Lester Zick wrote: > On 17 Jul 2006 14:15:19 -0700, "Karl Malbrain" <email@example.com> > wrote: > > > > >firstname.lastname@example.org wrote: > > > >> I don't find that to be the case for me; at least for the usual > >> meanings of the terms "believe" and "truth" /in this context/. > > > >truth: > > 1. The quality or being true; as: > > (a) Conformity to fact or reality; exact accordance with > > that which is, or has been; or shall be. > > (b) Conformity to rule; exactness; close correspondence > > with an example, mood, object of imitation, or the > > like. > > > >If a mathematical result conforms to the axioms you agree to opoerate > >within, you get mathematical truth. > > Not exactly. All you've got at that point is axiomatic truth, self > consistency between axiomatic assumptions and extraplated theorems.
And an expansion of the truth of the system.
> >> On the other hand, I do believe in the truth of the statement "if we > >> assume Euclidean geometry with the parallel postulate, then all > >> triangles have angles summing to 180 degrees"; but that is a belief in > >> the truth of the fact that it logically follows from the given axioms - > >> not a belief in the truth of the axioms themselves. > > > >Exactly. The axioms are not things in themselves. > > Sez who? Axioms are as much things in themselves as any other > assumptions.
As part of their system they go beyond that and become things-for-themselves.