must go on as it is going. That would be the sum and sub- stance of our theory of knowledge. And some might say " all the better "— 'Tis a lifelong toil till our lump be leaven. ; The better — wbaf a come to perfection perishes — Things learned on earth we shall practise in heaven ; Works done least rapidly Art most cherishes. And perhaps if there is an inner arcanum and sanctuary and impregnable rock of reason this is it, that her aim and tend- ency, if not yet her result, are right. But (2) there is another possible solution which may incline us to feel a fuller rehance on the inner core of knowledge, on the massive results of tradition, common sense, and the exactor sciences — reliance, not merely on their tendencies, but on their attained results, taken, of course, with the limitations which would be acknowledged in all careful statements of the sciences themselves. If it be pointed out that, at least to a less ex- tended experience, our methods would give fallible results, our answer might be, " Yes ; but our methods were not invented for an experience of that kind, but for our experience." The principles of induction claim to be true of the world that we know, claim to give us guidance as acting on the experience that we have ; they know nothing of another world nor of a different, narrower experience. Within a different experience to ours there is no reason why they should give truth at all, because they are not intended to apply to such an experience. So far from being the whole consideration, they might in such a case not be considerations worth attending to in the least. 510 KNOWLEDGE And this answer we for our part prefer, as pointed out by the character of the logical genesis of our inductive prin- ciples. They claim no a priori validity. They are strong, not because thought must accept them before it begins to act upon experience, and without reference to anything that experience may turn out to be, but because, reflecting on its own ways of dealing with experience, thought finds that these express the common character of all correctly working methods, while in no case, as applied in its experience, do they lead to results which cannot stand. We reply to the objection, therefore, by ruling it out of court. It lays down that our principles would, under certain circumstances different from ours, lead to false conclusions, and therefore cannot be maintained. Our reply is, that our principles are meant only for circumstances like ours ; and whether they would or would not hold under other circumstances it is not our business to inquire. This much only would remain to add. An ideal reasoned certainty would have taken everything into account that could bear upon the case in question. But what that exists could not bear upon it ? And how, then, could we get an ideal certainty without knowing the omnitudo realitatisl The results of this reflection would, at first sight, be to send us back to relativity once more, though in a new form. Certainty, it might be said, is a matter of degree, and the more certain belief is that which rests upon the greatest mass of judgment. Where in this process of increasing stability we come to actual fact is a point we cannot determine. It is enough to say, that where the greatest mass of judgments cohere there we have greatest certainty. It might be enough to leave the matter thus. But the view that certainty must be, after all, a definite stage of belief, grounded logically on some totality of considerations, should not be too hastily dismissed. If we resolutely keep to what we experience of reality as the basis of all we know or think of it, and as determining the estimate of our own attitude to it, the whole of our grounds for or against a belief must be found within experience. And that belief which stands the test of the whole of experience in the many-sided ways which our logic requires may thus be said to have encountered all the considerations justly bearing on it. Still, the old argu- ment comes back, further experience may modify. Well, this suggestion, again, is grounded in experience and applies prim- arfly to the less certain, i.e. less organised, results in which we now believe. But those things which we claim as the most certain, as the really certain, are just those which advancing THE VALIDITY OF KNOWLEDGE 511 experience is not found to modify, the broad tendencies of science, tradition, and common sense — understood all of them scientifically, i.e. with due limitations. The arguments from " limited experience " tell less and less as we approach them. Seeming exceptions really confirm this statement. The "miracles" of science which upset common-sense traditions, the modifications introduced by an extended science into its own original suppositions, really leave the mass of truth stand- ing as it was, but seen in new relations and differently phrased. It is the broad result for which we contended, not the pre- cise way in which that result is at any time understood or expressed. The theory of our theories and the expression of them are at all times among the most pliable portion of belief. But it is just these which bring the familiar truth into fresh and less certain relations. At this point, then, the negative argument disappears, as it were by absorption. The truth that knowledge now claims as the irreducible minimum of its rights is, as we learned in Pt. II. Chap. XVI., approximate truth, — truth, some of which is all true, all of which is nearly true, and which looks to fresh experience for further definition, and welcomes correction instead of being overthrown by it. It is the living organism absorbing fresh matter and making it its own ; and for the knowledge which so lives there is no death. The overthrow of particular facts is no analogy for its destruction. And so, in a sense, we have reached the same result as before. For the knowledge we claim is not final But there is a difference. Before we claimed only to be progressing ; now we claim a result, not final, but containing reality itself. Before we claimed only to be on the road to truth ; now we claim to dwell with truth. Here and there we trace her very outlines, though they be but outlines, and though our vision of them is not always clear. 5. But now, it may be asked, is not our whole theory of validity after all an assumption ? "We have chosen to formu- late a certain test which, if our reasoning has been correct, can indeed be consistently carried out, and is so far possible. But, after all, what guarantee is there that this is the test of truth ? Must it not in turn require proof ? — and what proof of it can be given which will not be found to assume it? Obviously none, if it is what it claims to be ; and as obviously this must hold of whatever is the test of truth. You cannot get a further test outside and above it ; and if you could find that elephant to support your world, you would still require a tortoise to support your elephant. Then must the test of 512 KNOWLEDGE truth in any case remain au isolated judgment, the one judg- ment that must be valid though isolated ? After all that we have said of proofs and tests, does our o-wn criterion of truth remain a mere assumption ? There are two things to be said in answer to this question. (i.) If we consider what we ordinarily mean by a " proof " on the one hand and an " assumption " on the other, we shall get some light. If we take any ordinary judgment IST and desire to prove it, we have to find some distinct judgment M which is certain independently of N, and from which N follows by an equally certain and independent process p. If it turns out that either M or p depends for its certainty on E", we are arguing in a circle, and our procedure is vicious. Now for the principle which we propose as the test of truth no proof of this kind can ex hypothesi be found. For supposing such a proof X, the process by which we brought X into use must be some method of connecting X with our proposition T. But since the content of T is precisely that truths are made valid by interconnection, the argument would be necessarily circular. The method connecting X and T could not be true unless T were also true. We cannot then prove our conception of val- idity in the way in which we can prove any particular truth ; just as we cannot explain the whole of reality in the way in which we can explain this or that fact. The reference to some- thing else must, as Aristotle told us,^ come to a stop somewhere. But now, an assertion which is unproven is ordinarily said to be an assumption. But what in ordinary cases is an assumption ? It may be said to present one or both of two features. Generally it is a suggestion, intrinsically uncertain, taken up for certain purposes which from a logical point of view may be legitimate or illegitimate. But if we connect this suggestion with other assertions, certain or probable, it ceases so far to be a mere assumption, and becomes a judgment for which some grounds may be given. The assump- tion, then, appears as an isolated assertion. It does not follow that every isolated judgment is an assumption in the first sense. For if there were any self-evident judgments, they might be isolated and yet require no grounds outside themselves. We must be careful, then, when we call a judgment, as though by way of stigma, an assumption, to know what we mean. We may mean merely that it rests on no extrinsic grounds, or we may mean that it is as it stands unwarranted. The latter meaning would not be involved in the former for any one who should allow self-evident judgments. For us, however, it may ^ Posterior Analytics, i. 3. THE VALIDITY OF KNOWLEDGE 513 be said, no consolation is to be found in this. For we have discarded self-evidence as a final test, and the isolated judgment must therefore, for us at least, be invalid. We can only get out of this, it may be urged, by a frank admission that the judgment of validity is an exception. And this, it might be sympathetically put, would not be so unreasonable. Grant- ing that everything else must be tested by interconnections, the judgment which tests all others falls, on that very ground, into an essentially different category, and we may be prepared to treat it differently. • But the reasons which would lead us to fall back on this reply are more apparent than real. The judgment of validity is not so isolated as appears. Consider first, not the principles by which vaUdity is assui'ed, but the completed result, the valid system. In this system we have a number of judgments, a, b, c, d . . . all interconnected, supporting one another. Any one of those judgments, then, is valid, tested, connected. Any one of them, a or b, apart from the system, before the system is formed, is unconnected, isolated. So with any judgment p that stands outside the system now formed. But what of the judg- ment M that recognises the system abed as a whole ? Is this judgment isolated ? Surely not ; it stands on the same footing as the component judgments abed. Certainly, it is isolated as compared with any foreign judgment p. But this only means that it is not yet final. Whatever connectedness or validity is rightly attributed to its component members, that connectedness and validity must be allowed to the system com- posed of them as a system. The system is involved in the components, just as the components depend on the system. We may again revert to the analogy of explanation. The part was explained when it found its true place in the whole. The whole was explained, not again by reference to another whole, but by presenting itself as a system of connected elements. So it is here. The single judgment is valid as falling into a system ; the recognition of the whole is valid as expressing an interconnected set of judgments. So far of the whole system of truth. Applying the same conception to the methods of forming judgments, we have found them to form similarly an interconnected whole, and the recognition of this whole as valid is no more an isolated judg- ment than that of any of the distinct but connected methods. In fact, in the concrete whole which knowledge forms there is not strictly a before and after. There is not first the whole, with its truth assured, and then the parts depending on it ; nor are there first the parts and then the whole. Knowledge 33 514 KNOWLEDGE in its fragments is a hierarchy where certain judgments of sacrosanct authority give or withhold credit as they list ; or it is a monarchy where a single principle rules with undivided sway, or delegates local authority to media axioimata of con- ditional value. But knowledge in its whole truth is a democracy where no element is before or, after another, but where the value and truth of each is bound up with the salvation of the whole, and the whole rests equally on the trustworthiness of every member. Now, the principle of