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From: bradb@ai.toronto.edu (Brad Brown)
Subject: Re: Artificial Intelligence and Intelligence
Message-ID: <88Nov18.111140est.6198@neat.ai.toronto.edu>
Organization: Department of Computer Science, University of Toronto
References: <484@soleil.UUCP> <88Nov15.170837est.707@neat.ai.toronto.edu> <392@itivax.UUCP>
Date: Fri, 18 Nov 88 11:11:30 EST

In article <392@itivax.UUCP> dhw@itivax.UUCP (David H. West) writes:
>In article <88Nov15.170837est.707@neat.ai.toronto.edu> bradb@ai.toronto.edu (Brad Brown) writes:
>>Godel's Incompleteness Theorem is a more general result
>>stating that any axiomatic system of sufficient power will
>>be fundimentally incomplete.  (NB  Systems that are not of
>>'sufficient power' are also not of sufficient interest to
>>consider for the purpose of AI)
>
>That's by no means obvious.  Formal reasoning is a relatively recent
>addition to the human behavioral repertoire...

I conceed that I don't have the backround to support this statement,
but my article was a followup to a proposal that because Turing 
machines could not compute some functions (eg the halting problem)
no computer could be made to compute "intelligence."  I was arguing
that the incompleteness of formal systems is not a sufficient to 
proof that formal systems cannot be intelligent.


>>[...] Godel
>>shows that there will exist theorems which are true within
>>a system that the system will not be able to prove true.
>[...]
>
>>a belief in a "magic" component to the brain that defies
>>rational explanation.  Sorry, but I just don't buy that.
>
>Eh?  You have to admit the possibility, because you've just declared
>your belief in theorems which are true-but-unprovable in a system.
>If that isn't "defying rational explanation" (within the system), I
>don't know what is.

NO!!  All Godel's theorem says is that every sufficiently powerful
formal system will not be able to prove the truth of some true
theorems.  I implied earlier in my article that I felt the brain
could not prove these truths *either*, so there is no contradiction.

				(-:  Brad Brown  :-)

				bradb@ai.toronto.edu