论维特根斯坦对哥德尔定理的评析

Remark on Wittgenstein's Comments on Gdel's Theorem

数学哲学的基础问题一直是维特根斯坦所关注的核心领域之一。20世纪30年代哥德尔提出的第一不完备性定理彻底地动摇了数学的逻辑主义、直觉主义和形式主义的基础。在这种背景下,中后期的维特根斯坦对哥德尔第一不完备定理进行了评论,但他的评论却受到了人们广泛的质疑和批评。很大一部分的原因是由于人们误解或误读了维特根斯坦的观点。基于此,在维特根斯坦数学哲学的语境下来分析和理解他的这些评论,并最终阐明其理论特色。

The basic problem of the philosophy of mathematics has long been of concern to Wittgenstein. Godel＇ s proposed First Incompleteness Theorem that has thoroughly shaken mathematics of logicism, intuitionism and formalism at 1930s. Wittgenstein commented Godel＇ s First Incompleteness Theorem in his mid-to-late period, but his comments were widely questioned and criticized. This is mainly because people misunderstood or misread Wittgenstein＇ s view. This paper will analyze and interpret his comments in the context of Wittgenstein＇ s philosophy of mathematics, and finally clarify his theoretical features.