The problem of reconciling the necessity of arithmetic with its applicability illustrates of the more general problem of explaining the applicability of the propositions of pure reason to experience. For Kant, it becomes urgent only in relation to propositions which, although in some sense the products of pure reason, nevertheless have a subject matter: the danger is that we conceive of this subject matter as consisting of objects existing in a realm wholly isolated from the world of experience, and it is then apt to seem puzzling how features of this abstract realm could possibly be relevant to reasoning about the empirical one. The key to the way out of this difficulty that Kant recommended is for us to contrive that those concepts and principles which we adopt a priori be used for viewing objects from two different points of view — on the one hand, in connection with experience, as objects of the senses and of the understanding, and on the other hand, using isolated reason that strives to transcend all limits of experience.
Keywords: Kant, arithmetic, pure reason, experience, analytic judgement, objects of the senses