Return-Path: Delivered-To: shoulson-kli@meson.org Received: (qmail 29405 invoked from network); 3 Mar 2000 15:14:03 -0000 Received: from zash.lupine.org (205.186.156.18) by pi.meson.org with SMTP; 3 Mar 2000 15:14:03 -0000 Received: (qmail 14076 invoked by uid 40001); 3 Mar 2000 15:14:02 -0000 Delivered-To: kli-mark@kli.org Received: (qmail 14073 invoked from network); 3 Mar 2000 15:14:00 -0000 Received: from fl.egroups.com (208.50.144.74) by zash.lupine.org with SMTP; 3 Mar 2000 15:14:00 -0000 X-eGroups-Return: sentto-44114-2156-mark=kli.org@returns.onelist.com Received: from [10.1.10.36] by fl.egroups.com with NNFMP; 03 Mar 2000 15:13:52 -0000 Received: (qmail 12307 invoked from network); 3 Mar 2000 15:13:46 -0000 Received: from unknown (10.1.10.27) by m2.onelist.org with QMQP; 3 Mar 2000 15:13:46 -0000 Received: from unknown (HELO hotmail.com) (216.33.241.194) by mta2.onelist.org with SMTP; 3 Mar 2000 15:13:46 -0000 Received: (qmail 64697 invoked by uid 0); 3 Mar 2000 15:13:45 -0000 Message-ID: <20000303151345.64696.qmail@hotmail.com> Received: from 200.41.247.39 by www.hotmail.com with HTTP; Fri, 03 Mar 2000 07:13:45 PST X-Originating-IP: [200.41.247.39] To: lojban@onelist.com MIME-Version: 1.0 Mailing-List: list lojban@onelist.com; contact lojban-owner@onelist.com Delivered-To: mailing list lojban@onelist.com Precedence: bulk List-Unsubscribe: Date: Fri, 03 Mar 2000 07:13:45 PST X-eGroups-From: "Jorge Llambias" From: "Jorge Llambias" Subject: [lojban] The Quine challenge Content-Type: text/plain Content-Transfer-Encoding: 8bit Content-Length: 2145 Lines: 59 From: "Jorge Llambias" > > A student at Yale may belong to zero or more clubs. > > Some clubs are final clubs. > > A final club is defined as "a club such that membership > in it >precludes membership in any other final club". I am assuming that "precludes" is not a symmetric relationship, i.e. "membership in A precludes membership in B" does not entail "membership in B precludes membership in A". In practical terms it does entail it, but I'm assuming that the definition of final clubs rests on the preclusion rules of each club and not on the practical preclusions resulting from the rules. Otherwise the problem has a different solution. Now, final clubs are well defined only in the following situation: Membership in every club that reciprocates all preclusions precludes membership in every other club that reciprocates all preclusions. (Note: clubs that have no preclusions against them count as trivially reciprocating all preclusions.) To see that this is necessary, assume it is not: then there are at least two clubs X and Y that reciprocate all preclusions, but membership in X does not preclude membership in Y. Then we could choose either X or Y to be a final club consistently with the definition, but not both. In such case club finality would not be well defined. In the situation in which final clubs are well defined, this is a non-circular definition: A final club is any club which reciprocates all preclusions. (i.e., any club X such that membership in X precludes membership in Y for any club Y such that membership in Y precludes membership in X.) Any takers? co'o mi'e xorxes ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com ------------------------------------------------------------------------ GET A NEXTCARD VISA, in 30 seconds! Get rates as low as 2.9% Intro or 9.9% Fixed APR and no hidden fees. Apply NOW! http://click.egroups.com/1/936/1/_/17627/_/952096428/ ------------------------------------------------------------------------ To unsubscribe, send mail to lojban-unsubscribe@onelist.com