>>33
Perhaps it's merely the semantical nature of the argument that leads to this confusion. It doesn't matter what the name of what defines mathematics is, but it can be said with certainty that mathematics does not define itself. "In maths you don't pick axioms because you believe them to be fundamentally true, you pick axioms because you want to study systems that you believe have those axioms." I've neither said, thought, nor implied that axioms are any sort of truths, in fact, they quite possibly contain the least amount of truth. They're merely truthy. Still, this fact does nothing to refute axioms' roots outside mathematics. To assert an axiom, you must use procedures derived outside of the field of mathematics, such as assumption. Mathematics only deals with the relationship between properties, which means that the actual basis for these relationships must be developed by an outside entity, for axioms are derived from no other property. Just think of philosophy and logic creating the axiom and mathematics creating the theorems; in a purely numerical instance, of course.