[FOM] Proof "from the book"
torkel at sm.luth.se
Tue Aug 31 04:45:29 EDT 2004
Arnon Avron says:
>That "if S is consistent then G is true" is provable not only in S (which
>might prove false sentences), but also in PA (which proves only true
>sentences). Hence I do say that if S is a (formal) consistent extension of Q
>then Godel's proof shows G to be true.
I don't understand your "hence". Since we can prove Godel's theorem for
consistent extensions S of Q such that we have no idea whether or not
the Godel sentence G of S is true, what do you mean by saying that
Godel's proof shows G to be true in such a case?
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