From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!qt.cs.utexas.edu!yale.edu!spool.mu.edu!uunet!mcsun!sunic2!sics.se!sics.se!torkel Tue May 12 15:49:06 EDT 1992
Article 5418 of comp.ai.philosophy:
Path: newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.ecf!utgpu!cs.utexas.edu!qt.cs.utexas.edu!yale.edu!spool.mu.edu!uunet!mcsun!sunic2!sics.se!sics.se!torkel
>From: torkel@sics.se (Torkel Franzen)
Newsgroups: comp.ai.philosophy
Subject: Re: Goedel's theorem proof without self-referencing?
Message-ID: <1992May5.154030.18664@sics.se>
Date: 5 May 92 15:40:30 GMT
Article-I.D.: sics.1992May5.154030.18664
References: <1992Apr23.183732.25378@kum.kaist.ac.kr>
	<1992May4.214051.16767@hellgate.utah.edu> <76781@netnews.upenn.edu>
Sender: news@sics.se
Organization: Swedish Institute of Computer Science, Kista
Lines: 20
In-Reply-To: weemba@sagi.wistar.upenn.edu's message of 5 May 92 14:33:49 GMT

In article <76781@netnews.upenn.edu> weemba@sagi.wistar.upenn.edu (Matthew P 
Wiener) writes:

   >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.

  Talk about undecidable sentences having to be self-referential is
indeed pretty nonsensical, but your remarks overlook the little nugget
of sense in this kind of comment. Godel's theorem is not at all the
assertion that a certain formal system is incomplete. Godel himself
was very carefully vague in his description of the result - "the
formal incompleteness of Principia Mathematica and related systems".
The nugget of sense consists in the observation that some form of
diagonalization is used in all proofs of Godel's theorem. Indeed, in
the case of the specific undecidable statement of Kirby and Paris,
they proved it to be undecidable in PA by proving that it implies the
consistency of PA, and the proof of Godel's second theorem uses the
Godel sentence.


