Note A — A LECTURE

I had already written my Critique of Sigwart’s notion of existence when I became aware of a note in his Logic, second ed, p. 390, a passage which, while it has not made it necessary to alter anything which I had written, has led me to insert it for the purpose of comparison. “Das Seiende überhaupt,” Sigwart writes, “kann nicht als wahrer Gattungsbegriff zu dem einzelnen Seienden betrachtet werden; es ist, begrifflich betrachtet, nur ein gemeinschaftlicher Name. Denn, da ‘Sein’ für uns ein Relationsprädikat ist, kann es kein gemeinschaftliches Merkmal sein, es müsste denn gezeigt werden, dass dieses Prädikat in einer dem Begriffe alles Seienden gemeinsamen Bestimmung wurzle.” I fear that the reader will, just as little as myself, attain by this explanation to clearness concerning Sigwart’s notion of existence. He will perhaps the better understand why all my efforts regarding it have proved futile.

II.

As Sigwart has failed to grasp the nature of judgment in general he is not, of course, able to understand that of the negative judgment in particular. He has gone so far in error as to deny to it an equal right as species along with the positive judgment; no negative judgment is, he thinks, a direct judgment, its object is rather always another actual judgment or the attempt to form such a judgment.

In this assertion Sigwart is opposed to some important psychological views which I have made good in my lecture. It would therefore seem fitting to resist his attack. For this purpose I shall show: (1) that Sigwart’s doctrine is badly founded; (2) that it leads to an irremediable confusion, as in that case Sigwart’s affirmative judgment is a negative judgment, while his negative judgment if indeed a judgment at all, and not rather the absence of one, is a positive judgment, and that moreover his positive judgment really involves a negative one, along with other similar confusions. (3) Finally I think it will be possible—thanks to Sigwart’s detailed explanations—to show the genesis of his error.

1. The first inquiry in the case of an assertion so novel and so widely diverging from the general view, will be as to its foundation. With regard to this, he insists above all (p. 150) that the negative judgment would have no meaning if the thought of the positive attribution of a predicate had not preceded. But what can this mean? Either there is here a clear petitio principii, or it cannot mean anything more than that a connection of ideas must have preceded. Now granting this for a moment (although I have in my Psychology shown its falsity) this would by no means prove his proposition, since Sigwart himself recognizes (p. 89 note, and elsewhere) that such a “subjective connexion of ideas” would still not be a judgment; that there needs rather to be added to it a certain feeling of constraint.

An argument follows later (p. 151) the logical connexion of which I understand just as little. It is rightly observed that in and for itself we have the right to deny of anything an infinite number of predicates, and it is with equal right added that in spite of this, we do not really pass all these negative judgments. And now what conclusion is drawn from these premisses? Perhaps this, that the fact that a certain negative judgment is warranted is not sufficient in itself to explain the entrance of the judgment. This we may without hesitation admit. But Sigwart concludes quite otherwise; he permits himself to assert, it follows from this that the further condition which is here lacking is that the corresponding positive affirmation has not yet been attempted. This is indeed a bold leap, and one which my logic at least is not able to follow. And why, if one were to inquire further, are not all the positive judgments here concerned really attempted? The most probable answer, judging by the examples given by Sigwart (this stone reads, writes, sings, composes; justice is blue, green, heptagonal, rotating), is, that this has not been done because the negative judgment has already been made with evident certainty; for this would best explain why there is no “danger of any one attributing these predicates to the stone or to justice.” If, however, any one prefer to answer that “the narrowness of consciousness” makes it impossible to attempt at the same time an infinite number of positive judgments, I am content with this expedient also, only it must then be asked if this appeal ought not to have been made directly and earlier, since Sigwart himself calls the possible negative judgments an “immeasurable quantity.”

It is also a curious error (Marty has already called attention to it), when Sigwart asserts that in contradistinction to what holds good of the negative judgment “every subject admits only of a limited number of predicates being affirmed.” But why? Can we not, for example, say a whole hour is greater than half an hour, greater than a third, greater than a fourth and so on ad infin.?... If then, notwithstanding, I do not really make all these judgments, there are evidently good reasons for this; above all that the “narrowness of consciousness” forbids it. But then this might also be applied most successfully in regard to negative judgments.

