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Article 5440 of comp.ai.philosophy:
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>From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Goedel's theorem proof without self-referencing?
Message-ID: <1992May6.183511.27360@sics.se>
Date: 6 May 92 18:35:11 GMT
References: <1992Apr23.183732.25378@kum.kaist.ac.kr>
	<1992May4.214051.16767@hellgate.utah.edu> <76781@netnews.upenn.edu>
	<1992May5.154030.18664@sics.se> <76916@netnews.upenn.edu>
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In-Reply-To: weemba@sagi.wistar.upenn.edu's message of 6 May 92 17:03:09 GMT

In article <76916@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu
 (Matthew P Wiener) writes:

   >>The nugget of sense consists in the observation that some form of
   >>diagonalization is used in all proofs of Godel's theorem.

   >That can get pretty loose, so I won't argue the point....

   There isn't really any argument here, but possibly a question of some
interest. Even though particular statements undecidable in (say) PA, and
the proofs of their undecidability, need not have anything to do with
diagonalization or self-reference, is there any reason why all proofs of
Godel's theorem should do so?

   >Goedel's proof of G2I does.  There are other proofs, for example, the
   >model-theoretic one in Smorynski's HANDBOOK OF MATHEMATICAL LOGIC article

  Quite true. Though I would not claim to have any insight myself into the
nature of the constructions used in that proof.


