从实用主义看反推数学  

A Study of Reverse Mathematics from the Perspective of Pragmatism

作　　者：康孝军[1] KANG Xiaojun(School of Philosophy and Sociology,Jilin University,Changchun,Jilin,130012)

机构地区：[1]吉林大学哲学社会学院,吉林长春130012

出　　处：《自然辩证法通讯》2023年第3期46-54,共9页Journal of Dialectics of Nature

基　　金：国家社会科学基金青年项目“反推数学的哲学基础研究”(项目编号:15CZX045)。

摘　　要：反推数学是从定理“反推”公理,每一位数学工作者都可利用这一新方法来开启新研究。追本溯源,反推数学是希尔伯特纲领的一种部分实现。这一相对实现除了延续了希尔伯特纲领的可靠性证明初衷外,无疑也继承了工具主义这一特征,是从实用角度来寻找数学真理。本文将尝试从实用主义哲学的视角出发,进一步探讨反推数学的哲学价值。具体而言,将从以下两方面来进行探讨:首先,结合数学史来论证数学自身的实用性;其次,在说明数学的可修正性之后,基于反推数学纲领,尝试探讨一种实用主义的数学真理观。该真理观以公理化系统为基础,是一种相对的、可修正的、可操作的实用主义真理观。Reverse mathematics is a program that seeks the axioms from the theorems and every mathematician can use this new method to start new researches.Historically,reverse mathematics was a partial realization of Hilbert’s Program,which not only continues the original intention of the reliability proof of Hilbert’s program,but also inherits undoubtedly the characteristics of instrumentalism,that is,to find the mathematical truth from a practical perspective.This paper will try to further explore the philosophical value of reverse mathematics from the perspective of pragmatic philosophy.Specifically,the discussion will be carried out from the following two aspects:firstly,the practicability of mathematics itself will be demonstrated from the perspective of the history of mathematics;and secondly,after explaining the revisability of mathematics,a pragmatistic view of the mathematical truth will be explored tentatively based on reverse mathematics.This view of truth is based on the axiom system and it is a relative,revisable,operable and pragmatistic view of truth.

关 键 词：实用主义 反推数学 希尔伯特纲领 数学真理 可修正性 

分 类 号：N0[自然科学总论—科学技术哲学] O1[理学—数学]