Somewhat later we meet a third argument which, as I have already by anticipation refuted it in my Psychology (book ii. chap. 7, section v.), will be treated quite shortly here. If the negative judgment were a direct one, co-ordinated with the affirmative judgment as species then, thinks Sigwart (p. 155 seq.), whoever in an affirmative categorical proposition regards the affirmation of the subject as involved must, to be consistent, regard the denial of the subject as involved in the negative proposition, which is not the case. The latter observation is correct, the former assertion, however, quite untenable, as it involves in itself a contradiction. For exactly because the existence of each part in a whole is involved in the existence of the whole, the whole no longer exists if but one of its parts is missing.

It only remains now to consider a point of language by which Sigwart believes himself able to support his view. A testimony for it is, he thinks, to be found in the fact that the symbol for the negative judgment is formed in every case by means of a combination with the symbol of affirmation, the word “not” being added to the copula. In order to judge what is here actually the fact, we will glance for a moment at the sphere of feeling. Sigwart agrees, I think, with me and everybody else that pleasing and displeasing, rejoicing and sorrowing, loving and hating, etc., are co-ordinate with each other. Yet a complete series of expressions denoting a disinclination of feeling are found in dependence upon the expression for the corresponding inclination. For example, inclination, disinclination; pleasure, displeasure; ease, disease; Wille, Widerwille; froh, unfroh; happy, unhappy; beautiful, unbeautiful; pleasant, unpleasant;—even “ungut” is used. The explanation of this is, I believe, not difficult for the psychologist, notwithstanding the equally primordial character of these opposite modes of feeling. Ought then the explanation of the phenomenon lying before us in the expression of the negative judgment, closely related as it is to the before mentioned phenomenon, to be really so very difficult, even assuming the primordial character?

As a matter of fact the case must be very bad when thinkers like Sigwart in making statements so important in principle, and at the same time so unusual, have to resort to arguments so weak.

2. The grounds on which Sigwart’s doctrine concerning the negative judgment rest have, therefore, each and all proved untenable. This must be so; for how could the truth of any doctrine be shown which would plunge everything into the greatest confusion?

Sigwart finds himself compelled to distinguish between the positive and the affirmative judgment, and the affirmative judgment—one hears and wonders at the new terminology—is according to him, closely examined, a negative judgment. On page 150 he says literally: “The primordial judgment can certainly not be termed the affirmative judgment, but is better described as the positive judgment, for only in opposition to the negative judgment, and in so far as it rejects the possibility of a negation, is the simple statement A is B an affirmation,” and so on. Inasmuch as it “rejects.” What else can that mean than “so far as it denies”? As a matter of fact only those negations can, according to this new and extraordinary use of language, be called affirmations! Yet this would really mean, and particularly when it is said that the proposition A is B is often such a negation (cf. the expressions just quoted), that the use of language would be reduced to a confusion quite unnecessary and altogether unendurable.

Not only is the affirmation—as set forth—according to Sigwart really a negation but also, paradoxical as it may seem, the negation, on close consideration, proves to be a positive judgment. It is true, Sigwart protests against those who, like Hobbes, would regard all negatives as affirmative judgments with negative predicates. But, following Sigwart, if this is not so, then these must be affirmative judgments with affirmative predicates, since he teaches that the subject is in every case a judgment, the predicate being the notion of invalidity. On p. 160 he says in the note the negation does away with a supposition, denies the validity, and this expression, considered in itself, might be taken to mean that Sigwart assumes here a special function of denial (absprechen) the contrary of that of affirmation (zusprechen). But no; a negative copula (cf. p. 153) according to him there is not.

