Re: [lojban] xorlo and masses

[Martin Bays <mbays@sdf.org>]

* Saturday, 2011-08-20 at 18:06 -0300 - Jorge Llambías <jjllambias@gmail.com>:

> On Sat, Aug 20, 2011 at 4:53 PM, Martin Bays <mbays@sdf.org> wrote:
> > * 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:
> >> > 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).
> 
> (Do you want "lo broda zo'u ro ri brode"? Otherwise "ro ri" goes in
> the x2 of "brode".)

(I know, but it still works as an example)

> I think we should be able to say "lo broda zo'u ro ri poi brodi cu
> brode" where "brodi" dismembers the broda-atoms into brodi-atoms.
> 
> To be more concrete:
> 
> lo bevri be lo jubme zo'u re ri cu verba
> "The carriers of table(s): two of them are children."
> 
> should not imply that two whole teams of table carriers are children,
> but is more likely just saying that two people among the table
> carriers are children..
> 
> This is basically saying that "lo broda" is "zo'e noi ke'a broda", and
> not "zo'e noi ro ke'a broda".

Hmm. These are tempting semantics, but I don't see how to formalise
them nicely.

We seem to want that a simple sumti, like {lo broda} or {ko'a}, should have
interpretation a Whole, which I'll denote [lo broda] resp. [ko'a].

Then you'd have that {re ko'a broda} means that in the set of wholes
    { X partof [ko'a] | broda(X) } ,
there are precisely two minimal elements?

That seems reasonable; but it doesn't explain {ro ko'a broda}.

How, without invoking absolute atoms, can you give a meaning to
{ro ko'a broda} based only on the Whole [ko'a] and on the meaning of
{broda}?

If broda is brodi-distributive (and brodi is considered somehow
canonical in this respect), you could have {ro ko'a broda} mean that
all brodi-atoms below [ko'a] satisfy broda. But what then about highly
non-distributive predicates like S(X) := {X sruri ko'e}? In general,
we can't expect to have anything better than S being S-distributive.
So following the same rule, {ro ko'a sruri ko'e} would mean that every
S-atom below ko'a satisfies S, which is an uninformative tautology.

I also don't see how to formalise your atomising poi.

> >> > {re lo bevri be su'o jubme cu ci mei .i pa ra verba}
> >
> > 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.
> 
> (Not really very relevant to your point, but why a bijection? Some of
> the Wholes could carry more than one table, and perhaps some of the
> tables were carried more than once, and maybe some tables were not
> carried at all.)

(sure; the setup was meant to be the simplest one, in which we do get
a bijection)

> > 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.
> 
> I don't like the idea of pronouns carrying more info than B. The
> reason is that some Wholes are more natural than others, and having to
> keep track of unnatural Wholes is... well, unnatural.

I agree. But as discussed above, I don't see how to get this working
without using global atoms.

(From which I would conclude that using global atoms is the right
thing to do)

> >> 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).
> 
> Suppose two people carry two (smallish) tables in the same action. It
> makes no more sense to say that the carrying is distributed over the
> tables than to say it is distributed over the people.

OK. I expect there would be disagreement in this case as to whether it
distributes over the tables. Probably in lots of other cases too.

> >> 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.
> 
> Yes, but what I'm trying to say is that the same word (say "bevri")
> can be used to represent (slightly) different predicates in different
> contexts, the slight difference being in this case its
> distributiveness type over its arguments.

Hmm. I'd be happier making the simplifying assumption when theorising
about the language that the meaning of a predicate is immutable and
consists of (in the first approximation) a Boolean truth function on
tuples of Wholes... but I agree that that's a theoretical abstraction
which would likely be ignored by actual language users.

> >> (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.
> 
> I suppose that's the kind of information that is meant to be given by
> the "(mass)" comments in the gi'uste.

Specifically indicating non-distributivity? Yes.

Martin

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