TY - JOUR

T1 - WEYL REEXAMINED

T2 - Das KONTINUUM 100 YEARS LATER

AU - Avron, Arnon

N1 - Publisher Copyright:
© 2020 The Association for Symbolic Logic.

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - Das Kontinuum

KW - Weyl

KW - foundations of mathematics

KW - predicative mathematics

UR - http://www.scopus.com/inward/record.url?scp=85098641412&partnerID=8YFLogxK

U2 - 10.1017/bsl.2020.23

DO - 10.1017/bsl.2020.23

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AN - SCOPUS:85098641412

SN - 1079-8986

VL - 26

SP - 26

EP - 79

JO - Bulletin of Symbolic Logic

JF - Bulletin of Symbolic Logic

IS - 1

ER -