Re: [lojban] Re: Holiday Present from the BPFK: The gadri Proposal Has Been Completed

["And Rosta" <a.rosta@v21.me.uk>]

xorxes:
> --- And Rosta wrote:
> > > The idea of plural reference
> > > is mostly taken from a paper by Thomas McKay, which can be
> > > read here: http://philosophy.syr.edu/
> > 
> > I've given the first 3 chapters a hurried but not perfunctory reading,
> > & find none of his arguments against singularism in the least 
> > persuasive. Nor do I see why the distinction matters. Are the
> > clinching arguments to be found later on? 
> 
> Probably not. I don't remember exactly, but the final chapters
> are very technical. We didn't adopt his plural quantifiers 
> anyway, Lojban quantifiers are still the ordinary singular ones,
> but unquantified sumti can have several referents.
> 
> The distinction matters if we want to give a general interpretation
> to quentifiers. {PA <sumti>} is quantification over the (usually
> more than one) referents of <sumti>. For any given sumti. 

I can't get my head around nonsingularist logic -- I understand it
to a certain extent, but doubt I could reason in it. But I don't
think this is a problem: "referent", in the sense that appears to
be used here, can be defined simply as "that which is quantified
over".
 
> >[I have also given a very 
> > hurried read through what I could find on the twiki; I didn't
> > see anything explanatory there, but maybe I missed it.]
> > But at any rate, I could rephrase my questiion: To say "3 of the-
> > individuals-among lo vo nanmu", one would need to use a predicate
> > meaning "is-an-individual-among" -- is that right? 
> 
> {ci lo vo nanmu cu klama}
> Exactly three of the referents of "lo vo nanmu" are goers.
> 
> There is no need for a predicate there, but {me <sumti>} gives the
> predicate "x1 is/are among the referents of <sumti>", so in general
> we have:
> 
>  PA <sumti> = PA da poi ke'a me <sumti>
>               PA x, such that x is among the referents of <sumti>.
> 
> > And "ci lo vo
> > nanmu" is "three quartets of men"?
> 
> No, that would be {ci lo gunma be lo vo nanmu}, or {ci loi vo nanmu}.
> The referents of {lo gunma be lo vo nanmu}, or of {loi vo nanmu}
> which is the same thing by definition, are quartets of men, so here
> with the quantifier we count quartets.  

At least xorlo makes good use of the PA lV--PA lVi distinction, and
uses it to make a key semantic distinction.

This said, I don't understand how come "ci lo vo nanmu" quantifies
over the four referents of "lo vo nanmu", yet "ci loi vo nanmu"
quantifies not over the one referent of "loi vo nanmu" but
rather over the quasi-infinite number of things that "loi vo
nanmu" can refer to. It's not that I see anything objectionable
to this -- indeed, it's expressively a good thing -- but I don't
understand the basis for the claim about PA me <sumti>.

--And.