Kant’s denial that psychology is a properly so-called natural science, owing to the lack of application of mathematics to inner sense, has garnered a great deal of attention from scholars. Although the interpretations of this claim are diverse, commentators by and large fail to ground their views on an account of Kant’s conception of applied mathematics. In this article, I develop such an account, according to which the application of mathematics to a natural science requires both a mathematical representation and (...) a metaphysical validation for the positive use of this representation to achieve a priori knowledge about nature. The second condition—that of metaphysical validation—has been overlooked in the literature. I show that psychology’s falling short of natural scientific propriety consists not in our lacking sufficient mathematical tools for the representation of inner states, according to Kant. After all, we can represent the mere temporality of inner states with the line and their intensities with numbers. Rather, the problem is that metaphysics does not validate the further use of such mathematical entities for the achievement of a priori knowledge about inner phenomena. (shrink)

Scholars working on Kant’s Anticipations of Perception generally attribute to him an argument that invalidly infers that objects have degrees of intensive magnitude from the premise that sensations do. I argue that this rests on an incorrect disambiguation of Kant’s use of Empfindung as referring to the mental states that are our sensings, rather than the objects that are thereby sensed. Kant’s real argument runs as follows. The difference between a representation of an empty region of space and/or time and (...) a representation of that same region as occupied by an object entails that, in addition to their extensive magnitude, objects must be represented as having a matter variable in intensive magnitude. Since it is the presence of sensation in a cognition that marks the difference between representing only the extensive magnitude of the object and the object as a whole, it is sensation that represents its intensive magnitude. (shrink)