validity, like every other principle, is taken out of the whole of knowledge by an abstraction, and it is so taken that it appears as an isolated judgment. But in truth it rests on the whole of which it forms a necessary element. Eecognising the whole system of connected judg- ments as true, recognising the connecting methods as reasonable, we include the assertion of the principle of validity as sound. Neither the principles nor the system which it helps to create can be proved aliunde as any portion of the system can be proved. There is at this point no question of proof in that sense. But neither is there assumption. Our assertion of the principle does not contradict its own requirements by remaining cut oti' from the rest of our thought. On the contrary, our principle approves itself as an essential element, the gmding element, in our complete system of belief. (ii.) If remaining at the abstract point of view, distinguish- ing the principle of validity from judgments which are valid, we required a support ab extra for our principle, there can be for us only one course, The principle cannot be " proved " by judgments taken as vaUd. It can only be led up to by judg- ments possessing definite psychic force ; and it is precisely in that way that we have tried to lead up to it. There are two ways in which we can regard judgments — as having validity, or as possessing so much felt force. Now, to " prove " the criterion of validity by means of judgments which you assume to be valid, or which are valid on submitting to that test, is either to prove by assumptions or to argue in a circle. But to appeal from the validity of judgments to their de facto force is simply to corroborate one thing by another. As apart from a criterion of validity, judgments simply possess so much force ; the only intellectual factor therefore remaining outside that test is this force ; and if by means of analysing and correlating certain judgments we establish the criterion of validity, we have used the only means in our power to that end. The only further condition which such a process must fulfil is that neither in the judgments used nor in the reasoning which connects them THE VALIDITY OF KNOWLEDGE 515 should there be any principle inconsistent with the theory of validity subsequently estabhshed. Lastly, if we establish the criterion of validity by means of the force of certain judgments, we may corroborate it further — not as valid, but in its felt strength — by the whole mass of judgments which it sets in order. The validity-judgment, and felt certainty do not always step by step coincide; but the synthesis of judgments which is the principle of validity is also a grouping or regrouping of feelings of belief which has a marked eiiect on the nature and direction of those feelings themselves. Thus we may feel little liveliness of behef about any judgment taken singly ; but when it has become united with many more the certainty of the whole becomes a feeling of great strength. More strictly, it is not a mere feeling but a power of acting on, producing, or abolishing feelings of certainty, a power which exceeds the most intense certainty which can be felt at any one moment. Hence the most clearly felt judgments fade away when brought to the point of inconsistency with some element of a well-knit system. The constraint, the obligation we feel to reverse our judgment, expresses the reaction (in terms of felt certainty) of this mass of felt belief upon the feeling which has first arisen within us. This subjugation of the immediate single feeling to the system is in its completeness a gradual work, and it is only as it becomes complete that the principle of validity triumphs over every opposing force. The principle of validity, then, has in a sense both a ground and a test ; but neither of these is, apart from the principle itself, valid, nor is it possible that it should be so. But it is led up to and confirmed by actual judgments in their character of felt certainty to which, and to which alone, it should on its own theory make appeal. We may now, in a few sentences, sum up our theory of the conditions and validity of knowledge. Our starting-point was the datum of immediate apprehension which we took to be fact. We assumed these data, and we postulated that they can be analysed into elements, that they can be remembered, and that any portion of the continuous stream which they form can be constructed into wholes for thought. The relations in which they are found are generalised, and that with certainty, except in so far as a conflicting generalisation can be formed from the apprehended data. By these five methods, judg- ments and inferences of all kinds are built up, and their validity is tested by their consilience, which similarly justifies 516 KNOWLEDGE the methods postulated. The resulting system, then, is know- ledge, and is valid. Memory, or construction, or any other postulate, is justified so far as it is (a) a method of forming beliefs which (/S) gives results coherent with one another, and with those formed by other methods. So far as it fails to satisfy these tests it cannot be relied upon. Such being the character of knowledge, it remains to con- sider further the character of the mind which possesses it, and of the reality with which it deals. CHAPTEE III The Conception of External Eealitt^ 1. We have now discussed the main conditions of knowledge, and have tried to show in what way a system of valid judg- ments, in other words scientific truth, may be built up from them. But we have to submit our hypothetical conditions to a further test. Certain conceptions pass current in our mental economy as solid and well-established truths. These concep- tions not merely hold facts together by universal laws, but, as we shall try to show, distinctly attribute to them a certain nature or manner of existence. Now, though we have no doubt often enough used these conceptions in preceding chapters, we have not yet made our references to them ex- plicit. We have been bent on explaining and justifying our knowledge of particular facts in the present or the past, of the wholes constituted by such particulars, and of the iinifor- mities in their relations and occurrence. We have now to ask whether the factors of knowledge so far assumed will further explain such conceptions of the nature of things as we name matter, mind, substance, power, attribute, etc. A few words may be prefaced as to the nature and limits of this inquiry. As to its nature, one general principle must be laid down, viz. that nothing must be taken as final until it is submitted to all known tests. This undoubtedly makes our inquiry more difficult. If, for example, we could take the notion of matter and its independence of mind as ultimate data, we should have to explain them by our theory of the conditions of knowledge. And if our theory as hitherto de- veloped failed to explain our knowledge of these data, we should have to say " so much the worse for the theory," and set about remodelling it. If, again, we could take our conditions of knowledge as certain and certainly exhaustive, we could make them an absolute test for the existence of matter ; and if 1 In regard to this chapter, I am under special obligations to Professor Case, and to his private teaching even more than to his published work. 517 518 KNOWLEDGE the knowledge of matter could not be explained in accordance with them, it would be that conception which would need revision. Hence, in fact, thinkers who have assumed one or other end of this problem as fixed have generally made very short work of the rest. In our theory, however, there can be no reason for taking one side of the question for granted rather than the other, and the only remaining alternative is to test both sides together, to be ready to abandon any element which stands out in manifest contradiction to the total system, and to accept, at least provisionally, any account which is harmonious throughout and consistent with everything that must be taken as fact. This short preface will also indicate the limits of our present inquiry. Our primary object, it will be remembered, is to lay down the conditions of valid judgment or knowledge. And for the discovery of these any judgment claiming validity may at least be useful. But to examine any and every kind of judgment made by man is clearly out of the question, and the problem is to get, within manageable reach, a fairly representative series of tests for the conditions we are sug- gesting, whatever these might be. This test is most readily obtained by examining, in connection with its conditions, each summum genus of conceptions. For if we can explain the formation of the genus we may fairly presume, at least until evidence to the contrary be produced, that the same mental operations applied to different material will also explain the species. If you can explain the genesis of the idea of matter, it will readily be seen that differences in the nature of the observed facts will distinguish solid and liquid, metal and non-metal, element and compound. So if we once postulate the conceptions of matter and motion, there would, I imagine, be no difficulty, so far as our problem is concerned, in ex- plaining the conceptions of force, energy, or momentum. Nor, again, postulating these, would there be any epistemological problem with regard to impact or gravity. But if we turn to the conception of mind the case is different, for here we have a conception which is at least primd facie generically different from any of those hitherto mentioned. And here oOx 'ian ihto,- /3avra i(7c,ai. Our assumed conditions might explain every species of concept under the one genus, while quite inadequate to the other. It will be observed, then, that our problem ends (as it should) where the questions of physical, and we may add psychological, science begin. The physicist does not consider how his fundamental conceptions of matter and motion are THE CONCEPTION OF EXTERNAL REALITY 519 found. Nor, therefore, does he criticise their ultimate value. His theory of matter, if he is concerned with one at all, is simply as exact a determination as possible of the results derivable from certain methods and certain conceptions which are taken for granted. The only question for him is what these methods prove or suggest, and what they prove is for him (and quite rightly) final. But whether the whole set of conceptions, from beginning to end, might not have to be re- modelled by a further criticism, whether, that is, the conceptions of the specialist at their highest perfection, express ultimate reality is a further question which does not concern him but does concern us. Our business is with what is to him the ultimate genus. And hence our inquiry, primarily concerned with the conditions of knowledge, comes also to fill up the gap left by the sciences in our knowledge of existence. The summa genera of reality belong to the problem of knowledge. A full theory of knowledge ought to enumerate these summa genera, and that from every possible point of view. It ought to decide how each of them is to be conceived, and what epistemological conditions are postulated by each severally and by all together, whUe as the parallel problem it should determine the measure of validity to be attached to each. I do not in the present and following chapters make any pretence to such completeness. I confine myself to the treatment of such conceptions as have played the most prominent part in the theory of knowledge, in order to see how far they present difficulties to our present conception of intellectual operations. 