数学初始公理严格性的实在论辩护  

The Realism Defence of the Strictness of Initial Axioms of Mathematics

作　　者：刘伟伟[1] 刘晓红 LIU Weiwei;LIU Xiaohong(School of Philosophy,Shanxi University,Taiyuan,Shanxi,030006)

机构地区：[1]山西大学哲学学院,山西太原030006

出　　处：《自然辩证法通讯》2024年第8期25-33,共9页Journal of Dialectics of Nature

基　　金：教育部青年基金项目“诠释学视域下数学证明的构造机理研究”(项目编号:22YJC720008)。

摘　　要：基于实在论的立场,数学概念所指称数学对象的实在性构成了数学初始公理严格性的前提和基础;数学初始公理的语义空间中蕴含着作为认识主体的数学家们对于具有实在性的数学对象之可能世界的一种真理性的认识论选择;可能世界语义学能够在方法论层面上为数学初始公理的严格性论证提供一种实在论的语义分析支撑;数学初始公理的生成是一种数学家们对于具有实在性的数学对象进行“理解-解释(心理)-解释(文本)”这一整体思维机制的“诠释学”方法论建构过程;数学公理系统所具有的以实在性的数学初始公理为起点的“诠释学循环”之方法论建构特征,不仅体现了数学公理系统在认识论层面上的稳固性,而且还使得数学初始公理的严格性得到了进一步的彰显与确证。Based on the standpoint of realism, the reality of mathematical objects referred to by mathematical concepts constitutes the premise and foundation of the strictness of initial axioms of mathematics;The semantic space of initial axioms of mathematics contains a epistemological choice with truthfulness of mathematicians as the knowing subject regarding the possible world of mathematical objects with reality;Possible world semantics can provide a semantic analysis support on the basis of realism for the strictness argument of initial axiom of mathematics at the methodological level;The generation of initial axioms of mathematics is a process of methodology construction of hermeneutics, in which mathematicians engage in an overall thinking mechanism of “understanding-explanation(psychology)-explanation(text)” about mathematical objects with reality;The “hermeneutic cycle” methodological construction feature of mathematical axiom system, which starts from initial axioms of mathematics with reality, not only reflects the stability of mathematical axiom system at the epistemological level, but also further demonstrates and confirms the strictness of mathematical initial axiom.

关 键 词：数学初始公理 实在论 严格性 可能世界语义学 诠释学 

分 类 号：O1-0[理学—数学] B025.7[理学—基础数学]