I think it's better to conceive of mathematical axioms as being part of mathematical system X or not, rather than as true or false. That is, they're not self-e

I think it's better to conceive of mathematical axioms as being part of mathematical system X or not, rather than as true or false. That is, they're not self-evident or universal or true according to some external standard, they're merely postulated as properties of a given mathematical structure. See http://en.wikipedia.org/wiki/Axiom#Non-logical_axioms http://en.wikipedia.org/wiki/Axiom#Non-logical_axioms