2. I begin with that distinction among objects of knowledge, which has probably played a greater part in the theory of knowledge than any other — the distinction between self and not-self. This distinction may be confounded with two others, viz. that between subject and object, and that between mind and matter. All these three are, in fact, separate antitheses. For the self may be object, as when I am aware of my own feelings, my own existence, etc. And again, the not-self may be either mind (e.g. you) or matter (e.g. my pen). Such, at least, is the priTud facie state of the case. In the present and following chapter I propose accordingly to develop the concep- tion of matter, first, negatively, by its distinction from the self which thinks, and then more positively by a consideration of the facts which combine to form it. We begin, then, by asking how in general do we come to distinguish that which is from that which is not ourselves. We must start by admitting, with Hume, that no particular 520 KNOWLEDGE perception ever makes this distinction for us with indubitable certainty. We may confess that whenever we try to think of ourselves we always "stumble upon" some particular percep- tion of love, hate, joy, anger, or what not. Likewise we must admit that there is no object of the " outer sense " so sure but that we may be deceived as to its externality. Nor, though we might correctly perceive its spatial externality, — its being outside that particular coloured pliable surface which we call our body, — would this be in any way the same thing as its actual existence independently of our mind. For the whole matter, outer body, space, and all, might be a creation of the mind's activity. We go back, then, to the primary data of apprehension, with the admission that there are not among those data as they stand any which could give us the distinction which we un- doubtedly make, and which we are required to explain. I apprehend a content which I describe as a hard, coloured surface. This I judge to be matter and not-self. I apprehend hot-throbbing-achy, and judge it to be feeling and a state of self. But, as we urged in Part I. Chap. I., in each case the second assertion is a true judgment, and is not a part of the apprehension. What is given or apprehended is in the first case hard-coloured-extended; and in the second, hot-achy- throbbing. Why is the second content referred to the self and the other to the not-self ? Or what are these concepts under which I bring my two particulars ? 3. The answer is to be found, not immediately or wholly in any character of the facts as given in apprehension, but in their behaviour and relation with facts similar or different. This will be clearer if we first define a little more narrowly the meaning of the contrast between self and not-self. Among the various contents of our apprehension we have some that are tangible, coloured, extended, that move in certain uniform ways, and to which under certain circumstances the natural man attributes taste, odour, or sound. We also observe feelings, emotions, ideas, beliefs, acts of will and effort ; and finally, the acts of apprehension, judgment, and other intel- lectual operations become in their turn objects for our obser- vation. A point of distinction and also of union between these two classes of facts is found in that particular coloured extended, etc. object which I call my body. For the first class of objects (with the exception of the bodily surface itself) are all located outside, the second all inside the body, this locating being, as Professor James has well shown, not an arbitrary operation of the mind upon the given object, but a part of the THE CONCEPTION OF EXTERNAL REALITY 521 given character itself. Calling the first provisionally the external world and the second the self, we find that the phenomena of each group vary for the most part independently of one another, " external " facts perishing while feelings, etc. change, or changing while feelings persist. No alteration in my feelings, emotions, will, etc., disturbs the walls of this room in their several relations. They look down cold and unmoved on my joy or my sorrow. They resist my will or aid my efforts with impassible neutrality. It is true that as an observed fact the said walls depend for their existence on a certain position of my body, which in its turn depends on will, and is accompanied by feelings, whether from the muscles or the joints. But here, again, a Uttle analysis shows that it is not the " inward " state of feeling which is really " relevant " to the appearance of the walls. If I am in the room and my eyes are open, all I have to do is to remain quiescent and they continue to appear. If I am out of the room a quite different set of inward feelings will precede their appearance — acts of will, muscular efforts, etc., and these again will differ according to the place from which I start and the door by which I enter. Putting all these facts together, it appears that the real condi- tion of the appearance of the walls is not anything in feeling, etc., as such,i but only the presence of my body in certain space relations to them and to various other objects (floor, door, passage, etc.). The result is that the content " wall " is inde- pendent of the contents, — feelings, will, beliefs, ideas, etc., — but that it is not yet shown to be independent of my body or my observing consciousness. Pause for a moment, however, to con- trast the case of a feeling. All the time that I am experiment- ing with the perception of the wall I am conscious of an acute pain in my left under-jaw. This pain is given as in my body ; it moves about with me, independently of all other space relations ; it is affected in some degree by concentration of the attention upon other things, but the mere presence of any spatial object affects it not. The two contents, in short, have entirely different modes of behaviour. Their interconnections, the laws of their appearance or disappearance, are as widely different as possible. Hence contents that range themselves along with my aches and pains as dependent on one another, or on my body, no matter in what part of space I am, become classed together as the self ; while, conversely, those which are given in permanent space relations, or as changing their relations in accordance with certain uniform laws of motion, are classed in their turn ' Feeling, of course, might operate more directly by affecting attention. That case will be covered by considerations advanced lower down. 522 KNOWLEDGE- as dependent, not on the stream of feeling, etc., but on them- selves or on one another. But now we must go back to the point from which we broke off. Independence of other psychical facts, it may be said, is easily proved. But our argument has not shown it also of the bodily presence and the perceptive consciousness. Of these points it would, I imagine, be allowed that the first followed from the second — my bodily presence could be taken as the condition of a fact's appearance only as it is the vehicle of my perceptive consciousness. We have now brought to a single point the question, what characteristics in a content make us attribute it to the not-self ? We distingmsh a content from self only when we believe it to exist whether we apprehend it or no. If, for example, I believe the content A which I now apprehend to continue in existence when my back is turned, then I may believe^ A to have an existence independent of me ; or whenever I believe a content Aj similar to A to exist, although I do not and never did apprehend it, then I can assert the existence of A independently of me. In the judgment " A has independent existence " there is therefore no characteristic at- tached to the content A which marks it off as a content from A as given. Independent existence is not a qualitative percep- tible character. It is a negative characteristic of the conditions of A's existence. It says, " The A which I now apprehend would exist now and would still be A even though I did not appre- hend it, and thus (for example) it may continue to exist though I should cease to apprehend it." "We shall see later that this " independence of the apprehending consciousness " applies to certain aspects of the self as well, but as it is the most import- ant and difBcult condition of the not-self, we may treat it in this early stage of our discussion as the only point to be considered. We are brought, then, at once to the question, How can this independence be known ? And the answer is, that it depends entirely on our success in discovering universal laws in the occurrences of phenomena. Thus if the relation A - B is uni- versal, and I am given A, I infer the existence of B. But if I do not in a given case apprehend B, I am forced to the belief that B exists without being apprehended. Or if we put B = A and take the continuance A -A to be universal, or universal under certain known conditions, then in any case of A plus those conditions I am led to the belief, not that A ceases to exist when I cease to contemplate it, but that it continues pre- cisely what it was to my apprehending consciousness. But is it ever possible to eliminate the fact of apprehension ' I.e. in the absence of other reasons for attributing A to the self. THE CONCEPTION OF EXTERNAL REALITY 523 itself from the conditions of a phenomenon ? I reach the uni- versal A is B by observing some case Aj - Bj. But now, what were the facts in their entirety ? Surely the apprehension of Aj followed by the apprehension of Bj. I may, by the methods of difference and agreement, show that ODE and the rest have nothing to do with B, but how am I to apply this eliminative process to the fact of apprehension itself. I can have no given case of A and B without the apprehension of both terms being given also to my reflective consciousness. Hence must I not conclude that it is the apprehended A which causes the appre- hended B ? This difficulty is dispelled by the case where B is given without A I am watching a landscape into which there suddenly dashes from its tunnel an express. In the previously apprehended contents, the landscape, no cause could be assigned for this new appearance (for we have, to go no further, the immediately suggested negative instance of the landscape un- changed for hours). The cause, then, by this instance, is in something unobserved. This alone would sufficiently demon- strate the existence of a something apart from observation, though it would not tell us what that something was. But by previous experience I have found certain positions and motions of a body to imply certain antecedent positions and motions, and I have " no reason to suppose " that any other cause exists which could produce these positions and motions here given. Hitherto, in- deed, I have had observed motion as the antecedent, but the present case operates as a negative instance eliminating the characteristic of being observed. This, then, is my case. For the given effect B I have been led by previous instances to suppose a cause to be discoverable within the total " observed A." The present instances show that the "observed" has nothing to do with' it. But B must have a cause. I have no reason to suppose that cause to lie outside " apprehended A." But A is [not here apprehended, hence A as such is the cause of B, and exists here unobserved. If it is replied that the case might equally be taken to prove that some X altogether different from A is the cause of B, that cannot be admitted. Only the observation that A was absent from the place, where according to previous experience it should be present, could go to prove this. But ex hypothesi we are not able here to observe all that place so as to see that A is not there. All we can say is, that we do not see that A is there. Our observation of A alone is absent, and it alone is accordingly excluded from the cause of B. To sum up, I believe the cause of B to lie in the observed A, and that accordingly that fact or some part of it preceded B here. But the observation of A did not occur here, therefore 524 KNOWLEDGE A unobserved, or some part of it, did occur here as the cause of B.i We may indeed put the whole matter more simply in ac- cordance with our final statement of the inductive process. The observed facts A and B always go together. We must therefore suppose them to do so in any case unless we have reason to the contrary. Now we observe A and we assert B, but B is not observed. This is no reason for denying B unless we have observed the place where B should be and found it absent. Hence if we have not examined B's " place " we assert B to exist there unobserved. And the inferences are converging. In the series A-B-C, I may observe A and C without observing B, whence both relations A-B, C-B converge on the assertion of B and strengthen one another. The result of non-observation of presence (as opposed to positive observation of absence) is thus to eliminate the qualification of " being observed " from the antecedent or conseqi^ent of a fact, but not in any other way to modify the character of the antecedent or consequent suggested by the uniformities observed. We conclude that an ordinary process of induction distinguishes for us the " outer " from the " inner " world in the sense of showing that this outer world does not depend for its existence on any of the feelings, activities, etc., which, along with the apprehending consciousness, itself we group under the conception of the ego and its states. 