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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: <4901@j.cc.purdue.edu>
Date: Mon, 3-Aug-87 11:32:23 EDT
Article-I.D.: j.4901
Posted: Mon Aug  3 11:32:23 1987
Date-Received: Wed, 5-Aug-87 04:45:18 EDT
References: <1404@cullvax.UUCP> <902@bsu-cs.UUCP>
Reply-To: ags@j.cc.purdue.edu.UUCP (Dave Seaman)
Organization: Purdue University
Lines: 36
Xref: mnetor sci.math:1739 sci.math.symbolic:117 sci.philosophy.tech:345

In article <902@bsu-cs.UUCP> dhesi@bsu-cs.UUCP (Rahul Dhesi) writes:
>In article <1404@cullvax.UUCP> drw@cullvax.UUCP (Dale Worley) writes:
>>campbell@utx1.UUCP (Tom Campbell) writes:
>[about paradoxes]
>>(Midaeval Catholic, about 1300?):  "Can God make a stone so large that
>>he can't lift it?"  
>
>Assumption:  God is all-powerful.
>
>Conclusion:  God *can* make a stone that he can't lift.  Then he *can*
>lift it.  For being all-powerful means having the ability to violate
>the rules of logic, for the rules of logic exist only because God
>allows them to;  therefore God can suspend the rules.

I hesitated to respond to this because I am not interested in starting a
religious debate, but there is something to be said here that lies in the
realm of logic rather than religion.  It is especially appropriate to the
ongoing discussion about paradoxes.

As others have pointed out, the true meaning of a paradox is that it is
time to re-examine your assumptions.  Russell's paradox, for example, means
you have to be careful about what you call a set.

The stone paradox can be formulated as follows:  Assume x is an omnipotent
being.  Let P(x) be the statement, "x can make a stone so big that x can't
lift it."  Is P(x) true, or is it false?  A little thought shows that it is
neither.

What do we conclude from the contradiction?  There must be something wrong
with the original assumption that there exists an omnipotent being.
Therefore no such being can exist.  Notice that I have never said that
there is any particular thing that x cannot do, or that there is any stone
that cannot exist.  It is x itself that cannot exist.
-- 
Dave Seaman	  					
ags@j.cc.purdue.edu