The supposed (to pass to another point) is in one aspect (M — P) quite certain and actual. It is in connection with S (as known) that M — P is but possible. And I may add that, where S itself is taken as possible only, the supposed is here doubly possible. But, essentially and always, what is supposed is taken as possible.
This statement may seem at first to be in conflict with plain facts, such as the example given on p. 87 (cf. Essays, pp. 37-40). I maY be told that possibility is here certainly excluded. I would on the other side, however, ask the reader to reflect whether certainty is not contrary to the very meaning of "If." And, since to my mind that point is clear, I conclude that any appearance to the contrary rests on what may be called linguistic or rhetorical artifice. I actually, that is, assert or deny some real connection, and so far there is no "If." But, for some unstated reason, I desire at the same time to suggest that things throughout might have been otherwise. And I convey at once my undoubting judgment and my doubtful suggestion by licentiously applying " if" to the undiscriminated compound. "The destruction of the barometer (§ 50) caused the absence of warning— and it need not have been so." And " since you are well (which you might not have been)" is the double meaning conveyed in "si vales bene est." We may notice further in this connection that it is common to refute an asserted S — P by showing it as true only if the impossible is supposed.
41 "The fact is the quality in the man's disposition." (i) It is so here, but even here a " disposition " apart from any circumstances is an impossible abstraction. Further (ii), if "disposition" is used to explain "conditional," then obviously, since the very meaning of H2 THE PRINCIPLES OF LOGIC BOOK I " disposition " involves a standing " if," the explanation is circular (see Appearance, Index, s. v. Dispositions), (iii) The objection to "quality" is that it seems merely to repeat (what we knew before) that things are so; and to admit (if we add "latent") that we do not know how (Cf. Appearance, p. 362.).
42 " A quality which has appeared...experiment." This state ment (see above) may involve a vicious abstraction.
43 There is much here that requires correction, (i) I surely, in the case of every categorical judgment, am not forced to make it. The " arbitrary " character of all judgment and inference is discussed in T. E. I and II. (ii) Logical compulsion means merely that the object is so, whatever else I am pleased to fancy. And if a hypotheti cal judgment did not say that much, it would be no judgment at all. (iii) And further, to make the result of the "experiment" disappear from the reality is in principle vicious.
44 "Were very different." The "very" here is objectionable. See 45 With regard to the limits of explanation I will merely state here that — except in a relative sphere where assumptions are made — all judgments and all truth on my view involves what is inexplicable. There is in every case a certain amount of unknown condition (x). The question in any particular case will be as to the nature and amount in the end of this x. See Appearance, p. 581 and its Index, and that of Essays, s. v. Inexplicable.
46 The conclusion drawn in §§ 53-56 is, I think, sound on the whole, though in part perhaps inaccurate. Even in the case of a designated particular we can hardly say broadly that this falls outside the sup- posal. On the other hand certainly we fail to get this, as merely designated, within the supposal and the judgment. The judgment therefore will, more or less against our wish, turn out to be abstract merely and only conditional — though neither in form. See Essays, pp. 38-40, and the Index of that work, and of this, s. v. Designation.
47 " It does not assert the existence." Yes, it does assert this and must do so. But what existence and where is in every case the ques tion. See on § 2 and Chap. I, § 10.
48 For the doctrine that all judgments are conditional see Essays, Index, s. v. Judgment.
49 Cf. T. E. I and IX, and Essays, pp. 299 foil.
50 The real truth...actual." This is the doctrine for which I have now for so many years contended. See Appearance and Essays, the Indexes. Relations exist only in and through a whole which can not in the end be resolved into relations and terms. " And," "together" and "between," are all in the end senseless apart from such a whole. The opposite view is maintained (as I understand) by Mr. Russell, and was perhaps at last tacitly adopted by Prof. Royce. But, for myself, I am unable to find that Mr. Russell has ever really faced this question. See Essays, Index, s. v. Unity.
51 In "orthodox Christianity," the "orthodox" was meant to be emphatic.
CHAP. 11 FORMS OF JUDGMENT 113 52 On the actual content of the " this " see T. E. IV and V, and the Index.
53 On conditioned and conditional see T. E. II, and Essays, the Index.
54 " There is no because," i.e. of the character which you assume and require. The argument here is, in my opinion, sound, but it is perhaps better put as follows. The condition, on which the judgment holds, is unknown, and it admits also the opposite of what is asserted. The judgment therefore, in its present form, is at once both true and false. See Essays, Index, s. v. Conditional.
