Date: Thu, 10 Jul 2008 01:03:40 -0400
"Marshall" <marshall.spight_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
>> 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.
I don't think so: axioms are sentences that are suppposed to be true. 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 - 00:03:40 CDT