Re: [lojban] xorlo and masses

[Martin Bays <mbays@sdf.org>]

* Saturday, 2011-08-20 at 11:39 -0300 - Jorge Llambías <jjllambias@gmail.com>:

> On Sat, Aug 20, 2011 at 7:52 AM, Martin Bays <mbays@sdf.org> wrote:
> >
> > One issue with this approach, though (and maybe this is what you
> > meant, actually?) is that quantification only makes sense when we have
> > an idea of what atoms are relevant. So in {lo broda ro ri brode}, {ri}
> > would have to carry as information not only what Whole {lo
> > broda} refers to, but also that quantification of it is to be taken
> > with respect to broda-atoms.
> 
> What I meant was that it is "brode", not "ri", that needs to carry
> that information.

How would that work, sorry?

Having it in the sumti seems coherent, and I'm starting to think it
might even be usable (and barely diverge from current usage and
prescription).

> > That's conceptually slightly ugly, and I don't know how intuitive it
> > would be.
> >
> > (Example of use: in the context of people carrying tables,
> > {re lo bevri be su'o jubme cu ci mei .i pa ra verba}
> > would mean that two of the tables are being carried by threesomes, and
> > one of the tables is being carried by a group which consists entirely
> > of children.
> 
> I'm not sure I see that that follows. "ra" should have the same
> referents as "lo bevri be su'o jubme". The natural distribution of
> "verba" is over people, so I would interpret "pa ra verba" as saying
> that one of the carriers of tables is a child, with no information as
> to whether the child is in one of the two threesomes. But that's only
> assuming the most natural distribution of "verba".
>
> You are assuming that from the context the natural distribution
> shifts from prenu to "cimei [be lo prenu]", and further that the
> referents of "ra" are not the same referents of "lo bevri be su'o
> jubme" but those of "lo bevri be su'o jubme be'o poi ci mei [be lo
> prenu]".

I wasn't, although I see that the english translation I gave could
give that impression.

Let me give in painful detail the meaning I meant to give the lojban,
and how I derive it:

The interpretation of {lo bevri be su'o jubme} has data (B,P) where B
is the Whole of the people carrying the tables, and P is the predicate
 P(x) :== (x carries >=1 table) ;
the P is recorded to indicate that when the sumti is quantified, the
quantification is over those P-atoms which are parts of B.

By definition of B and P, a P-atom below B is precisely the Whole
which carries one of the tables. So the P-atoms below B are in
bijection with the tables. 

Now {ri} also has data (B,P). So {pa ri verba} means that exactly one
of the P-atoms below B satisfies {verba}. Since {verba} is
x1-distributive wrt people, this claims that all of the people who are
part of this P-atom are children - i.e. that all of the carriers of
the corresponding table are children. There may or may not be three of
them.

> > Assuming {bevri} is distributive in x2 with respect to tables, {lo
> > prenu cu bevri lo jubme} would accurately describe the situation, and
> > {ro lo prenu cu bevri lo jubme} would be false.)
> 
> Right, but it is not a general property of "bevri" that it is
> distributive in x2 with respect to tables. In some other context we
> may need that it not fully distribute with respect to tables.

Maybe so (although I can't actually think of an example).

> What I was getting at is that it is not generally part of the
> meaning of a predicate how it distributes in any of its arguments
> with respect to other predicates, although in a lot of cases there
> is an obvious natural choice.

Well... technically it is part of the meaning, if we accept that the
meaning of a predicate includes the information as to when it is true
of given arguments.

> (We could try to define predicates in such a way that how they
> distribute with respect to other predicates is always determined,
> but I don't think it would work from a practical usage point of
> view.)

Agreed, although hints like "usually distributive over foos" could be
helpful when indicating meaning.

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