Date: Thu, 10 Jul 2008 18:26:06 -0700 (PDT)
On Jul 10, 5:59 am, "Brian Selzer" <br..._at_selzer-software.com> wrote:
> "Marshall" <marshall.spi..._at_gmail.com> wrote in message
> > And for most proofs, (and this is my big objection to
> > your position) we don't even need to consider any model,
> > or even whether there is a model. For example, consider
> > the group axioms. It is a theorem of group theory that
> > the identity element is unique. Why can we say such a
> > thing without specifying *which* interpretation of the group
> > axioms we mean? Because it *doesn't matter* which
> > interpretation we are talking about: the naturals under addition,
> > the nonzero rationals under multiplication, translations in the
> > Cartesian plane, whatever. It's true for *all* interpretations.
> Isn't it true that even the most primitive axioms range over a collection of
> arbitrary objects?
Sure. "Arbitrary" in that the theory doesn't specify what that collection is.
Marshall Received on Thu Jul 10 2008 - 20:26:06 CDT