康德的先验感性论对数学的奠基意义

The Foundational Significance for Mathematics in Kant's Transcendental Aesthetics

对于数学来说,康德在《纯粹理性批判》的"先验感性论"部分对时空观念进行先验研究的意义在于,此框架不仅可以为现实的数学成就提供一种哲学辩护,而且还确立了某种主体性的认知结构对于数学结构的奠基关系。康德之后的一些哲学家对其数学哲学的批评某种程度上来源于对感性论与数学关系的误解,但康德本人也有一定责任。先验哲学可以从认知主体的角度为数学的实际形态提供某种必要性的解释,这条进路直至今日仍具有生命力。

Kant's philosophical foundations for mathematics and the relationship between philosophy and mathematics must be critically analyzed in the context of his first part of Critique of Pure Reason,which includes the concepts of space and time as well as aesthetic features. The misunderstandings on Kant amongst the later philosophers are mainly caused by the misreading on his aesthetics which is not sufficiently illustrated. Essentially speaking, a genuine and transcendental philosophy of mathematics is capable of supporting a necessary explanation for cognitive subject, and it still works today.