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From: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Newsgroups: comp.ai.philosophy
Subject: Minds, machines, and Godel
Message-ID: <1991Jan16.035058.7465@bronze.ucs.indiana.edu>
Date: 16 Jan 91 03:50:58 GMT
Sender: chalmers@bronze.ucs.indiana.edu (David Chalmers)
Organization: Indiana University, Bloomington
Lines: 27

Dull around here.  How about everybody tries to give the decisive refutation
of the Lucas/Penrose arguments that use Godel's theorem to "show" that human
beings are not computational (or more precisely, to "show" that human beings
are not computationally simulable)?

Just to refresh your memory, the argument goes like this: if I were a
particular Turing Machine T, there would be a mathematical sentence G (the
"Godel sentence" of T) that I could not prove.  But in fact I can see that G
must be true.  Therefore I cannot be T.  This holds for all T, therefore I am
not a Turing machine.

The argument goes through equally well if we replace "am a Turing Machine" by
"am simulable by a Turing machine", so that's not a problem.  The Penrose
version of the argument is similar, except that it applies to the level of
the mathematical community rather than to the level of the person (thus
avoiding the problem that in practice individual people may not be perfect
mathematicians; the mathematical community can conquer all).

I actually think that most of the standard replies are flawed (or can be
overcome) in one way or another.  But I'm interested to see the wisdom of
the net.  Please reply only if you have a good grasp of Godel's theorem and
of the theory of computation.  No hand-waving or mystical mush.

-- 
Dave Chalmers                            (dave@cogsci.indiana.edu)      
Center for Research on Concepts and Cognition, Indiana University.
"It is not the least charm of a theory that it is refutable."