Kant’s Argument that Mathematics is the Science of Magnitude: Comments on Daniel Sutherland’s Kant’s Mathematical World

Abstract

The main claims of Kant’s Mathematical World are that for Kant mathematics is a science of magnitudes, the world of experience is a world of magnitudes, and there is an essential role for intuition in representing magnitudes. This paper critically examines the argument for these main claims. It articulates an eight-step “Master Argument” that connects magnitude to mathematics through a series of intermediary concepts. Some of these steps are left unclear in Kant’s Mathematical World , and I argue that the book’s silence on syntheticity and the role of intuition in proof is a partial cause for this unclarity.