The Foundational Role of Intuition in Kant's Philosophy of Mathematics

The role of intuition in Kant's philosophy of mathematics has often been misunderstood. The present essay aims to remedy this misapprehension by offering an in-depth analysis of the most crucial passages of the Critique of Pure Reason for Kant's philosophy of mathematics. First, I argue that the role Kant ascribes to intuition in mathematical practice should not be interpreted as a remedy for the defects of Aristotelian logic, as has been argued by several authors. Instead, it should be understood as a necessary condition for the objective validity of mathematics. Second, I argue that the often-neglected `Axioms of Intuition' should be given more attention in Kant scholarship since they constitute Kant's proof that mathematics indeed has objective validity. In order to explain the `Axioms of Intuition,' a detour is taken through the so- called `subjective deduction' in which Kant unravels his theory of the threefold synthesis.