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Article 5417 of comp.ai.philosophy:
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>From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
Newsgroups: comp.ai.philosophy
Subject: Re: Goedel's theorem proof without self-referencing?
Message-ID: <76781@netnews.upenn.edu>
Date: 5 May 92 14:33:49 GMT
References: <1992Apr23.183732.25378@kum.kaist.ac.kr> <1992May4.214051.16767@hellgate.utah.edu>
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Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
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In-reply-to: tolman%asylum.utah.edu@cs.utah.edu (Kenneth Tolman)

In article <1992May4.214051.16767@hellgate.utah.edu>, tolman%asylum (Kenneth Tolman) writes:
>>My questions are : 1) Is there any proof of Goedel's 1st incompleteness
>>without using self-referencing technique? 

>No, there are not.

This is nonsense.  Goedel's theorem is the assertion that a certain formal
system (PA=Peano Arithmetic) is incomplete.  Goedel's proof was both
ingenious and significant, but that does not make it the only proof.  Any
independence result from PA will suffice.

Gentzen's proof was proof-theoretic.  He analyzed the logical complexity
of PA-based proofs, and showed that they only went so far.  So statements
beyond that complexity were independent--no self-reference.

Kirby and Paris gave a model-theoretic proof.  They analyzed non-standard
models of arithmetic, and showed which properties of their models correspond
to which fragments of PA.  When they went far enough, they had independence
results.
-- 
-Matthew P Wiener (weemba@sagi.wistar.upenn.edu)


