we have as Leibnitz’s remaining legacy to later logicians the conception of Characteristica Universalis and Ars Combinatoria, a universal denoting by symbols and a calculus working by substitutions and the like. The two positions that a subject contains all its predicates and that all non-contingent propositions—i.e. all propositions not concerned with the existence of individual facts ultimately analyse out into identities—obviously lend themselves to the design of this algebra of thought, though the mathematician in Leibnitz should have been aware that a significant equation is never an identity. Leibnitz, fresh from the battle of the calculus in the mathematical field, and with his conception of logic, at least in some of its aspects, as a generalized mathematic,[1] found a fruitful inspiration, harmonizing well with his own metaphysic, in Bacon’s alphabet of nature. He, too, was prepared to offer a new instrument. That the most important section, the list of forms of combination, was never achieved—this too was after the Baconian example while the mode of symbolization was crude with a = ab and the like—matters little. A new technique of manipulation—it is, of course, no more—had been evolved.
It may be said that among Leibnitz’s successors there is no Leibnitzian. The system as a whole is something too artificial to secure whole-hearted allegiance. Wolff’s formalism is the bastard outcome of the speculation of Leibnitz, and is related to it as remotely as Scholasticism is to Aristotle. Wolff found a sufficient reason for everything and embodied the results of his inquiries in systematic treatises, sometimes in the vernacular. He also, by a transparent petitio principii, brought the law of the sufficient reason under that of non-contradiction. Wolff and his numerous followers account for the charge of dogmatism against “the Leibnitzio-Wolffian school.” They are of importance in the history of logic for two reasons only: they affected strongly the German vocabulary of philosophy and they constituted the intellectual environment in which Kant grew to manhood.
A truer continuator of Leibnitz in the spirit was Herbart.
iii. Kant’s Logic.
Herbart’s admitted allegiance, however, was Kantian with the qualification, at a relatively advanced stage of his thinking, that it was “of the year 1828”—that is, after controversy had brought out implications of Kant’s teaching not wholly contemplated by Kant himself. The critical philosophy had indeed made it impossible to hark back to Leibnitz or any other master otherwise than with a difference.
Yet it is not a single and unambiguous logical movement that derives from Kant. Kant’s lesson was variously understood. Different moments in it were emphasized, with a large diversity of result. As interpreted it was acquiesced in or revolted from and revolt ranged from a desire for some modifications of detail or expression to the call for a radical transformation. Grounds for a variety of developments are to be found in the imperfect harmonization of the rationalistic heritage from the Wolffian tradition which still dominates Kant’s pure general logic with the manifest epistemological intention of his transcendental theory. Or again, within the latter in his admission of a duality of thought and “the given” in knowledge, which within knowledge was apparently irreducible, concurrently with hints as to the possibility, upon a wider view, of the sublation of their disparateness at least hypothetically and speculatively. The sense in which there must be a ground of the unity of the supersensible[2] while yet the transcendent use of Reason—i.e. its use beyond the limits of experience was denied theoretical validity—was not unnaturally regarded as obscure.
Kant’s treatment of technical logic was wholly traditional, and in itself is almost negligible. It is comprised[3] in an early essay on the mistaken subtlety of the syllogistic figures, and a late compilation by a pupil from the introductory matter and running annotations with which the master had enriched his Formal Logic. interleaved lecture-room copy of Meyer’s Compendium of 1752. Wolff’s general logic, “the best,” said Kant, “that we possess,” had been abridged by Baumgarten and the abridgment then subjected to commentation by Meyer. With this traditional body of doctrine Kant was, save for matters of minor detail, quite content. Logic was of necessity formal, dealing as it must with those rules without which no exercise of the understanding would be possible at all. Upon abstraction from all particular methods of thought these rules were to be discerned a priori or without dependence on experience by reflection solely upon the use of the understanding in general. The science of the form of thought abstracted in this way from its matter or content was regarded as of value both as propaedeutic and as canon. It was manifestly one of the disciplines in which a position of finality was attainable. Aristotle might be allowed, indeed, to have omitted no essential point of the understanding. What the moderns had achieved consisted in an advance in accuracy and methodical completeness. “Indeed, we do not require any new discoverers in logic,”[4] said the discoverer of a priori synthesis, “since it contains merely the form of thought.” Applied logic is merely psychology, and not properly to be called logic at all. The technical logic of Kant, then, justifies literally a movement among his successors in favour of a formal conception of logic with the law of contradiction and the doctrine of formal implication for its equipment. Unless the doctrine of Kant’s “transcendental logic” must be held to supply a point of view from which a logical development of quite another kind is inevitable, Kant’s mantle, so far as logic is concerned, must be regarded as having fallen upon the formal logicians.
Kant’s transcendental teaching is summarily as follows: “Transcendental” is his epithet for what is neither empirical—i.e. to be derived from experience—nor yet transcendent—i.e. applicable beyond the limits of experience, the mark of experience being the implication Definition of “Transcen-dental.” of sense or of something which thought contra-distinguishes from its own spontaneous activity as in some sense “the given.” Those features in our organized experience are to be regarded as transcendentally established which are the presuppositions of our having that experience at all. Since they are not empirical they must be structural and belong to “the mind”—i.e. the normal human intelligence, and to like intelligence so far as like. If we set aside such transcendental conditions as belong to sensibility or to the receptive phase of mind and are the presuppositions of juxtaposition of parts, the remainder are ascribable to spontaneity or understanding, to thought with its unifying, organizing or focussing function, and their elucidation is the problem of transcendental analytic. It is still logic, indeed, when we are occupied with the transcendent objects of the discursive faculty as it is employed beyond the limits of experience where it cannot validate its ideas. Such a logic, however, is a dialectic of illusion, perplexed by paralogisms and helpless in the face of antinomies. In transcendental analytic on the other hand we concern ourselves only with the transcendental “deduction” or vindication of the conditions of experience, and we have a logic of cognition in which we may establish our epistemological categories with complete validity. Categories are the forms according to which the combining unity of self-consciousness (synthetic unity of apperception) pluralizes itself through the various functions involved in the constitution of objectivity in different types of the one act of thought, viz. judgment. The clue to the discovery of transcendental conditions Kant finds in the existence of judgments, most manifest in mathematics and in the pure science of nature, which are certain, yet not trifling, necessary and yet not reducible to identities, synthetic therefore and a priori, and so accounted for neither by Locke nor by Leibnitz. “There lies a transcendental condition at the basis of every necessity.”
Kant’s mode of conceiving the activity of thought in the constitution of objects and of their connexion in experience
- ↑ Nouveaux essais, iv. 2 § 9, 17 § 4 (Gerhardt v. 351, 460).
- ↑ Critique of Judgment, Introd. § 2, ad. fin. (Werke, Berlin Academy edition, vol. v. p. 176, l. 10).
- ↑ Kant’s Introduction to Logic and his Essay on the Mistaken Subtlety of the Four Figures, trans. T. K. Abbott (1885).
- ↑ Loc. cit., p. 11.
