quantifiers

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

sos:
> It is not at all clear to me what a person saying "Ax(Fx => Gx)
> assumes, but someone who says "Every unicorn is blue" seems pretty
> clearly to be assuming that there are unicorns.
Yes, otherwise that person would have no reason to say that. But that
seems to be just a conversational implicature. When the same person
says "everyone who answers all questions correctly will get an A"
it seems equally clear that they are not predicting that someone
will answer all questions correctly.
pc:
Well, it has been argued that ALL of this is conversational implicature,
but part of logic has been pretty consistently to make as much of
implicature over into explicit entailment (cf. the various "or"s).  In any
case, if the speaker wants to make it clear that he is NOT assuming that
there will be a perfect paper, he had better say "ANYONE who answers
all questions correctly"

xorxes:
That person [who assumes that unicorns exist] is accomodated in any
case already: {ro lo su'o pavyseljirna cu blanu} leaves no doubt about
the assumption that there is at least one unicorn. But for the general case,
it seems better to leave it unspecified as to whether there are or
not.
pc:
But, as the apparent complaint about the conditional form goes, that
structure is long and complicated -- too much so for the frequency of its
use (it is the general case, after all, though there are those who deny that
fact).  Oh yes, "and not commonly used."
sos:
> I am not sure this is non-specific (or is it non-distinctive or
> whatever?).  To be sure we cannot identify the apples, but they remain
> the ones -- whichever they were -- that I bought.
Isn't that what nonspecific is supposed to be? Compare with: "there is an
apple such that I buy it for three dollars". Just the same for this case:
"there is a mass of apples (a submass of the mass of all apples) such that
I buy it for three dollars".
pc:
I long ago gave up on specific/definite.  What I want to say is that this is
a described submass, not just a random one; it is characterized by an
expanded predicate structure, not just be a non-specific quantifier.  I am
not sure whether this will turn out to matter, but it does open up some
lines of investigation.

xorxes:
I thought we had agreed that {piro loi plise} was [the expression to
*refer to* the mass of all apples], and that
{pisu'o loi plise} was a mass whose components were the members
of a subset of the set of all apples, or a "submass" for short.
pc:
But _piro loi plise_ can't be the referring expression, precisely because it
contains (local) quantifiers.  Now, it may be that we can work around
this somehow by stretching the metaphor from the partial cases to this
one as well (as I suppose we should), but the partial cases are none of
them referring expressions either, since they are non-specific (or
whatever).  This needs some more work all around, although I thank you
for reminding once again of  the lu'a set as a possible source for some
solutions here (not the offical versions, alas.

xorxes:
I don't think it follows.
(A) No one who knows there are no unicorns says X.
(B) Someone who says X believes there are unicorns.
To my mind, B does not follow from A, since A does not preclude
someone who doesn't know whether there are unicorns to say X.
In other words, it is not necessary to either believe that there
are unicorns or to believe that there are no unicorns. It is
possible to not know and not believe either of them. Which is what
I went on to say:
pc:
The possibility of getting off in the messiness of "know" was why I
reworded the issue to
"No one in a universe that does not include unicorns would say X."
Now from iy does follow that "Anyone who says X is in a universe that
includes unicorns" (well, under the universal assumption that saying
anything puts one in some universe or other).

sos:
>.  Why, exactly, all the
> fuss?
The fuss comes from the fact that you are pulling the carpet from
under my feet. I have been learning Lojban thinking that the universal
quantification in Lojban was treated as it is usually treated in
all the logic books I've read, and now you are telling me that in
Lojban it is different (and to no advantage that I can see).
You are saying that I can't pass a negation across a {su'o} by
changing it to a {ro} and viceversa.
I understand that it is possible to define things so that {ro}
implies {su'o}, but I don't see any advantages to doing that, and
I do see a lot of complications. That's why all the fuss from me.
pc:
But the rug was never there, at least not in the time xorxes was learning
the language (after _da poi_ and _lo_ fell together).  I am just bringing
the message, as he says.  How did xorxes, one of the most meticulous
students of Lojban, who has quoted to me many an obscure obiter
dictum from the draft textbook, miss this rather central point when he
was  learning the language?
        I fear that the answer may be that the draft textbook, like so
many drafts, has been revised piecemeal, with the results that there are
many fossils buried in among the latest words.  In particular, there may
be pieces of the original _lo_ construction still around, which
construction was approximately the present _ro lo_ but was described as
allowing that the set being taken distributively (and conjunctively) might
be empty and that that situate defaulted to true.  For good reasons of
likely usage, we decided that the default form should be _su'o_ instead
of _ro_ and that made the empty reading no longer viable (as _ci lo re
broda_ is not).  So, the old contrast between _lo broda_ and _ro da poi
broda_ disappeared.  But I think some of the text from the earlier
situation is still around.  As I have said, I can remember weeding out a
bit about _lo ro broda_ allowing the empty set within the last year and a
half.  And I suppose that, given a choice of an exstnetial import or not,
some people will choose the free form and assume the other is the
mistake.
        As for how quantifiers are treated in "all" the logic books, it is a
pretty rare (or bad) one in which "all" does not imply "some" (a couple
of books on free logics or a chapter on that in maybe a half dozen texts).
That is just counting texts on mathematical / symbolic / formal logic.
But Logic did not come into existence with Frege or even Boole and for
the couple of millennia and change before the mathematicians got into
it, the existential import of at least affirmative universals, even of the
restricted sort, were -- following natural language usage -- taken for
granted, and -- latterly -- even argued for.

