quantifiers

["John E. Clifford" <pcliffje@CRL.COM>]

Yes, veion, we have been here before from various other angles.  I am only
trying to get some systematic understanding of where it is we are, using
the reasonably well-established concepts and notation of formal logic
(which is, after all, supposed to underlie Lojban) as a tool.  It does
seem that what we are finding is that the underlay is the logic of Russell
and, latterly, Quine, where referring gives way to "being the value of a
bound variable."  It works - - no task goes undone, and expressions map in
natural ways and yet the explanation sounds very odd.  Linguists who know
logic (McCawley always pops up here) and logicians (well, philosophers --
Strawson, e.g.) who know (weeeell) linguistics find the diffe rences
disturbing, even when the mechanics work out right.  It does seem odd to
be able to talk about everything but never about any particular thing,
since we tend to take the latter kind of talk as basic and talk of
generalities as an abstraction from talk about individuals.  But, as JCB
used to point out, this late neolithic language Loglan is not bound by the
prejudices of earlier-lithic languages (as witness the "basic" vocabulary,
largely unavailable to even our grandparents -- mine anyway).

xorxes:
>I thought {ro} never had existential import. You are saying that it does
>in {ro broda} but it does not in {ro da poi broda}. I guess that if it's
>defined like that then that's that, but I really don't see the point of
>complicating {ro} in such a way. Is it just to copy the behaviour of the
>English "every"? It doesn't seem to be a very good reason. A much better
>translation for {ro} in any case is "each". Does "each" have existential
>import in English? It is very unsettling to find out that {ro} changes
>meaning with context.

In logic, the universal quantifier always has existential import; that is,
the domain of discourse is never empty (except in one special field, which
turns out to rest on the error of assuming that the domain of discourse
must be the class of existents).  The question is only about what set is
said to be non-empty and comes to the fore in translating categorical A
sentences, All S are P.  If that is read, as it usually is in modern
logic, as "for all x, if Sx then Px", then only the domain of discourse is
said to be non-empty, but the set of Ss is not guaranteed to be.  In fact,
if there are no Ss, then "All S are P" is true on this version (false
antecedent means true conditional).  On the other hand, if "all S are P is
read as a restricted quantifier to S, "for all x that are S, Px,"  the
universal covers only the Ss and thus claims that there are some of them,
since whatever the range of the universal, it is non-empty.  So, if there
are no Ss, the second version is false.  These two versions correspond
exactly (indeed, the Lojban was designed to represent directly) the two
sentences, ro da broda nagi'a brode (actually the fully sentential version
of this, ro da zo'u da broda [whatever the sentential version of the
predicative form is] da brode) and ro da poi broda cu brode (or, again, ro
da poi broda zo'u da brode), respectively.  ro does not change its
meaning; only the kind of thing its claims that there are changes, from
unrestricted to restricted. The odd "universal true even when there are no
Ss " is a feature of the conditional, not of the universal.  Notice, the
"there are S version" has several forms: ro broda = ro lo broda = ro da
poi broda.  (I trust xorxes' grammar so much that I have revised my
understanding of all this mess to accomodate his insistence on just this
equation and others related to it.  So, I did not say RECENTLY that some
of these have existential import and some don't, all of these are the same
and requires that there be brodas.) By the way, "each" does have
existential import in English and, indeed, requires that there be more
than one of the critters and that we can line 'em up ("every" is
etymologically "ever each", "line 'em up and run through the whole lot one
by one").  "All" is about as neutral as English gets, since "any" clearly
does not have existential import (an etymological curiosity).  See
Vendler's article or the the appropriate section in the Dictionary of
Philosophy.

xorxes:
> > > >         ro da poi broda cu brode
> > > >         ro da broda nagi'a brode
> > >
> > > If there are no brodas, the first is false while the second is true,
> > > regardless of what brode is.

>And the explanation for why the first was false was that {ro da poi broda}
>was supposed to be Ax e {broda}.

Actually, I said
>Restricted quantifier sentence are false when restricted to an empty set
> (existential import).
That does, unfortunately, use set talk (a logician's habit), but the set
is inessential: a restricted quantifier sentence is false when there are
no things of the sort to which it is restricted.  I would have written
(and did somewhere, I thought) this as Ax such that x broda, not with
set-membership notation.

xorxes:
>Talking about sets is a convenience, and when the set
>exists it makes little difference whether you use it or not to explain
>the meaning of {lo broda}. But when there is no corresponding set,
>the expression is still meaningful
Agreed.  The point of using set talk is to find a
coherent way of dealing with all the descriptors and a way that was
different from the purely quantifier versions, i.e., to match in logic the
differences in Lojban structure.  So, we will say these are th e classes,
not the sets, if we want to stick to the pattern, which is the point of
this exercise. But whether we use the sets or not, or even classes or not,
the quantifiers remain and that is the crux of non-referring part.

        Since, as I have said, we can always manage equipollence between
the two systems, I don't suppose I can give contrasting cases.  If I say
it one way or the other, they describe the same situation, are true or
false together and necessarily so.  But suppo se that in fact there is
exactly one thing of a certain sort, S, and I want to say that it has a
further proerty, P.  Then "Every S is P" and "The S is P" turn out to be
equipollent, yet one of them is overtly a general claim, about everything
or at least every S and the other is a singular claim that refers to a
particular thing and says something about it.  The first does say
something about that particular thing, but only as falling under a general
category, without referring to that thing at all.  If there were several
Ss and one of them were John, then "All Ss are P" would say something
about John without referring to him, and it would certasinly not mean the
same thing as "John is a P."  But the cardinality of a class (so long as
it is not a wrong-sized class) should not change the significance of a
quantified sentence where the quantifier is restricted to that class, so
something is different between the two even when they come out to describe
the same state of affairs.  Since all the descriptors t hat can have them
have real quantifiers, they all fail to refer to the members of the sets
they are restricted to, for "refers to" is just what the "the S" and
"John"  sentences have that the quantified sentences lack (well, don't
have, anyhow).  I think (looking at this) that this aamounts to saying
that referring expressions refer and others don't and so the claim is just
that le, lo, and la are not referring expressions, however much they may
act like them at a practical level.  I do not know whether t here might be
interesting Whorfian effects from this odd difference (it looks like just
the sort of thing that Whorf would have thought to be source for such
effects -- if he thought there were such things -- since he seemed to
think that Hopi time refere nces that worked functionally as near as you
like to SAE but were based on a totally different "metaphysic" was the
mark of a profound difference).