摘要
在有关模态的哲学问题中,数学真理常被哲学家们视作是形而上学必然的。然而由于弗雷格的逻辑还原并不成功,因此这实际上是缺少充分解释的。这篇论文将首先澄清形而上学必然性的准确含义,然后分别总结近年来出现的基于逻辑主义策略的、集合论基础主义策略的、数学实践承诺策略的三种不同的辩护基础数学真理的形而上学必然性的方案,最后指出三种辩护方案均需要不同程度的诉诸某种本质主义纲领来回避各自的困难,然而这并非是没有代价的。因此,如何完整的论证基础数学真理的形而上学必然性仍旧是一个亟待解决的问题。
In the debate concerning modality, pure mathematical truths are always understood as metaphysically necessary. But it lacks of enough explanation because of Frege’s failure. This article first clarifies the concept of metaphysical necessity, and then analyzes three arguments based on logicism, set-theoretic foundationalism, and mathematical practice commitment, respectively. Finally, the author attempts to show that both of arguments have to be completed by some versions of essentialism at the expense of various difficulties. Hence, it’s still an open question to prove the metaphysical necessity for pure mathematical truths completely.
作者
陈培阳
CHEN Pei-yang(School of Humanities,University of Chinese Academy of Sciences,Beijing 100049,China)
出处
《自然辩证法研究》
CSSCI
北大核心
2022年第4期115-121,共7页
Studies in Dialectics of Nature
关键词
形而上学必然性
逻辑主义
集合论基础主义
数学实践
本质主义
metaphysical necessity
logicism
set-theoretic foundationalism
mathematical practice
essentialism
