Herman Weyl's intuitionistic mathematics
Herman Weyl's intuitionistic mathematics
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赫尔曼·韦尔的直觉数学
DOI：
10.2307/421038
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
D. Dalen
中科院分区：
文献类型：
--
作者：
D. Dalen
众所周知，赫尔曼·韦尔曾一度与布劳威尔一起追求根据直觉主义原理对数学进行修订。然而，文献中几乎没有阐明韦尔的角色，特别是布劳威尔对韦尔效忠直觉主义事业的反应。这个简短的插曲无疑提出了许多问题：是什么让韦尔放弃了他自己在《连续论》中阐明的计划，韦尔如何对布劳威尔的新直觉主义如此了解，韦尔的直觉主义与布劳威尔的直觉主义在哪些方面不同，布劳威尔如何看待韦尔的观点，……？对于其中一些问题，至少可以根据一些现有的信件和注释提出部分答案。本文将主要集中讨论韦尔职业生涯中直觉主义事件的历史问题。 1920 年，韦尔发表了轰动一时的论文《论数学的新基础危机》，轰动一时地卷入了基础性争论。 1918 年，他凭借专着《连续统》[18]，在数学基础领域一举成名。除了连续统的技术逻辑数学构造之外，它还包含对基于任意（因此也是命令式戴德金割断）的连续统传统构造的缺点的相当广泛的讨论。
It is common knowledge that for a short while Hermann Weyl joined Brouwer in his pursuit of a revision of mathematics according to intuitionistic principles. There is, however, little in the literature that sheds light on Weyl's role and in particular on Brouwer's reaction to Weyl's allegiance to the cause of intuitionism. This short episode certainly raises a number of questions: what made Weyl give up his own program, spelled out in "Das Kontinuum", how did Weyl come to be so well-informed about Brouwer's new intuitionism, in what respect did Weyl's intuitionism differ from Brouwer's intuitionism, what did Brouwer think of Weyl's views,... ? To some of these questions at least partial answers can be put forward on the basis of some of the available correspondence and notes. The present paper will concentrate mostly on the historical issues of the intuitionistic episode in Weyl's career. Weyl entered the foundational controversy with a bang in 1920 with his sensational paper "On the new foundational crisis in mathematics".' He had already made a name for himself in the foundations of mathematics in 1918 with his monograph "The Continuum" [18]; this contained in addition to a technical logical-mathematical construction of the continuum, a fairly extensive discussion of the shortcomings of the traditional construction of the continuum on the basis of arbitrary-and hence also impredicativeDedekind cuts.