From pycyn@aol.com Sat Mar 04 06:58:42 2000 Received: (qmail 25038 invoked from network); 4 Mar 2000 14:58:57 -0000 Received: from unknown (10.1.10.27) by m3.onelist.org with QMQP; 4 Mar 2000 14:58:57 -0000 Received: from unknown (HELO imo-d03.mx.aol.com) (205.188.157.35) by mta2.onelist.org with SMTP; 4 Mar 2000 14:58:57 -0000 Received: from Pycyn@aol.com by imo-d03.mx.aol.com (mail_out_v25.3.) id h.37.2215e88 (3888) for ; Sat, 4 Mar 2000 09:58:52 -0500 (EST) Message-ID: <37.2215e88.25f27eac@aol.com> Date: Sat, 4 Mar 2000 09:58:52 EST Subject: Re: [lojban] Final clubs - a basket demonstration To: lojban@onelist.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 4.0 for Windows sub 30 X-eGroups-From: Pycyn@aol.com From: pycyn@aol.com Well, if you start with a totally non-exclusive club (compatible with every club) then you get all of the remaining clubs in the "rest" basket and intuitively have the wrong club in the final set as well (it is not preclusive, but is final only because it is alone). Now, I suppose that the point is that, if there is a final club, then there is no such unexclusive club (given our symmetrical exclusiveness) but, in fact, this is not so, since only membership in final clubs is exclusive, so that such a club -- so long as it is not final -- is possible. And, also possible if it is the only final club. Back to maximally proclusive clubs again. The solution is not with the intersection -- as previously noted -- but with any such set. How to pick which one: the largest (or, this being Yale, the smallest), if there is one, or the one which is first in alphabetic order (clubs have unique names after all, so this is a well-ordering) or the one with the highest prestige (again this is Yale). Any of these will give a unique reading, so there are different sets of rules, each of which works. pc