Path: utzoo!attcan!uunet!husc6!mailrus!ames!zodiac!joyce!sri-unix!garth!smryan
From: smryan@garth.UUCP (Steven Ryan)
Newsgroups: comp.ai
Subject: Re: The Ignorant assumption
Message-ID: <1418@garth.UUCP>
Date: 16 Sep 88 01:58:53 GMT
References: <1411@garth.UUCP> <2381@uhccux.uhcc.hawaii.edu>
Reply-To: smryan@garth.UUCP (Steven Ryan)
Organization: INTERGRAPH (APD) -- Palo Alto, CA
Lines: 16

>" ... We all know (I hope) formal systems are either
>" incomplete or inconsistent.
>
>I don't know that.  Can you show this for predicate logic?

Either a system is too simple (like propositional calculus) to
do number theory (which is equivalent to everything else) or it's
powerful enough in which Godel's theorem come into play: any
system powerful enough for number theory is either incomplete or
omega-inconsistent.

Simple systems like propositional calculus are complete within their domain,
but their domain is incomplete with respect to number theory and all
other formal system.

(Predicate calculus includes quantifiers; propositional calculus does not.)