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.