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Date: Fri, 23 Sep 2011 21:07:23 -0400
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plural variable
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* Friday, 2011-09-23 at 12:55 -0700 - John E Clifford <kali9putra@yahoo.com=
>:

> {pi PA lo brodacu brode} doesn't seem to me to be an abuse; it merely
> signifies that a subbunch the size of .PA of lo broda brodes.  It's
> a bit ickier with a proper name or a clear atomic individual (well.
> not so atomic anymore) but not really improper or even difficult to
> understand.  I still don't see what the {su'o} adds -- unless you
> always write the decimal place 0. Ah!  thew {su'o} allowa that there
> might be more than one such fragment, but so does just {pi za'u}, as
> far as I can see.

Yes, {pi za'u} is looking like a plural existential quantifier to me.

I think, having thought further, that anything like {ro pi} for the
universal is too much of an abuse of {pi}. Probably the universal is of
limited use, anyway.

> So, I suppose that {za'u} is a particular quantifier of a sort -- the
> sort that says how big the new bunch is.  Would {su'o pa} take members
> one at a time,

Yes, there seems to be agreement that usual "whole" quantifiers
({re}, bare {ro} and {su'o}, {so'e} etc) are singular quantifiers.

> where, as a plural quantifier, {su'o} might take larger sub bunches?

{su'o} on its own should be singular, I believe.

> Well, "worlds" is a slippery term (and the obvious replacement
> "situation" is no better).  And its referent tends to get mixed up
> with domains or universes of discourse, which bunches of things we
> drawn from wherever we will to talk about.  I suspect that situations
> and maybe even worlds could be defined to more or less match up with
> universes (or conversely), but I wonder if it would be worth the
> effort.  In a discussion, we have a universe (a bunch of things and an
> interpretation of terms and predicates, just like a world) except that
> the things may not be all from one world and the interpretation of the
> predicates may take into account interpretations from several worlds,
> as needed.

I'd prefer to work as Montague does: we have one universe, i.e. one set
of individuals, but predicates are really maps from worlds to extensions
in that universe.

The problem with having different universes for different worlds is that
we want to be able to say things like "this child will die" - meaning
that we must be able to make predications of the referent of "this
child" in future worlds. So you'd need to introduce a family of
bijections between the worlds' universes indicating what individuals
correspond to what - which is essentially the same as working with
a single universe (the quotient).

> There are many variations but this is the core.  So,
> presumably  (though not obviously) you are in this world and the glass
> in some other and the the eating is evaluated in a universe where both
> occur.  Alternately, of course, both you and the glass are in a single
> other world where the eating takes place.  But then it is a little
> hard to see what that all has to do with you here and now, since that
> glasseater is neither.

Yes, this is precisely the kind of confusion which Montague's approach
avoids. The individual which in this world is the referent of "me" also
exists in all other worlds (although it may not be the referent of "me"
in all of them), because it's an element of the unique universe.

> This is not detailed, but the details take too long for me to work out
> precisely again to participate in this discussion.  It is worth
> noticing that the universe of a particu;ar discussion is dynamic: it
> expands and sometimes contracts as the discussion proceeds. Ahah!
> something that make matters clearer is to note that universes have
> worlds within them, on which they draw.


> (Incidentally, calling {su'o} and existential quantifier is somewhat
> misleading because not everything in the universe -- the range of the
> quantification -- exists, generally speaking).

I'd say that {ro da ca'a ca zasti} is false.

Martin

> ----- Original Message ----
> From: Martin Bays <mbays@sdf.org>
> To: lojban@googlegroups.com
> Sent: Fri, September 23, 2011 1:57:10 PM
> Subject: Re: [lojban] {zo'e} as close-scope existentially quantified plur=
al=20
> variable
>=20
> * Friday, 2011-09-23 at 13:14 -0400 - John E. Clifford <kali9putra@yahoo.=
com>:
>=20
> > I'm not sure what {pi za'u} might mean.  I suppose the default is
> > either 0 or 1, so not that different from {pisu'o} after all.  What
> > did you mean to say?
> > {pi su'o lo broda} is an u specified subbunch but, if a quantifier,
> > it, like {pi ro lo}, is over the domain of only lo broda.  Oh! Just
> > saw the point of {za'u}, assuming that it's default is 0.  But then
> > I don't understand {su'o pi za'u} as adding anything.
>=20
> The {su'o} before the {pi} was just to explicitly make it an existential
> quantifier... of course it's a horrible abuse of {pi}, which is meant to
> be a decimal point, but not a new abuse.
>=20
> So {su'o pi za'u ko'a}, which might or might not be the same as just {pi
> za'u}, would mean "one or more subbunches of ko'a", where a subbunch of
> ko'a is a sum aka plurality aka bunch (I understand these all to mean
> the same things, and to agree with Chierchia's setup, at least modulo
> the intensionality issues below) the atoms below which are also below
> ko'a; i.e. it is any ko'e such that ko'e me ko'a, if {me} is our Among
> relation.
>=20
> In other words, {su'o pi za'u ko'a} would be the plural quantifier
> \exists X AMONG ko'a
>=20
> > Yes, bunches can include things from various worlds because domains
> > often contain such: we talk about imaginary things and past things and
> > so on, all not from this world but some other. This world only has
> > what exists in this world in it.  There is a much longer way of laying
> > this out, but that is the gist.  We need this to make general claims
> > (along with other reasons), since we often want to generalize not just
> > about the current whatevers but about past and future ones as well.
>=20
> Naturally.
>=20
> But the way I'm understanding the tense system, {lo} and {zo'e} would
> only ever get evaluated *after* we've selected a world.
>=20
> e.g. {mi ka'e citka lo blaci} means that in some possible world I eat
> something which is glass *in that possible world*, i.e. it means
> something like (ignoring all subtleties of {lo} for a moment)
> \exists w. \exists b. (blaci_w(b) /\ citka_w(mi,b))
>=20
> (where the first quantifier is over worlds, and the second quantifier is
> over the domain, and blaci_w and citka_w are the interepretations of
> blaci in the world w, being relations on the domain).
>=20
> I really don't see how it could work any other way. Could you explain in
> detail how you see it doing so?
>=20
> Martin
>=20
> --=20
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