Re: quantifiers

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

xorxes:
If you think that {lo broda cu brode lo brodi} is _not_ equivalent
to {lo brodi cu se brode lo broda} in any interesting sense, then
please explain, preferably giving an example.
pc:
I do think they are equivalent, which is why I am unsure about the set
theoretic version of  _lo broda_, since I do not see how to get them
equivalent on that form, even with set theory (but I have not spent a lot
of time on it, since I am not sure I want or need the set theory version
anyhow).

sos:
> AxEyFxy does not entail (and so is not equivalent to)
> EyAxFxy, so the two do not seem to be coordinate.
I didn't say they were. The first is (i) and the other is (ii)=(iii).
pc:
I guess I just didn't see what is meant here by "coordinate," since it
clearly did not mean "order indifferent."  Apparently (see my later
comments then) the talk about conversion is largely irrelevant, although
if two quantifiers do convert they are coordinate.

sos:
>         1. Universals are not affected by superordinates (and so are
> coordinate with them?)
>         2. Universal otherwise affect what is subordinate to them
>         3.  Particulars do not affect subordinates (and so are coordinate
> with them?)
>         4.  Particulars are otherwise affected by any superordinate
>         5.  Numerics affect subordinate numerics
> These are all true and mean that there are several cases where
> (assuming
> some connection between order and subordination)  order does not
> matter.  But it also leaves a lot of cases where it does and wouldn't it > be
> nice to have a handy way of dealing with them and perhaps a uniform
> way for all the others as well?  So far as I can see, we do not at the
> moment.
I don't disagree with any of that.
pc:
Then I really do not get your point at all: it is not about order or nesting
or conversion or affecting selections.  What else have we talked about
in this context?  And, more importantly, what relevance does it have to
the issues at hand (other than the issue of what cases are coordinate)?

iain:
Of course, from my point of view, the alternative you suggest is pretty
implausible, since a proposition like (3x) (3y) F(x,y) cannot be
understood by breaking it down into its component parts, e.g. as (3x)
G(x),
where G(x) is (3y) F(x,y), but can only be interpreted as a whole.
pc:
Remind again why (3x)(3y)Fxy can't be broken down sequentially.
Now, it is the case that (3x man)(3y dog) x pets y expands in a bit more
complex fashion, it still seems to me to be complex to component
expansion.  I suspect  -- from something iain says elsewhere -- that
problem may be about what there are three of: men (in the first case) or
men-who-pet-three-dogs.  I take it that the answer is "men" and that
iain holds with "men who pet three dogs,"  in spite of what the
componential analysis seems to say.  The first view has some technical
problems, the second gives the wrong readings some times.  I'll try both
and see what works out.  Evidence:
iain:
The point is that we were discussing multiple quantifiers,
where the F in Ax(Fx => x=... ) is itself defined as a numerically
quantified expression, whose leading particular quantifier thus
comes within the scope of that universal.  You obviously don't
consider this situation to arise in the case of _consecutive_
numerics, and it is not clear whether you have some alternative
means of expressing that situation.
pc:
I take it that F in this case is just "is a man" (in the first instance) or "is
a relevant man" or "is a member of [the 3leton declared at the
beginning], none of which contains any further quantifiers at all.

nss:
> pc:
> Even if there are no unicorns, what compels us to claim that _ro
> pavyseljirna cu blanu_ is true?  It is a universal claim, so the
> minimum
> truth value of its instances.  It has no instances, so, presumably, it has
> no
> truth value.
At first glance, it may not be obvious what such a value should be.
But it turns out that the practical way to define the minimum of
an empty set is the maximum possible value, and conversely for
the maximum.  This is a fairly well-known trick where I come from.
It appears counter-intuitive when you first come across it, but
it works, and you soon get used to it.
pc:
The well-known trick is of course commonly used in circles where it is
ASSUMED that the right result is the conditional one.  The trick has no
other justification and flies in the face of the established rules for all
the connectives and quantifiers, but, yes, it does work to get the value
that has been imposed on the empty case.  That is, it gives the wrong
value outside the mathematical context but the right one inside.

iain:
What's a "multiply referring expression", that you don't
think we've covered.  You've covered {la bab. e la djan. e la haris.}
and {le ci nanmu} yourself above, so it's neither of those.
pc:
Beats me.  This is xorxes expression as far as I can trace it back and I
am not sure what he means by it either, since he and I cannot seem to
come to any communication about what a referring expression is, as
opposed to a quantified one.

iain:
If your question is how to say it in Lojban, my preferred solution
at the moment would be an explicit {ro}
        ro ci nanmu cu rapypencu ro ci gerku
which would be equivalent to
        ro lo ci lo nanmu cu rapypencu ro lo ci lo gerku
pc:
Oh drat!  Is that first one legal?  I thought I got shot down earlier for
trying something like those collapses of  QLQLQ sequences.  And since
I really don't understand double  descriptors (partly because of that
earlier shoot down) I am not sure whether this works.  I do hope so, so
that Lojban can say this, but I do wish I could see the interpretation rule
here.  How is this related to _le ci lo nanmu cu  rapypencu le ci lo
gerku_, which I can figure out how it might mean what is wanted (if it
is legal)?

nss:
> Since the first of these
> was created exactly to have a universal quantifier with existential
> import,
Unfortunately, nobody told us that. :-)
pc:
Last time I looked (a while ago, admitedly), it was in the commentary,
where it had been for several years.

In general, I am not saying anything about masses this time around.  I
agree that the rule of thumb is a bust beyond the simplest cases.  I also
think that the semantics that I thought was agreed upon forces _loi
broda_ to be the mass of all brodas.  I gather that what I took to be
agreement either was not or has been withdrawn in the light of further
evidence, throwing _loi broda_ back to an indefinite description (still,
at least, not a quantified expression).  At that point, the rule works
better but no longer says what it did originally.  I am beginning to go
back now to an earlier claim that the notion of a mass is simply
ambiguous and that there are at least two radically different concepts
here, one from English plurals and one from Quine & Malinowski (or
some such bodies).  If that is true, we clearly want to focus on the first
of these, the one that in English gets muddled with distributive claims
and claims about averages.  But keep the data coming in, please.
        Hence I will not say muc in reply to

On Wed, 20 Sep 1995, Don Wiggins wrote:

> >         When someone says in the ordinary course of events (well, not
> > all that ordinary in this traditional example) "All unicorns are white,"
> > the response "There aren't any unicorns" is neither intended nor
> > understood as confirming the original claim.  It is a challenge to the
> > original claim, a contrary claim to it, as much as "Some are blue" is.  It
> > is this fundamental fact that logic has always taken into account in its
> > treatment of quatifiers, abetted of course by the fact that we usually do
> > not talk about what is not, except with conscious care.
>
> This reminds of the conundrum which goes something like:
>
> "Do you enjoy beating your wife?"
>
> "Yes" means that you beat beat your wife and you enjoy it.
>
> "No" means you beat your wife, but you don't enjoy it, sort of doing it out of
> a sense of duty.
>
> "Mu" means 'I deny the premise of your question', i.e. I don't  beat my wife
> (the set of events of I beating my wife is null).  Mu as I read about it
> is supposed to be of Oriental origin and would be the appropriate response
> to .i piro loi pavyjirna cu blanu vau
>
Except to say that _piro loi pavyseljirna_ probably has no
presuppositions, the massification of the empty set is probably just the
empty mass..  It is almost certainly not blue, however.
pc>|83