KANT'S ANTITHESIS OF DOGMATISM AND CRITICISM. 213 undertakes to prove that Space and Time are pure percepts underlying the concepts of mathematics. He does it by showing that in mathematical judgments the predicates are " necessarily and universally " connected with the subjects a priori, and yet are not discoverable by a mere analysis of the definitions of the subjects. Geometry, for example, " is a science which determines the properties of Space synthetically and yet a priori. What, then, must the idea of Space be, in order that such a knowledge of it should be possible ? It must, primarily, be a perception ; for out of a mere concept no propositions can be drawn which go beyond the concept itself l as do the propositions of geometry. But this percep-i tion must be found in us a priori, and hence, must be a pure] non-empirical perception. For geometrical propositions are ' all apodictic, that is, they involve the consciousness of their! own necessity ; and such propositions cannot be empirical " (second ed., p. 41). Evidently, however, since the sup- posed fact that Space is a reine Anschauung is inferred from the fact that geometrical theorems are necessary a priori, the necessity and apriority of those theorems cannot in turn depend upon a proof that Space is a reine Anscliaunng. Kant here, in a word, not only accepts the logical method of the ' dogmatists,' but even uses it to establish that principle which, so far as mathematical reasonings are concerned, is in the same sentence supposed to show the illegitimacy of their logical method. His own language exhibits better than any commentary how irrelevant is the doctrine of the pure per- cepts to the epistemological questions concerning the criteria of a priori knowledge, which are the only questions at issue ! between himself and the AVolmans. And now, in the third place, the theory that judgments a priori presuppose a pure percept, refers only to mathematical judgments ; and it there- fore does not affect Kant's admission, already noted, that there may be valid a priori judgments of which the predicates are (like those in mathematics) attributa rationata, but which being sufficiently explained by the principle of contradic- tion do not require the mediation of any such pure percept. Only one point more needs to be touched upon. It may be urged, in Kant's behalf, that he at least is distinguished from his predecessors and is more ' critical ' than they in that j he limits the scope even of our valid a priori judgments to " objects of possible experience," and professes no knowledge I of the transcendent. Upon this much might be said, if' 1 Note again that this is inconsistent with the admissions which Kant makes in the Reply to Eberhard. 15
