Tom Caylor wrote:
> 1Z wrote:
> > Tom Caylor wrote:
> > > 1Z wrote:
> > > > Tom Caylor wrote:
> > > >
> > > >
> > > > > > Again, the kind of formalism that says
> > > > > > everything can be brought under a single
> > > > > > formal scheme (the Hilbertian
> > > > > > programme) is different from the kind
> > > > > > that says mathematical truths are dependent on axioms,
> > > > > > and different truths will be arrived at under different
> > > > > > axioms. Of course the key point here
> > > > > > is "different truths". Tom is not entitled to assume that
> > > > > > all roads lead to Rome.
> > > > >
> > > > > If your definition of truth is limited to logical inference given a
> > > > > certain set of axioms and inference rules, then what are we trying to
> > > > > do on the Everything List?
> > > >
> > > > That's *mathematical* truth.
> > >
> > > Mathematical logic is richer than that.
> >
> > Mathematical logic can't conjure up existential conclusions
> > without making existential assumptions.
> >
>
> True. ;)
>
> > > This is what Bruno is saying,
> > > that the math path points toward Rome. And it is no more scary (a la
> > > possible spirits lurking under/in every rock) than the matter path.
> > > Limiting math as you are doing, and as Brent Meeker does in his
> > > response to my (X and not-X) note, is ignoring such evidence as the
> > > proofs of Godel and Tarski's Indefinability Theorem.
> >
> > They do not disprove formalism, as I have explained.
> >
>
> True. Formalism is an existential assumption.
Well, a non-existential assumption.
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Received on Thu Oct 26 2006 - 18:37:23 PDT