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212 ARTHUR O. LOVEJOY: forth this ground of the possibility of such propositions, show- ing that it can be nothing but the pure percept underlying the concept of the subject. Only in such a pure percept is it possible to connect a synthetic predicate with a concept a priori." Thus the theory of the reine Anschauung constitutes the last trench into which Kant retires to defend his antithesis of dogmatism and criticism. About this theory three things may be said, of which only the two last are indispensable to our present inquiry. First, the whole idea of a ' pure ' per- cept, which we are under no conditions to be allowed to think as a concept, and which gets some peculiar demon- strative efficacy from its perceptual character is a logical chimera that belongs with the other hybrid monsters of antiquity. But this is unimportant. Second, and what is- more to the point, the theory, though it were true, is, by Kant's own showing, not essential to the proof of the logical validity of the a priori judgments in question ; and it is therefore irrelevant to the issue. Wolff and Baumgarten had, in effect, declared that, when you have analysed your concepts to the uttermost and still find that two of them, not denned as possessing the same essence, coinhere indivulso- nexu, you have reached the ultimate point of verification ; beyond this de facto psychological necessity, this " internal mark of truth," it is both needless and impossible to go. 1 Now even if it be a fact that a reine Anschauung ' underlies *" our mathematical judgments, a knowledge of this fact is not necessary in order to establish the truth of those propositions- a priori (in so far as they are true a priori) ; nor does ignor- ance of the fact subtract anything from the evidence of their truth. The fact would be an interesting piece of psycho- logical information ; but the truth of the propositions, as propositions a priori, would still require to be tested by in- quiring whether, when the meaning of the concepts involved , as concepts, is fully understood, the contraries of the proposi- tions prove to be inconceivable. All of which is admirably A : illustrated by Kant's own procedure when, in the Kritik, he I 1 This must not be understood as implying that there is anything in common between the Wolffian theory of knowledge and the uncritical affirmation of anything of which one has " clear and distinct ideas, or a strong " emotion of conviction ". The prior analysis of concepts is pre- supposed, the careful framing of definitions, the clear discrimination of the several sorts of predicables, and the testing of attribute by the attempt to think the given definition with the given attribution negated. But the Wolffian logicians had rightly maintained that the touchstone in this final test can be nothing but the ultimate and inexplicable mental fact that the proposed negation is actually unthinkable.