弗雷格的《算术基本规律》

Frege's Grundgesetze der Arithmetik

弗雷格被看作是分析哲学的奠基人和数理逻辑的创始人,然而,他的毕生工作都致力于建立一种被称为逻辑主义的数学哲学。他在《算术基本规律》一书中给出了执行逻辑主义方案的形式系统。然而,由于罗素悖论的发现,很少有人关注弗雷格的《算术基本规律》。本文将主要介绍《算术基本规律》一书,包括其符号系统的说明,公理、规则、定义和定理的说明,罗素发现的悖论以及弗雷格的补救措施。

Frege is regarded as the founder of mathematical logic and the father of analyticphilosophy,but most of his career is devoted to a kind of philosophy of mathematics,Logicism.He presented his logical system in his book Grundgesetze der Arithmetik.Dueto Russell’s paradox,only a few people focus on the details of Grundgesetze der Arithmetik.This paper mainly introduces to Chinese-speaking world,including the explanationof symbols,axioms,rules,definitions,important theorems and Frege’s response toRussell’s paradox.