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A footnote to The crisis in contemporary mathematics
Historia Mathematica ( IF 0.5 ) Pub Date : 2018-05-01 , DOI: 10.1016/j.hm.2018.03.002
Boris Katz , Mikhail G. Katz , Sam Sanders

We examine the preparation and context of the paper "The Crisis in Contemporary Mathematics" by Errett Bishop, published 1975 in Historia Mathematica. Bishop tried to moderate the differences between Hilbert and Brouwer with respect to the interpretation of logical connectives and quantifiers. He also commented on Robinson's Non-standard Analysis, fearing that it might lead to what he referred to as 'a debasement of meaning.' The 'debasement' comment can already be found in a draft version of Bishop's lecture, but not in the audio file of the actual lecture of 1974. We elucidate the context of the 'debasement' comment and its relation to Bishop's position vis-a-vis the Law of Excluded Middle. Keywords: Constructive mathematics; Robinson's framework; infinitesimal analysis.

中文翻译:

当代数学危机的注脚

我们研究了 Errett Bishop 于 1975 年在 Historia Mathematica 上发表的论文“当代数学危机”的准备和背景。Bishop 试图缓和 Hilbert 和 Brouwer 在逻辑连接词和量词解释方面的差异。他还评论了罗宾逊的非标准分析,担心这可能会导致他所谓的“贬义”。“贬低”评论已经可以在毕晓普演讲的草稿中找到,但在 1974 年实际演讲的音频文件中找不到。我们阐明了“贬低”评论的背景及其与毕晓普立场的关系 -可见排中律。关键词:建构性数学;罗宾逊的框架;无穷小分析。
更新日期:2018-05-01
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