Date: Thu, 10 Jul 2008 03:31:55 -0700 (PDT)
On Jul 10, 6:03 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "Marshall" <marshall.spi..._at_gmail.com> wrote in message
> > On Jul 9, 8:36 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> >> Logical propositions without an intended interpretation are when written
> >> just squiggles--something akin to doodles--with no significance or
> >> utility
> >> whatsoever, and are when spoken just noise--they do not rise even to the
> >> level of being a tale told by an idiot: they're just noise.
> > That turns out not to be the case. Axioms are just sentences in
> > a language, for example. A first order theory is just a bunch
> > of syntactic statements. There may be a variety of different
> > possible interpretations, or models. There may be exactly
> > one, or there may be none at all.
> > Marshall
> I don't think so: axioms are sentences that are suppposed to be true.
I can only really echo Marshall's comments. The "truth" (whatever that means) of axioms is irrelevant as far as a theory is concerned (and i'd make pains to distinguish between the scientific and everyday uses of the term theory).
> Truth is determined through interpretation. Therefore, axioms are sentences that
> are supposed to be true under an interpretation--the intended
> interpretation. So a logical theory consists of a set of sentences that are
> supposed to be true under an interpretation along with that which can be
> derived from those sentences.
Received on Thu Jul 10 2008 - 05:31:55 CDT