Re: lu'a

[jorge@PHYAST.PITT.EDU]

pc:
> >       lu'i mu lo plise: a set of exactly five apples.
> This and similar items seem to be no problem: xorxes' interpretation
> coincides with the
> one I hypothesized.  mu lo plise gives  us five apples distributively and
> lu'i groups them
> into a set, a five-membered subset of lo'i plise (here we really are
> forced to use set talk).

I don't think we really need to appeal to lo'i plise. It is true that
lu'i mu lo plise is a subset of lo'i plise, but it need not be defined
in terms of it.

> The set is presumably definite (or is it specific) even though the
> members have not been
> identified.

I would say it is indefinite. Its default quantifier should be {su'o}.
We can also talk of re lu'i mu lo plise: two sets of five apples.

> Presumably lu'o mu lo plise would mean the five apples were
> massifed for
> both of us.

I'm not sure how that matters. The five apples are the elements of the
set, they don't enter in any other relationship. They are internal to
the sumti.

> But I suspect that lu'a mu lo plise may be treated
> differently.  Indeed, I am not
> sure how to treat it, because I do not know what the implicit quantifier
> on lu'a is, ro or
> su'o.

I think it has to be su'o.

> If it is ro, then I would take the lu'a as being redundant, since
> mu lo plise already
> takes all the five apples distributively.

I disagree that {lu'a mu lo plise} gets you apples. As you say, if you
want to talk about apples, you don't need {lu'a} at all.

> If lu'a is su'o lu'a then this
> would distribute only
> some of the original five.

But that's {lo mu lo plise}. No need to use "a component of X" when
X already is a component-type thing.

> I am unclear how, in that case, lu'a mu lo
> plise is related to lo
> mu lo plise (or even le mu lo plise, which seems a particularly useful
> notion, if I
> understand it: the old "a" - "the" game in English, though that has
> better explanations
> within logic).

lo mu lo plise: (At least) one of some five of all apples.
le mu lo plise:  Each of the five of all apples.

The second says nothing different from {le mu plise}. I'm not sure
whether the first says anything different from {lo plise}, since the
first selection of 5 is indefinite, so as far as I can tell has no
logical effect (other than saying that there are at least five apples
in all) but it may have some connotation of there being some especially
relevant five-apple group.

> But I see that this is clearly not what xorxes has in mind:
> >> lu'a ci le selcku might make sense, bringing us down to a new set
> >> (assuming that I was calling more than three things selcku originally).
> >No, to talk about one of the three books one would say {lo ci le selcku}.
> >{lu'a ci le selcku}, if it makes any sense, should be a component common
> >to each of the three books in question.
> I cannot see how lo ci le selcku means "one of the three books"; it seems
> literally to mean
> "some of the three things which are among the books," i.e., " at least
> one of some three of
> the books," selecting distributively from a selection already made (but
> not specified)
> from the specified books.

Sorry, yes, that's what I meant. Presumably that's also what you meant by
{lu'a ci le selcku}. What I meant is that you don't need to use {lu'a} to
do the job that {lo} already does.

> But that
> gets us no
> nearer to understanding  xorxes' lu'a ci le selcku: whence comes this
> "component
> common to each of the three books"?  There is nothing about that either
> in ci le selcku,
> which is just some three books, or in the notion of the members of a set
> or component of
> a mass (neither of which ci le selcku refers to anyhow).

I'm saying that lu'a X will refer to components of X. If X is a set or
a mass whose components we know, then there is no problem, {lu'a} refers
to them. If X does not have explicit components, then we will have to
guess what they are from context. I don't think there is anything wrong
with {lu'a ta} for example. Here again it is not well defined what are
the components of the thing I am pointing at, but if context is clear
why should that be a problem?

> >>  Massification is a logical operation, not a
> >> Waring blender.
> >Of course it is. but you don't need to refer to the mass always in terms
> >of its components. Consider this:
> >       lei pare plise cu gunma  i mi citka re lu'a le gunma
> >       The twelve apples are a mass. I eat two components of the mass.
> >The second sentence should not say that I eat two masses. To say that
> >I can simply say {mi citka re le gunma}.
>         I don't quite understand the latest example here: lei pare plise
> cu gunma is
> analytic, "the mass of  (the) twelve apples is a mass."  But the second
> part is very unclear,
> even given xorxes reading.  le gunma refers to all the masses the speaker
> has in mind,
> presumably the one mass of 12 apples.

