This paper discusses the concept of heterogeneity and the problem of application in the Schematism of pure concepts, the first chapter of the Analytic of principles in Kant & PRIME;s Critique of Pure Reason. It puts forward a distinction between the thesis of heterogeneity as metaphysical independence between concepts and intuitions, on the one hand, and heterogeneity as lack of homogeneity in the components of judgment, on the other. The paper claims that the latter, not the former, generates the problem of the application of categories to appearances. It also claims that, although the concept of application is present in the problem of the objective validity of the categories in the Transcendental deduction, application only appears as a problem in the Schematism chapter. On these grounds, and in contrast to those continuist readings which take the Schematism chapter to be a part of the problematic raised in the Deduction, this essay proposes that Schematism represents a new problem in Kant & PRIME;s program of a critique of pure reason. Although akin to Mario Caimi & PRIME;s "discontinuist" reading of Schematism (2015 and 2017), my proposal differs from it in one vital point, namely, on how to understand the distinction between transcendental schemata and schemata of empirical concepts. According to my proposal, heterogeneity as lack of homogeneity arises only for the application of categories to appearances, but not for empirical and mathematical concepts, so the role of schemata for these is not as a mediator between concepts and their objects. Finally, the paper argues for a central, exemplary role for mathematical schemata in the solution to the application problem. Kant takes the idea of schemata as ruled processes from his view of mathematical cognition, and it is precisely in this role that transcendental schemata are meant to solve the application problem.
