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From: ags@j.cc.purdue.edu (Dave Seaman)
Newsgroups: sci.math,sci.math.symbolic,sci.philosophy.tech
Subject: Re: Russell's set of sets which... paradox
Message-ID: <4913@j.cc.purdue.edu>
Date: Tue, 4-Aug-87 10:17:40 EDT
Article-I.D.: j.4913
Posted: Tue Aug  4 10:17:40 1987
Date-Received: Thu, 6-Aug-87 04:08:46 EDT
References: <1404@cullvax.UUCP> <902@bsu-cs.UUCP> <4901@j.cc.purdue.edu> <918@bsu-cs.UUCP>
Reply-To: ags@j.cc.purdue.edu.UUCP (Dave Seaman)
Organization: Purdue University
Lines: 24
Xref: mnetor sci.math:1745 sci.math.symbolic:119 sci.philosophy.tech:352

In article <918@bsu-cs.UUCP> dhesi@bsu-cs.UUCP (Rahul Dhesi) writes:
  [ regarding the stone paradox ]
>Let me throw this at you:  
>
>     Omnipotent Being n. A being with the power to invalidate any or
>     all possible sets of axioms.
>
>Now try again.

But of course.  I know what omnipotent means, and my proof depends on it.
I grant you that an omnipotent being could invalidate all possible sets of
axioms IF IT EXISTED.  But the proof shows that it doesn't, and it does so
without denying the being's ability to do any particular thing, including
denying axioms.

You may, of course, claim that there is an omnipotent being who has
presented us with a logic that appears to work in all cases that we can
verify, but which does not apply to herself.  The argument then reduces to
"either there is no omnipotent being, or all of logic (and all of
mathematics) is just an illusion."  Obviously the continuation of that
argument does not belong in sci.math.
-- 
Dave Seaman	  					
ags@j.cc.purdue.edu