WikiDiscuss

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wrote:

> --- John E Clifford wrote:
> > > What
> > > > more can using a gadri do?
> > >
> > > It allows you to use the reference to make
> a
> > > claim about
> > > its referents.
> >
> > But I have already done that in the first
> place;
> > even though it is the whole sentence which
> makes
> > the reference it does also make a claim about
> > that referent.
>
> Consider these three cases:
>
> (1) Exactly three cows are white.
> (2) At least three cows are white.
> (3) At most three cows are white.
>
> With (1), I suppose you could argue that you
> made a reference
> to all the cows that are white, and claimed
> about them that
> they are white. I would not say that, I would
> say that all
> one does is say how many white cows there are
> without referring
> to the white cows.

I would, of course, like to submit here that what
I am talking about is {ci (lo) bakni cu blabi} or
some such so it is not "exactly three" in the
sense that none other are, but just "three" — as
you pointed out before. This does not make a lot
of difference but I try to keep the cases clear
in case it does.
> With (2), the presumed referents are more
> doubtful. Are they
> all the white cows, or any group of at least
> three white cows?
> I would say that all one does with (2) is say
> how many white
> cows there are without referring to the white
> cows.
>
> With (3), we are not even sure that there are
> any white cows,
> so talking of reference is even more iffy. I
> would say that
> (3) just says how many white cows there are
> without referring
> to the white cows.

The referring in each case is through the
particular quantifier (as it were), which is all
of these, though admittedly buried in very
different ways. All that the last case says is
that what is referred to may not be white. the
second says that we don't know how many are in
the group referred to — often the case even with
definite descriptions.

> True references to the white cows would be "the
> exactly three
> cows that are white", "the at least three cows
> that are white"
> and "the at most three cows that are white". In
> lojban:
>
> lo ci bakni (poi blabi)
> lo su'o ci bakni (poi blabi)
> lo su'e ci bakni (poi blabi)

These have some of the same problems as the cases
above — we don't know how many are involved in
the lastt two cases and in the last case the fact
that there may be none with the resultant
problems about claims that, taken grammatically,
are true but referentially false (Oh, I suppose
you are going to allow nonreferring sumti to
participate in true atomic sentences, but causes
a different set of problems, which I don't know
how you would deal with).

> PA bakni cu blabi
>
> says that the number of cows that are white is
> PA. It does
> not refer to PA cows and say of those that they
> are white.
> The latter is meaningless for some PA, and iffy
> for others.

Well, it is not exactly meaningless when PA =
{no}, it is just that its meaning does not flow
out in the usual pattern, which pattern says
exactly that reference does not occur in this
case. Otherwise they all get treated the same
way (with some tranlation work required for
proportional and relative quantifiers).

As McKay points out, descriptions are just
quantifiers (and, I suppose, conversely). That
is, a description is a function from a
sentence-matrix to a sentence as much as a
quantifier is. (This was always one of the
hardest pieces of Montague grammar to get one's
head around but it is very old in logic --
singular propositions are on a par with
universals and particulars, just different functions).