4. Scepticism may object that another explanation of the fact is possible. The de facto continuity of sensible things and their apparently universal connections may be accounted for on the supposition that there exists an external order quite different qualitatively from that which we perceive. Let a be continuous through observation and permanent in successive observa- tions. We have inferred from this that a exists continuously whether we perceive it or not, and is therefore independent of our perceiving consciousness. But it may be alleged, what really exists continuously is some A which never enters into the range of my observation at all, but which is such as to produce a by acting upon my consciousness. And similarly with regard to change. If I could so establish the universality of a - /3 that it should be beyond all doubt ; then given 3 perceived, it follows that a exists unperceived, and is therefore independent of the perceiving consciousness. But according to our own theory of induction we can only establish an 1 It would similarly be a misconception to object that the argument is circular on the ground that it must prove A present in order to prove it the cause, while it proves it present because it is the cause. A is proved to be the cause by being present in other cases. Being the cause, it is inferred to exist here. THE CONCEPTION OF EXTERNAL REALITY 525 universal a — (S by some method of elimination, a method which is a bruised reed as soon as we rely on it as against the suggestion of unobserved concomitants. Hence supposing a pair of universal correlates A — B, themselves unperceived, but acting on consciousness so as to cause that reaction which would constitute the apprehension of a — /S, no inductive method could eliminate these concomitants. Whence it must be conceded that their existence remains a possibility. Yes, but an unmotived possibility. As we showed above, there can be no ground for assuming any unobserved cause except failure of uniformity within the range of observation. Now, the theory suggested, which is in effect the thing-in- itself hypothesis in its relatively reasonable shape, wants us to assert an unobservable cause precisely where uniformity is found. If we inquire for a moment on what analogies the theory really relies we shall see how truly it may be described as groundless. Certain illusions, for example, are very easUy explained as the effect of some reaction of our nervous organisa- tion on a given physical agent. The same explanation may even be extended to some at least among " secondary qualities." Thus the sensation of heat may be " explained " as a mental reaction upon a certain stimulus of the nervous periphery by the molecular motions of an adjacent solid or fluid mass. Well, granting this, whence does the explanation derive its plausibility? From two considerations — (1) the observed •phenomena of heat by which, through ordinary inductive methods, physicists have inferred the probabilities of vibratory motion, explaining, as such motion would, the facts of radiation, conduction, reflection ; and, again, expansion, change of form, and so on. And (2) the ohserved inconsistency of our perceptions of heat — the old facts of the water which is hot and cold to the two hands, on which Locke quite rightly relied. Now mark these two points. As long as you have observed facts to support your explanations your position is strong enough. You are " explaining " in the only way in which that operation can be genuinely carried out, viz. by assign- ing the effect to observed antecedents, or subsuming the operation under an observed law. But when, instead of pointing to an observable antecedent, you assume the operation of one that ex Jiypothesi cannot be observed, you can have no law by which to explain the operation you suggest, no analogy by which to make it plausible, no fact to give it reasonable ground. The truth is, that while Locke, in his plain, half- naive way, took the action of primary qualities of matter as 526 KNOWLEDGE the ultimate account of all sense-perception, the thing-in-itself theory used this analogy in an illegitimate manner. For the unknown, indescribable thing was supposed to act on the mind after the fashion of the part-observed, part-inferred action of the familiar physical thing through the bodily organism on the sensitive subject. Eeally, from the terms of the hypothesis there could be no analogy. But it may be objected, we are going a step too far. Grant that there is no analogy in the manner of operation, there is at least the fact that the sense-perceptions referred to may be said to deceive us so far as we attribute them to outward things. If the action of physical agents in the hands of a conjurer can produce temporary illusions, why should it not be an arch- conjurer who dazzles us with this vain show of a physical order ? Or if we reply, that the cases of actual illusion are too few and unimportant to constitute a serious argument, what do we say to the constant and regular perception of secondary qualities ? If the " reference " of heat and colour to an external world is iUusory, if it is to be explained by the action of a colourless substance devoid of temperature, is not this deception on a large enough scale to justify us in carrying doubt still further ? The answer to this brings up our second point. The alleged subjectivity of certain "secondary qualities," certainly in Locke and in some degree in Democritus,^ was based on the de facto irregularity of the deliverances of consciousness upon those qualities. It was really this which suggested that they could not be " in the thing." Now this, so far as it goes, was good argument, and if the alleged want of uniformity cannot be explained away, the conclusion is just. But where no such want of uniformity exists, i.e. where we have reduced the phenomena of the senses to an orderly, coherent body of facts without assuming any agents beyond those observed, what need we of further hypotheses ? The reason for them fails at the point where irregularity gives way to uniformity.^ As to the thing-in-itself, then, the argument may be ' See Theophraatus de Sensu 61, quoted by Ritter and Preller, Hist. Phil. 6th ed. 1S2 : " a-rifiehi' S^ (is ouk dal (fiian ri fiij raira Train (palveaBai rots fc^ois," etc. ; and of. Burnet, Early Greek Philosophy, p. 358, and note. ^ It may be said that at least there is nothing to negative the suggestion before us. An outer reality conditioning our perceptions, yet never perceived, cannot, it may be urged, be contradicted by our inductions, because ex hypothesi they never come into contact with it. But this is not so. Our inductions go to prove that, e.g., the observed fact A is the total ground of the observed fact B, that A becomes B, and so on. All this would be untrue if it is not A that becomes B, but an unperoeived M which is responsible now for our perception THE CONCEPTION OF EXTERNAL REALITY 527 summed up thus. According to our theory of induction any suggestion must have grounds in observation : a cause of un- known character may be logically assumed only when observable facts present us with breaks of uniformity which cannot be otherwise explained. Hence, where a mass of inferences con- verge on the conclusion that a certain reality persists or changes in accordance with a uniform law, to suppose an un- observable external agency breaking up ^ that uniformity is to reject the strongest inferences we have on the ground of an unmotived suggestion. There is, accordingly, no reasonable ground for supposing such an outer order. The reference of a content to the external order is an act which stands or falls by the same logical test as any other. If it harmonises with other references which we make, it is con- firmed by them ; and if we have a coherent system of judgments making such reference, we must accept their residt in this respect as in others. Here, as elsewhere, the isolated judgment frequently breaks down, and so it is not necessarily this apparent colour or this perceived shape that belongs to the object, but the " corrected " colour or " true " shape as tested by the remaining judgments which we make upon the object. That which forms the only basis for a harmony of judgments is here, as elsewhere, the reality. 5. An argument closely connected with the thing-in-itself theory must be noticed here, though a brief allusion to it will be enough, as we have discussed its main principle in another connection. It wUl be said that the kind of independence for which we have argued is not in question. No one supposes that a previous state of my consciousness is the whole cause of my present perception. But the contention is that granting a real world operating on the mind in perception, still the per- ception itself is a state of mind, and as such determined in part by the constitution of the mind itself. This argument may be put in a special or in a general form. Specifically, it is alleged that the sensible fact on which we rely as giving us a glimpse of the external order is of an ambiguous character. The true A, and presently for our perception B. Granting the validity of science and its laws, they are therefore directly incompatible with this form of phenomenalism. It may be added, that the very instances on which the suggestion relies cut both ways. If the "real " order is often misapprehended, we find this out by the contradictions in which our misapprehensions involve us. And this is evidence, not only that other misapprehensions are possible, hut also that they will betray themselves by their inconsistencies — in fact, that ~ parallelism of the kind and extent suggested by the theory is not possible. ^I .say " breaking-up " because the uniformity which the thing would substitute is different from and largely incompatible with that which we actually infer. 528 KNOWLEDGE unit of knowledge is the representation, and to this the forms of space and time are contributed by the structure of the sensibility itself, while the unity, substantiality, etc., that we seem to find in objects is really in the same way the contribution of our understanding. Thus the result whicli is for our consciousness the primary fact is at the same time a product in most essential respects of that very intelligence which seems merely to appre- hend it as a passive spectator. This conception of Kant we have already rejected. The formless sense-datum postulated by the theory we believe to be a myth, the product of a false abstraction. We can verify no fact of sense that has not duration, nor any spaceless fact that subsequently becomes for us extended. True, it was Kant's own contention that space and time existed from the first in our representations, but it was a contention that proved fatal to the very theory which it came forward to support. For the unverified character of that formless multiplicity of sensation on which half the Kritik rests is thereby openly confessed. And as witli space and time, so with the constitu- tive categories. "When I judge " this is an ink-pot," I do not superinduce a conception of unity on a number of data which are without it. It is true that the data are multiple, but they also present a unity of outline, spatial position, and so on, which is as real an element in the given total as the multi- plicity itself It is true, again, that the category of unity, in the sense of the fact of unity, is implied in the term ink-pot. It does not follow that the fact of unity, or the conception of it, logically or psychologically preceded the fact or conception of the ink-pot. You have not the unity before you have things that are one any more than you have the things that are one without a unity. If Kant had been merely arguing against an empiricist who did not know his business, and wished to show that logically the fact of unity is implied in the first single object we come across, and coixld not be derived from a multitude of disconnected data, there would be nothing to be said against him. But the disconnected data into which unity is introduced are as fictitious as the disconnected data from which unity is derived. Unity as well as multiplicity is found in things. The conception of unity is arrived at by analysis of objects that are one. In this relation the abstract is not prior but posterior to the concrete, the concept to the fact of sense. But logically there is no such relation : the element of unity is contained in the thing that is one. The regulative or dynamical categories are indeed in a different position. Our treatment of substance is not now in THE CONCEPTION OF EXTERNAL REALITY 529 question, so I say nothing of it. Bub the causal relation is clearly not given in the way in which a space relation is given. It is not to be found in sense by a mere analysis. But, then, this very fact puts it out of court in the present discussion. "We are not now considering the validity of the principles which build up our conception of reality by means of complex syntheses of given fact. We are considering whether the perception from which these syntheses start can itself be taken as giving us any glimpse of an external order, or whether what we know of the constitution of such perceptions is fatal to this behef. Only such categories, then, as are alleged to determine the actual building up of the separate representation (Kant's mathematical or constitutive categories) can come into con- sideration here. The Kantian relativity, then, is bound up with a theory of sensation which we cannot accept. 