Re: quantifiers

[jorge@PHYAST.PITT.EDU]

> Historically, the question of existential import has only arisen for universal
> quantifiers; it has been assumed for the rest, although the best version
> of the original problem, categorical logic, has both negative proposition
> types lack existential import (which is why the logical transformation is
> simpler).  It is false that every member of the empty set is a member of
> every set, because there are no members of the empty set and "every" has
> existential import in English.

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.


> Gee, I hope I did not say that ro da poi broda involved {broda}; only ro
> lo broda does (if I have this system right)

Yes, you said this:
> > > >         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}.


> Assuming I have the grammar right -- and I got it from xorxes --

-- which increases the possibilities you don't have it right :) --

> then lo
> expressions always refer distributively to sets, as shown by the internal
> caardinal and the external quantifier -- even if the cardinal is one.

In my opinion, the introduction of sets is merely accessory. It makes it
easier to describe the meaning of {lo broda}, but in no way should using
{lo broda} commit you to the existence of the set. There is nothing
ill-formed about an expression like {lo selcmi poi ke'a na cmima ke'a}
"a set which is not a member of itself", even though no set of all such
things exists. 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.


> Thus they always have the form Ax e {"broda"} (the set of things I have
> in mind anc choose to describe as brodas).

That one is {le broda}, and it talks not of the set, but of each of
the things.

> That is the quantify over, not refer to, individuals.

I'm still unable to see the difference between quantifying over a one
element set and referring to the individual member, when the set in
question is known to the speaker and listener to have one member.
Could you give an example where the two differ?

> And la expressions are just le expressions
> with the predicate being "called "...""

To me {la djan} is one individual, but I think Lojbab will argue that
it can be many individuals each of which is called "djan". In practice,
I have only seen it used as true names, not as the predicate version.

> So they do not refer either.

In my opinion they do.

> It
> is, if not in the book (such as there is), at least in the corpus of this
> list over the last year and a half.  At most (and this is even unsure)
> the deictics and the personals (ti, ta, mi, etc.) refer.  I should add
> that this is not necessarily a problem; it is only odd in a human language.

I don't believe {la djan} behaves in Lojban any different from "John"
in English. What's odd about it?

Jorge