Subject: Re: [lojban] Re: [jboske] Quantifiers, Existential Import, and all that stuff

From: Edward Cherlin <[email-masked]>
Date: Sat, 09 Mar 2002 12:56:57 -0800

On Friday 08 March 2002 11:34, [email-masked] wrote:
> ...when Lojban has {ro
> da} the quantification is over the universal set, which {da}
> represents, not over whatever might come after it...

There is no universal set in any consistent set theory, since the set 
of subsets of a given set is larger (has strictly greater 
cardinality) than the original set. Is there a Lojban term for 
'class' as the term is currently used in set theory? (Crudely, a 
collection of sets must be a class rather than a set if 
contradictions would arise from it being a set. For precision, see 
any of the axiom sets for successful set theories of this kind.) 

Do we think that 'ro da' can refer to the members of a class rather 
than a set? In that case your statement could be rescued by a 
reference to a universal class in some appropriate theory. But the 
phrase "*the* universal class" would still be inadmissible, unless 
you mean to express "what-I-describe-as-the universal class".

-- 
Edward Cherlin
[email-masked]
Does your Web site work?