Weyl Reexamined: `Das Kontinuum' 100 Years Later

Arnon Avron aa at tauex.tau.ac.il
Wed Jun 17 03:12:32 EDT 2020

At September 2018 there was a workshop at Leeds on the subject
"Das Kontinuum - 100 Years Later" (https://weyl100.wordpress.com/).
Following that meeting  (and Feferman's paper:
"Weyl Vindicateded:  `Das Kontinuum' 70 Years Later" ),
I wrote a new paper on Weyl's book, called:

"Weyl Reexamined:  `Das Kontinuum' 100 Years Later".

My article has just been published on Cambridge Core in The Bulletin of Symbolic Logic,
and is available at http://dx.doi.org/10.1017/bsl.2020.23.

Here is its abstract:

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 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.

Comments  are most welcome!

Arnon Avron

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