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From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan17.093035.13716@sics.se>
Date: 17 Jan 91 09:30:35 GMT
References: <1991Jan16.035058.7465@bronze.ucs.indiana.edu>
	<91Jan16.135532edt.1132@neuron.ai.toronto.edu>
	<1991Jan17.040803.8205@bronze.ucs.indiana.edu>
	<JMC.91Jan16213907@DEC-Lite.Stanford.EDU>
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In-Reply-To: jmc@DEC-Lite.Stanford.EDU's message of 17 Jan 91 05:39:07 GMT

In article <JMC.91Jan16213907@DEC-Lite.Stanford.EDU> jmc@DEC-Lite.Stanford.EDU
 (John McCarthy) writes:

   >The Penrose argument against AI of most interest to
   >mathematicians is that whatever system of axioms a computer is
   >programmed to work in, e.g. Zermelo-Fraenkel set theory, a man
   >can form a G\"odel sentence for the system, true but not provable
   >within the system.

  Surely this can't be Penrose's argument. Obviously anybody can *form*
the Godel sentence. If Penrose has an argument it must be that human
beings, but not the machine at issue, can realize the truth of the
Godel sentence (again assuming the interpretation of the theory to be
agreed on). Again: it is not in general the case that the Godel sentence
for a theory (=the set of arithmetical theorems generated by the machine)
is true, nor have we any reason to believe that we can in general establish its
truth in those cases when it is true.