Re: quantifiers

[jorge@PHYAST.PITT.EDU]

pc:
> My point is that even "such that/ which is a" cannot cover
> both of these
> connectives, that  poi cannot be both conditional and conjunctive.

Why not? The conditional or the conjunction are a consequence of {ro}
and {su'o}, not of {poi}. I am certainly not saying that you can replace
word by word to go from one type of formula to the other. That is
certainly not the case.

Let me try to write everything down, otherwise I'm totally lost.

The Lojban expressions in question are the following:

1a      ro broda cu brode
1b      ro da poi broda cu brode
1c      ro da broda nagi'a brode

2a      su'o broda cu brode
2b      su'o da poi broda cu brode
2c      su'o da broda gi'e brode

My position is that 1a, 1b and 1c mean all the same thing, and likewise
2a, 2b and 2c mean all the same thing.

Since we have no disagreement about the meaning of 1c, I think you are
saying that either one or both of 1a and 1b mean something different,
namely:

1d      su'o da broda ije ro da broda nagi'a brode

I think that it is not worth it to complicate matters by giving
1a or 1b or both the meaning 1d, and I don't see a problem with
that position. We can of course give that meaning to one or both
of 1a and 1b, but that only makes manipulating formulas more
complicated, and I don't see the advantage. The existential import
can always be recovered anyway using an explicit inner quantifier
{ro lo su'o broda}.

> The Gricean (conversational implicature) explanation of existential
> import is a
> completely plausible one and may even be true for English a lot of the
> time (though it
> does not readily explain the differences among the four universals, each,
> every, any, and
> all).

Well, the special thing about "any" are its scope properties, they
are different from the others. The special thing about "each" is that
it blocks massification. The special thing about "all" is that it
strongly suggests massification (at least to me, not a native speaker)
and the special thing about "every" is that it has nothing special about
it, as far as I can tell...  :)

> Still, the habit in logic and one of the explicit goals in Lojban
> (well, at least Loglan)
> is to move as many as possible of these logically significant differences
> from pragmatics
> (or wherever Grice is buried these days) to overt differences in form.

I'm not against that, of course. I just don't think that the form with
existential import should be the standard one. The standard one should
be the logically simpler, which means no existential import.

> Given the variety
> of forms available in Lojban for universals (etc.) this asignment seems
> natural.

I don't agree. I think the natural assignment should make 1a, 1b and 1c
equivalent. Each of these forms is needed for separate reasons, and the
existential import can always be forced when required, anyway.

> >The supposed greater complexity of negation shifting with
> > restrictive quanti fiers could be dealt with by introducing from categoric
> > logic the O quantifier to match the existing A,I, and E
> A: All S is P (ro)
> E:  No S is P (no -- if that is still the word)
> I:   Some S is P (su'o)
> O: Some S is not P (xu'o?)
> A and O are contradictories, as are E and I; the other relations among
> these depend upon
> what we do with existential import (Does A imply I or E O?)

I see. Yes, it would be nice to have such {xu'o}. If the default
for the complement of {da'a} was "at least 1", rather than 1, I think
that would be it.

But anyway, if {ro} and {su'o} are to be duals there has to be no
existential import, and I think that relationship between them is
important. I don't think A should imply I, nor E O.

(BTW, conversationally, usually I implies O and O implies I, but we
don't force that one on the quantifiers. Why should we force the
others?)


> I do not see any reason to think that prenex and shifted forms are
> equivalent, since
> shifting does not take the sumti out of the core sentence, while
> prenexing does and that
> fact is crucial to the difference in results.

I guess it's just a matter of aesthetics. To me these two should be
exactly equivalent:

        re da poi nanmu cu pencu re de poi gerku
        re da poi nanmu ku re de poi gerku zo'u: da pencu de

And the same should hold for:

        re nanmu cu pencu re gerku
        re nanmu re gerku zo'u: ny pencu gy

I guess you could define them as being different, but I would find it
aesthetically wrong.

> As for the re prenu e re
> gerku form, that has to
> expand into a conjunction of two sentences, each with a single sumti in
> the prenex.

I don't see why, since they are not filling the same argument place.
Anyway, it would be just a consistent convention. Another possibility
would be using {jo'u}, which doesn't seem to have any use.

>  My version does technically put one
> in the scope of
> the other, but since it is indifferent which is in the scope of which
> (the two are
> equivalent), this does not force the separate instantiations

It is indifferent if you define it like that, otherwise it wouldn't be :)
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. Of course, you can also
define it to have equal scope and read it as "there are exactly two men
and there are exactly two dogs such that..., but I thought we had agreed
that this was not the most useful way of doing it. (I don't know what
are Skolem functions.)

Jorge