6. The general principle of the Kantian view has been put perhaps in its most seductive form by Lotze, and to this general conception we must now direct attention. Lotze reminds us ^ that when a state b arises in a substance B under the influence of a change a in A, it is a common but obvious error to refer b to a alone. Eeally b is dependent on B as much as on A. Thus the wax (B) takes the image (b) of the seal (A), not merely because I press (a) the seal upon it, but because of the nature of the wax — at once yielding and firm enough to " set " in its new form. So it is with any mental act. Suppose an external agency (A) operating (a) on my consciousness (B), then my consciousness will be stimulated to evolve out of itself an act of sense-perception (b) : and the character of the perception will be as much dependent on the nature of my mind as on that of the object which it perceives. Thus, to give an analogy, the barrel-organ (A) grinding in the street (a) sends the little boys (Bi, Bj, Bg . . . B^) into raptures (b), while it drives me (C) to exasperation (c). And so it is with per- ception, as we can even make out in detail for certain stimuli. Thus my judgment of the temperature of a body palpably depends on the temperature of my own skin at the point of contact. My judgment of colour depends upon complex relations of contrast, etc ; my judgment of the degree of any sensible fact on the total stimulus operating, and so in a thousand other cases. But it is also possible that in some cases and in some degree we are built so as to see askew ; in other cases and other relations we are built so as to see straight. Granting — what cannot be denied — that my perception is a mental fact, referable as an effect as much to my mental or ' See, for instance, Logic, bk. iii. chap, iii. § 325 ff. 34 530 KNOWLEDGE physical constitution as to the nature of the object operating through waves of ether on my second cranial nerves, or by waves of air on my eighth, it is quite possible that I am so constituted, eyes, ears, nerves, brain, mind, and all, that the state aroused in me as the net result is precisely one in which T am aware of that object which has just set this ether or the air in motion in my direction. Just as one object acting on me may arouse a feeling bearing no relation whatever to the character of the object, so another object may arouse a per- ception which does relate to the object itself. It depends on the way in which our minds happen to have been built. If Descartes' almighty Puck built us all as a gigantic joke to see how much he could take us all in, then I grant it is likely that our perceptions bear no more relation to a perceived object than a sense of nausea to the movement of a ship. But failing evidence for this kind of creation by way of joke, we may leave the question how we are built open and may decide if we can by the ordinary logical test of consilience as between the deliverances of the perceptive consciousness. So far as my per- ceptions tolerate and support one another, so far I take them as correct in fact ; and if the synthesis of these perceptions involves me in the belief that the facts they report are external to my consciousness, I accept their evidence. Their inner aspect, their dependence on my inward constitution, is not in point, because it decides nothing as to the way in which I am constituted. If I am so formed that under given stimulus I judge facts to be " there " which are not " there," why, then, I judge, and always shall judge, wrong. And if I am so con- stituted that under the same stimulus I judge that to be true which is true, then I shall judge right. But in which way I am constituted the theory does not and cannot tell us. And there seems but one test by which we can learn — our old acquaintance, the consilience of results. In fact we may say that these tests operate in the very cases which might be relied on by an opponent as analogies for the relativity view. Optics, and in a lesser degree acoustics, actually do reconstitute our world of perception in some degree. And this strictly on the ground of consistency as between the dehverances of consciousness. Take one instance. The shriek of the locomotive as it rushes towards me rises in pitch, while to you at the other end of the platform it seems to fall. Here is a discrepancy which is rectified at once by a simple deduction from the theory of sound explaining both phenomena at one stroke, and at the same time leading both of us to correct our first judgment and hold instead that the THE CONCEPTION OF EXTERNAL REALITY 531 pitch in fact remains constant. If the whole mass of our per- ceptions were systematised after this fashion, the corrected values which they would give would be the true external order. In fact, Lotze's theory would have weight only against some crude theory of emanation, or efflux, which should treat the perception as an actual copy within the mind of the external fact. It is not a copy. It is not like the external fact. If, so to put it, you could get at my perception of this tree, and perceive it as I perceive the tree, it would not look at all like the tree. It would not strictly " look " at all, i.e. it would not itself be visible. It would not be a sort of retinal image with the soul for retina, but it would be an act of con- scwisness referring to the tree, recognising the existence of the tree — as disparate from the tree itself, as the tree is disparate from the motions of the ether or the molecular changes in the optic nerve and the occipital lobes which " intervene " between the appearance of the tree in the line of vision and my percep- tive act. The perception is undoubtedly qua perceptive act the mind's own creation. It is thoroughly psychical in character. But this does not for a moment prevent it from being a correct recognition of its object. 7. But another difficulty occurs. How is it psychologically or metaphysically possible that we should get to know anything of an order of things independent of the mind ? The primary fact of perception is that which is present to our consciousness, and surely that which is present to is also "in" our consciousness, in the sense of being some one of its states, modes, or manifestations. Granting this, can we ever arrive at a knowledge of external things ? I should answer, certainly not. Inference, as we have been contending all along, goes by resemblance, and if we are asked to infer an external order from the facts of perception, we must ask in reply where is the experience of any similar order given. Fx hypothesi it is in no case given. Therefore neither can it be inferred.^ To illustrate. It is sometimes urged that though direct perception is confined to the world of mental representation, we must yet infer an external order of some kind as the cause of such representa- tions. But how, ultimately, do we know any causal relation ? By observation and experiment. And this involves observation of both terms, the cause as well as the effect. If, then, we could once observe an external object A acting upon the mind so as to produce the presentation or representation a, we might make such an observed relation a basis on which we might rest subsequent explanations of the presentations /3, y, etc. J Cf. Professor Case, Physical Eealism, p. 69. 532 KNOWLEDGE But since ex hypothesi we can never observe A, such a basis of inference entirely fails us. We must accordingly give up the notion that a world external to mind can be known by infer- ence alone, while direct perception is confined to the mind's own inward states.^ Either, then, we must admit direct perception of an external order or we must refuse knowledge of such an order altogether. To have direct perception means, in the phraseology used in this work, to have a fact given in apprehension or present to apprehension. Now, how can a fact be present to the mind without beconiing part of the mind ? We may answer this first by an analogy. What happened to me yesterday is known to me at this moment by an act of memory. This act is an asser- tion made at this moment. " I was sitting here writing at this time yesterday morning " is a judgment which I make now, and which asserts a past state or action of myself. Now, that past state is in a way present, and its being present is no accident, but is the essential point of my remembering it. But whatever interpretation we may give to its "presence," what- ever theory of the mind and its nature that fact may suggest to us, we cannot so interpret its " presence " as to do away with its reality in the past. This would be to destroy the very memory-judgment, which, as argued above (in Pt. I. Chap. IV.), includes the pastness of the fact as part of its content, upon which our whole reasoning in the matter rests. The true interpretation of the facts, neither taking away nor adding any- thing, is that I now make an assertion of a fact that existed in the past. That the fact is now in my present consciousness in the sense of being referred to by it does not in the least affect the truth that it really was in the past and is not now. Similarly, I apprehend a fact external to my own conscious- ness. That is, there is within my consciousness an assertion of a fact external to it. That the external fact is referred to in my assertion does not make it a part of my asserting conscious- ness any more than the past fact was made merely present by the reference of my present consciousness. But this is only an analogy, and still the question remains whether there may not be a difference. Have we not said that apprehension is always of fact, while perception is notoriously fallible ? How then can we speak of direct apprehension of external objects ? To answer this, to clear up the parallelism ^ This point Berkeley may fairly be said to have proved, whence, granting his initial assumption, taken from Locke, that the object of immediate know- ledge is always an "idea" in our own consciousness, his conclusion follows rigorously. THE CONCEPTION OF EXTERNAL REALITY 533 between memory and apprehension, and to see what precisely is the part played by apprehension in our knowledge of the external order, we must go a little further into the theory of apprehension and of assertion in general. In relation to every assertion we may, at least in thought, distinguish three points. There is, 1st, the abstract fact of assertion — the fact that an assertion is made ; there is, 2nd, the content of the assertion regarded as quaUfying the assertion itself as a mental event ; and, finally, there is, 3rd, the content regarded as the fact which, if the assertion is true, exists. Thus in my memory- judgment there was involved, first the fact that I formed the judgment, then the content of the judgment (" I was sitting here, etc., yesterday "). Now, this content, whether the judg- ment was true or false, undoubtedly qualified my asserting con- sciousness at the moment of assertion, and was then as a quality of a mental event undoubtedly real. But if the judgment was true, the content " I was sitting," etc. existed also as a fact, independently of the present memory-judgment — existed in truth, whether that judgment should ever be formed or no. Now, an assertion qua mental event is undoubtedly an element in my consciousness, and in my present consciousness to boot. The same is true of its content qua a quality of the assertion itself. But this does not apply to the content qua fact asserted. In this sense the content is not necessarily an element in my consciousness at all. The idea that it is so rests on an inexplicit confusion between the fact asserted and the fact that I assert it. And this confusion is as fatal to memory — or to any judgment about self, past or future — as to perception of an external reality. For the assertion that I make now is an element in my pt'esent consciousness ; and if assertion and thing asserted are confused, my past or future state must really be present, and memory and expectation dis- appear. On the other hand, once understand that the fact asserted need not exist in the conscious act of asserting it, and there is no reason why it should exist as a part of the history of that consciousness, i.e. there is no reason why it should not be independent of or external to the conscious series just as it is independent of and external to the " passing thought." ^ Coming now to the truth or falsity of an assertion, we may have three different cases. (1) The assertion may, like the memory-judgment just instanced, assert a content as existing 'As to the "relativity" involved, according to dialectics of the cruder sort, in the very notion of an "object," it is enough to retort with Eiehl, "Relativist . . . nicht das Sein der Objecte, sondem ihr Objectsein " (op. eU. ii. 2, p. 150). 