不可分的直观——康德数学哲学浅析

在20世纪关于数学基础的争论当中,直觉主义流派往往将康德认作是其理论的鼻祖。然而,回到解析几何与微积分诞生不久的18世纪,康德所提出的“纯粹数学是如何成为可能的问题”,并不容易被已经惯用这两种数学工具的现代人所理解。本文拟通过对“这个问题是如何提出的、为了解决这个问题康德所提出的猜想、康德怎样证明这个猜想”三个方面的分析,来理解康德所提出的这个问题的含义。从中可以看到,“不可分的直观”成为康德数学哲学区别于其他数学哲学流派的核心概念。

The Indivisible Intuition——An Elementary Analysis on Kant's Philosophy of Mathematics

In the dispute about the foundation of mathematics in the 20th century, philosophers approving Intuitionalism usually take Kant for the originator of their theory. However, back to the 18th century when analytic geometry and calculus had just been invented, the question " How is the pure mathematics possible" , which was presented by Kant, is not easy to be understood by the modern people who have been accustomed to using these mathematical techniques. How was the question presented? What is the hypothesis that is put forward by Kant in order to solve this question? How does Kant prove this hypothesis? This paper intends to understand this question by answering these three questions. It can be found that the " indivisible intuition" is the core concept which makes Kant's philosophy of mathematics rather different from others'.