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From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Minds, machines, and Godel
Message-ID: <1991Jan17.104913.15692@sics.se>
Date: 17 Jan 91 10:49:13 GMT
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In-Reply-To: jmc@DEC-Lite.Stanford.EDU's message of 17 Jan 91 05:39:07 GMT


  To amplify my previous comment: John McCarthy's remarks correctly
emphasize that machines just as well as people can use Godel's theorem
in its positive application, i.e. as a means of indefinitely extending
the set of formal principles which we recognize as valid.

  The point I wish to make is that Godel's theorem cannot even be used
to refute the bald assertion that the set of arithmetical theorems
provable by human beings is recursively enumerable (and thus equal to
the set of theorems produced by some Turing machine, or provable in
some formal system). For we have no reason to believe that we would be
able even to convince ourselves of the truth of the Godel sentence for
such a formal system.