On Thu, 20 Jul 2006 11:50:15 EDT, "Dave L. Renfro" <email@example.com> wrote:
>Dave L. Renfro wrote (in part): > >> Axioms are true by definition. Of course, >> a certain axiom A for Theory T may be false >> in Theory T'. However, in any (consistent) >> theory for which A is an axiom, A will be true. > >Actually, I think "truth" only makes sense >once a model is specified, so "for Theory T" >should be "in Model M for Theory T", and >similarly for the other references to "theory" >above.
And into what model do "model M and theory T" fall precisely?
Modern appeals to model theory and models are simply naive alternatives to being able to demonstrate what's actually true and false. Models are not mechanically exhaustive. That's why they're models of what we suppose to be true and not what's actually demonstrably true and appeals to models instead of truth merely demonstrate the rankest kind of faith based mathematics.