悖论与数学基础问题(Ⅱ)

Antinomies and the Foundational Problem of Mathematics (Ⅱ)

中文摘要:

      在本文中,主要讨论悖论定义问题,此外,还将对‘悖论的起源’、‘数学三次危机’和‘Zermelo解决悖论的方案’等内容作简要的综述和评论。至于Russell对悖论的解决方案与悖论成因等内容的讨论将在本文的续篇中给出。

英文摘要:

      This expository article centers on discussing the question of how to define more comprehensively the concept of antinomy (or paradox) in mathematical science. Also included in the present discourse are expositions about the origin of antinomies, three mathematical crises and Zermelo 's program for resolving antinomies, etc.