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Re: [lojban] About plural 'ro'

Jorge Llambías, On 22/04/2010 22:34:

On Thu, Apr 22, 2010 at 11:44 AM, And Rosta <and.rosta@gmail.com> wrote:

If every possibly combination of individuals constitutes a
group/bunch/set/collectivity, so that there is no doubt over the
definitiion, is it necessary, and is it advantageous, to invoke plural
quantification/predication?


Plural reference is useful to say things like:

    lo tadni cu dasni lo xunre mapku gi'e sruri lo dinju
    "The students wore red caps and surrounded the building."

With groups instead of plural reference, we would have to split the
claim into two: each student (not the group) wore red caps, and the
group (not each student) surrounded the building.

Or else, change one of the predicates to something like "participated
in the surrounding of the building", or "has members each of which
wore red hats". That's less appealing than just saying of the students
that they wear hats and that they (the same students that wear the
hats) surround the building.


OK. But consider "The students are men and women", where you don't mean to claim that anybody is both a man and a woman. I take that to mean "Each of the predicates is-a-man and is-a-woman is predicated of some subcollectivity of the students". Likewise, your example is "Each of {wore red caps, surrounded the building} is predicated of some subcollectivity of the students".

So the difficulty with Lojbanizing your English example doesn't really have to do with problems with mixing 'collective' and 'distributive' predicates, and the solution is one that would also handle my example.


For that, we only need plural reference, not plural quantification.
According to pc, we can't have plural reference without plural
quantification. I don't have a problem with introducing let's say
"ro'oi" and "su'oi" for the plural universal and existential
quantifiers. As long as we leave "ro" and "su'o" for the usual
singular ones, which are the ones most often needed.


OK. This is sensible. So my question is limited to the necessity or advantage of plural reference.


That's the case for plural reference.

A second issue, completely separate from the above, is the meaning of
an expression like:

    ro <sumti> cu broda

given that "ro" is the singular universal quantifier, and <sumti> is a
term with plural reference.

Now, a quantifier needs a domain of quantification. A term with plural
reference has a number of referents. What to do?

I know! Let's use the set of referents of the sumti as the domain of
quantification for the quantifier! (What else?)

But what if instead of a singular quantifier, we have a plural quantifier:

    ro'oi <sumti> cu broda

Now, a plural quantifier also needs a domain of quantification. Again,
we note that a term with plural reference has a number of referents.
What to do? How about... let's use the set of referents of the sumti
as the domain of quantification for the plural quantifier!


It's not entirely a separate question, because if there is no plural reference then different answers to your questions are needed. To my way of thinking, the ro'oi one would involve quantifying over subcollectivities of <sumti> and the ro one would involve quantifying over primitive subcollectivities of <sumti> (where primitive = a subcollectivy with no subcollectivity but itself).

(When I say "to my way of thinking", I mean about the semantic representations, not about what Lojban locutions are supposed to mean.)


Now comes a third issue, independent of the other two issues.

We know (or at least don't argue much about) how sumti such as ti, ta,
tu, mi, do, ri, ra, ko'a, di'u, etc. get their referents, which can be
one or many. 

It's not clear to me that the referent can be many (rather than being a collectivity, if that is different from being many).


But how does a sumti like "lo broda" get its referents?

No matter how it gets them, we know that they must satisfy the broda
predicate, i.e. "lo broda cu broda". Is it necessary that each of the
referents satisfy the predicate? No. Is it necessary that they satisfy
it all collectively? No. Is it necessary that they satisfy it in
groups of seven? No. In groups of varying numbers? No, that's not
necessary either. All that is required is that its referents must
satisfy the predicate "broda", in whatever arrangement they do it,
i.e. "lo broda" = "zo'e noi ke'a broda", it is a sumti whose
referent(s) satisfy the predicate broda.


OK. But it's plain to see how if there's only one referent then this is all so much simpler.


When we need to specify how exactly the referents of "lo broda" broda,
we have to do it by some other means, because "lo broda" by itself
doesn't say. Similarly, in "lo broda cu brode", when we need to
specify how exactly the referents of "lo broda" brode, we need to do
it in some other way, because neither "lo broda" nor "brode" do it.

What means do we have at our disposal? One is the singular universal
quantifier "ro":

     ro lo tadni cu dasni lo xunre mapku
     "Each one of the students wears a red cap."

What about the surrounding of the building? Well, we could say, for example:

     pa djine be lo tadni cu sruri lo dinju
     "One ring of students surrounded the building."

Or:

     ci djine be lo tadni cu sruri lo dinju
     "Three rings of students surrounded the building."

After all, there are many different configurations in which the
students could surround the building together. If we are not too
concerned about the exact configuration, but we still want to insist
that they did it as a group (in case that's not obvious from the
context), we could say:

     lo gunma be lo tadni cu sruri lo dinju
     "A group of students surrounded the building."

As someone once said, the price of infinite precision is infinite verbosity.


I pretty much agree with all this. Translated into my terms, "Some subcollectivity of <sumti>" is similarly vague.

--And.

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