From jjllambias@hotmail.com Fri Mar 3 14:54:50 2000 X-Digest-Num: 383 Message-ID: <44114.383.2187.959273826@eGroups.com> Date: Fri, 03 Mar 2000 14:54:50 PST From: "Jorge Llambias" Subject: Re: final clubs la karl cusku di'e >Perhaps the definition is flawed. I assumed that the >designation 'final' was applied to clubs _after_ they were >subjected to the test condition (that they precluded >membership in each other). It is applied at the same time, since it is a circular definition. You take the proposed set of final sets and test if they comply. If you test {B, C} it passes. If you test {A} it also passes. (Assuming no existential import in the definition.) Therefore, there is no well defined set of final clubs, as there are two competing suitable and incompatible candidates. >That is to say, they're >final clubs because they're mutually exclusive, not >mutually exclusive because they're final clubs. Both things. > > ... You cannot join both B and C, but > > that is not enough to make them final. > >Excuse me? That is _exactly_ the definition of a final club, Yes, when it gives a single set of final clubs. But not when more than one set is possible. >I disagree. You could call A final if there weren't any >other candidates for final clubs, but there aren't any >conditions in A's bylaws to license that deduction in >any non-vacuous way. If what you object to is the vacuous satisfaction of the definition by A, then use this new definition for well defined final sets: Final sets are all sets with some preclusion. In your example, the situation is one where B and C are well defined final sets. To prove my new definition wrong you need a situation where a club with some preclusion is not final. co'o mi'e xorxes ______________________________________________________ Get Your Private, Free Email at http://www.hotmail.com