In a fascinating book entitled "The Mathematical Experience," [Davis and Hersh], I found:
- Mathematical axioms have the reputation of being self-evident, but it might
seem that the axioms of infinity and that of God have the same character as far
as self-evidence is concerned. Thus, ...'Axiom of Infinity: An infinite set
exists.' Axiom of God: (Maimonides: Mishneh Torah, beginning):
The basic principle of all basic principles and the pillar of all the sciences is to realize that there is a First Being who brought every existing thing into being.
Which is mathematics and which is theology? Does this lead us to the idea that an axiom is merely a dialectical position on which to base further argumentation, the opening move of a game without which the game cannot get started?"