基于数学实践进路的数学基础多元论辩护  

The Defense of Pluralism in Mathematical Foundation Based on the Approach to Mathematical Practice

作　　者：李娜[1] 叶发扬[1] LI Na;YE Fa-yang(School of Philosophy,Nankai University,Tianjin 300350,China)

机构地区：[1]南开大学哲学院,天津300350

出　　处：《科学技术哲学研究》2024年第4期22-28,共7页Studies in Philosophy of Science and Technology

基　　金：国家社会科学基金重点项目“基于哲学逻辑的集合论研究”(16AZD036);中央高校基本科研业务费专项资金资助项目(ZB21BZ0109)。

摘　　要：近年来,在数学基础的研究中,存在着集合论、范畴论和一价基础三大相互竞争的基础理论,并逐渐形成了数学基础的一元论与多元论之争。学界对相关哲学立场的辩护存在不同的进路,其中最重要的一条是数学实践进路。基于该进路,以作为数学实践事实之实践对象和实践方法为依据,“自然的”数学基础多元论获得了成功辩护。但该辩护并不充分,因其面临数学实践的可靠性质疑和论据的不全面性问题。鉴此,通过表明数学实践的可靠性,并在“自然的数学基础”意义之基础上,从“数学基础”层面提供论据补充,才能真正实现对数学基础多元论的充分辩护。In recent years,there have been three competing foundational theories in the research of mathematical foundations:set theory,category theory,and univalent foundations.This has sparked a debate between monism and pluralism in the foundation of mathematics.Various approaches within the academic community have been taken to defend different philosophical positions,with the most significant being the focus on mathematical practice.On this approach,the pluralism of“natural”mathematical foundation has been successfully defended,based on practical objects and methods as mathematical practice facts.However,the defense is inadequate due to the concerns about the reliability of mathematical practice and the incompleteness of arguments.In view of this,by demonstrating the reliability of mathematical practice and providing additional evidence about“mathematical foundation”,based on the meaning of“natural mathematical foundation”,we can achieve a full defense of the pluralism about mathematical foundation.

关 键 词：数学基础 数学实践 集合论 范畴论 一价基础 

分 类 号：N02[自然科学总论—科学技术哲学]