> So if we sing a canonical song and claim axioms are true > of the lyrics we don't actually have to demonstrate the > truth of the axioms but are simply allowed the luxury > of assuming their truth because our song is canonical?
What do you mean by the truth of an axiom? I thought axioms were true by definition, at least if we're not dealing with an inconsistent axiomatic theory. Not only that, but axioms can be proved quite easily. Here's an example I posted back on June 20: