- The Philosophy of Science Society, Japan
- 科学哲学 (ISSN:02893428)
- vol.43, no.2, pp.2_67-2_79, 2010 (Released:2011-04-01)
This paper aims to interpret Jean Cavaillès' 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 Gödel'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, Cavaillès uses this transcendental structure to propose a new idea about the problem of the foundations of mathematics.