Re: tech:logic matters

[Iain Alexander <ia@stryx.demon.co.uk>]

In message <822426847.6847.0@cunyvm.cuny.edu> pcliffje@crl.com writes:

> &
> > &: But why should {suo no lo ro broda} mean that there are brodas?
> > pc: Because the internal _ro_, properly understood, says that there
> > are some brodas, even if none of them do whatever the predication goes
> > on to claim.
> That's what I don't understand.
> pc:
> Well, the internal quantifier says how big the referred-to set is.  In
> this case, it has all members.  That implies, as "all" does, that it has
> some members, i.e., at least one.  What is the problem?  (This is not
> even about restricted quantifiers this time.)

(and earlier)
> > They are the quantifiers of natural language ...

You keep insisting on this, but McCawley doesn't appear to think
that it's quite so clear cut.

        ... while 6.3.4b would probably be interpreted as including
        members who incurred no bills among those to whom the 10 percent
        discount is offered:
        ...
        6.3.4 b. Any member who paid all his bills by the fifteenth
        of the month was entitled to a 10 percent discount on
        their publications.

(I've only dipped into the book, so it's possible he might give
the lie to this later, but I don't believe I've quoted totally
out of context.  He does of course give examples where there
is an existential implication, but gives several reasons as to
how it might arise, not just from the quantifier itself.)

> pc:
> Right!  So, the standard for Lojban syntax for quantifiers ought to be
> _Q broda cu brode_  matching the semantics as closely as feasible.
> this form claims there are brodas except for the cases of _no_ and
> whatever is the denial of _ro_ (?_ronai_? _nairo_? something else
> altogether?).

{naku ro} or {da'a su'o}

Given that we want to be able to express both "one and all"
(universal with existential import) and "any and all"
(universal which may be vacuous) in simple forms such
as the above, we need a quantifier for each.  I previously
offered you something like {ro su'o} as an existential-
universal to contrast with plain {ro} as a possibly-vacuous
universal, but you weren't impressed.  You did not however
offer me a possibly-vacuous universal in return, except
as a circumlocution, which the above seems to indicate
you agree is undesirable.  I am therefore forced to
propose my own, {ro su'o no}, which is not particularly
pretty, but I can always hope that usage will eventually
establish that a naked {ro} is at least ambiguous between
the two possibilities, as it is in English, and preferably
that {ro su'o no} is the default interpretation, at least
barring pragmatic indications to the contrary.

(I have no particular objections to particular constructions
such as {ro lo broda} carrying existential import, providing
it can be explained in such a way that this is not part of
the meaning of {ro}, but arises from the context as a whole,
for instance by a default {su'o} inner quantifier.  If it could
also be explained using your definitions, and still end up
with the same meaning, then we might both be satisfied, but I
won't hold my breath.  In any case, I think we need some explicit
quantifiers, such as discussed above, up our sleeves, to override
whatever implications might arise from the context.)

The other thing that needs to be worked out is how the
existential-universal interacts with (bridi) negation.
You may consider it to be a trivial exercise for the
reader, but it's a significant part of the negation
paper, and virtually part of the definition of what
{na} and {naku} mean.

(I'll try one example just to see how it goes.
{naku rosu'o da poi broda zo'u:  da brode} <=>
{su'o da poi broda zo'u:  da na brode .ija ro da zo'u:  da na broda})

co'o mi'e .i,n.
--
Iain Alexander                    ia@stryx.demon.co.uk
                    I.Alexander@bra0125.wins.icl.co.uk