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From: sarima@tdatirv.UUCP (Stanley Friesen)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <109@tdatirv.UUCP>
Date: 29 Jan 91 20:31:34 GMT
References: <1991Jan16.035058.7465@bronze.ucs.indiana.edu> <1991Jan16.182120.20961@sics.se> <1991Jan18.012527.20104@news.cs.indiana.edu> <93@tdatirv.UUCP> <2291@sirius.ucs.adelaide.edu.au>
Reply-To: sarima@tdatirv.UUCP (Stanley Friesen)
Organization: Teradata Corp., Irvine
Lines: 31

In article <2291@sirius.ucs.adelaide.edu.au> jbaxter@adelphi.physics.adelaide.edu.au.oz.au (Jon Baxter) writes:
|This line of reasoning has already been discussed at great length in this
|thread. Even if a human mathematician does use heuristic methods to arrive
|at mathematical theorems, the proofs are generally correct and when they
|are not they are (usually) quickly overturned by the rest of the mathematical
|community. So surely we can idealize away from the--perhaps slightly
|inconsistent--human mathematician, to the completely consistent one.

Perhaps so, but I believe that by that point we have something that is
uninteresting from an AI point of view (something with no 'intelligence').
I maintain that such a generalized, consistant mathemetician has lost 'his'
ability to be original (to invent new theorems or concepts) except in a
very restricted sense.  It is the 'willingness' to make mistakes that allows
new ideas to be generated.  Thus a model that didn't include at least a
sub-component that was 'unreliable' would be incapable of doing anything
except *check* theorems proposed to it.  That is in idealizing away the
error you have idealized away the mathmetician and left nothing but a
'vetter' as you call it.

|To do this all one has to consider is a mathemetician who feeds her
|"proofs" to another very large group of mathematicians that reject
|anything they decide is invalid. The system consisting of the original
|mathematician plus her "vetters" can be made virtually as reliable as you
|like, so simulate the lot of them on a Turing machine and you have got
|yourself an error-free "mathematician".

I suspect you would end up with an 'error-free' mathematical 'vetter' that
needs a real mathematician to feed it new ideas.
-- 
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uunet!tdatirv!sarima				(Stanley Friesen)