论希尔伯特公理化方法的哲学意义  

The Dispute of the Foundation of Geometry and its Solution:Examining the Philosophical Significance of Hilbert’s Axiomatic Method

作　　者：钱立卿[1] QIAN Liqing

机构地区：[1]上海社会科学院哲学研究所

出　　处：《哲学分析》2022年第4期152-163,199,共13页Philosophical Analysis

基　　金：上海市哲学社会科学规划一般课题“当代数学哲学的现象学诠释”(项目编号:2018BZX011)。

摘　　要：科学理论中隐藏的哲学疑难未必能在思辨性的争论中解决,许多争执需要在后续的发展过程中逐渐显示其意义和效果。弗雷格与希尔伯特关于几何学基础的论争是这种争辩发展模式的一个实例。尽管希尔伯特的公理化方案与形式主义真理论观点无法为弗雷格同意,但相比传统的几何观念,公理化几何具有独特贡献,其典型表现之一就是揭示了几何中的对偶关系的实质。公理化思想最终通向了关于此论争的模型论解决方案,这个结局兼有着数学的外观和哲学的内核。The philosophical problems hidden in scientific theories may not be resolved in speculative debates,and many disputes manifest their significance and effects diachronically in the subsequent development process.The debate between Frege and Hilbert on the foundation of geometry is an example of such debates.Although Hilbert’s axiomatic program and formalist theory of truth are not accepted by Frege,axiomatic geometry has its unique contribution compared with traditional geometric concepts.One of its typical manifestations is to reveal the essence of duality in geometry.The axiomatic thought finally leads to the model theory solution to this dispute,which has both the appearance of mathematics and the essence of philosophy.

关 键 词：公理化 对偶性 几何学 现象学 

分 类 号：B15[哲学宗教—世界哲学]