Date: Feb 3, 2013 3:23 AM
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

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

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

Regards, WM

For older §§ see