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From: drw@cullvax.UUCP (Dale Worley)
Newsgroups: sci.math,sci.math.symbolic,sci.philosophy.tech
Subject: Russell's set of sets which... paradox
Message-ID: <1404@cullvax.UUCP>
Date: Tue, 28-Jul-87 18:03:50 EDT
Article-I.D.: cullvax.1404
Posted: Tue Jul 28 18:03:50 1987
Date-Received: Thu, 30-Jul-87 01:57:58 EDT
Organization: Cullinet Software, Westwood, MA, USA
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Xref: mnetor sci.math:1675 sci.math.symbolic:111 sci.philosophy.tech:315

campbell@utx1.UUCP (Tom Campbell) writes:
> I would like to know if a *satisfactory explaination* has ever
> been given regarding Russell's well-known set theory paradox.

Perhaps the best way to phrase the solution is as a consequence of a
really very subtle principle of modern mathematics:  "There are
syntactically well-formed sentences, which nonetheless don't mean
anything."  A particular example of this is "the set of all x's which
have property P(x)" -- this phrase denotes a set for only certain
properties P, and "non-self-membership" isn't one of them.

The earliest example that I know of is from the Scholastic philosophy
(Midaeval Catholic, about 1300?):  "Can God make a stone so large that
he can't lift it?"  The solution, of course, is that there can be no
such stone.

Dale
-- 
Dale Worley	Cullinet Software		ARPA: cullvax!drw@eddie.mit.edu
UUCP: ...!seismo!harvard!mit-eddie!cullvax!drw
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