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From: franka@mmintl.UUCP
Newsgroups: sci.philosophy.tech
Subject: Re: Incompleteness (was: Re: Uncertainty in life)
Message-ID: <2173@mmintl.UUCP>
Date: Mon, 8-Jun-87 22:44:00 EDT
Article-I.D.: mmintl.2173
Posted: Mon Jun  8 22:44:00 1987
Date-Received: Sat, 13-Jun-87 08:01:34 EDT
References: <6762@mimsy.UUCP> <3977@sdcc3.ucsd.EDU> <8135@ut-sally.UUCP> <1192@epimass.EPI.COM> <19216@ucbvax.BERKELEY.EDU>
Reply-To: franka@mmintl.UUCP (Frank Adams)
Organization: Multimate International, E. Hartford, CT.
Lines: 19

In article <19216@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes:
>The upshot of Goedel's incompleteness theorem is the unprovability of
>necessarily true statements, i.e., statements true in every model, for
>sufficiently powerful systems.  That there are *some* statements your
>system can't prove is a good thing: but this is the requirement of
>consistency, not completeness.  First order predicate calculus is both
>consistent and complete.

Perhaps; but let us understand that "sufficiently powerful systems" means
"second order systems" in this conclusion -- which is not at all the same as
the "sufficiently powerful" requirement for the systems to which the
incompleteness theorem itself applies to.

And even then, every unprovable statement is false in some model if you
fudge the definition of "model" a bit.
-- 

Frank Adams                           ihnp4!philabs!pwa-b!mmintl!franka
Ashton-Tate          52 Oakland Ave North         E. Hartford, CT 06108