Re: quantifiers

[jorge@PHYAST.PITT.EDU]

> 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."

Well, a reasonable notation should be order indifferent for the
coordinate case. "Order" is a property of the notation, "coordinate"
is not a property of the notation, it is one of the cases that we
want our notation to take care of.

> 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
> 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.

It is about all of those things. My point is this: given two quantifiers
(including numerics) in general there are three possible scope interactions.

When one of the quantifiers is {ro} or {su'o}, the three possibilities
actually are reduced to two, because the coordinate coincides with
one of the other two possibilities. When both quantifiers are {ro},
or both are {su'o}, all three cases collapse into one.

But in the general case, there are three possibilities.

Let's say the quantifiers in question are {ci} and {vo}, and to simplify
things we select from the unrestricted universe.

The three cases are:

{ci} superordinate to {vo}: For each of three x there are four y
                            such that: F(x,y)

{ci} coordinate with {vo}:  There are three x and four y such that: F(x,y)

{ci} subordinate to {vo}:   There are three x for each of four y
                            such that: F(x,y)


The simplest notation of Lojban does not allow for three possibilities,
it allows at most for two: {ci da vo de zo'u} and {vo de ci da zo'u}.

We have two choices: assign those to the superordinate and the
subordinate cases respectively, or assign them both to the coordinate
case.

You seem to be saying that there is some reason why the only possible
choice is assign them both to the coordinate case.

Some of us seem to prefer to use the two simple cases for the
superordinate and subordinate cases. That would entail that _in general_
two quantifiers do not commute.

> 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)?

You say that "by logic" {ci da vo de zo'u} has to be a representation of
the coordinate case. I don't see how that has to be so by logic. That is
one of the possible choices of a consistent notation. Not the only choice.

> 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.

Yes, that's my expression, but for something that you have been
insisting that Lojban used to have and doesn't have anymore.

We more or less agree on what singular terms are. They refer.
They are immune to any scope problems. They are great.

You said that there are plural terms like that also, which refer
to more than one object individually at the same time. I called them
"multiple referring expressions". You never gave an example. I can't
see how you can have such scope immunity with multiple reference.

What would it take for {le ci gerku} to be a referring term?
What would the consequences be? You say that many scope problems come
from {le ci gerku} having lost its reference power that it once had,
but you never explain, with an example, what that would mean.

> > 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?

It is legal, al PAs can be strung together legally.
{ropirociropimu nanmu} is legal too, although rather meaningless.

The meaning that Iain proposes is not the standard one as explained
in the reference grammar, but it is one that seems to me more useful.

>  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)?

{le ci lo nanmu} is essentially the same as {le ci nanmu}: "each of the
three dogs in question". It is atually "each of the three dogs in question
out of all the dogs that there are", but because of {le}'s specificity
that's the same as {le ci nanmu}. The specific/definite three dogs I'm
talking about. I would say that it refers to those three dogs, but now
I'm scared of using the word "refer".  :)

{ro lo ci lo nanmu} is each of some three dogs, which is not the same
thing. The three dogs remain indefinite/nonspecific/whatever.

{roci nanmu} is proposed as a shorthand for this, instead of the
current meaning, that is essentially that the claim is true both
for {ci nanmu} and for {ro nanmu}, so that three men are all the men
that there are.

Jorge