534 KNOWLEDGE independently of itself, and then the judgment may be true or false according as the content does or does not, did or did not, will or will not, exist. (2) The assertion may he only of a content qualifying the asserting consciousness. To this asser- tion memory itself may be attenuated, e.g. "You may attach what weight to it you please, but I assure you that I have the distinct remembrance of being there." Here the assertion is of the remembrance as qualifying my present consciousness. Lastly (3), we may simply not distinguish between the content as qualifying consciousness and the content as independently existing. " Tarn Pearce's old mare doth appear gashly white " ; but whether it is only an appearance or the veritable animal "in her rattling old bones" is a point to which we do not commit ourselves. Now, apprehension we have all along treated as a form of assertion — its differentia being that it asserts only the present. Then in apprehension we may distinguish, at least in thought, the same three aspects — the fact of apprehension, its content as qualifying the apprehension, and its content as that to which the apprehension refers. Thus, primd facie treating apprehension like other assertions, we should expect to find on the one side the act of apprehension with the content quaUfy- ing it ; on the other, the fact apprehended. And this it may be said we do find in those apprehensions which we call percep- tions. There is the oblong white shape before my eyes (this paper); here is my perception with its own definite quality. What the perception asserts is not as such its own quality, but determines that quality, and while distinct from the fact of the perception is present to the perception. The perception, in short, is an act of reference to the object, just as the memory- judgment was an act of reference to the past event. The only difference is ip the nature of the reference. The memory asserted its content as past ; the apprehension is aware of its content as present to it. With this difference, perception and memory are in other ways analogous in relation to their object. Passing to the class of apprehensions which we call feeling, the analysis is more difficult. Here the content asserted is such that it can only be taken to exist as qualifying the appre- hending consciousness itself. My headache is non-existent if I am not aware of it ; while, conversely, the fact that I am aware of it proves its existence. Here, then, the "esse is percipi," and the content asserted and the content as qualifying the assertion tend ^ to fall into one. I am asserting an element ' Tend, because as long as consciousness maintains itself the element of recognition, admission, or attention to the content is still a feature of it. THE CONCEPTION OF EXTERNAL REALITY 535 in my own asserting consciousness, and in reality the assertion and the fact asserted are here bound up together. At this stage, then, the distinction of the content as qualifying the assertion and the content as fact asserted falls to a mere difference of aspects. The painfulness of my headache may be looked at indifferently as an object felt or as characterising my recognition of my present state. "We may then distinguish acts of apprehension as consisting of (a) feelings and (&) perceptions. In the case of percep-' tion we contend that an external reality is the fact present to the apprehending consciousness. One word here will be enough to remind the reader that though this is so, apprehen- sion cannot, on our principles, be aware that it is so. There is no intuitive perception of the externality of the object. There is " intuitive," i.e. direct, perception of objects which are in fact external, but not intuitive knowledge that they are so. This knowledge is gained by a system of inferences from the relations and behaviour of the contents themselves. To assert independent existence or to deny it is equally to assign rela- tions, causal or other, to the given content, and such relations are not given in the mere apprehension of that content. Let us rehearse our description of the facts in order to see if there is any inconsistency. In fact (let it be supposed), in a given case the object E' present to our apprehension is a fact external to our consciousness. Our apprehension A has the quality E". Now, what constitutes the difference between E' and E" ? Not the internal constitution of the contents, not their attributes or character, but certain relations in which they stand. E' is, according to our hypothesis, an element in a " material," E" in a mental, totality. On this question of the relation of the contents before it, apprehension has no business to decide. It therefore simply asserts E without considering whether this particular E be E' or E", i.e. whether it has one set of relations or another. Further observation of the rela- tions, comparison of one set of relations with another, and of the behaviour of E in comparison with that of D or F, lead us to the belief that E (say) is a permanent reality, that accord- ingly it remains in existence when we do not perceive it, and that therefore it is to be regarded as independent of our minds. All this is the content of judgment and the work of compared observations and inferences, as shown above. In another case we apprehend I", which is in fact internal. Here it is I" itself which qualifies the apprehending C", and we are aware of what is in fact a state of ourselves. Still, as merely apprehending, we do not determine this. All we say 536 KNOWLEDGE i3 " I," not " I"," and it is again comparison of observations upon the behaviour of I and similar contents which leads us to the judgment " I is merely a fact of our own immediate consciousness." Thus the content of apprehension qud apprehension is fact. But this is so merely because apprehension decides nothing as to the relations in which its content stands, or (we shall see reason for the phrase later) the totality to which it belongs. The I white figure which I see at the foot of my bed on the stroke of midnight is a reality qud apprehended. Either it is " there " or it is " in my consciousness." The important question Which ? is decided by reflective comparison of its continuous or successive appearances with those of other phenomena. Our position, then, may be summed up. Apprehension is always a definitely qualified state of consciousness. Its object may be its own quality or it may be an independently existing fact. "Which is the case in any instance or class of instances must be decided by a comparison of different contents. In one case our reflective consciousness analysing the whole facts would decide that there is really an external fact present, that the apprehension is of that fact, and that the content of the apprehending consciousness corresponds with it. In the other, we should decide that there is no external fact present, and that the content asserted is in truth a qualification of the asserting consciousness itself, and only as such has any reality. Thus, as our result, an external order may be directly present to apprehension, otherwise such an order could never be known ; but apprehension does not itself assert that the order given is external, otherwise apprehension might be false. It will probably be objected here that in any case, if the apprehending consciousness is really qualified by the content it asserts, it must be as qualifying it that the content is really present, whence every apprehension in fact asserts its own quality and nothing external. This is really the objection answered at the outset. The content present in apprehension determines the quality of the perceptive act. The content present to apprehension is not as such an element in it. No assertion takes cognisance of its own quality because it is its quality, but takes its quality from the fact to which it refers. In simple feeling, where to be and to know coincide, this dis- tinction falls to one of aspects. But this is only one case. Elsewhere the fact asserted is distinct from any element of the asserting consciousness in reality as well as in thought. All apprehension asserts is the presence of the content E or I. Further reflection may decide that this content existed only THE CONCEPTION OF EXTERNAL REALITY 537 within the apprehending consciousness, or that it exists apart from it. In this latter case a still further reflection shows that the apprehension must, as a mental event, have been definitely qualified in correspondence with its object E. But we can no more infer from this that what was present to apprehension, and what apprehension asserted, was its own quality than we can say that memory is an assertion of a fact now present. What has been called the " moment of reflection " shows me my apprehending consciousness with its quality on the one hand and the thing apprehended on the other. It docs not show me that I apprehended a quality of my own consciousness, but rather that in this case an outer object was present to my apprehension, and this presence gave rise to its quality as an assertion. The existence of the content as qualifying the apprehending consciousness is, in short, as much an inference from the comparison of facts as its existence as an independent object. The mistake of natural or intuitive realism is to start with the assumption that the independence of the percept is immediately given ; ^ the mistake of any subjective idealism is to assume that the object is first given as inward. To our view it is, in fact, not given as either. It is given as a content present to an inward state. Whether it is the kind of con- tent which exists merely as a qualification of such a state, or whether it is such as to exist independently, is to be found out only by studying its behaviour and relations, and the con- clusion is in any case a judgment depending on inference.^ ^ Cf., for example, Hamilton, Lectures on Metaphysics, vol. ii. p. 106 : " In an act of perception I am conscious of something as self and of something as not-self ; this is the simple fact. " ^ It may be urged, that the subjective idealism which we have been com- bating is no longer held by any thinker of repute ; and that the real question is whether the facts of perception and of knowledge in general do not postulate an eternal or universal consciousness as the subject for which alone they can be real. But the arguments urged in support of this view simply assume the position of subjective idealism as their premisses, while they reject it in their conclusion. Thus, e.g., Green is constantly telling us that everything real is "determined by relations, " and relations depend on an intelligence. "There must then be something other than the manifold things themselves which combines them. . . . With such a combining agency we are familiar as our intelligence" (Prolegomena, p. 31, and passim). This is why "Common objects of experience, ... in the only sense in which they are objects to us or are perceived at all, have their being only for, and result from, the action of a self-distinguishing consciousness " (p. 68). We might think this pointed to subjective idealism; but not at all. "But we cannot suppose that those relations of fact or objects of consciousness which constitute any piece of know- ledge of which a man becomes master " (p. 74) cease to be real if he forgets them. "They must e.xist as part of an eternal universe." Here we seem suddenly to have got back to natural realism. What I know is something which is there for me to know, and is there whether I know it or not. But the very next words undeceive us — "and that a spiritual universe or universe 538 KNOWLEDGE of consciousness.'' The "universe," the " unchanging order," is not independ- ent of consciousness ; for it is an "order of relations — and even if relations of any kind could be independent of consciousness, certainly those that form the content of knowledge are not so. As known, they exist only for conscious- ness ; and if in themselves they were external to it," we cannot conceive how they could get in (p. 75). To put it shortly, things are proved to exist only for consciousness because they depend on relations, and relations " as known exist only for consciousness." But for what consciousness do relations as known exist? Unless your consciousness or the universal consciousni'ss is given to me in immediate apprehension, clearly for my own (cf. Balfour, Mind, N.S., No. 8, p. 435). But then, how can related facts be taken as existing apart from me ? You may say, ' ' Oh, we abstract from your individual consciousness ; relations exist apart from that." I quite grant it ; but then I do not see how the universal consciousness comes in. In short, if you stand on the ground that relations (or reality as such, it does not matter which you take) are given as existing only for consciousness, you mean