>email@example.com wrote: >> Karl Malbrain wrote: >>>Belief means you agree with the axioms. >> >> Consider: >> >> http://en.wikipedia.org/wiki/Elementary_group_theory >> >> I don't "agree" or "disagree" with the axioms that define a group. What >> could it even mean to "disagree" with the axiom "for every element, >> there exists an inverse"? > >Obviously it makes no sense to agree or disagree with the group axioms. >It does make perfect sense to agree or disagree, or remain agnostic >about, that there exists a measurable cardinal, or that a particular >primitive recursive ordering of naturals has no primitive recursive >infinite descending sequences. > >> I happen to agree; a common definition of "mathematical truth" is >> "follows logically from a particular set of axioms". > >That's a very silly definition, even if one does in fact run into it >from time to time in the "philosophical" outpourings of some mathematicians.
One needn't believe or disbelieve any set of axioms to extrapolate theorems from them and demonstrate their consistency or lack of consistency between theorems and axioms. This doesn't imply the axioms themselves are truer or falser mathematically or otherwise.