its effects in some mistaken views we may proceed to notice.
(a) Judgment is not inclusion in, or exclusion from, a class. The doctrine that in saying, " A is equal to B," or " B is to the right of C," or " To-day precedes Monday," I have in my mind a class, either a collection or a description, of " things equal to B," or " to the right of C," or " preceding Monday," is quite opposed to fact. It is as absurd as the assertion that, in " It is our son John," or " It is my best coat," or " 9 = 7 + 2," I think of a class of " our sons John," or " my best coats," or " that which is equal to 7 + 2." If the view stood apart from implied preconceptions, and by itself as an interpreta tion of fact, it would scarcely, I think, be so much as discussed. And, as we shall be forced to recur to it hereafter (Chap. VI.), we may so leave it here.
lion and Intuition, 2nd ed. 1880). But he, I find, treats Prof. Bain's third edition (1875), in which an earlier edition of his own criticism is treated with the greatest respect, as if it either had no existence, or at all events was somehow irrelevant to the issue. For myself I must say that for the reason given above I confine myself to the earlier theory.23 22 THE PRINCIPLES OF LOGIC BOOK I (b) Judgment is not inclusion in, or exclusion from, the subject. By the subject I mean here not the ultimate subject, to which the whole ideal content is referred, but the subject which lies within that content, in other words the grammatical subject. In " A is simultaneous with B," " C is to east of D," "E is equal to F," it is unnatural to consider A, C, and E as sole subjects, and the rest as attributive. It is equally natural to reverse the position, and perhaps more natural still to do neither, but to say instead, " A and B are synchronous," " C and D lie east and west," " E and F are equal." The ideal complex, asserted or denied, no doubt in most cases will fall into the arrangement of a subject with adjectival qualities, but in certain instances, and those not a few, the content takes the form of two or more subjects with adjectival relations existing between them. I admit you may torture the matter from the second form into the first, but, if torture is admitted, the enquiry will become a mere struggle between torturers. It requires no great skill to exhibit every subject together with its attributes as the relation between independent qualities (subjects), or again even to make that relation the subject, and to predicate all the remainder as an attribute. Thus, in " A is simultaneous with B," it is as easy to call " exists in the case of AB " an attribute of simultaneity, as it is to call " simultaneous with B " an attribute of A. We may finally observe that existential judgments do not lend themselves easily to the mistake we are considering. And such negative judgments as " Nothing is here," will be found hard to persuade. But on both these points I must refer to the sequel (Chaps. II. and III.J.
(c) Judgment is not the assertion that subject and predi cate are identical or equal. This erroneous doctrine is the natural result of former errors. You first assume that in judgment we have a relation between two ideas, and then go on to assume that these ideas must be taken in extension. But both assumptions are vicious; and, if we consider the result, asking not if it is useful but whether it is true, we can hardly, I think, remain long m hesitation. That in " You are standing before me," or " A is north of C," or " B follows D," what we really mean is a relation either of equality or identity is simply incredible; and torture of the witness goes CHAP. I THE GENERAL NATURE OF JUDGMENT 23 to such lengths that the general public is not trusted to behold it.* However useful within limits the equation of the terms may be found, if you treat it as a working hypothesis (vid. Book II. Part II. Chap. IV.), yet as a truth it will not bear any serious examination. Let us look at it more closely.
(i) If what is asserted be equality, then that of course is identity in quantity, and is nothing else whatever27. And I must venture to complain of the reckless employment of this term. To use the sign — for qualitative sameness, or for individual identity (I do not ask here if these are different), is surely barbarous. No harm perhaps may come, but there should be some limit to the abuse and confusion we allow ourselves in practice. Let us then first take equality in its proper sense, to stand for an identity in respect of quantity. But, if so, if the subject and predicate are equated, if " Negroes are men," when written " All negroes = some men," is on a level with 2= 12 — 10 — if what is said and signified is that between the terms, if you compare them numerically, there is no difference whatever, we can at once pass on. It is certain that some judgments, at least, can not express this relation of quantity, and it is certain again that, of those which can, it is only a very small class which do. Illustration is hardly wanted. " Hope is dead " would mean that, " In hope and a fraction of dead things there is exactly the same sum of units." And, in asserting that " Judgment is not an equation," I should express my belief that to divide both by 2 would not give the same quantity.
But the sign = does not seem to mean equality. It does not mean that the units of the subject and predicate are iden tical in quantity. It would appear to mean that they are the same altogether. The identity it asserts is not quantitative, but seems absolute. In " All Negroes = some men," the " = " rep resents exclusion of difference both quantitative and qualitative.
