Re: [lojban] Sets etc.

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

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


la djan cusku di'e

>Sets can be sliced into members in only one way: masses, in many
>different ways.

{ko'a joi ko'e} can only have two members, ko'a and ko'e.
{lei pano mlatu} can only have 10 members, each of the cats.
Maybe some masses can be sliced in different ways, but I can't
think of any example. Unless you are thinking of things like
{lo djacu} as a mass, but that is not a mass in the
grammatical sense.

> > I'll give it a shot. Let's use {girzu} for "club", and
> > {mulgirzu} for "final club". This should work:
> >
> >             ca'e ro da poi girzu cu mulgirzu
> >             I define: Every club is a final club.
> >
> > I think that is the only way that what you called a
> > definition can really define final clubs.
>
>This definition is too inclusive.  Here's an example.
>
>Membership in Club A does not preclude membership in any club.
>Membership in Club B precludes membership in every other club.
>Membership in Club C precludes membership in Club D.
>Membership in Club D precludes membership in Club A.
>Membership in Club E precludes membership in Clubs A and C.
>There are no other clubs.

Obviously I misunderstood the definition. I thought that
"a club such that membership in it precludes membership in
any other final club" was a description of a final club
for a given state of students being members of clubs.
I took "precludes" as descriptive of a situation, not as
a membership rule of the club! I thought, for example,
that any club with no members was a final club, not because
of any internal rule of the club but because membership
in it trivially precludes membership in any other club,
and thus in every final club.

But then consider this other example:

Membership in Club X precludes membership in Club Y.
Membership in Club Y precludes membership in Club X.
Membership in Club Z precludes membership in Club W.
Membership in Club W precludes membership in Club Z.
There are no other clubs.

Here either X and Y are final, or Z and W are final,
but not both. So in this case the definition is not a
real definition. It is not enough to tell us which
clubs are final.

So the definition of final club has to preclude some
sets of membership rules like the one above to be
a real definition.

What is Quine's answer? That there is no non-circular
definition?

co'o mi'e xorxes

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