56 " You may say &c." It is of course the English empiricist of 1883 who is being addressed here. As to how far the criticism is now out of date, the reader must judge for himself.
57 " The whole or part of the series of phenomena," i.e. as such.
ss " The present." Cf. §§ii foil.
59 " The assertion seems not false." On the other side, since it depends on an unknown condition, and since therefore its opposite also is possible, it has not absolute truth. In this point, and so far, it is like the " analytical judgment of sense." On the other hand it is higher and truer because, and so far as, its condition is less unknown and less dependent on mere " matter of fact."
60 "Does not ascribe...real." This, we have seen (Note 3) is wrong. But, if " existence " meant my " real world " of events, it could stand. On the " quality " see Note 41.
61 If "existence" (Notes 3 and 33) means my " real world," then to say of anything that its existence is implied in there being such a world, is, so far, unconditional assertion. But on the other hand, so far as this world itself is not absolutely real and true, the assertion becomes, so far, merely relative, and dependent on an unknown con dition. If you could say that P, as such, is implied in the real, that would make P true absolutely.
To " the consequence of a false hypothesis &c.," we should, I think, add "unless by an abstraction the hypothesis is taken as merely false."
62 ' It must cease to predicate— real " should be " It must cease to predicate its elements, as such, of the perceived real."
63 "Immersed in matter." For "matter of fact" see Essays, pp.
64 " Assert the existence...that " should be " assert their content of that." And "can ascribe...as such" should be changed to "can ascribe to reality its content unconditionally."
65 The division made in § 80 is (we have seen) indefensible, if only because the "imaginary" is left out. See Note 33- And for the " awkward assumption " cf. § 32.
66 " Soul to soul." Cf. Note 31. And (lower down), to the question raised by "Either here or nowhere," the answer, I think, must be " in the end nowhere." But for the sense of this reply I must refer to my Appearance and Essays.
CHAPTER III l THE NEGATIVE JUDGMENT § I. After the long discussion of the preceding chapter, we are so familiar with the general character of judgment that we can afford to deal rapidly with particular applications. Like every other variety, the negative judgment depends on the real which appears in perception. In the end it consists in the declared refusal of that subject 2 to accept an ideal content. The suggestion of the real as qualified and deter mined in a certain way, and the exclusion of that suggestion by its application to actual reality, is the proper essence of the negative judgment.
§ 2. Though denial, as we shall see, can not be reduced to or derived from affirmation, yet it would probably be wrong to consider the two as co-ordinate species. It is not merely as we shall see lower down (§7), that negation presupposes a positive ground. It stands at a different level of reflection. For in affirmative judgment we are able to attribute the content directly to the real itself. To have an idea, or a synthesis of ideas, and to refer this as a quality to the fact that appears in presentation, was all that we wanted. But, in negative judgment,3 this very reference of content to reality must itself be an idea. Given X the fact, and an idea a — b, you may at once attribute a — b to X; but you can not deny a — b of X, so long as you have merely X and a — b. For, in order to deny, you must have the suggestion of an affirmative relation. The idea of X, as qualified by a — b, which we may write x (a — b), is the ideal content which X repels, and is what we deny in our negative judgment.
It may be said, no doubt, that in affirmative judgment the real subject is always idealized. We select from the whole that appears in presentation, and mean an element that we do not mention (Book III. I. Chap. VI. § 12). When we point to a tree and apply the word " green," it may be urged that the subject is just as ideal as when the same object rejects the CHAP. Ill THE NEGATIVE JUDGMENT HtJ offered suggestion "yellow." But this would ignore an im portant difference. The tree, in its presented unity with reality, can accept at once the suggested quality. I am not always forced to suspend my decision, to wait and consider the whole as ideal, to ask in the first place, Is the tree green? and then decide that the tree is a green tree. But in the nega tive judgment where " yellow " is denied, the positive relation of " yellow " to the tree must precede the exclusion of that relation. The judgment can never anticipate the question. I must always be placed at that stage of reflection which sometimes I avoid in affirmative judgment.
