The role of Anschauung in Kant’s conception of geometry

Abstract

Far from being outdated, Kant’s philosophy of mathematics offers valuable insights to modern scholarship. This paper focuses on Kant’s notion of Anschauung (commonly translated as intuition) within geometry. Contrary to a widely held view, it will be shown that appealing to Kantian intuition is, in some cases, still necessary. After reviewing past and recent objections to Kant’s arguments, a new interpretation of A 716-717/B 744-745 of the first Critique (CPR) will be proposed. The role that Kant assigns to intuition in this passage, which I term 'revelatory,' remains indispensable despite modern advances in mathematics and logic. Notably, almost all English translations of the CPR, as well as the official translations in French and Greek, have disregarded this function of intuition. This paper aims to show why these interpretations are inconsistent with Kant’s philosophy of mathematics and to argue that the revelatory function of intuition withstands objections to the classical reading.