(ii) The identity is (a) not likeness; it is not a relation con sisting in a partial qualitative identity, definite or indefinite. " Iron — some metal " can hardly mean " Some metal is similar to iron." Not only do the facts exclude this interpretation, but the theory would not work with it. If " similars " and " like- * Vid. Jevons, Principles of Science, Chap. i. § 12.
24 THE PRINCIPLES OF LOGIC BOOK I ness " are phrases that occur, this is a proof that here, as in the case of =, the theory does not mean what it says, or quite know what it is doing. That when A is like B you may write one for the other, is of course quite untrue (cf. Book II.).
(b) The identity again is not definitely partial, consisting in sameness in some particular point or points of quality. For, on this interpretation, you could make no advance, until the point of sameness had been specified. And even then the equational theory would not work.
(c) Unless we suppose that both sides differ only in name, and that this difference of names is the import of the judgment — a view we shall glance at in a future chapter (Chap. VI.) — we must take the sign = to mean total sameness to the exclusion of all difference. But, if so, the theory must reform itself at once, if it desires to be consistent. It will not be true that " Negroes = some men," for certainly " some men " are not " = negroes." Nor again will it be true that negroes are equal to a certain stated fraction of mankind. That stated fraction is an universal adjective which might be applicable to other men as well as to negroes. If "is " or " = " stands for " is the same as," then it is as false to say " A is H B," as it was before to say " A is some B." " Some B" covers not only the B which is A; it may hold just as much of the other B, which we take as not-A. And it is so with " ^ B "; that applies just as much to the % which are not-A, as it does to the third which is identical with A. The quantification of the predicate is a half-hearted doctrine, which runs against facts, if " = " does mean equal, is ridicu lous if " = " comes to no more than plain " is" and is down right false if " = " stands for " is the same as."
To be consistent we must not merely quantify the predi cate, we must actually specify it. The men that are negroes are not any and every set of men, who have a certain number. They are those men who are negroes, and this is the predicate. Negroes = negro-men, and iron = iron-metal. The predicate now really and indeed seems the subject, and can be substi tuted for it. The idea is a bold one, and its results have been considerable; but if we look not at working power but at truth, the idea is not bold enough, and wants courage to remove the last contradiction.
CHAP. I THE GENERAL NATURE OF JUDGMENT 25 That A should be truly the same as AB, and AB entirely identical with A, is surely a somewhat startling result. If A = A, can it also be true that to add B on one side leaves the equation where it was? If B does not mean o, one would be inclined to think it must make some difference. But, if it does make a difference, we can no longer believe that A = AB, and AB = A. If "iron-metal" is the same as "iron," how misleading it is to set down the two sides as different terms. If there really is a difference between the two, then your statement is false when by your " = " you deny it. But if there is no difference, you are wrong in affirming it, and in opposing " iron " to " iron-metal."
There is only one issue. If A is AB, then the A that is AB is not A but — AB. Both sides of the assertion are just the same, and must be so stated. Negro-men are negro-men, and iron-metal is iron-metal.* For consider the dilemma. B either is or is not an addition to A. If it is not an addition, its insertion is gratuitous; it means nothing on either side, may fall upon whichever side we choose, is absurd on both alike, and should be got rid of — then A = A. But if B is an addition, then A = AB cannot be true. We must add B on both sides, and AB = AB. In short B must disappear or have a place on each side.
We have now reached consistency, and the reader may ask, Is the result still false? I do not like to seem obstinate, and I prefer to reply, Do you think it is true? 1 will accept your answer. If you say that identical propositions are all false, I shall not contradict you (cf. Chap. V. § i), for I also believe that a judgment which asserts no difference is nothing. But if you pronounce on the side of truth, I should like to ask a question. For an assertion to be true must it not assert something, and what is it that you take to be asserted above? That where there is no difference, there is no differ ence, that AB will be AB as long as it is AB? You can hardly mean that. Is the existence of AB what is secretly asserted? But, if so, we should say openly " AB exists," and our reduplication of AB is surely senseless. We know that it exists, not because we double it, but, I suppose, because we know of its existence.
* Cf. Lotze, Logik, 80-2.
