Date: Dec 7, 2012 1:34 AM
Subject: Matheology § 173

Matheology § 173

The question of language is also particularly relevant, for Brouwer
would continue to emphasize that mathematics does not depend on
language or logic, being prior to language and logic. Language is
merely an instrument of social domination, and it makes impossible a
real communication: ?nobody has ever communicated his soul to someone
else by means of language.? In 1908, this line of thought would derive
into a denounce of classical logic and of axiomatic systems, which
obviously from his standpoint cannot be the real foundation of
mathematics. [...] Brouwer stressed that he had been elaborating these
ideas since 1907, before his involvement with topology, and mentioned
how (in his opinion) they also forced him to disagree with Hilbert?s
conviction that all mathematical problems are solvable. He emphasized
that the foundations for set theory provided both by the logicists and
Zermelo were to be rejected.
[José Ferreirós: "Paradise Recovered? Some Thoughts on Mengenlehre and
Modernism", (2008)]

Regards, WM