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Brouwer and Hausdorff: On reassessing the foundations crisis

Published online by Cambridge University Press:  19 September 2024

David E. Rowe
David E. Rowe*
Affiliation:
Mainz University
*
Email: rowe@mathematik.uni-mainz.de
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Abstract

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.

Keywords

Cantorian set theoryGerman mathematics journalsWeimar politicsmathematical power strugglesfoundations crisis

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Type
Research Article
Information
Science in Context , Volume 35 , Issue 4: Modernism in science and mathematics: A second look at Herbert Mehrtens , December 2022 , pp. 395 - 413
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© The Author(s), 2024. Published by Cambridge University Press

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