Newsgroups: comp.ai.philosophy,alt.consciousness.mysticism,alt.consciousness,alt.paranormal.channeling,talk.philosophy.misc,alt.atheism
Path: cantaloupe.srv.cs.cmu.edu!nntp.club.cc.cmu.edu!godot.cc.duq.edu!news.duke.edu!MathWorks.Com!europa.eng.gtefsd.com!howland.reston.ans.net!news.sprintlink.net!demon!betanews.demon.net!news
From: paul@morat.demon.co.uk (Paul Andrew King)
Subject: Re: rereRe: The end of god
Message-ID: <492@morat.demon.co.uk>
Sender: news@demon.co.uk (Usenet Administration)
Nntp-Posting-Host: morat.demon.co.uk
Organization: home
References: <36vt2m$g6m@scapa.cs.ualberta.ca> <371epj$8gn@engnews2.Eng.Sun.COM> <IECbkKlrZkPU070yn@gagme.wwa.com>
Date: Sun, 9 Oct 1994 11:40:21 GMT
Lines: 36


In article <IECbkKlrZkPU070yn@gagme.wwa.com> whitroth@gagme.wwa.com (mark)
writes:
>In article <371epj$8gn@engnews2.Eng.Sun.COM>, tlw@Eng.Sun.COM (Tom Wetzel)
wrote:
>> Kevin Wiebe writes:
><snip> 
>Sorry, you blew it on your examples. Euclidean geometry is a *perfect*
>example of *incompleteness*, since it requires...(been a buncha years)
>five, I think, axioms, which are unprovable within the system, such
>as parallel lines, etc.

Get a clue.  "Incomplete" doesn't mean having axioms (if it did then
Godel's theorem would be utterly trivial, instead of one of the most 
significant discoveries in mathematics).

1) *All* formal systems start with axioms.
2) The axioms are trivially proved within the system (simply by restating
them)
3) If an axiom could be derived from the *other* axioms then it wouldn't be
an axiom.

Incomplete means that there are statements in the system which are true,
but not derivable from the axioms (I repeat that each axiom can be "derived"
from itself)
>
>And neither God (tm), nor this level of math is really appropriate for
>many of these newsgroups, and alt.pagan is one for which it ain't.
>Can you prune your crossposting list?
>
>    mark

I agree that the list needs pruning, but my setup is very unreliable at
fiddling with crossposts.

Paul K.
