[FOM] CH and mathematics
James.Hirschorn at univie.ac.at
Wed Jan 23 22:52:14 EST 2008
On Tuesday 22 January 2008 00:46, Bill Taylor wrote:
> Alex Blum writes:
> > Is Feferman's question in effect an expression of doubt about
> > the meaningfulness of CH? Would you say that the same would have been
> > true of Fermat's last theorem would have been proved independent of
> > the axioms of arithmetic?
> These are in no way parallel. FLT is arithmetical, so is subject
> to the usual straightforward quantifier-extension in meaning as explicated
> from Hilbert to Tarski. No such remarks apply to set-theoretical
> results, as Feferman was at pains to make clear in his quote, I feel.
I'm not sure what the "quantifier-extension in meaning" is.
> And BTW, FLT is a bad example, being Pi-0-1. If it was undecidable
> it would automatically be true. Twin-primes would have been better.
I think Alex makes 2 very valid points in his above quote:
1) Is "inherently vague" the same thing as "meaningless"?
Presumably "meaningless" would imply "uninteresting".
2) There is (I think) the remaining question of whether the current proof of
FLT can be formalized within PA. If it cannot, does that mean Wiles' proof of
FLT is inherently vague?
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