Re: Set Theory Woes

[Ashley Yakeley <AshleyB@HALCYON.COM>]

At 1997-12-24 03:38, Logical Language Group wrote:

>>Worse still, "ce" is inconsistently defined in the refgram. On page 354,
>>"A ce B" is defined as the set with elements A and B (or {A, B}).
>>Logically, and together with the left-grouping rule, this means that "la
>>frank. ce la .alis. ce la djeimyz." means {{Frank, Alice}, James}, that
>>is, a set with the two members James and the set of Frank and Alice. Page
>>355 inconsistenly assigns this sumti to the more useful meaning {Frank,
>>Alice, James}.
>
>I would not think that left grouping constitutes bounding of the set.

It's not left-grouping alone that bounds the set: it's the binary nature
of "ce" (as defined on p354) together with left-grouping that bounds the
set.

The only solution is to define "A ce B ce C ce D..." as a special form
where the "ce"s cannot be considered separately. It's irregular, inasmuch
as "A ce B ce C" is a set with three members, and "A ce B" is a set with
two members, but "A" is not typically a set with one member.

>If you want to formally get into mathematical set spectification, then you
>need to goi fully into Mex, where you have parenthesis to set bounds on the
>set definition.

Fine, but this kind of mathematical set specification may turn up in
ordinary Lojban utterances.

--
fe'oca'emi'e tricrfraksizeicecmu .iji'a ca'emi'e .aclin.