Re: final clubs

["Jorge Llambias" <jjllambias@hotmail.com>]

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