> 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. 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.
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