Now what in the world is one to understand by “denial” (absprechen)? Does it mean the simple suppression (Aufhörenlassen) of the positive judgment upon the given subject matter, that is, according to Sigwart, the falling away of the feeling of compulsion previously given in a connexion between ideas? This is impossible, since the removal of this would bring about a condition in which the connexion of ideas remains, without being either affirmed or denied. How often does something of which we were previously certain become uncertain without our on this account denying it. What then is this denying? May we perhaps say that according to Sigwart it is a feeling oneself compelled (sich-genötigt-fühlen) to annul, whereas affirming is a feeling oneself compelled to posit? We should then have to say that all the while we are passing a negative judgment, we are in reality always seeking to pass a positive judgment, but that we experience a hindrance in so doing. The same consciousness, however, is felt by one who is clearly aware of the entire absence of a positive ground. For how can any one succeed in believing anything which he at the same time holds to be entirely ungrounded? Of no one, especially if Sigwart’s definition of the judgment be applied as the standard, is this conceivable; that is to say, every one in such a case will experience failure in such an attempt. Accordingly there is, as yet, no negative judgment. If then the rejection does not signify a negative copula it must manifestly be regarded as an instance of the affirmation of the predicate “false,” or (to use Sigwart’s term) as its “identification” with the judgment which in this case should be the subject. This “false” also cannot simply mean “untrue,” for I can assert “untrue” of thousands of things with regard to which the predicate “false,” which appears in certain judgments, would not be in place. If only judgments are true, then of everything which is not a judgment the predicate “untrue” must be affirmed, though certainly not on that account the predicate “false.” “False” must therefore be regarded as a positive predicate; and so from Sigwart’s point of view absolutely false in principle, certain as it is that the merely not being convinced (nicht-überzeugt-sein) is no denial, it is equally certain that we have actually no choice; we should be compelled to regard every negative judgment as a positive judgment with a positive predicate. So we arrive at a second and greater paradox.

But here a third factor enters which completes the confusion. If we examine Sigwart’s view as to the nature of judgment in general, it may be shown in the clearest manner possible that the simple positive judgment itself involves in turn, a negative judgment. That is to say, following Sigwart, every judgment involves besides a certain combination of ideas, a consciousness of the necessity of our “identification” (unseres Einssetzens) and the impossibility of its contradictory (cf. espec. p. 102), the consciousness, moreover, of such a necessity and impossibility valid for all thinking beings (cf. pp. 102 and 107), which, by the way, is of course quite as false as Sigwart’s whole view of the nature of judgment in general. All judgments without exception are, on account of this peculiarity, called by Sigwart apodictic: nor will he admit the validity of any distinction between the assertorical and apodictic forms of judgment (cf. p. 229 seq.). I now ask: Have we not here a negative judgment distinctly involved? Otherwise what meaning can be given to the statement when we hear Sigwart speak of a “consciousness of the impossibility of the contradictory.” Further I have already shown in my Psychology how all universal judgments are negative, since to be conscious of universality means nothing else than to be convinced that there exists no exception; if this negative be not added, the most extensive list of positive assertions will never constitute a belief in universality. When therefore, a consciousness that every one must so think is here spoken of, there is in this fact a further proof of what I have asserted, namely that according to Sigwart’s doctrine of judgment the simplest positive acts of judgment must involve a negative act of judgment. And yet we are called upon at the same time to believe that the negative judgment, as set forth (p. 159 seq.), arose relatively late, and that therefore on this, as well as on other grounds, it is unworthy of being placed side by side, with the positive judgment as a species equally primordial! Sigwart would surely not have expected this of us had he been conscious of all that I have here set forth in detail, and which is the more clearly seen to be involved in his exposition, often so difficult to comprehend the more carefully it is submitted to reflection. Of course expressions may be found where Sigwart, respecting this or that point of detail, asserts the contrary of what is here deduced; for what else can be expected where everything is left in such ambiguity, and where the attempt to make things clear exhibits the most manifold contradictions?

3. Finally, we have still to show the genesis of the error in which this able logician has involved himself in a relatively simple question after having once mistaken the nature of the judgment. The proton pseudos is to be sought in a delusion which has come down to us from the older logic that to the essence of the judgment there belongs the relation of two ideas with one another. Aristotle has described this relation as combination and separation (σύνθεσις καἰ διαίρεσις) although he was well aware of the imperfect propriety of the expressions, adding at the same time that in a certain sense both relations might be described as a combination (σύνθεσις, cf. de Anima, iii. 6). Scholastic and modern logic held fast to the expressions “combination” and “separation”; in grammar, however, both these relations were termed “combination,” and the symbol for this combination the “copula.” Sigwart now takes seriously the expressions “combination” and “separation,” and so a negative copula seems to him a contradiction (cf. p. 153), the positive judgment, on the other hand, appears to be a presupposition of the negative judgment, since, before a combination has been set up, it cannot be separated. And so it appears to him that a negative judgment without a preceding positive judgment is quite meaningless (cf. p. 150 and above). Consequently we find this celebrated inquirer in a position which compels him to put forth the most strenuous efforts all to no purpose—the negative judgment remains inexplicable.

