前期维特根斯坦对数学中形而上学预设的批判  

Early Wittgenstein’s Criticism on Metaphysical Presupposition in Mathematics

作　　者：朱文瑞 Zhu Wenrui(School of Marxism,Anhui University of Finance and Economics,Bengbu 233030,China)

机构地区：[1]安徽财经大学马克思主义学院,安徽蚌埠233030

出　　处：《洛阳师范学院学报》2023年第9期6-10,共5页Journal of Luoyang Normal University

基　　金：教育部人文社会科学研究规划基金项目(21YJA720005)。

摘　　要：前期维特根斯坦致力于祛除数学哲学中的形而上学预设。在数学对象的实在性方面,他主张数学对象并不存在,实在性唯当在科学中谈论才有意义;在数学命题的真理性方面,他则主张数学命题不表达思想,更不关乎命题真假问题,真理性概念也只涉及科学命题。前期维特根斯坦从运算方向上给出了数的形式定义与等式的形式证明。这类定义与证明消解了逻辑主义的发问方式,使得逻辑主义框架下诸如“数学对象存在吗”“算术命题可以证明吗”这类问题丧失了意义。Wittgenstein in the early stage was committed to dissolving the metaphysical presupposition in the philosophy of mathematics.In terms of the reality of mathematical objects,he advocated that mathematical objects did not exist,and that reality was meaningful only when it was talked about in science;in terms of the truth of mathematical propositions,he advocated that mathematical propositions neither expressed any thought nor involved truth or falsity,and the concept of truth only involves scientific propositions.Wittgenstein gave the formal definition of the number and the formal proof of the equation from the operational direction.This definition and proof dispelled the questions such as“Is there any mathematical object?”and“Can arithmetic propositions be proved?”,and these questions lose their meaning under the framework of logicism.

关 键 词：维特根斯坦 数学对象 数学命题 运算 形而上学 

分 类 号：B085[哲学宗教—哲学理论]