Date: Jan 25, 2013 5:17 PM
Author: mueckenh@rz.fh-augsburg.de
Subject: Matheology § 199
Matheology § 199

Gödel makes a rather strong comparison between "the question of the

objective existence of the objects of mathematical intuition" and the

"question of the objective existence of the outer world" which he

considers to be "an exact replica."

Gödel's rejection of Russell's "logical fictions" may be seen as a

refusal to regard mathematical objects as "insignificant chimeras of

the brain."

Gödel's realism, although similar to that of Locke and Leibniz, places

emphasis on the fact that the "axioms force themselves upon us as

being true." This answers a question, untouched by Locke and Leibniz,

why we choose one system, or set of axioms, and not another; that the

choice of a mathematical system is not arbitrary.

Gödel, in the "Supplement to the Second Edition" of "What is Cantor's

Continuum Problem?" remarked that a physical interpretation could not

decide open questions of set theory, i.e. there was (at the time of

his writing {{and that did never change}}) no "physical set theory"

although there is a physical geometry.

[Harold Ravitch: "On Gödel's Philosophy of Mathematics"]

http://www.friesian.com/goedel/

http://www.friesian.com/goedel/chap-2.htm