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WEYL REEXAMINED: “DAS KONTINUUM” 100 YEARS LATER

Part of: General logic History of mathematics and mathematicians Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  10 June 2020

ARNON AVRON
ARNON AVRON*
Affiliation:
SCHOOL OF COMPUTER SCIENCE TEL AVIV UNIVERSITYTEL AVIV6997801, ISRAEL E-mail: [email protected]
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Abstract

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Hermann Weyl was one of the greatest mathematicians of the 20th century, with contributions to many branches of mathematics and physics. In 1918, he wrote a famous book, “Das Kontinuum”, on the foundations of mathematics. In that book, he described mathematical analysis as a ‘house built on sand’, and tried to ‘replace this shifting foundation with pillars of enduring strength’.

In this paper, we reexamine and explain the philosophical and mathematical ideas that underly Weyl’s system in “Das Kontinuum”, and show that they are still useful and relevant. We propose a precise formalization of that system, which is the first to be completely faithful to what is written in the book. Finally, we suggest that a certain set-theoretical modern system reflects better Weyl’s ideas than previous attempts (most notably by Feferman) of achieving this goal.

Keywords

WeylDas Kontinuumpredicative mathematicsfoundations of mathematics

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 03B30: Foundations of classical theories (including reverse mathematics) 01A60: 20th century
Type
Articles
Information
Bulletin of Symbolic Logic , Volume 26 , Issue 1 , March 2020 , pp. 26 - 79
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Association for Symbolic Logic

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