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Article 1971 of comp.ai.philosophy:
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>From: torkel@sics.se (Torkel Franzen)
Newsgroups: rec.arts.books,sci.philosophy.tech,comp.ai.philosophy
Subject: Re: Existence
Message-ID: <1991Dec9.113942.4957@sics.se>
Date: 9 Dec 91 11:39:42 GMT
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In-Reply-To: jmc@SAIL.Stanford.EDU's message of 7 Dec 91 22:00:31 GMT

In article <JMC.91Dec7230031@SAIL.Stanford.EDU> jmc@SAIL.Stanford.EDU 
(John McCarthy) writes:

   >Not only did Goedel hold this view, which was rather unpopular
   >throughout his life, but this view motivated his three greatest
   >pieces of work, his completeness theorem for first order logic,
   >his even more famous incompleteness theorem and his work on
   >the continuum hypothesis.

  I believe a piece of pedantry is in order here, for Godel's peculiar
talent for making something mathematically substantial out of
philosophical ideas covered a wider range than that which you describe.
In particular, his proof of the consistency of the continuum hypothesis
did not involve countable models (although Cohen's work did). The
set-theoretical universe L in which Godel proved that the (generalized)
continuum hypothesis holds in fact contains every ordinal. Godel
arrived at L, the universe of constructible sets, by analyzing and extending
in formal terms a concept from constructive mathematics, viz.
Russell's ramified hierarchy of types, establishing that iterating this
constructive notion into a non-constructively infinite hiearchy yielded
all of classical set theory. His so-called Dialectica interpretation, which
is also usually counted among his fundamental work, similarly analyzed concept
of constructive mathematics. So not only Platonism and the logical paradoxes,
but constructivistic ideas were analyzed and exploited by Godel with a
peculiar finesse.


