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Path: utzoo!watmath!watnot!watdcsu!dmcanzi
From: dmcanzi@watdcsu.UUCP (David Canzi)
Newsgroups: net.philosophy
Subject: Re: Sc--nce Attack (self-awareness)
Message-ID: <1765@watdcsu.UUCP>
Date: Fri, 18-Oct-85 07:35:13 EDT
Article-I.D.: watdcsu.1765
Posted: Fri Oct 18 07:35:13 1985
Date-Received: Sat, 19-Oct-85 05:47:08 EDT
References: <45200016@hpfcms.UUCP> <1605@pyuxd.UUCP>
Reply-To: dmcanzi@watdcsu.UUCP (David Canzi)
Organization: U of Waterloo, Ontario
Lines: 34
Keywords: Turing machines vs. the mind
Summary: 

In article <10642@ucbvax.ARPA> tedrick@ucbernie.UUCP (Tom Tedrick) writes:
>My understanding is that Godel's incompleteness theorems prove
>(assuming the consistency of Arithmetic) that no Turing machine
>can possibly simulate the human mind.
>
>This is because for any particular Turing machine there are certain
>statements that the human mind can recognize as true (again with
>the consistency assumption), that the machine cannot recognize
>as true.

What Godel proved was that, if the axioms of arithmetic are consistent,
there is some arithmetical statement, G, which can neither be proved
nor disproved by applying the rules of logic to the axioms of
arithmetic.  Ie. neither G nor ~G is a theorem of arithmetic.

Godel proved this by going "outside of" arithmetic, and constructing a
theory about statements and proofs in arithmetic.  Ie.  while the
axioms of arithmetic are statements about numbers, the axioms of this
newly constructed theory are statements about statements and proofs.
He constructed a statement of arithmetic, G, and proved, from the
axioms of his new theory, that neither G nor ~G could be proven from
the axioms of arithmetic.  Even though G couldn't be proven from the
axioms of arithmetic, Godel was able to prove G by reasoning from the
new axioms.

Now, what does this have to do with Turing machines?  No Turing machine
can generate a proof of G from the axioms of arithmetic.  But then
neither can any human.  Godel proved G by using a different set of
axioms.  I don't see any evidence that a Turing machine can't simulate
Godel and do the same.
-- 
David Canzi

There are too many thick books about thin subjects.