2,6 THE PRINCIPLES OF LOGIC BOOK I But what then do we assert by AB = AB? It seems we must own that we do not assert anything. The judg ment has been gutted and finally vanishes. We have followed our premises steadily to the end, and in the end they have left us with simply nothing. In removing the difference of subject and predicate we have removed the whole judgment.* § 17. We have seen the main mistakes of the foregoing doctrines. It is a more pleasing task to consider the main truth which each one of them has seized, (i) The views we began to criticize in § 13, have avoided the error of subject predicate and copula. They have seen that in judgment the number of ideas is not the main question, and that the essence of the matter does not lie in the ideas, but in some thing beyond them. Nor, to be more particular, is the impli cation of will in all judgment a complete mistake. It is true that, in an early stage of development, the intelligence is so practical that it hardly can be said to operate independ ently. It is true again that, in the evolution of self-con sciousness, the opposition of idea and reality depends, to a degree I will not here discuss, upon volitional experience. And in these points there is truth in the theory, which, how ever much he may abandon it, we shall place to the credit of Professor Bain. And the view that in judgment we have an association of idea with sensation, and a coalescence of both elements, is far from being wholly destitute of truth. For (as we shall see in the following Chapter) the subject in all judgment is ultimately the real which appears in per ception; and again it holds good that the lowest stage, in the development of judgment and inference alike, is the red integration of ideal elements with sensuous presentation, in * It is not worth while to criticize in detail a doctrine we can show is fallacious in principle. Cf. Chap. V. But among minor objections to the quantification of the predicate is its claim to silence you, and prevent you from saying what indubitably you know. It tells you you must not say "A is B," unless you also certify how much of B is A. But, even supposing that " so much of B " is the truth that you would affirm if you could, in numerous cases you can not affirm it. You know that A possesses a quality B, and, as to how the B, that is A, stands in extent to the B which is not A, you have no information. You must either then decline to quantify, or must abstain from speak ing the truth you know. But it is not worth while to criticize in detail.
CHAP. I THE GENERAL NATURE OF JUDGMENT 27 such a manner that the two are not distinguished, but run into one whole.
(ii) And from the second class of errors we may also collect important results. In the first place it is true that the content asserted is always complex. It can never be quite simple, but must always involve relations of elements or distinguishable aspects. And hence, after all, in judgment there must be a plurality of ideas. And, in particular, (a) though it is false that the predicate is a class in which the subject is inserted, and a fundamental error to take the universal in the form of a collection, yet it is entirely true that the predicate must be always an universal. For every idea, without exception, is universal. And again (&) though assertion is not attribution to a subject in the judgment, though it is false that the grammatical subject is the reality of which the predicate is held true, yet in every judgment there must be a subject. The ideal content, the adjective divorced, is made real once again by union with a substantive. And (c) the doctrine of equation, or identity of the terms, has itself grasped a truth, a truth turned upside down and not brought to the light, but for all that a deep fundamental principle.
Turned upside down, and made false, it runs thus. The object of judgment is, despite their difference in meaning, to assert the identity of subject and predicate when taken in extension. But turned the right way up it runs thus. The object of judgment is, under and within the identity of a subject, to assert the synthesis of different attributes. When ever we write " = " there must be a difference, or we should be unable to distinguish the terms we deal with (cf. Chap. V.). And when a judgment is turned into an equation, it is just this difference that we mean to state. In " S = P " we do not mean to say that S and P are identical. We mean to say that they are different, that the diverse attributes S and P are united in one subject; that S — P is a fact, or that the subject S is not bare S, but also S — P. And the reason why the theory of equation works, and is not mere nonsense, is that in fact it is an indirect way of stating difference. " The subject is the same " implies, and may be meant to convey, the truth that the attributes differ. We must refer to the sequel for further explanation, but at present our concern is 28 THE PRINCIPLES OF LOGIC BOOK I briefly to point out that an identity must underlie every judg ment.
But how is this possible? A is " prior to B," or " to the left of C," or "equal to D." The judgment asserts the equality, or sequence, or position of two subjects, and it surely does not say that both are the same. We must try to explain. We saw that all judgment is the attribution of an ideal content to reality, and so this reality is the subject of which the content is predicated. Thus in " A precedes B," this whole relation A — B is the predicate, and, in saying this is true, we treat it as an adjective of the real world. It is a quality of something beyond mere A — B. But, if this is so, the reality to which the adjective A — B is referred is the subject of A — B, and is the identity which underlies this synthesis of differences.
