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 -