From: Christian Szegedy (szegedy@t-online.de)
Date: Tue Oct 19 2004 - 17:35:58 MDT
I must say, that I did not have time to thoroughly read the Godel Machine
paper, so it may be completely stupid what I will write.
> In more familiar terms, it would seem that Schmidhuber's Gödel Machine
> must prove a new proof system is consistent in order to accept it,
and that
> runs smack dab into Gödel's original theorem. Any system that can prove
> its own consistency is inconsistent.
Perhaps I misunderstand what you want, but it seems to me that you want too
much from yor self-rewriting AI. It does no have to prove absolute
consistency,
only consistancy relative to its original system.
> Maybe the Gödel Machine's first proof system would start with ZFC set
theory.
> ZFC suffices to prove the consistency of Peano Arithmetic, and might
accept a
> rewrite implementing a proof verifier that accepted PA proofs
I don't really understand, what you want to accomplish. I don't think
that a self
rewriting AI should really enhance or restrict the theorems it accepts:
it must typically improve the run-time of its parts.
> Lest any despair of AI, remember that humans can think about this
> stuff without going up in flames, ergo it must be possible somehow.
Humans (even mathematicians) are far from theorem proving systems.
Humans are error tolerant systems and a mathematician says that
a theorem is proven, if it can be embedded into his mindset seamlessly.
Of course, there are a lot of mistakes, but fortunately I do not go up
in flames if I produced a wrong proof.
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