布劳威尔与豪斯多夫:关于重新评估基础危机

IF 0.3 4区 哲学 Q2 Arts and Humanities
David E. Rowe
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引用次数: 0

摘要

与康托尔集合论相关的认识论问题是1900年以来基础理论争论的焦点。历史学家赫伯特-迈尔腾斯(Herbert Mehrtens)认为,这场 "基础危机 "是以大卫-希尔伯特(David Hilbert)为首的现代派与各种反现代派之间更大冲突的一部分。在反现代派中,L.E.J. Brouwer 更进一步,根据他的直觉主义哲学提出了新的基础原理。同时,费利克斯-豪斯多夫(Felix Hausdorff)成为新现代风格的主要倡导者。在这篇文章中,我对基础危机进行了重新评估,强调了所涉及的各种思想问题的次要性。相反,我将重点放在德国数学界内部的紧张关系上,并由此引发了一场争夺《数学年鉴》杂志控制权的戏剧性权力斗争。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Brouwer and Hausdorff: On reassessing the foundations crisis

Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen.

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来源期刊
Science in Context
Science in Context 综合性期刊-科学史与科学哲学
CiteScore
0.80
自引率
0.00%
发文量
1
审稿时长
>12 weeks
期刊介绍: Science in Context is an international journal edited at The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, with the support of the Van Leer Jerusalem Institute. It is devoted to the study of the sciences from the points of view of comparative epistemology and historical sociology of scientific knowledge. The journal is committed to an interdisciplinary approach to the study of science and its cultural development - it does not segregate considerations drawn from history, philosophy and sociology. Controversies within scientific knowledge and debates about methodology are presented in their contexts.
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