firstname.lastname@example.org 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.
-- Aatu Koskensilta (email@example.com)
"Wovon man nicht sprechen kann, daruber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus