Newsgroups: comp.ai.philosophy,sci.logic
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From: dave@prim.demon.co.uk (Dave Griffiths)
Subject: Re: Godel, Lucas, Penrose, and Putnam
Message-ID: <1994Dec29.130707.376@prim.demon.co.uk>
Organization: Primitive Software Ltd.
References: <3ddp99$tc@usenet.ucs.indiana.edu>
Date: Thu, 29 Dec 1994 13:07:07 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:24124 sci.logic:9224

In article <3ddp99$tc@usenet.ucs.indiana.edu> chalmers@bronze.ucs.indiana.edu (David Chalmers) writes:
>
>Penrose's second argument proceeds, in essence, by saying "suppose I *am*
>formal system F", and then arguing that with this assumption in place, he
>can see the truth of statements that are beyond F's powers, even if F is
>supplemented by the assumption that it is F.  Let F' be the system derived
>by supplementing F with the assumption that it is F.  Then for the usual
>reasons F' cannot see the truth of its Godel sentence G(F').  But Penrose
>argues that (under the assumption that he is F) he can see the truth of
>G(F'): he knows that he is consistent, so (under the assumption that he is
>F) he knows that F is consistent, and indeed that F' is consistent, so he
>knows that G(F') is true.  This contradicts the initial assumption that he
>is F.  Similar reasoning shows that he cannot be any formal system.

I haven't read the Penrose book yet but is he arguing that because a
computer _does_ comprise a formal system it can never see the truth of G(F')?
This begs the question of what we mean by "see the truth of". I would argue
that all a computer has to do is be as sure as we ourselves are about the
truth of a Godel sentence, ie fairly certain but not totally.

>This argument avoids the obvious flaws with the Lucas argument and the
>first Penrose argument, as it nowhere requires that he is directly able to
>determine the soundness of F.  It simply requires that he can know that he
>himself is sound.

How does he differentiate between the reality of himself being sound and the
illusion that he is sound?

Dave
