The Transcendental Structure in the First Works of Jean Cavaillès

Abstract

This paper aims to interpret Jean Cavailles' philosophical position proposed in his early works as a reconstruction of Kant's epistemology. Kant's mathematical epistemology consists of three principal components: (a) the pure concept of the understanding, (b) intellectual and sensible schemata produced by the imagination, and (c) sensible intuition. First, as a result of Godel's incompleteness theorems, Cavailles extends (c) to cover intellectual intuition. Then, under the influence of Hilbert's conceptions of sign, he replaces (b) with the concept of sign as intellectual-sensible mixture, and (a) with certain mathematical concept. Finally, Cavailles uses this transcendental structure to propose a new idea about the problem of the foundations of mathematics.