From jjllambias@hotmail.com Fri Mar  3 07:13:45 2000
X-Digest-Num: 382
Message-ID: <44114.382.2157.959273826@eGroups.com>
Date: Fri, 03 Mar 2000 07:13:45 PST
From: "Jorge Llambias" <jjllambias@hotmail.com>
Subject: The Quine challenge
X-Yahoo-Message-Num: 2157


> > A student at Yale may belong to zero or more clubs.
> > Some clubs are final clubs.
> > A final club is defined as "a club such that membership > in it 
>precludes membership in any other final club".

I am assuming that "precludes" is not a symmetric
relationship, i.e. "membership in A precludes membership
in B" does not entail "membership in B precludes
membership in A". In practical terms it does entail it,
but I'm assuming that the definition of final clubs
rests on the preclusion rules of each club and not on
the practical preclusions resulting from the rules.
Otherwise the problem has a different solution.

Now, final clubs are well defined only in the
following situation: Membership in every club that
reciprocates all preclusions precludes membership
in every other club that reciprocates all preclusions.

(Note: clubs that have no preclusions against them
count as trivially reciprocating all preclusions.)

To see that this is necessary, assume it is not: then
there are at least two clubs X and Y that reciprocate
all preclusions, but membership in X does not preclude
membership in Y. Then we could choose either X or Y to
be a final club consistently with the definition, but
not both. In such case club finality would not be well
defined.

In the situation in which final clubs are well defined,
this is a non-circular definition:

     A final club is any club which reciprocates
     all preclusions.

(i.e., any club X such that membership in X precludes
membership in Y for any club Y such that membership in Y
precludes membership in X.)

Any takers?

co'o mi'e xorxes


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