In article <firstname.lastname@example.org>, Lester Zick <DontBother@nowhere.net> wrote:
> On 19 Jul 2006 14:33:26 -0700, "Dave L. Renfro" <email@example.com> > 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.
Axioms are only true "for purposes of argument", in order to see what can be derived from them. and their consequences are only conditionally true as consequences of those axioms, not true in any absolute sense.
There is no absolute unconditional truth available to us in mathematics.