[FOM] Proof "from the book" of the incompleteness theorem
torkel at sm.luth.se
Sun Aug 29 14:34:44 EDT 2004
Arnon Avron says:
>This is indeed the first proof (out of 3) that Smullyan presents
>in his book on the incompleteness theorems. The trouble with this
>proof is that it misses one of the most important aspects of Godel's
>proof: the actual construction of a *true* sentence which the system
>fails to prove, and a *proof* that it is true.
Godel's proof does not establish that the Godel sentence of a theory
is true. It would be unfortunate if it did, since the Godel sentence
of a theory is sometimes false.
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