From cburke@MITRE.ORG Fri Mar 3 14:34:28 2000 X-Digest-Num: 383 Message-ID: <44114.383.2184.959273826@eGroups.com> Date: Fri, 03 Mar 2000 17:34:28 -0500 From: Carl Burke Subject: Re: final clubs Jorge Llambias wrote: > From: "Jorge Llambias" > > > > >Club A imposes no conditions on its members > > > >Club B requires members to swear a loyalty oath, > > > > and to swear no other oaths > > > >Club C requires members to swear a loyalty oath, > > > > and to swear no other oaths > > > > > > How can you tell in that example that it is B and C that > > > are final, and not that A is the only final club? > > la xod cusku di'e > > >Because you can't be a member of B and C, unless you join them > >simultaneously. If A was final and {B, C} were not, you could join both B > >and C. > > Sorry, I don't understand. A can be final by itself: > Membership in A precludes membership in any other > final club (which happen to be none). > Membership in B or C does not preclude membership > in A, which is the only final club, so they are not > final clubs. This is consistent with the definition > of final clubs. 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). That is to say, they're final clubs because they're mutually exclusive, not mutually exclusive because they're final clubs. > ... 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, that membership in one precludes membership in all other final clubs. You cannot join both B and C, therefore they must be final. Since B and C must be final (because their bylaws preclude membership in each other), A cannot be final (unless you can have multiple sets labeled 'final', which are mutually exclusive internally but not across set boundaries.) > Of course, B and C being final and A not final is > also consistent. That is why final clubs are not well > defined in this situation. We have two possible > answers. 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. -- Carl Burke cburke@mitre.org