Date: Jan 25, 2013 5:17 PM
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"]