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From: jbaxter@physics.adelaide.edu.au (Jon Baxter)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <2291@sirius.ucs.adelaide.edu.au>
Date: 24 Jan 91 12:08:00 GMT
References: <1991Jan16.035058.7465@bronze.ucs.indiana.edu> <1991Jan16.182120.20961@sics.se> <1991Jan18.012527.20104@news.cs.indiana.edu> <93@tdatirv.UUCP>
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In article <93@tdatirv.UUCP> sarima@tdatirv.UUCP (Stanley Friesen) writes:

.........
>
> I suppose idealization is OK, but it does leave us with an almost uninteresting
> result! I do not believe that a generalized resoning system can be designed
> that is not subect to mistakes.  I.e. being able to reach arbitrary conclusions
> without scope limitations automatically implies the possibility of error.
>
> Of course with humans it goes even deeper than that, since we operate almost
> entirely on pattern matching (i.e. guessing).  This is true in *all* fields
> of human endeavor, even (or especially) mathematics.  I do not believe that
> any system could match human performance in mathematics except by using
> pattern matching to arrive at new hypotheses 'from scratch'.  And pattern
> matching is intrinsically unreliable.
>
> What am I saying here?  I am saying that humand mathemeticians arrive at
> conclusions based on prior experience, intuition, training &c. and only
> produce mathematical proofs as an final step.  The real work is in the
> leaps of intuition.

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.
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".
--
Jon.                            "Life's too short for death."