为什么韦尔认为埃米-诺特让代数成为公理数学的极乐世界?

Iulian D. Toader
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摘要

本文试图澄清魏尔将艾美-诺特代数比喻为公理学中的 "埃尔多拉多"。论文讨论了魏尔早期对公理的看法,这是他对戴金德和希尔伯特的批判的一部分,其动机是魏尔默认了关于正确性的现象学认识论,然后论文描述了诺特在代数学方面的工作,特别强调了其与戴金德和希尔伯特著作的祖先关系,以及她的数学方法,其特点是非元素推理,即脱离数学对象的推理。然后,论文转向韦尔对诺特工作的评论,反对将她在代数学中使用的公理化方法与他晚期关于公理化的观点相提并论,理由是后者抵制诺特的脱离原则。
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Why Did Weyl Think that Emmy Noether Made Algebra the Eldorado of Axiomatics?
The paper attempts to clarify Weyl's metaphorical description of Emmy Noether's algebra as the Eldorado of axiomatics. It discusses Weyl's early view on axiomatics, which is part of his criticism of Dedekind and Hilbert, as motivated by Weyl's acquiescence to a phenomenological epistemology of correctness, then it describes Noether's work in algebra, emphasizing in particular its ancestral relation to Dedekind's and Hilbert's works, as well as her mathematical methods, characterized by non-elementary reasoning, i.e., reasoning detached from mathematical objects. The paper turns then to Weyl's remarks on Noether's work, and argues against assimilating her use of the axiomatic method in algebra to his late view on axiomatics, on the ground of the latter's resistance to Noether's principle of detachment.
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