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From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Godel's Proof (was Re: Help!).
Message-ID: <1990Nov27.145243.6214@sics.se>
Date: 27 Nov 90 14:52:43 GMT
References: <1306@ucl-cs.uucp>
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Organization: Swedish Institute of Computer Science, Kista
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In-Reply-To: G.Joly@cs.ucl.ac.uk's message of 27 Nov 90 11:49:20 GMT

In article <1306@ucl-cs.uucp> G.Joly@cs.ucl.ac.uk (Gordon Joly) writes:

   >Godel only produced one major work; his brain was fallible and he
   >suffered from depression for the latter part of his life.

   This is a piece of misinformation. Godel produced a number of
results of very great importance for the development of logic. His
major contributions were 1) the completeness theorem for predicate
logic, 2) his two incompleteness theorems, 3) his definition of the
constructible hierarchy in set theory and the basic result L |=AC+GCH,
4) the ("Dialectica") interpretation of arithmetic by means of
higher order primitive recursive functions. (Add to this e.g. his
observations concerning intuitionistic logic and axioms of infinity,
and his philosophical writings.) An astonishing proportion of work in
logic and set theory directly or indirectly derives from Godel's work.

  Of course there is no reason to believe that this work is of interest
in AI. In particular, I have seen no invocation of Godel's theorem in
this context which might not as well be replaced by an invocation of the
fact that there exist non-recursive r.e. sets.