Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!uunet!seismo!ll-xn!cullvax!drw 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 Lines: 21 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 From the Temple of St. Cathode of Vidicon: