Bruno Marchal wrote:
> Le 27-oct.-06, à 00:40, 1Z a écrit :
> >>> Tom Caylor:
> >>> 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.
> >>> Tom
> >> Brent Meeker: But as I understand it, Bruno wants to identify
> >> "mathematical existence" with true existence statements about
> >> mathematical objects.
> >> Some of these are unprovable. They can be consistently added to the
> >> axioms. But also their negation can be consistently added to the
> >> axioms. But not both. So there are disjoint realms of consistent
> >> mathematics - some are Rome, some are Athens, some are Tuva, most are
> >> Harry Potter's home town.
> > 1Z (Peter Jones): I suppose that is why he wants to base his case on
> > the
> > subset of arithmetic everyone agrees on.
The manoeuvre addresses the mathematical objections to
Platonism whilst doing nothing about the philosophical.
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