In a note (p. 159) he gives us, as a result of such attempts, a remarkable description of the process by which we arrive at the negative judgment—a result in which he believes himself finally able to rest satisfied. In this account the false steps which he successively makes become, each in turn, evident to the attentive observer. Long before the point is reached where he believes himself to have come upon the negative judgment, he has as a matter of fact already anticipated it.

He sets out with the correct observation that the first judgments which we make are all positive in character. These judgments are evident and made with full confidence. “Now, however,” he continues, “our thought goes out beyond the given; by the aid of recollections and associations, judgments arise which are at first also formed in the belief that they express reality” (which means, according to other expressions of Sigwart, that the ideas are combined with the consciousness of objective validity; for this (xiv. p. 98) belongs to the essence of the judgment) “as, for example, when we expect to find something with which we are acquainted in its usual place or pre-suppose respecting a flower that it smells. Now, however, a part of what is thus supposed contradicts our immediate knowledge.” (We leave Sigwart to show here how we are able to recognize anything as “contradictory” when we are not as yet in possession of negative judgments and negative notions. The difficulty becomes still more sharply apparent as he proceeds:) “when we do not find what we expected, we become conscious of the difference between what exists merely in idea and what is real.” (What does “not find” mean here? I had not found it previously; obviously I now find that what was erroneously supposed to be associated with another object is without it, and this I can only do by recognizing the one and denying the other, i.e. recognize it as not being with it. Further what is meant here by “difference”? To recognize difference means to recognize that of two things the one is not the other. What is meant by existing “merely in idea”? Manifestly, “what exists in idea which is not at the same time also real.” It would seem, however, that Sigwart is still unaware that in what he is describing the negative function of the judgment is already more than once involved. He continues:) “That of which we are immediately certain is another than that” (i.e. it is not the same, it is indeed absolutely incompatible with that) “which we have judged in anticipation, and now” (i.e. after and since we have already passed all these negative judgments) “appears the negation which annuls the supposition and denies of it validity. And here a new attitude is involved in so far as the subjective combination is separated from the consciousness of certainty. The subjective combination is compared with one bearing the stamp of certainty, its distinction therefrom recognized, and out of this arises the notion of invalidity.” This last would almost seem to be a carelessness of expression, for if invalid were to mean as much as “false” and not “uncertain” it could not be derived from the distinction between a combination with and a combination without certainty, but only from the opposition existing between combination which is denied and one which is affirmed. As a matter of fact, the opposite affirmative judgment is not at all necessary to it. The opposition, the incompatibility of the qualities in a real, is already evident on the ground of the combination of ideas representing the opposite qualities which, as I repeat once more, cannot, according to Sigwart himself (p. 89 note; and p. 98 seq.), be called an attempt at positive judgment. Although this may now and again happen in the case of contradictory ideas, it certainly does not happen always. If, for example, the question is put to me: Does there exist a regular chiliagon with 1001 sides? then—assuming that I am not perfectly clear in my own mind, as will be the case with most men, that there does exist a regular chiliagon, I certainly do not attempt to form a judgment (i.e. according to Sigwart, confidently assume) that there exists a regular chiliagon having 1001 sides before forming the negative judgment that no such figure exists on the ground of the opposition between the qualities.

Sigwart himself, as his language frequently betrays (cf. e.g. pp. 152 and 150) recognizes at bottom, as he is bound to recognize, in spite of his attack upon the negative copula, that negation and denial are just as much a special function of the judgment as affirmation and recognition. If this be granted, then the range of their application is by no means so limited as he erroneously asserts. It is false that in every case where a denial takes place the predicate denied is the notion “valid.” Even of a judgment we may deny now its validity, now its certainty, now its à priori character. And just in the same way the subject of the judgment can change most frequently. Of a judgment we may deny certainty, and validity; of a request, modesty; and so in every case, universally expressed, we may deny B of A. Sigwart himself, of course, does this just like any one else. Indeed he sometimes speaks unintentionally far more correctly than his theory would admit, and witnesses, as it were, instinctively to the truth; as, e.g. p. 151, where he declares not—as he elsewhere teaches—that the subject of a negative proposition is always a judgment, and its predicate the term “valid,” but “that of every subject ... a countless number of predicates may be denied.” This is certainly true and just on this account the old doctrine holds that affirmation and denial are equally primordial species.