Re: [lojban] final clubs

[Carl Burke <cburke@MITRE.ORG>]

From: Carl Burke <cburke@MITRE.ORG>

Jorge Llambias wrote:
> From: "Jorge Llambias" <jjllambias@hotmail.com>
> 
> > > >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


------------------------------------------------------------------------
DON'T HATE YOUR RATE!
Get a NextCard Visa, in 30 seconds!  Get rates as low as 
0.0% Intro or 9.9% Fixed APR and no hidden fees.
Apply NOW!
http://click.egroups.com/1/2120/1/_/17627/_/952122695/
------------------------------------------------------------------------

To unsubscribe, send mail to lojban-unsubscribe@onelist.com