by it. Even mathematics is not to be taken for granted; its validity must be proved on grounds that are independent of it. That mathematical propositions are more than figments of the brain, that they are true of real objects, is, says Riehl, no assumption, but the demonstration of the Critique.
This controversy, like so many others, can be settled only by a study of Kant's own utterances in the light of his philosophical development. But one point in the argument just given may be immediately disposed of. Though the method of the Critique is synthetic, that is, descends from conditions to facts, while the method of the Prolegomena is analytic, that is, ascends from facts to conditions, the minutest examination and comparison fails to discover any difference in their attitude towards the question now under consideration.[1] The presupposition of both is that there are a priori synthetic judgments which are objectively valid. And this corresponds with the history of the psychological development of the critical problem in Kant, while the contrary assumption that the Critique was to prove the validity of mathematical and other a priori synthetical judgments, is absolutely irreconcilable with that history. Such knowledge, apart from metaphysics, was never problematic to Kant, though it was long a problem. And the nature of the problem is already clearly described in that letter to Herz of the 21st of February, 1772. We have through pure reason a knowledge of objects; yet objects are independent of us; whence, then, the correspondence between the deliverances of reason and objective facts? Not a proof of the correspondence, which it never occurred to this scion of rationalism to doubt, but an explanation of it, of the "mystery" and "miracle" of knowledge, which ordinarily depends upon experience of objects, yet originating without such experience. Kant did not originally speak of proving the validity of mathematics; his language is to "explain" or "render intelligible" the fact of such a priori knowledge. For it surely is a puzzle that the mind should be able to say in advance what the laws of the
- ↑ So Erdmann, Kant's Kriticismus in der ersten und in der zweiten Auflage der Kritik d. r. V., 172, 186, and similarly in his introduction to Kant's Prolegomena, XXX.