§ 3. And this distinction becomes obvious, if we go back to origins and consider the early development of each kind. The primitive basis of affirmation is the coalescence of idea with perception. But mere non-coalescence of an idea with perception is a good deal further removed from negation. It is not the mere presence of an unreferred idea, nor its unob served difference, but it is the failure to refer it, or identify it, which is the foundation of our first denial. The exclu sion by presented fact of an idea, which attempted to qualify it, is what denial starts from. What negation must begin, with is the attempt on reality, the baffled approach of a qualification. And in the consciousness of this attempt is implied not only the suggestion that is made, but the subject to which that suggestion is offered. Thus in the scale of reflec tion negation stands higher than mere affirmation. It is in one sense more ideal, and it comes into existence at a later stage of the development of the soul.* § 4. But the perception of this truth must not lead us into error. We must never say that negation is the denial of an existing judgment. For judgment, as we know, implies belief; and it is not the case that what we deny we must once have believed. And again, since belief and disbelief are incom patible, the negative judgment would in this way be made to depend on an element which, alike by its existence or its disappearance, would remove the negation itself. What we deny is not the reference of the idea to actual fact. It is the mere idea of the fact, as so qualified, which negation ex- * Compare on this whole subject Sigwart, Logik, I. 119 and foil. I do not, however, wholly accept his views.
l6 THE PRINCIPLES OF LOGIC BOOK I eludes; it repels the suggested synthesis,4 not the real judg ment.
§ 5. From this we may pass to a counterpart error. If it is a mistake to say that an affirmative judgment is presup posed in denial, it is no less a mistake to hold that the predicate alone is affected, and that negation itself is a kind of affirma tion. We shall hereafter recognize the truth which this doc trine embodies, but, in the form it here assumes, we can not accept it. The exclusion by fact of an approaching quality is a process which calls for its own special expression. And when we are asked to simplify matters by substituting " A is Not-B " for " A is not B," we find an obvious difficulty. In order to know that A accepts Not-B, must we not al ready have somehow learnt that A excludes B? And, if so, we reduce negation to affirmation by first of all denying, and then asserting that we have denied, — a process which no doubt is quite legitimate, but is scarcely reduction or simplification.
§ 6. There is a further objection we shall state hereafter (§ 16) to the use of Not-B as an independent predicate. But at present we must turn to clear the ground of another error. We may be told that negation " affects only the copula; " and it is necessary first to ask what this means. If it means what it says, we may dismiss it at once, since the copula may be wanting. If the copula is not there when I positively say " Wolf," so also it is absent when I negatively say " No wolf." But, if what is meant is that denial and assertion are two sorts of judgment, which stand on a level, then the statement once again needs correction. It is perfectly true that these two different sorts of judgment exist. The affirmative judgment qualifies a subject by the attribution of a quality, and the negative judgment qualifies a subject by the explicit rejection of that same quality. We have thus two kinds of asserted relation. But the mistake arises when we place them on a level. It is not only true that, as a condition of denial, we must have already a suggested synthesis, but there is in addition another objection. The truth of the negative may be seen in the end to lie in the affirmation of a positive quality; and hence assertion and denial cannot stand on one level.5 In " A is not B " the real fact is a character x belonging to A, and which is incompatible with B. The basis of negation is really CHAP. Ill THE NEGATIVE JUDGMENT 117 the assertion of a quality that excludes (#). It is not, as we saw, the mere assertion of the quality of exclusion (Not-B).
§ 7. Every negation must have a ground, and this ground is positive. It is that quality x in the subject which is in compatible with the suggested idea. A is not B because A is such that, if it were B, it would cease to be itself. Its quality would be altered if it accepted B; and it is by virtue of this quality, which B would destroy, that A maintains itself and rejects the suggestion. In other words its quality x and B are discrepant. And we can not deny B without affirming in A the pre-existence of this discrepant quality.6 But in negative judgment x is not made explicit. We do not say what there is in A which makes B incompatible. We often, if asked, should be unable to point out and to dis tinguish this latent hindrance; and in certain cases no effort we could make would enable us to do this. If B is accepted, A loses its character; and in these cases we know no more. The ground is not merely unstated but is unknown.
§ 8. The distinctions of " privation " and " opposition " (Sigwart, 128 foil.) do not alter the essence of what we have laid down. In a privative judgment the predicate " red " would be denied of the subject simply on the ground that red was not there. The subject might be wholly colourless and dark.7 But if " red " were denied on the ground that the subject was coloured green, it would be the presence of an opposite quality that would exclude, and the judgment would then be based on positive opposition. This distinction we shall find in another context to be most material (cf. Chap. VI. and Book III. II. Chap. III. § 20); but, for our present purpose, it may be called irrelevant. In the one case as in the other, the subject is taken with a certain character; and by addition as well as by diminution that individual character may be destroyed. If a body is not red because it is uncoloured, then the adding-on cf colour would destroy that body as at present we regard it. We may fairly say that, if the predicate were accepted, the subject would no longer be the subject it is. And, if so, in the end our denial in both cases will start from a discrepant quality and character.
