FOM: determinate truth values, coherent pragmatism
V.Sazonov at doc.mmu.ac.uk
Tue Sep 5 13:13:19 EDT 2000
Harvey Friedman wrote:
> Reply to Davis 1:43PM 9/4/00:
> >Set theorists explore this territory as utterly remote from
> >everyday human experience as quarks. They must look for theoretical
> >cohesiveness. As Goedel suggested years ago, such axioms can justify
> >themselves on the basis of their consequences - and here again it is you
> >who are doing so much to bring this about.
> But the justification for the general math community is not along any idea
> of truth. It is rather along the lines of coherent pragmatism. Because the
> possibility of experimental confirmation is nonexistent - or at least
> inconceivable at this point - truth plays no significant role in the
> equation. Only coherent usefulness.
> >Yes. But they will want more. They will hardly regard them as acceptable,
> >however convenient, unless they have reason to believe that their
> >arithmetic consequences are true.
> The only way they have of testing truth of arithmetic consequences is that
> there is no contradiction. So this just amounts to faith in consistency.
> This they will gradually accept after there is enough well worked out
> theory and enough smart people are using them to gain confidence there are
> no problems and to get a vested interest in their use. Notions of truth
> seem utterly irrelevant for this process in the general mathematical
Dear Prof. Friedman,
Is there any essential difference of the above point of view with
the formalist's one?
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