for my consciousness. If you do not mean that, your assertion has not the remotest plausibility. Having said so much, you can take your stand on what is given, and refuse to allow any abstraction at all. Then, you stick to my individual consciousness, and must deny any reality beyond it. Or you allow abstraction, and then you come to the relations or the reality existing apart from consciousness altogether. But by merely abstracting individuality you come, not to the universal consciousness as a great reality, but merely to a consciousness which is nobody's consciousness, and is not as it stands real at all, but a thin abstraction. And even so, why allow this much abstraction and no more ? If relations can exist otherwise than as they are given, what becomes of your whole argument ? It is really Berkeley's fallacy over again. You argue that the perceived can exist only as your per- ception. Then your inner sense of reality reasserts itself, and you admit that somehow the perception is independent of your perceiving it. But to save your first position it must exist for some consciousness if not for yours, and so the permanence of things comes to be their being in the mind of God. But when you have once admitted the content perceived to be independent of your per- ceiving it, you have leapt the chasm at which you halted at first. You have admitted that what you know is not as such a state of you or of your conscious- ness, and, having admitted that much, you have no right to argue that it must be a state of any other consciousness. In one word, can you perceive or think of a real fact which does not depend for its reality on your perception or thought ? If not, your knowledge must be confined to your own mental history. If yes, you have on this ground no shadow of excuse for taking such real fact as existing in or depending on any other consciousness whatever, eternal or fleeting, universal or individual. In such a presentment as Mr. Bosanquet's (Essentials of Logic, chap. i. p. 7-20), the idealist position is attenuated to the point of ambiguity. Take this sentence, "The world for each of us is our course of conscious- ness, looked at in that way in which it presents a systematic, organ- ised picture of interacting objects, not in that way in which it is a stream of ideas and feelings, taking place in our several heads " (p. 16). Observe the position: my consciousness, my "self," is a conception which I have built up out of certain experiences in contrast with certain others. Subjective idealism held the contrast an illusion and identified the world with this self. Attenuated idealism admits the contrast, no longer identifies the world with the self, as we ordinarily understand the term, and yet reduces self and world alike to the "course of consciousness." What, then, we must ask, is this course of con- sciousness ; for what do the words stand ? Not for the " course of consciousness " which I refer to my own "head," which constitutes myself. For what, then ? Why, says our passage, for the " organised picture of interacting objects." But are these a course of consciousness ? Well, they are grasped by consciousness, i.e. they are known. In other words, attenuated idealism proclaims the truth that the known world is an object of knowledge. The reduction of all things to the course of consciousness is a mere expression tor the abstract truth or THE CONCEPTION OF EXTERNAL REALITY 539 truism tliat all the known world comes within the sphere of the knowing mind. But just here comes the danger. It is but the alteration of a preposition, or even of an emphasis, and this dull truism is converted into a weighty paradox. What is within the sphere of mind must be in mind, must have its existence in the medium of consciousness. "With this we are back in something very like subjective idealism, we rest on essentially the same fallacy — that consciousness must in some way sustain in its existence the reality that it knows, that what exists for knowledge exists only by our knowledge. The transition from the truism to the fallacy is excellently illustrated by Mr. Bosanquet when he tells us that the common-sense theory assumes a world existing " outside miW, " and proceeds to refute it by showing that what is "outside perception" is "out of our reach" (loc. cit. p. 10, the italics are mine). Here is the whole thing in a nutshell: "Existing outside mind" means to common sense, ' ' existing whether known to exist or not " ; " existing outside perception " means, " in a world beyond the scope or reference of perception." That these two meanings coincide is the whole sum and substance of the fallacies of idealism. CHAPTEK IV Substance So far we have been concerned purely with the negative character of the external order — its distinction as the not-self from our own feeling and perceiving consciousness. We have now to pass to its positive characterisation as matter or substance with powers and attributes of its own. Of course, the whole complex variety of its nature, resting as it does on the particular data of experience, does not concern us here. All we have to point out is, the manner in which these grand structural concepts are formed into which particulars are fitted. We have, in a word, to define and explain the terms just used — substance, power, attribute, etc. We shall discuss this subject under two main heads — that of the unity of various attributes in the thing, and that of the permanence of substance in the midst of qualitative changes. We shall try to show that our structural conception of matter rests on these two notions, that each notion is a definite and valid conception, and that its growth may be readily explained on the principles of knowledge which we have already admitted. I. The Unity of the Thirig. 1. According to Berkeley, a thing was a bundle. Several attiibutes, a certain odour, taste, sound, hardness, figure, and so forth "go constantly together," and from experience of their " conjunction " we come to believe in their universal and necessary uaion. We group them together in our fancy, and the group or bundle which we form of them is what we mean by a thing. I believe this description, after all that has been said against it, to be near the truth, and to fail mainly through being too abstract. I recall it here to illustrate by contrast the account which I believe to be the truth. Two attributes, on this view, are referred to one thing, not when they follow closely upon one another in a fixed order, but when they are apprehended as occupying one and the same space at one and 640 SUBSTANCE 541 the same time.'' Facts may be closely and constantly related to one another without being judged to form one substance. Thus a blow is followed by a pain, but the blow and the pain are not constituted attributes of one thing. The four walls of my room are objects that go constantly together, but they are not on that account conceived as one wall. On the other hand, the content white-shiny-cylindrical given by sight, and hard-cylindrical given by touch, are both referred to one single space, and form for me a single thing — the pen I at this moment hold in my hand. The thing, penholder, is that which is at once to sight and touch combined white, hard, etc. The attributes which constitute it do not follow one another, nor are they like any other attributes merely coexistent in space, but their coexistence is of a peculiar kind, they jointly occupy the same part of space. It is true that one thing cannot both be white and not white in the same time, space, and relation ; but it is quite possible that it can be both white and hard in the same space and at the same time, and it is just this doubleness or multiplicity of character that constitutes it a thing and not an attribute. Two opposite objections may be taken to this view. First, it may be urged that our conception is not specific enough. Any content, it may be said, refers different facts to the same space (for the future the words "at the same time" may be taken as written in this connection). Thus in the example of the pen, the visual perception taken alone contains different attributes which it refers to the same space. Thus white and cylindrical, or even white and shiny, are distinguishable attributes. Hence the visible character of the pen taken alone should constitute it a thing. To answer this, we must draw a distinction between attributes which we may name re- spectively concrete and abstract. A concrete attribute is, or may be, the full content of an individual act of apprehension. Thus the visual perception of my pen presents it to me as shiny- white-cylindrical, etc. This is its visible character, and may form the content of a single act of apprehension without the addition of further elements, and its visible character is a concrete attribute of the thing. On the other hand, these terms, white, shiny, cylindrical, etc., are each taken severally abstract attributes. They are marks of the concrete attribute, ' Cf. James, vol. ii. p. 183. Professor James seems to think, however, that the mind effects the unification. I cannot think that this is so, or that the "great intellectual law of economy" has anything to do with the case. I cannot see that it would be economical to impose a unity on contents not given as one. And I can only suppose the statement that " Whatever sensible data can be attended to together we locate together " to be unintentional. 542 KNOWLEDGE elements in the actual given content as it is apprehended. They cannot, any one of them, ever be apprehended by themselves. Each one of them may be conjoined with quite different elements in any other given content, but they must always be given conjoined, with something. We never see a colour that is not extended, nor a "shine" that is not a shine of some colour, nor a colour that has not some degree of shininess (luminosity), and so on. Now, a thing is constituted by the reference to one space, not of abstract, but of concrete attributes ; not of the elements of a single apprehended content, but of the contents of what can be, and in other cases are, separate acts of apprehension. 2. It may next be asked how we can know this fact of co- existence in a single part of space ? There can be only one answer to this, namely, by direct apprehension. "When I press the table with my finger, and at the same time look at it, attending to both facts at once, my total perception is of a coloured-hard-surface in contact with my finger. I may doubtless shift my attention so as to consider only the visible aspect of the table and its relation to other points of the field of vision ; or, again, to contemplate only its tangible properties. But I can also attend to both facts at once, and they then form for me a single given content in which the identity of the attri- butes, their existence in a single part of space, is an element. This view would seem less strange if a habit had not arisen among thinkers of describing a sensation as being " referred to " a given place, as being localised by the perceiving con- seiousuess. This language suggests the wholly unwarrantable view that the sensation qud sensation has no locality or position, that it is originally " given " to the mind positionless, and the mind assigns it due position. This notion is applied to bodily feelings as well as to optical sensations or sounds. Thus I am said to " locate " a pain in my left leg, or a sound to my ri"ht, as though the pain or the sound turned up in my mind as a detached kind of article which must be put away somewhere, and gets sent to my leg or to the next room because those are' the places I happen to have unoccupied just now. As long as we regard two sensations, one, say, of sight and one of touch, as " given " spaceless and positionless, and " re- ferred " by some act of intellectual synthesis, or what not, to their positions in space, a difficulty would certainly arise when we come to the question how two sensations of different kinds apprehended by means of different organs come to be referred to the same point in the same space. There seems indeed, no manner of reason why a positionless unextended' SUBSTANCE 543 content should be referred to any position at all, much less to the same position as some other. If, however, a sensation as given is extended and has position, if the position is a part of what is given, then there is no question about the psychological nature or logical value of the assertion of that position. It is simply a part of the act of apprehension. And this being under- stood, there is no more difficulty in supposing two contents appre- hended in one space than in apprehending them in continuous contact or at a distance of two feet. The total content in such cases is, in fact (e.g.), " hard-coloured-surface " or " single surface hard and coloured " given in a single apprehension ; not " hard- there " in one act, " coloured-there" in another, and " first there = second there " in a third. Such at least is the basis of this percep- tion of unity. That, the basis once laid, it may also in any case be " constructed " by three separate perceptions we may also admit. The difficulty here is in fact physiological or psychological, not logical. In logic the given is ultimate, in pyschology we may have to ask how the given comes to be given. Thus in the present case we have assumed that the eye and the finger- tip can identify a portion of space, and through it an object, that I can " feel " — as a matter of immediate sentiency — that the object which I see about eighteen inches from my eye is also the object which feeling locates at the end of my finger. At first sight, indeed, the whole thing might seem a question of sight. For you see your finger, and see it in contact with the coloured surface, and so " of course " it is that surface which is the seat of the hardness that you feel. But why of course ? Two things at least are involved here — first, that the hardness felt is felt as in contact with the finger. This may, I think, pass as a true analysis of the fact of tactual feeling. Second, that the finger-tip of your vision is the same as that of your feeling. But why this sameness ? whence comes it? — only from the iden- tification of the positions of the feeling and sight of my finger. "Which brings us back to the same point, namely, that perception as it stands in the developed man gives us space relations iden- tical or diverse, as the case may be, between the contents of vision and touch ; in short, as it is sometimes put, that the space of sight and touch is one space. Now this identification certainly raises a psycho-physical question of great interest. The nervous affections, that we must suppose as intermediaries in visual and tactual perception of the same object, are very diverse in origin, and presumably in character. In the one case the physiological disturbance starts with the fibrils permeating the skin of the finger-tip ; in the other, with the rods and cones of the retina. How physiological 544 KNOWLEDGE impressions so distinct in origin should come to give impressions with any element of identity is certainly a puzzle. N"or does the relation between them appear to be a pre-established harmony. Babies in the first two or three months of their existence, when they begin to " take notice," seem to make no connection between visual and tactual perception at all. They grasp what is put into their fingers, they follow with their eyes any chance object that interests them, and they suck anything put into their mouths. But they do not integrate these three worlds of perception. A distinct step forward is taken in the baby's education when he looks at the thing he holds in his hands, and then unfailingly carries it to his mouth. This stage is followed almost immediately by the attempt to grasp what he sees, and the absurdity and awkwardness of the first efforts in this direction show how inadequately the spaces of hand and eye are as yet integrated. A baby not only makes bad shots at objects within reach, but grasps quite confidently at distant objects — crying for the moon is only an extreme in- stance. We must therefore admit that the identification of the spaces of different sense organs is an educated perception.^ Nevertheless, it is a perception still, and as such for logic a primitive fact. This is no isolated peculiarity of the perception now before us. Not to go beyond sight itself, we have a parallel distinction between the logical and psycho-physical points of view. The paper on which I am writing is given me as a con- tinuous surface, but the mechanism by which this perception is effected is the stimulation of a vast number of separate nerve endings in my retina. What is the physical or " psychic syn- thesis " by which these separate stimuli produce a single con- tinuous sensation ? That we do not know, but two things are clear — that the physical unit is the stimulation of the single nerve ending, and the mental unit the perception of surface which is due to countless stimulations of countless nerve end- ings. In building up our knowledge of the world we start from the mental unit. In physiological psychology we start from the physical unit. Admitting, then, the psychological difficulties of the existence of the perception of identity on which our theory rests, we have still to stick to the fact of that perception, and to start from it as the basis of our knowledge of things. 3. The identification of concrete qualities is peculiar in its re- sults no less than in its genesis. It makes us further qualify an ^ As a further analogy we might point to our sound-space, which for most individuals is never very accurately measurable in terms of sight and touch. Here again the well-known powers of the blind show the effect of cai-eful attention in educating discrimination. SUBSTANCE 545 already apprehended content. When I analyse a given optical appearance and say it is rhomboidal in shape, crystalline in appearance, etc., I am analysing out by simultaneous or suc- cessive acts of attention the several abstract qualities or elements of the apprehended whole. I am not assigning some further quality to that whole other than is given in the apprehension of it. Again, when I judge A before B, or to the right of C, I assert relations of A but not qualities, i.e. characteristics given by attention to A alone. But when I add to the seen crystalline shape the perception of hardness, smoothness, sharpness, a certain weight, coolness, etc., I am further qualifying the eon- tent first given. These new facts do not merely stand in relation to the first fact, but are qualities of it in the sense above assigned to that word of facts discernible by attention to the content itself. Of course, we may invert the process. The visual may be said to qualify the tactual content, or vice versd. All I want to bring out is, that in this case the one content is the other — not merely is related to it, but is it. If we try to make this " is " a little more precise, we may put it that the two con- tents which I will call V and T have the common element P — the position they occupy in space and time. Now, any com- parable content-s have a common element in a certain sense, namely, their generic character, but this common element is a name for their similarity, or, if you prefer it, for the two elements, one in each several content which are precisely alike. There is no numerical identity. Here there is such identity. The same portion of space and time is given in the two contents, and that is their precise ground of union. They are one as to a portion of their composition. But what, after all, is the thing — is it the one attribute or the other, or the space in which they are ? Or is it, again, none of these, but a mysterious something that " is " all of them or manifests itself in all ? The first two views are clearly out of court at once. As to the third, we no doubt (on sufficient general grounds) believe that there is more " in " things than meets the eye or all the other senses together. But we cannot admit that this possible more is the thing to the exclusion of that which we do not surmise but know in it. The perceived contents themselves, as united in a single space, in the peculiar union constituted by that fact, make what we know as the thing. When I say, " The thing is that which is at once hard, round, white, cold, dull-sounding, acid," etc., I do not mean that the thing is some fact other than the union of these attributes which determines or possesses them, as I possess my hat or determine my line of conduct. I mean to name " the 35 546 KNOWLEDGE thing," this list of contents, in the form of union above de- scribed. This whole so united, then, is the thin^, each part its attribute. Note two things further. Any attributes, whatever they be, found in one space are referred to the same thing ; and there cannot be two things — though there can be many attributes — in one space. Certain classes of attributes exclude one another, and hence are called contradictory. It is contradictory attri- butes which a thing cannot have at the same time. It being understood that a thing can have any other attributes together, it will be seen without difficulty that whatever attributes are simultaneously presented wUl be referred to one thing. It might indeed be taken as the differentia of a thing that it is that which excludes from the same space all contents except those which form elements in itself. And if we suppose a person confined solely to the sense of touch, this would perhaps be the only notion of a thing that he would have. It might, however, be questioned whether he could then be said to conceive things as we do at all. In any case, whatever the definition, the total character of things is, we believe, such as is described above. II. The Permanence of Substance. 4. The question, " What the Thing is," which we have already found difficult enough, is still further complicated when we take into account, what we have hitherto neglected, its dura- tion in time. The further subtleties and difficulties here arise from two sources, the empirical observation of the changes undergone by the thing, and on the other hand the apparent intellectual necessity of referring all changes to some per- manent existence which we call substance. We will consider this abstract need first, our object being to show precisely what is postulated on this head by our intelligence, and •why. In our notion of substance, apart from the ideas already considered, there appear to be three elements that are constant and pretty clear, along with one that is fluctuating and un- certain. First of all, substance is the permanent in reality ; it is that which neither comes into being nor ceases to be ; it changes in the sense that it is the subject of change, but is not itself increased or diminished. It is the string on which the variegated row of phenomena are strung. Secondly, sub- stance is contrasted with attribute, state, event, relation, etc., as that which has independent reality with that which can only exist in something else. The attribute must be an attribute of a substance, the event must in fact be a change SUBSTANCE 547 in a substance or substances, and so on, as we learnt from Aristotle. True, this distinction becomes imperilled when we ask with Locke what then this substance is which is to be distinguished from every attribute — from everything that could make it anything. And if the point is pressed, substance threatens to turn into a being which is not anything in par- ticular — a conception which will be rightly dismissed by Berkeley as " the most abstract and inconceivable of all other," and correctly proved by Hegel to be in fact indistinguishable from nothing. That which is nothing in particular is nothing at all. This second conception, however, may have derived some help from the third point, which is, that substance, as existing independently of other facts, is self-subsistent, and in this self-subsistence we find the ground of its permanence. Now, can any meaning be attached to " self-subsistence," or is it but another name for that causa sui which Schopenhauer tells us to be a mere Baron Munchausen, Kfting himself horse and all out of the river by his own pig-tail ? If a complex set of facts a/Syi is the true cause of a second complex abed, we have seen reason to hold that a^yi must pass continuously into abed. Whether directly or through intermediate stages, the first group of facts becomes the second. This is sometimes expressed by saying that the cause and effect are the same thing in different aspects or in different phases. There is an element of vagueness in this expression which appears when we ask what is meant by the "same thing." "What sameness is there between the antecedent and conse- quent ? Primd facie there is a total change in every particular, and the only sameness that appears is not a qualitative like- ness, but that very continuity which was our starting-point. Bub let us slightly alter the case. Suppose the universal relation with which we started to be, not a change a^yi — abed, but a state of quiescence a — a, or abed — abed, there is here a true permanence of quaUty : the same character of reality a persists through the two moments of observation. Here, then, is a complete identity. In abc-aby a partial identity. But in either case there really is something the same in the antecedent and consequent. And looking back now to our first case, aiSyJ — abed are so far the same that both are real. Some thing, some reality, persists through the two stages. Now we may have persistence without determination. Just as a change b may foUow a without being the eifect of a, so an unchan