§ 9. It may be answered, no doubt, that the subject, as it is now and as we now regard it, is not the same thing as the Il8 THE PRINCIPLES OF LOGIC BOOK I subject itself. In the one case, the subject rejects a sugges tion through a quality of its own, in the other it may reject on the strength of our failure. But I must persist in denying that this objection is relevant. In both cases alike the subject is taken as somehow determined; and it is this determination which (whatever it comes from) does give the subject a positive character, which in both cases lies at the base of the denial. No subject could repel an offered suggestion simply on the strength of what it was not. It is because the " not- this " must mean " something else'' that we are able to make absence a ground for denial. We shall all agree that the nothing which is nothing can not possibly do anything, or be a reason for aught.8 These distinctions do not touch the principle we stand upon, but I admit they give rise to most serious difficulties.9 And, mainly for the sake of future chapters, it may be well if we attempt here to clear our ideas. And (i) first, when we have a case of " opposition," there the subject repels the offered predicate because it has in its content a positive quality, filling the space which the predicate would occupy, and so expelling it. If a man has blue eyes, then that quality of blueness is incompatible with the quality brown. But (ii), when we come to privation, two cases are possible. In the first of these (a) within the content of the subject there is empty space where a quality should be. Thus, a man being eyeless, in this actual content lies the place where his eyes would be if he had them. And this void can not possibly be a literal blank. You must represent the orbits as somehow occupied, by peaceful eyelids, or unnatural appearance. And so the content itself gets a quality, which, in contrast to the presence of eyes, may be nothing,* but which by itself has a positive character, which serves to repel the suggestion of sight.
§10. But privation can rest on another basis (&). The *I may mention that, though contrast can not always be taken as holding true of the things contrasted, yet for all that it may rest n a positive quality. Thus, even in the case of a word like blind ness we should be wrong if we assumed that the blind man is qualified simply by the absence of sight from the part which should furnish vision. His mind, we can not doubt, has a positive character which it would lose if another sense were added.
CHAP. Ill THE NEGATIVE JUDGMENT 1 19 content of the subject may contain no space which could pos sibly be qualified by the presence of the predicate. What rejects the predicate is no other determination of the con tent itself, but is, so far as that content itself is concerned, an absolute blank. It is difficult to find illustrations of this instance. If I say "A stone does not feel or see," it may rightly be urged " Yes, because it is a stone, and not simply because it is nothing else." But we can find an example of the privation we want in the abstract universal. The univer sal idea (cf. Sigwart, 130), if you keep it in abstraction, repels every possible extension of its character. Thus " tri angle," if you mean by it the mere abstraction, can neither be isosceles nor scalene nor rectangular; for, if it were, it would cease to be undetermined. We may invent a stupid reductio ad absurdum: This isosceles figure is certainly a triangle, but a triangle is certainly not isosceles, therefore.
If we release the universal from this unnatural abstraction, and use it as an attribute of real existence, then it can not sup port such a privative judgment. For, when referred to reality, we know it must be qualified, though we perhaps can not state its qualification. Once predicate triangle of any figure, and we no longer can deny every other quality. The triangle is determinate, though we are not able to say how. It is only the triangle as we happen not to know it, which repels the suggestion of offered predicates. It is our ignorance, in short, and not the idea, which supports our exclusion of every sug gestion.
