Re: quantifiers

[jorge@PHYAST.PITT.EDU]

On existential import: to me, what pc calls the "modern" version is the
one that makes sense. The other seems more complicated, but in the
end it is just a matter of aesthetics, since both are of course
self-consistent.

On the blessed three dogs:

> But then, since ci da poi nanmu ku ci de poi gerku zo'u da pencu de
> "means the same as" ci de poi gerku ku ci da poi nanmu zo'u da pencu de
> (and do not even have different connotations that I can think of), and
> since, in the latter the dog reference is clearly not in the scope of the
> man reference, it must not be so confined in the former either.

Of course, if the first two mean the same then the scopes must be equal.
The question is, are we to define the first two as meaning the same?
You seem to assume that this is already pre-established, but I don't
really see why.

> That is,
> this is just the thing for the three-dog, three-men assertion.  The
> reason that this works is because both quantifiers have been overtly
> separated from the matrix which joins them, pencu, which, thus, plays no
> part in the specification of the ranges of the quantifiers. In the
> simpler form, ci da poi nanmu cu pencu ci de poi gerku, the fact that
> the quantifiers are embedded in the matrix forces us to take the matrix
> even into account in defining the range of at least the dogs.

The two expressions are:

1)      ci da poi nanmu ku ci de poi gerku zo'u da pencu de

2)      ci da poi nanmu ku ci de poi gerku ku pencu

Placing the second argument in front of the predicate in (2) should
change nothing, I just do it for effect.

I'm not sure what matrix {pencu} introduces in one but not the other,
since neither expression means anything without it. The writing of the
prenex as a separate thing is purely a clarificational notation,
I don't think it should have additional semantical content.

> Xorxes
> claims that this is just one way of specifying how to do it but has
> neither proposed an alternate way of achieving the differentiation he
> wants (his will not work, as noted)

I have proposed several alternatives in the past. One was:

        ro lo ci lo nanmu cu pencu ro lo ci lo gerku

where internal quantifier selections would always have maximum scope.

In any case, as And pointed out, none of them was general enough
to cover all the cases with three and more arguments. Your version
of giving a different meaning to the prenex version is also not enough
to cover that.

> nor shown in what way this proposal
> -- which is completely general and motivated by Lojban syntax as well as
> logical syntax -- is inadequate

I wouldn't say inadequate, it's just that I don't like giving any
significance to the prenex notation itself.

> nor has he proposed an alternative. The
> And proposal involves sets essentially -- and xorxes disapproves of them
> -- and -- insofar as it has been spelled out -- does not seem to differ
> significantly from my proposal in any other way.

Well, And made a very involved proposal, with something like eight new
cmavo or so, that never got much discussed because we were suddenly
discussing much more basic stuff.

>  pc: I am not clear just where definitions come into this, once the
> grammar of Lojban has been set up, which was done in respense to a number
> of factors which have nothing to do with the present problem.

I'm not sure I understand this argument. The grammar has been set up
as far as saying which word orders are allowed, but I don't see how that
settles this problem.

> The most
> that seems left is to say that this radical change in structure has an
> insignificant effect on the meaning of the sentence.  Again, the cases
> involved here are but special instances of quite general alterations (or
> relationships between two structures) and I think it can be demonstrated
> that the general rules under which these fall have generally significant
> effects on meaning.  So, what xorxes really needs at this point is a
> reason why these few cases should be exceptions.  The simplest case is to
> follow the general rule, not introduce an exception.

Of course I don't want exceptions. Could you explain what is the general
rule that you mean? I thought my rule was at least as general.

>         All of this does make me long again for referential expressions,
> which do spare us all the scoping problems of quantifiers.

You've mentioned referential expressions before, but you never explained
how they would differ from what we have (or what I believe we have).


> sos:
> > xorxes:
> > I would read it as "there are exactly two men for which there are
> > exactly two dogs such that...", i.e. for each of the men.
> > pc:
> > I do not see why you want to read the "for which" in there, since it is
> > not in there.
> To make the English clearer
> pc:
> Why not just use "and," which isn't there either but makes the English
> clearer without introducing an extraneous element of subordination?

Well, I would use "and" to explain the second possible meaning, as I believe
I did. When we started discussing this with And, I favoured the "and"
reading, but then I changed to the And reading which seemed more useful.
You say that we don't have a choice, and that one of the readings is forced
by some prior rule, but I don't see it.

> xorxes:
> [I]t is a matter of definition which notation expresses which claim.
> pc:
> I am not sure that I agree, but if it is, then let us agree to take a
> nice simple form -- only appropriately more complex than the simplest one
> for the simplest case -- and use it for the other related case. Again I
> offer the prenex form, which is about t he right size and is at least
> free from obvious defects under existing and independently motivated rules.

I agree it is a possibility, but I don't like giving semantic relevance
to prenex vs. non-prenex notation. A general solution (covering three
and more argument cases) will require something else anyway.

Jorge