从康德的观点看数学

康德在理性的根源处探讨数学和物理学“是怎样可能的”,《纯粹理性枇判》的“先验感性论”和“先验逻辑”两部分,可以分别看作康德的“数学哲学”和“物理学哲学”。康德以“先验的位置论”分别给数学和物理学的可能性基础定位,数学属于验前的感性直观能力,物理学属于验前的知性判断能力。与“逻辑主义”、“形成主义”的数学观不同,康德的“数学哲学”认为数学的对象是验前的感性直观形式,数学概念是从纯粹直观中验前地“构成”的。

Mathematics in Kant's View

Kant discussed in the origin of reason about the question of "how could mathematics and physics be?". The sections of "Transcendental Aesthetic" and "Transcendental Logic" in the Critique of Pure Reason seem to be Kant's "mathematics philosophy" and "physics philosophy". Kant positioned the possibility basis of mathematics and physics by "transcendental position". This article listed the main arguments of Kant's "mathematics philosophy" and also compared Kant's view of mathematics with the concepts of mathematics in "logicism" and "formalism".