Re: [lojban] Sets etc.

[John Cowan <jcowan@reutershealth.com>]

From: John Cowan <jcowan@reutershealth.com>

Peter Moulder wrote:

> Does `any' above mean `all' or `some'?  I've taken it to mean `all'.

Me too.

> Consider the case where there are two or more clubs, and no club
> precludes membership in any other club.  What answer would you want
> the "definition" to give in this case?

I think we can afford to ignore cases where the definition doesn't converge.
After all, there really is a Yale and it really does have clubs,
some of which are really final.   What we want, to paraphrase
Chip Delaney, is to know what we are talking about when we are talking
about them. 

> For all values of (C, E, F) within the above domain:
> 
>  final(C, E, F) <=>
>    (all[C1]
>      ((C1 \in C)
>       => ((C1 \in F)
>           <=> (all[F1]
>                 ((F1 \in F)
>                  => ((C1 = F1)
>                      ; (pair(C1, F1) \in E)))))).

Looks correct to me.

-- 

Schlingt dreifach einen Kreis vom dies! || John Cowan <jcowan@reutershealth.com>
Schliesst euer Aug vor heiliger Schau,  || http://www.reutershealth.com
Denn er genoss vom Honig-Tau,           || http://www.ccil.org/~cowan
Und trank die Milch vom Paradies.            -- Coleridge (tr. Politzer)

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