论希尔伯特几何公理的综合性质  

On the Syntheticity of Hilbert’s Axioms of Geometry

作　　者：周浩 ZHOU Hao(School of Philosophy,Universite Paris 1 Panthéon-Sorbonne,Paris 75005,France,Paris 75005,France)

机构地区：[1]巴黎第一大学哲学院,巴黎75025

出　　处：《科学技术哲学研究》2021年第3期1-7,共7页Studies in Philosophy of Science and Technology

基　　金：法国高等教育、科研与创新部AMX研究基金项目“论先天综合:数学、科学与哲学”。

摘　　要：受时代局限,康德基于欧氏几何宣称几何命题的先天综合性质。欧氏几何的现代数学表达为希尔伯特几何公理系统,并且后者可以方便地演化出非欧几何。于是,论证希尔伯特几何公理的先天综合性质可以在现代数学的背景中为一般几何命题的先天综合性质提供支持。希尔伯特几何公理的先天性不言而喻。继反驳石里克对希尔伯特几何系统的公理定义所作的分析性论证之后,对希尔伯特几何公理的综合性质的正面论证在于,阐明蕴涵定义超出分析性程序的方法论本质,揭示希尔伯特几何公理对业已被证明为先天综合知识的算术的双重依赖,并利用多种几何并存的局面展示享有唯一性地位的算术系统所不能彰显的先天综合知识的独特模态。Confined to his epoch,Kant affirmed the synthetic apriority of geometric propositions on the basis of Euclidean geometry.Euclidean geometry is expressed in modern mathematics as Hilbert’s system of geometric axioms and the latter can easily evolve non-Euclidean geometry.Thus,the demonstration of the synthetic apriority of Hilbert’s axioms of geometry can in the context of modern mathematics support that of general geometric propositions.The apriority of Hilbert’s axioms of geometry is self-evident.After the refutation of Schlick’s arguments for the analyticity of the axiomatic definition of Hilbert’s geometric system,the arguments for the syntheticity consist in expounding the methodological nature of implicit definition which is beyond analytic procedures,revealing the dual dependence of Hilbert’s geometric axioms on arithmetic whose synthetic apriority has been proved,and utilizing the coexistence of multiple geometries to show the special modality of the synthetic a priori that cannot be manifested by the arithmetic system which is apodictic.

关 键 词：先天综合 希尔伯特几何公理 蕴涵定义 非欧几何 

分 类 号：N02[自然科学总论—科学技术哲学]