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

From: [email-masked]
Date: Sat, 9 Mar 2002 17:18:46 EST

In a message dated 3/9/2002 2:57:35 PM Central Standard Time, 
[email-masked] writes:

> 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.) 

Thanks for the reminder; we get so involved in the give and take that we 
forget to check on basics from time to time. Yes, it is a universal class 
that is wanted and just which one is very hard to say. It is easier in a 
formal language when the types are all in a row, but Lojban reduces 
everything to one type, as it were (but so do most natural languages), so 
what all can be quantified over is not at all clear. Everything that can be 
successfully referred to in Lojban is clearly in and a lot more besides (all 
of set theory and hence of mathematics is in, for example). In any case, it 
is unlikely to be a recognizable class from some organized theory, though the 
classes from a number of theories probably get into it (it may not be 
formally coherent, though presumably non-contraditory, since it is the stuff 
of reality).