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From: thornley@cs.umn.edu (David H. Thornley)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan17.233234.17164@cs.umn.edu>
Date: 17 Jan 91 23:32:34 GMT
References: <1991Jan17.040803.8205@bronze.ucs.indiana.edu> <JMC.91Jan16213907@DEC-Lite.Stanford.EDU> <1991Jan17.170401.8536@bronze.ucs.indiana.edu>
Organization: University of Minnesota, Minneapolis, CSci dept.
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Before we continue with this discussion, I would like to ask how we
are to see that something is true.  Most of the time, I don't "see"
truth, I have to work at it.

If we have a program that will pass the Turing test, we presumably
can make some sort of equivalent logical system, and derive a Godel
number corresponding to an undecidable statement, given infinite
resources.  It is not at all clear to me that we can see that this
statement is true; what if a slight mistake occurred during the
process?  How can we tell?

Further, the Godel process, as well as I can tell, results in the
proposition P reading "Proposition P cannot be proved in this system",
which is obviously unprovable in that system, and hence true, provided
the system is consistent.  This seems, to me, to be precisely equivalent
to statement S:  "Statement S cannot be asserted by Chalmers".
I will point out that that statement is true iff Chalmers is
consistent, and challenge Chalmers to stay consistent while
agreeing with me.

I'm not talking psychology here, I'm talking about assertions and
logical consistency.  No system of logic can be both complete and
consistent, and neither can a human.  Any arguments that human
beings are different from logical systems will have to start somewhere
else.

DHT