Yes, I think we can trust a cooperative listener to understand that.

> lu'a le gunma is then said to be a
> component
> common to all of these, i.e., a component, in this case, of the one mass
> referred to.

Right.

> Ahah! we are to wander through the la'e/sa'e (old style -- what have they
> become? the
> symbol for a referent and the referent of a symbol) complex here.

la'e is the referent of a symbol, and lu'e is the symbol for a referent.

> That
> might be very
> useful, in fact, if it does not interfere with more fundamental uses.

I think it doesn't interfere. If we want to select individuals from
individuals we can always use le/lo directly. lu'a is useful to select
components, even from individually referred masses.

> But what then
> becomes of a case where we DO refer to a mass throughits components: what
> is lu'a le'i
> pare plise

{lu'a le'i pare plise} is at least one member of the set of twelve apples,
there's no problem since {le'i pare plise} is a set. I would never say
that instead of {su'o le pare plise} = at least one of the twelve apples,
but that's another story. Sets can always be avoided in normal
conversation.

> or, worse, lu'a le pare plise?

That would be a component of each of the twelve apples. It doesn't make
much sense because apples usually don't have common components, but
that's a problem of the semantics not the logic. If it was something like
books instead of apples it might make more sense.

> There does not seem to be any
> components here,
> since this phrase does not refer beyond itself.

I don't understand what that means.

> But, in fact, we want to
> get back to the
> same apples.

If we want the apples we shouldn't use {lu'a} there. lu'a gets to
components of whatever the internal sumti refers to. Apples don't have
obvious components, so talking of {lu'a lo plise} does not make much
sense, but not because they are individuals. Other individuals do have
components. {lu'a le pare selcmi} means at least one member of the
twelve sets.

> I'm not convinced that this is a consistent interpretation,
> as the one I
> guessed at is (even if useless -- which I don't think it is).

I don't see the inconsistency, and everything in your interpretation
can be covered with this one too.

> >       lu'i re lu'o mu lo plise: a set whose two elements are masses
> >                                of five apples each.
> Presents another set of problems, since presumably re lu'o mu lo plise is
> not legitimate,
> masses getting at most fractional quantifers (and  those only on
> idiomatic sufferance).

I don't think that's right. A mass of all of something can get only
fractional quantifiers, just like a set of all of something. But masses
of five apples (like sets of five apples) there are aplenty.

> Thus, there is no form to add lu'i to.  I suspect that somewhere here we
> have stepped over
> from making new descriptions to introducing new predicates.  There are,
> of course, many
> lu'o mu lo plise, since there are many ways to meet the conditions of mu
> lo plise, but I
> think to start talking about this multiplicity, we have to introduce
> gunma.

Why? I don't see the problem. What's wrong with this:

        ro le ci pipno cu se bevri lu'o mu nanmu
        i le ci lu'o mu nanmu cu bevri lo pipno

        Each of the three pianos was carried by a mass of five men.
        Each of the three masses of five men carried a piano.

Why should we need a predicate {gunma} for the second one and not for
the first which says more or less the same thing?

> But then I am
> still unsure just how this is to work.  It does seem to offer some useful
> devices if they can
> be made to work consistently, but I need some explanation -- or an
> enormous number of
> examples -- before I can begin to be convinced.

This is how I see it:

lu'a ko'a:  at least one component of the referent(s) of ko'a.
lu'i ko'a:  at least one set whose members are the referents of ko'a.
lu'o ko'a:  at least one mass whose components are the referents of ko'a.

For lu'a, one would normally expect the referent of ko'a to be a set
or a mass. If it isn't, then what are its components will have to come
from context.

For lu'i the referent of ko'a might be a set, in which case the set
referred to by {lu'i ko'a} will be a set of sets, nothing strange about
that.

Jorge