Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!uunet!seismo!husc6!mit-eddie!uw-beaver!tektronix!reed!mojo From: mojo@reed.UUCP (definition) Newsgroups: sci.math,sci.math.symbolic,sci.philosophy.tech Subject: Re: Russell's set of sets which... paradox Message-ID: <6678@reed.UUCP> Date: Thu, 23-Jul-87 14:13:25 EDT Article-I.D.: reed.6678 Posted: Thu Jul 23 14:13:25 1987 Date-Received: Sat, 25-Jul-87 11:22:21 EDT References: <1214@utx1.UUCP> Reply-To: mojo@reed.UUCP (definition) Organization: The Phrench Phry Contingency Lines: 27 Keywords: set theory, paradox, logic Summary: no answer expected Xref: mnetor sci.math:1636 sci.math.symbolic:101 sci.philosophy.tech:298 In article <1214@utx1.UUCP> 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. } }For those who are not familar with it, here it is. } }Let S' be a set such that S' has as its elements all and only those }sets which have the following property: } } They do not have themselves as elements. } }QUESTION: Is S' a set which does not have itself as a member? } } } Thanks, TDC What would you consider a "satisfactory explanation"? The only reasonable analysis I can imagine goes to the point of saying that S' is a member of itself iff S' is not a member of itself, then breaks down into paradox. This is a little like asking for a satisfactory explanation of the "This sentence is false" paradox. "Paradox is its own explanation" Nathan Tenny ...tektronix!reed!mojo