Date: Dec 7, 2012 1:34 AM
Author: mueckenh@rz.fh-augsburg.de
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