Path: utzoo!attcan!uunet!ginosko!xanth!ames!uhccux!lee
From: lee@uhccux.uhcc.hawaii.edu (Greg Lee)
Newsgroups: comp.ai
Subject: Re: intelligence and the initial conditions of the universe (BANG!!!)
Message-ID: <4558@uhccux.uhcc.hawaii.edu>
Date: 13 Aug 89 13:13:06 GMT
References: <0YtCI7a00V4G40XHNL@andrew.cmu.edu>
Organization: University of Hawaii
Lines: 22

From article <0YtCI7a00V4G40XHNL@andrew.cmu.edu>, by jk3k+@andrew.cmu.edu (Joe Keane):
\In article 1989Aug11.114022.481@IDA.ORG> rwex@IDA.ORG (Richard Wexelblat)
\writes:
\>In article <1490@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes:
\>>     The mathematics is independent of the universe.  
\>
\>You beg the question.  How do you know this is so?
\
\Because we state in advance what assumptions (axioms) we're using.  Everything
\else can be derived from them. ...

In advance of doing the mathematics?  But that's not so, in general.
Axioms have usually been discovered after some significant mathematics
has been done.  If there were no interesting or useful mathematics in
some area, why would anyone bother to axiomatize it?  It is also not
true that axioms have a logical priority.  The theorems that follow from
a set of axioms are also sufficient to deduce the axioms.  Besides, if
axioms _were_ stated in advance, how would that show that mathematics is
independent of the universe?  And besides _that_, where did you get
the idea that only mathematics can be axiomatized?

				Greg, lee@uhccux.uhcc.hawaii.edu