spatial world must be. Nor is this mode of statement limited to mathematics. Quite generally Kant says in the first edition of the Critique: "It is a fact that we are in possession of different kinds of synthetical knowledge a priori, as shown by the principles of the understanding which anticipate experience."[1] And "to understand the conditions which render every kind of them possible"[2] is declared to be, on the same unimpeachable authority, the task of the critical philosopher. With such passages before us, it is unnecessary, though it would be legitimate, to appeal to the wealth of confirmation to be found in the Prolegomena and the second edition of the Critique, of which, however, use has already been made in our exposition of the Kantian problem.
There is, however, an important truth which we owe to the school of commentators whose main contention we have just rejected. While they have failed to show that the object of the Critique is to prove the validity of mathematics and the other rational sciences, they have made clear that these are not, on the other hand, the proof of the Critique. That mathematics and physics are the "premisses" of Kant is a common statement. Yet it is utterly misleading. It implies that Kant weaves them into an argument from which a new conclusion is drawn, after the analogy of a syllogism. But they are not in any sense materials of proof. They are objects of investigation. The problem is not, What can be inferred from a priori synthetic judgments? but, What are the conditions on which they themselves depend? It is a matter of explanation alone.
Yet the explanation of a fact may under certain conditions become the proof or justification of that fact. If you have not seen the flash of light which accompanies the detonation of a cannon, I may by the help of those acoustical, optical, and physiological principles which explain these phenomena, prove to you that it really existed, if not that it was actually perceived by me. It is in the presence of doubters who question a fact, but must accept principles from which that
