3. Should Sigwart wish in this passage to widen the notion of existence to such a degree as to think that existence is that which can either be perceived or inferred from some perceivable object, or again, stands in some sort of causal relation to what is perceivable, it might be replied—if indeed such a monstrous notion of existence still require refutation—that even this notion is still too narrow. If, for example, I say: It may be that an empty space exists but this can never with certainty be known by any one, I thereby confess that existence may perhaps belong to empty space; but I deny most definitely that it is perceptible, or that it is to be inferred from that which is perceptible. In regard to relations of cause and effect on the other hand, it is of course impossible that empty space (which is certainly no thing) can stand in such a relation to anything perceivable. We should thus once again arrive at an absurd meaning in interpretation of an assertion in no way absurd.
How wrongly Sigwart has analysed the notion of existence is also proved very simply by means of the following proposition: A real centaur does not exist; a centaur in idea, however, certainly exists, and that as often as I imagine it. Whoever does not clearly recognize here the distinction of the “ὂν ὡς ἀληθές i.e. in the sense of existing, from ὂν in the sense of real (wesenhaft) will I fear hardly be brought to recognize it by the fullest illustrations which might be furnished by further examples. We may, however, also consider briefly the following point: According to Sigwart, the knowledge of the existence of anything consists in the knowledge of the agreement of something represented in idea with, let us say, χ, since I do not clearly understand with what. What now is necessary in order to recognize the agreement of something with something else? Manifestly, the knowledge of everything which is required in order that this agreement should really exist. But this requires (1) that the one element exist, (2) that the other element exist, and (3) that between them there exist the relation of identity since what does not exist can be neither like something nor different from it. But the knowledge of the first element constitutes already in itself a knowledge of existence. Hence the knowledge of the two remaining elements is no longer necessary to the recognition of any existence, and Sigwart’s theory leads to a contradiction. (Cf. with what has been said here, Sigwart’s polemic against my Psychology, book ii. chap. vii. in his work; The Impersonalia, p. 50 seq., and Logic, vol. i. second edition, p. 89 seq. note, as well as Marty’s polemic against Sigwart in the articles: “Über Subjectlose Sätze” in the Vierteljahrsschrift für wissenschaftliche Philosophie, viii. i. seq.)[A]
[A] 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.