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From: calhoun@hobbes.kzoo.edu (William Calhoun)
Subject: Re: Penrose and human mathematical capabilities
Message-ID: <1995Jul14.211534.3484@hobbes.kzoo.edu>
Organization: Kalamazoo College, Kalamazoo MI 49006
References: <3tra4b$em9@netnews.upenn.edu> <3tsi61$t7g@nnrp.ucs.ubc.ca> <3ttskd$fo7@netnews.upenn.edu>
Date: Fri, 14 Jul 1995 21:15:34 GMT
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Xref: glinda.oz.cs.cmu.edu comp.ai.philosophy:30210 sci.logic:12424

In article <3ttskd$fo7@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu 
(Matthew P Wiener) writes:

[much discussion deleted]>

>There have been no correct challenges to Goedel's proof.  The theorem
>is valid, and in the context of a programmed robot, there is no such
>thing--no ifs ands or buts--as a consistent, complete "truth judgement"
>that extends beyond such AI victories as checkers and other finite junk.
>

No one has challenged Godel's proof.  Only Penrose's assertion that
it follows that human thought *cannot* be computational.  

We know Godel's theorem.  So what?  So does ZFC.
  

Note: I am *not* making an argument for or against any particular 
position on AI.  I am saying that Penrose does not prove that human
thought is not computational.  In fact he, *says* that he can't prove
that.  But he claims that the loop holes in his argument all lead to 
bad positions for AI.  For instance, if human thought *is* computational, 
but the algorithm is unknowable then (he claims) AI is doomed. And he
says that this possiblity seems unlikely to him.

It seems to me that when it gets down to brass tacks, Penrose is relying
on his *intuition* that human "understanding" is not computational.
That's fine, but I would have prefered that he leave out the weak 
attempt to patch up Lucas's arguement and admit that he's playing a
hunch.

-Bill Calhoun
-Kalamazoo College
-calhoun@kzoo.edu
  
