Re: quantifiers on sumti - late response

[jorge@PHYAST.PITT.EDU]

And & Dylan:
> > > So what is "a set of boxes"? {pisuho lohi tanxe}?
> > That works, I think.  How about {lo se cmima be lo tanxe} or {lo'i
> > su'o lo tanxe}?
> Ah, yes. {lohi suo tanxe}.

Well, not really.  I'm not 100 percent sure, but I think {lo'i} works
like {lo}, that means "the set of all boxes, of which there are at least
one".  The inner quantifier of {lo'i} is always equivalent to {ro}.

It is not _a_ set of boxes, with at least one element, but _the_ one and
only set of boxes, with at least one element.

> Jorge:
> > > {ci da stedu loe prenu} is probably false (or at
> > > least conceptually really weird),
> > Yes, but for the opposite reason that you think, I think. There are
> > in fact many more than 3 human heads. (I prefer to talk about {stedu
> > be lo'e remna} rather than {be lo'e prenu}. I don't think the number
> > of heads is very relevant or easy to determine for general {prenu}.)
> Ah. So you'd say {suo ci da stedu loe remna} is true. I can see why.
> Weird. If you go off an find every human head, you find they each
> belong to loe remna. But if you encounter loe remna you find that
> Signor(a) Remna has one head. Cor.

But you never encounter {lo'e remna}. Or rather, you can't conclude
anything about {lo'e} remna from properties of the one you encounter.
Let me try to be more clear:

        mi penmi lo'e remna
        I had a human encounter (to put it some way).

        le se penmi be mi se stedu pa da
        The one I encountered is beheaded by exactly one thing.

But that does not allow me to conclude that:

        lo'e remna cu se stedu pa da.
        Human heads are only one.


Just like from:
        mi penmi pa remna
        I meet exactly one human.

        le se penmi be mi se stedu pa da
        The one I meet has exactly one head.

I can't conclude that:

        pa remna cu se stedu pa da
        Exactly one human has exactly one head.

Because {lo'e remna}, like {su'epa remna}, does not refer to a
particular individual.  You can't substitute it directly.

In some sense, {zi'o} works like that, too.  If you say {mi penmi zi'o}
(supposing that makes sense) and then say something about {le se penmi
be mi}, that doesn't let you conclude something about {zi'o}, as if it
had some particular referent.

> > If you want to claim that only {pa da stedu lo'e remna}, then that
> > {pa da} has to be a {lo'e} type object as well, and only {lo'e}
> > objects could be in relationship with {lo'e} objects, which would
> > limit its usefulness enormously.
> No, I don't want to claim this. But I would like to know how to
> say loe remna has exactly one head, two arms, two legs.

It doesn't, in my opinion, because {lo'e remna} is not a sumti with a
fixed referent, to which you can give properties, much like {pa remna}
is not a sumti with a fixed referent to which you can give properties.
Or rather, you could put {lo'e remna} in the x1 of a selbri meaning {x1
has exactly one head}, but you couldn't relate it with some one thing by
the relationship {stedu}.

> One of the selling points in the Lojban publicity pack I received
> however many years ago was that it might Whorfianly reshape one's
> world view. I think myopic singularity is the thing that's
> done that for me.

I've changed my view of the world back and forth many times since I
started learning Lojban, and I haven't settled on one yet.

> > (In fact, I'm tempted to write {ta tanxe reno lo'e plise} for
> > "that's a box for twenty apples", i.e. a twenty-apple box, not
> > necessarily for any particular twenty apples.)
>
> Ooh no - please - rather {ta tanxe loe re no mei plise}.

Ok, but make it {lo'e plise renomei}, which is slightly less ambiguous.
How do you like {lo'e reno plise}?

> > > and {ci da stedu lee prenu} is probably
> > > false too, if we're referring to a person,
> > But {le'e prenu} doesn't refer to any person, only to the particular
> > idea of person that you have in mind.
>
> I think referents are ideas of things. What I meant was "if {lee prenu}
> is here used +veridically" (i.e., I suppose, indistinguishably from
> {loe prenu}).

Well, ok, by "idea of person" I meant particular idea of indeterminate
person.  It may happen that there are only three heads that can be said
to fit that particular idea of person you have in mind.  It is not
indistinguishable from {lo'e prenu}, even if used +veridically, because
you may have lots of additional in-mind restrictions.

> > > while {ci da stedu loi prenu}
> > > can be true, if the person mass contains three people.
> > No doubt. Exactly three things are heads of some fraction of the
> > mass of all persons.
> "Exactly three things are head of some person-age". ["-age"=/@dZ/]
> "There are exactly three things such that there is some person-age
> that they are head of." Actually, make my example {loi remna se
> stedu ci da}, because I reckon there must be some universal
> quantification hidden here.

They are equivalent, as far as I can tell.  Existential quantifiers
commute with each other.

> Consider:
>
>   Three of my sisters have a pair of blue eyes.

How would you put that in lojban? If you say:

        ci le mi mensi cu se kanla lo blanu remei

You are saying:  There are three of my sisters, and there is a pair of
blue things, such that each sister is be-eyed by the blue thing.

In prenex form:

        ci da poi mensi mi ku'o de poi blanu remei zo'u: de kanla da

Which is also equivalent to:

        lo blanu remei cu kanla ci le mi mensi

What you really mean is:

        ro lo ci le mi mensi cu se kanla lo blanu remei
        For each of three of my sisters, there is a blue pair that
        be-eyes them.


> They don't all have the same pair. So, it should go something
> like this:
>
>   Ex, cardinality of x is 3, Ay y in x: y is sister of me, Ez,
>     z is pair of blue eyes of y

Right, but {ci le mi mensi} doesn't expand like that, as far as
I understand.

> Contrast
>
>   A pair of eyes belongs to three of my sisters.
>
> To me this supports my view that the logical form of {(ci) lo broda} is
>
>    Ex (cardinality of x is 3), Ay, y in x: y is broda
>
> and the logical form of {le (ci) broda} is:
>
>   (cardinality of X is 3) Ay, y in X: y is broda

That's not how I've understood things so far. For me:

        mi dunda re cukta re prenu

means that I give two books to two people, that is, there are two books,
and two people, such that I give each of the books to each of the
people.  Four events, but only two books and two people involved.

With your expansion, it would mean that I give each of two books to two
people, so there may be up to four people getting books.  I'm not at all
sure what is the official position on this, but I've always assumed that
numbers were essentially existential quantifiers.

> How, incidentally, does one actually say "le do", "lo do", "loi do",
> "loe do", etc.? I presume these are ungrammatical. Would {le suo do,
> (lo) suo do, loi suo/ro do, lei suo do, loe suo do} be okay?

Yes.

Jorge