§ ii. In a judgment of this kind the base of denial is neither the content of the subject itself, nor is it that content plus a simple absence; for a simple absence is nothing at all. The genuine subject is the content of the idea plus my psycho logical state of mind. The universal abstraction, ostensibly unqualified, is determined by my mental repulsion of qualities. And the positive area which excludes the predicate really lies in that mental condition of mine. My ignorance, or again my wilful abstraction, is never a bare defect of knowledge. It is a positive psychological state. And it is by virtue of relation to this state, which is used as content to qualify the subject, that the abstraction, or the ignorance, is able to become a subject of privation. We shall see that, in this form, the THE PRINCIPLES OF LOGIC BOOK I universal may more truly be called particular (Chap. VI. § 35); for it is determined and qualified, not by any develop ment of the content, but simply by extraneous psychological relation.10 § 12. The various kinds of negative judgment follow closely the varieties of affirmation. The immediate subject may be part of the content of present perception (" This stone is not wet "); or it may be found in some part of the series of space, or again of time, which we do not perceive (" Marseilles is not the capital of France," " It did not freeze last night "). Again what is denied may be a general connection ("A metal need not be heavier than water"). In this last case it is of course the unexpressed quality at the base of the hypothesis (Chap. II. § 50) which the real excludes.11 But, in all negative judgment, the ultimate subject is the reality that comes to us in presentation. We affirm in all alike that the quality of the real excludes an ideal content that is offered. And so every judgment, positive or negative, is in the end existential.
In existential judgment, as we saw before (Chap. II. § 42), the apparent is not the actual subject. Let us take such a denial as " Chimaeras are non-existent." " Chimaeras " is here ostensibly the subject, but is really the predicate. It is the quality of harbouring chimaeras which is denied of the nature of things. And we deny this because, if chimaeras existed, we should have to alter our view of the world. In some cases that view, no doubt, can be altered, but, so long as we hold it, we are bound to refuse all predicates it excludes. The positive quality of the ultimate reality may remain occult or be made explicit, but this, and nothing else, lies always at the base of a negative judgment.
§ 13. For logical negation can not be so directly related to fact as is logical assertion.12 We might say that, as such and in its own strict character, it is simply " subjective: " it does not hold good outside my thinking. The reality repels the sug gested alteration; but the suggestion is not any movement of the fact, nor in fact does the given subject maintain itself against the actual attack of a discrepant quality. The process takes place in the unsubstantial region of ideal experiment. And the steps of that experiment are not even asserted to exist in the world outside our heads. The result remains, and CHAP. Ill THE NEGATIVE JUDGMENT 121 is true of the real, but its truth, as we have seen, is something other than its first appearance.
The reality is determined by negative judgments, but it can not be said to be directly determined. The exclusion, as such, can not be ascribed to it, and hence a variety of ex clusions may be based on one single quality. The soul is not an elephant, nor a ship in full sail, nor a colour, nor a fire- shovel; and, in all these negations, we do make an assertion about the soul. But you can hardly say that the subject is determined by these exclusions as such, unless you will main tain that, after the first, the remainder must yield some fresh piece of knowledge. You may hold that " all negation is deter mination," if you are prepared to argue that, in the rejection of each new absurd suggestion, the soul exhibits a fresh side of its being, and in each case performs the special exclusion by means of a new quality. But it seems better to say that nothing is added by additional exclusions.13 The develop ment and application of these may proceed ad infinitum, but the process is arbitrary and, in the end, unreal. The same quality of the soul which repels one predicate, repels here all the rest, and the exclusion itself takes place only in our heads.
I do not mean to deny that a thing may be qualified by the exclusion of others, that the real character of a fact may depend on what may be called a negative relation. What I mean to say is that the negative judgment will not express this. It asserts that a predicate is incompatible, but it does not say that either the predicate, or the incompatibility, are real facts. If you wish to say this you must transcend the sphere of the negative judgment.
§ 14. We must not, if we can help it, introduce into logic the problems of the " dialectical " view.14 It may be, after all, that everything is just so far as it is not, and again is not just so far as it is. Everything is determined by all negation; for it is what it is as a member of the whole, and its relation to all other members is negative. Each element in the whole, itself the whole ideally while actually finite, transcends itself by mere self-assertion, and by mere self-emphasis brings forth the other that characterizes and negates it. If everything thus has its discrepant in itself, then everything in a sense must be its own discrepancy. Negation is not only one side of reality, I22 THE PRINCIPLES OF LOGIC BOOK I but in the end it is either side we please. On this view it would be doubtful if even the whole is positive; for it is just so far as by position it disperses itself in its own negation, and begets from its dispersion the opposite extreme. It is doubt ful if we may not transform the saying that " Everything is nothing except by position," into " Everything by position is its proper contrary, and nothing by position is all and every thing."
If this is so, there would remain no quality which is simply positive; and logical negation, in another sense than we have given it above, becomes the soul and, we sometimes are inclined to think, the body of the real world. But we are not called upon to discuss this view (cf. Chap. V.), for our result will stand in any case, I think, in its principal outline.