On 19 Jul 2006 14:33:26 -0700, "Dave L. Renfro" <firstname.lastname@example.org> wrote:
>Lester Zick wrote (in part): > >> 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?
Whether an axiom is true or not.
> I thought >axioms were true by definition,
Of course they are. Because we define our assumptions of truth as defintions of what's true. Remarkably useful concept.
> 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: > >Axiom R: All right angles are congruent. > >Theorem: All right angles are congruent. > >Proof (2-column format): > > Statements Reasons > >1. All right angles are congruent. 1. Axiom R.
You mean mathematikers can rely on circular reasoning to demonstrate modern math theorems? How nice. Certainly supports every speculative conjecture I've made concerning the intellectual content of modern math. Don't prove it; just assume it; then claim you've proven it.