Date: Feb 3, 2013 3:23 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 208
Matheology § 208

In Consistency in Mathematics (1929), Weyl characterized the

mathematical method as

the a priori construction of the possible in opposition to the a

posteriori description of what is actually given. {{Above all,

mathematics has to be consistent. And there is only one criterion for

consistency: The "model" of reality.}}

The problem of identifying the limits on constructing ?the possible?

in this sense occupied Weyl a great deal. He was particularly

concerned with the concept of the mathematical infinite, which he

believed to elude ?construction? in the naive set-theoretical sense.

Again to quote a passage from Das Kontinuum:

No one can describe an infinite set other than by indicating

properties characteristic of the elements of the set?. The notion that

a set is a ?gathering? brought together by infinitely many individual

arbitrary acts of selection, assembled and then surveyed as a whole by

consciousness, is nonsensical; ?inexhaustibility? is essential to the

infinite.

Small wonder, then, that Hilbert was upset when Weyl joined the

Brouwerian camp.

[John L. Bell: "Hermann Weyl", Stanford Encyclopedia of Philosophy

(2009)]

http://plato.stanford.edu/entries/weyl/index.html

Regards, WM

For older §§ see

http://www.hs-augsburg.de/~mueckenh/KB/Matheology.pdf