The whole matter is, however, still further complicated by the distinction, which we have already noted, between real and ideal possibility. Are the given synthetic _a priori_ judgments valid? That is one question. Can the Critical philosophy discover, completely enumerate, and prove in a manner never before done, all the possible synthetic _a priori_ principles? That is a very different problem, and when raised brings us to the further discussion of Kant’s transcendental method. The question at issue is no longer merely whether or not certain given judgments are valid, and how, if valid, they are to be accounted for. The question is now that of discovering and of proving principles which have not been established by any of the special sciences. This shifting of the problem is concealed from Kant himself by his omission to distinguish between the undemonstrated axioms of the mathematical sciences and their derivative theorems, between the principles employed by the physicist without enquiry into their validity and the special laws based upon empirical evidence. As regards the mathematical axioms, the problem is fairly simple. As we shall see later, in the _Aesthetic_, they do not require a deduction in the strict transcendental sense. They really fall outside the application of the transcendental method. They require only an “exposition.” But in regard to the fundamental principles of natural science we are presented with the problem of discovery as well as of proof. Unlike the axioms of the mathematician, they are frequently left unformulated. And many postulates, such as that there is a _lex continui in natura_, are current in general thought, and claim equal validity with the causal principle. Kant has thus to face the question whether in addition to those principles employed more or less explicitly by the scientist, others, such as might go to form an immanent metaphysics of nature, may not also be possible. B. (_a_)[185] =Psychological and logical possibility.=--Both have to be recognised and accounted for. Let us consider each in order.