数学原理

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作品 · 分析哲学

数学原理

1910 · 作者：伯特兰·罗素 & 阿尔弗雷德·诺思·怀特海

从逻辑推导出数学——由此可推出1+1=2的命题，直到第一卷第379页的*54.43才出现。

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简介

Russell and Whitehead worked on the book for about a decade; its three volumes appeared in 1910, 1912 and 1913, and the authors had to contribute to the printing costs. The aim was logicism: to derive mathematics from a small number of logical axioms and definitions. To avoid the paradox Russell had found in Frege’s system, the book uses a theory of types, which arranges entities and classes in levels, supplemented by the disputed axiom of reducibility. A planned fourth volume on geometry was never written. Its notation, adapted from Peano, shaped modern logic, and Gödel formulated his incompleteness theorems of 1931 for “Principia Mathematica and related systems”.