弗雷格与希尔伯特的几何学基础之争——兼论胡塞尔对几何学起源的分析  

The Debate on the Foundation of Geometry Between Frege and Hilbert:With a Discussion on Husserl's Analysis of the Origin of Geometry

作　　者：钱立卿[1] 

机构地区：[1]上海社会科学院哲学所

出　　处：《世界哲学》2015年第2期137-145,161,共9页World Philosophy

摘　　要：在读到希尔伯特的《几何基础》第一版以后,弗雷格与希尔伯特展开了几轮通信,表达了自己对公理化方法的三项质疑。希尔伯特在回信中解释了自己的立场,并强调了公理化方法的全新视角以及它与19世纪数学哲学的根本差异。与此同时,胡塞尔也在发展出现象学的过程中获得了系统的数学哲学观念,这种思想最终表现在《逻辑研究》第一卷及随后的著作里。胡塞尔对几何学的哲学基础和公理化方法的看法虽然总体上倾向于希尔伯特,但亦批判其对形式的片面强调。本文首先考察弗雷格与希尔伯特的争论,随后从现象学角度回顾这场争论,探讨公理化思想的哲学意义。Frege questioned the program of axiomatization on three related points right after the first publication of Hilbert's The Foundations of Geometry,Hilbert defended his standpoints,stressing the new perspectives of his program and its superiority to the views before him.Meanwhile,Husserl developed a systematic doctrine of the philosophical foundations of mathematics,whose basic points were closer to Hilbert's.Yet Husserl recognized the weakness of the philosophical concerns on mathematical formalization,which was revealed and attacked by Frege.A phenomenological reflection on Frege-Hilbert debate and the origin of modern geometry may help us to get better understanding of the essence of axiomatization.

关 键 词：几何学 公理化 流形论 弗雷格 希尔伯特 

分 类 号：B81-051[哲学宗教—逻辑学]