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Article 2320 of comp.ai.philosophy:
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>From: gerry@zds.com (gerry)
Subject: Re: Godel's theorem and AI criticism
Organization: Zenith Data Systems, Buffalo Grove, IL
Date: Fri, 20 Dec 1991 20:13:39 GMT
Message-ID: <1991Dec20.201339.12600@zds.com>
References: <1991Dec17.043358.111702@cs.cmu.edu>

In article <1991Dec17.043358.111702@cs.cmu.edu> kck+@cs.cmu.edu (Karl Kluge) writes:
>Godel's theorem, like NP completeness, talks about worst cases. There is no
>good reason (as far as I can see) to believe that useful concepts would have
>generating functions which were Godel sentences.  For that matter, there is
>no evidence (and can be no evidence) that given a set of axioms that
>includes the axioms of arithmatic over the integers, humans can recognize
>true sentences which have no finite proof from the axioms.  It is therefore
>far from clear to me what the supposed implications of Godel's theorem are
>for computational models of human cognition.

Of course, there is no good reason to believe in the non-existence of useful
concepts with Godel sentences as generating functions.  The fact of the matter
is that the nature of the generating function could be what will determine
which of these is true.  Now you have the task of first proving that the
set of "useful" functions is "complete" in the same sense that we were talking
about "truth" with Godel.  Your point about whether humans can in any sense
"recognize" the truth of statements without finite proofs, is right on.
Sloppy thinkers are always assuming that humans do have some type of ability
to "see" the truth or falseity of these sentences.

What we can build a case for is that natural selection has made sure that our
"generating function" will produce a large fraction of the truths necessary
for survival with a small enough delay to act on this discovered truths.
That's how our brains are designed; natural selection produces good and
ever better solutions to problems, but the process is necessarily blind to
many unexpected catastrophies, and organisms do get into dead end situations.
There is no "rational" reason to expect that any type of "global" intellegence
exists in terms of "global" coherences, nor is there any way to rule them out.
Here we stand on the threshold of an Abyss.

Gerry Gleason



