Path: utzoo!utgpu!news-server.csri.toronto.edu!neuron.ai.toronto.edu!tap
Newsgroups: comp.ai.philosophy
From: tap@ai.toronto.edu (Tony Plate)
Subject: Re: Minds, machines, and Godel
Message-ID: <91Jan16.135532edt.1132@neuron.ai.toronto.edu>
Organization: Department of Computer Science, University of Toronto
References: <1991Jan16.035058.7465@bronze.ucs.indiana.edu>
Date: 16 Jan 91 18:55:43 GMT
Lines: 29


Dave Chalmers writes:
>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.

A flaw in this "proof" is that it is incomplete.  To make it complete
we must prove that for all candidate T, there exists a sentence G
which cannot be proved by T, but which I can see is true.

The briefest statement of this argument would be that people can prove
anything, therefore, people are not turing machines.

I can't see how you could ever prove that "people can prove anything".

I think that it is necessary to have the universal rather than
the existential quantifier in the "people can prove anything"
part of the argument.  Otherwise, we could take the Turing machine T'
which can indeed prove G, and combine it with T to get a new
candidate Turing machine.

-- 
---------------- Tony Plate ----------------------  tap@ai.utoronto.ca -----
Department of Computer Science, University of Toronto, 
10 Kings College Road, Toronto, 
Ontario, CANADA M5S 1A4
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