It is identical, not because it is simply the same, but because it is the same amid diversity. In the judgment, beside the mere distinction of the terms, we have an opposition in time of A to B. And the subject of which A — B is asserted, being subject to these differences, is thus different in itself, while remaining the same. In this sense every judgment affirms either the identity which persists under difference, or the diversity which is true of one single subject. It would be the business of metaphysics to pursue this discussion into further subtleties. We should there have to ask if, in the end, every possible relation does not involve a something in which it exists, as well as somethings between which it exists, and it might be difficult to reconcile the claims of these prepo sitions. But we have already reached the limit of our enquiries. The real subject which is implied in judgment,28 will meet us again in the following Chapter; and that, we hope, may make clearer some points which at present remain obscure.
III. § 1 8. We have given some preliminary account of judgment, and have tried to dispose of some erroneous views. We pass now to our third task, and must make some remarks on the development of the function. As we have defined it above, judgment does not show itself at all the stages of psychical evolution. It is a comparatively late acquisition of the mind, and marks a period in its upward growth. We CHAP. I THE GENERAL NATURE OF JUDGMENT 2Q should probably be wrong if we took it as a boundary which divides the human from the animal intelligence; and in any case we should be ill-advised to descend here into the arena of theological and anti-theological prejudice (vid. Book III. Part I. Chap. VII.). It is better to treat the mind as a single phenomenon, progressing through stages, and to avoid all discussion as to whether the lines, by which we mark out this progress, fall across or between the divisions of actual classes of animals. Thus with judgment we are sure that, at a cer tain stage, it does not exist, and that at a later stage it is found in operation; and, without asking where the transition takes place, we may content ourselves with pointing out the contrast of these stages. The digression, if it be such, will throw out into relief the account we have already given of judgment. For judgment is impossible where truth and false hood, with their difference, are not known; and this difference cannot be known where ideas are not recognized and where nothing exists for the mind but fact.29 § 19. I do not mean that the lower forms, or that any form, of soul-life is confined to the apprehension of simple sensations. If the soul is ever the passive recipient of a given product, to which it does not contribute and which it does not idealize, yet in all actual mind a further step is made, and we always possess more than what is given through sense.30 The impression, so to speak, is supplemented and modified by an ideal construction, which represents the results of past experience. And thus, in a sense, the lowest animals both judge and reason, and, unless they did so, they must cease to adjust their actions to the environment. But, in the strict sense, they can neither reason nor judge; for they do not distinguish between ideas and perceived reality.
That the thing as it is, and as it appears in perception, are not the same thing, is, we all are aware, a very late after thought. But it is equally an afterthought, though not equally late, that there is any kind of difference between ideas and impressions. For a more primitive mind a thing is or it is not, is a fact or is nothing. That a fact should be, and should yet be an appearance, should be true of, and belong to, something not itself; or again should be illusion, should exist and yet be false, because its content is an adjective 3O THE PRINCIPLES OF LOGIC BOOK I neither of itself nor of any other substantive — these distinc tions are impossible for an early intelligence. A nonentity is not anything it can apprehend, and to it an error is never an illusion. And hence for this mind ideas never could be sym bols. They are facts because they are.
§ 20. The presentations of the moment, the given sensa tions, are received into a world of past experience, and this past experience now appears in the form of ideal suggestion. In the lowest stages of mind there is as clear a difference between the datum that is given and the construction that is made, as there can be in the highest. But it is one thing to have a difference in the mind and another to perceive it; and for an early intelligence this contrast between sensation and idea, is quite non-existent. A presentation AB, by a feeling d, produces an action de, or, by an ideal transition b-d, is trans formed into ABD; or may become AC, by the action of a-g, if g banishes B, and c is supplied. But, in all these cases, and in any other possible case, the process remains entirely latent. The product is received as a mere given fact, on a level with any other fact of sense.
If the object, as first perceived, could be compared with the object as finally constructed, there might be room for a doubt if the fact has become, or has been made by the mind. And still more if the ideas which perception excludes were ever attended to; if rejected suggestion, conflicting supple ment, wrong interpretation, and disappointed action, were held before the mind, then a reflection might take place, which would antedate the slow result of development; and the sense of illusion would awaken the contrast of idea and reality, truth and falsehood. But all this is impossible. For the leading feature of the early mind is its entire and absolute practicality.31 The fact occupies the soul no longer and no further than it tends to produce immediate action. The past and the future are not known except as modifications of the present. There is no practical interest in anything but the given, and what does not interest is not anything at all. Hence nothing is retained in its original character. The object, in its relation to present desire, changes ceaselessly in conformity with past adventures of failure or success. It contracts or extends itself, as the case may be, but it still remains the mere given object.
CHAP. I THE GENERAL NATURE OF JUDGMENT 31 And while the ideas it assimilates become part of presentation, the ideas it excludes are simply nothing at all.