Re: tech:logic matters

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

In message <822795303.5467.0@cunyvm.cuny.edu> pcliffje@CRL.COM writes:

> i,n:
> > > 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.
> pc:
> See earlier.  Notice here that the question is not about "all"  but
> "any,"

No, I disagree.  The point here is about the number of bills
which have been paid, i.e. "all".  McCawley admits that in
this case, "all [his] bills" includes the possibility of
"no bills".

> which notoriously does not have existential import

I agree that "any" does not have existential import.

> i,n
> > whatever is the denial of _ro_ (?_ronai_? _nairo_? something else
> > altogether?).
> {naku ro} or {da'a su'o}
> pc:
> Neither of these work very well, given everybody's habit of pushing
> negations around, in the first case, and the existential import in the
> second.

Yes, I agree, the second suggestion was poor.
The former, however, is accurate pe'i, and led into my later point that
I believe we need to know _how_ to push negations around correctly.

> When the restricted quantifiers were introduced, the
> quantifier set was expanded to contain the fourth corner to the
> traditional square -- contradictory to _ro_, subaltern to _no_ and
> subcontrary to _su'o_ -- but I have lost all track of the form used.
>
> i,n:
> 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.
> pc:
> Why we had four quantifiers in the final set: negations carried to the
> diagonally opposite quantifier with all else unchanged.

That appears to be of limited use, even if you fully understand
what all four possibilities mean.  It tells you how to convert
{naku Q} to {naku Q'}, but it doesn't tell you how to interpret
{Q naku}.

> i,n:
> 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.)
> pc:
> We have all of these things -- in various degrees of complexity and
> with various theories about what expression means what -- already.

I'm not sure we're on the same wavelength here.  I'm talking about
numbers and you're talking about expressions.  (I need to come
back to this.  Bedtime.)

> The only thing we do not have is a universal affirmative quantifier
> that does not have inherent existential import.   Since I cannot quite
> imagine why anyone would want to talk about a universe which was
> totally empty (or, indeed, what one could say about it), this lack
> seems far too minor to be worth hassling about.

Perhaps, but I cannot quite see the relevance of the emptiness
or otherwise of the universe to any logical statement.

> Even _ro su'o no_
> (which does not make much sense to me, as indeed does not _ro
> su'o_)  seem way too short an expression for the purpose, which has
> not yet turned up in any text.

I don't much like the particular expressions - you're welcome
to suggest better.

I'm not sure what you're last means.  I certainly can't claim
to be aware of _all_ the text, and I (no disrespect) doubt that
you are either, to the extent of spotting whether someone used
{ro} with the intention of allowing the zero option.  (Obviously
you don't mean the particular expressions {ro su'o} and
{ro su'o no} which are too recently invented to have appeared.)

ro da poi te janta fi ro de nagi'a pleji pu li pamu po ro masti
cu jerna panoce'i me'ardi'a be ro lo vo'a selpapri

Is _that_ what you want us to say?
co'o mi'e .i,n.
--
Iain Alexander                    ia@stryx.demon.co.uk
                    I.Alexander@bra0125.wins.icl.co.uk