[FOM] Godel, Wittgenstein etc.
praatika@mappi.helsinki.fi
praatika at mappi.helsinki.fi
Thu May 8 03:30:06 EDT 2003
[The following remarks, which I first presented in a private
correspondence, may perhaps clarify what I said in my earlier posting.]
My point was that we can apply Godel's theorem also to a theory S about
whose consistency we are less confident (e.g. ZFC + some new strong axiom)
and prove the conditional:
If S is consistent, then there is a true but unprovable-in-S sentence G (in
L(S).
So what can we then say about the truth of G (for S). I think that the
right conclusion is that we have exactly as much (or little) reason to
believe in the truth of G as we have reason to believe in the consistency
of S.
(An amusing historical example is Quine's orginal version of ML (1940) - in
the end of the book he presented a proof of Godel's theorem for his system.
But ML was later proved to be inconsistent. Hence his G (for ML) was
false!)
Best
Panu
Panu Raatikainen
PhD., Docent in Theoretical Philosophy
Fellow, Helsinki Collegium for Advanced Studies
University of Helsinki
Address:
Helsinki Collegium for Advanced Studies
P.O. Box 4
FIN-00014 University of Helsinki
Finland
E-mail: panu.raatikainen at helsinki.fi
http://www.helsinki.fi/collegium/eng/Raatikainen/raatikainen.htm
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