xorxes:
We understand the word "scope" differently, but it doesn't really
matter.
pc:
It may matter, for we may just be arguing about words here (but it does
not seem so).  By "scope" I mean all of the utterance from the beginning
of a quantifier expression through the last part of the utterance where
that expression affects the interpretation of the utterance.  This is
vague because Lojban does not seem to have a good syntactic rule for
characterizing scope.  Maybe, :from the beginning of the quantier
expression until the variable/expression is reset explicitly (by a "reset all
variables" operator) or implicitly (by requantifiying the same
variable/expression)."  And you mean...?

xorxes:
I have suggested several [ways to represent the three dog- three men pet].
I think the question is what does the
simple form mean. It is always possible to come up with more
involved forms in order to express the less frequent meanings.
I don't think Lojban is so fragile that we would make things
impossible to say just by having this or that minor convention.
pc:
Aside from the recent one involving double descriptors, which I do not
necessarily agree say what is wanted because I am still having trouble
with the structures, the only one I can find is the one with a conjunction
in the prenex, which gives gibberish under the textbook rules for these
structures.  My point, however, is that if we have to have subordination
whenever we have sequence then we can never get some structures out,
no matter how complicated we make them -- and we soon come to
unreasonable lengths for what we want to say.  That is, the
order=subordination feature which we happily exploit for _ci nanmu cu
pencu ci gerku_, is not a minor convention if it applies universally; it is
a major restriction.

xorxes:
. Even with the set interpretation [two orders of particular quantifiers]
are equivalent (as they should be, since the talk of sets is purely
clarificational, it doesn't change the meaning): there is a set of
at least one dog such that for every dog of that set there is a set
of at least one man such that each man of that set pets the dog. It
all comes out as saying that there are at least one dog and one man
such that the man pets the dog. (In this case, talk of sets muddles
everything, but it comes out to be the same in the end.)
pc:
I don't see it: how do we equivalently push particular quantifiers across
universals to convert from  Ex(x/=0 & x c {man} & Ay(y e x => Ez(z/=0
& z c {dog} & Aw(w e z => y pets w)))) to Ez (z/=0 & z c {dog} &
Aw(w e z => Ex(x/=0 & x c {man} & Ay(y e x => x pets y)))).  Maybe
we can manage using some principles of set theory (which may be
appropriate, given we have introduced sets) but the general pattern does
not transform in logic.  But xorxes may have some other notion of
equivalence or subordination here.

xorxes:
Given two quantifiers Q1 and Q2, there are three possibilities of
subordination:
(i)     Q1(Q2)  i.e. Q2 subordinate to Q1
(ii)    Q2(Q1)  i.e. Q1 subordinate to Q2
(iii)   Q1-Q2   i.e. Q1 and Q2 are coordinate.
In the case of the men and dogs, (iii) is the round robin,
and (i) and (ii) are three independent dogs for each man and
three independent men for each dog, respectively.
But when the quantifier is {ro} or {su'o}, these three cases
are degenerate.
If Q1 is {ro}, then (ii) and (iii) are the same.
If Q2 is {ro}, then (i) and (iii) are the same. And so if both
Q1 and Q2 are {ro}, then all (i), (ii) and (iii) are the same,
which is right, since multiple {ro}s commute.
If Q1 is {su'o}, then (i) and (iii) are the same.
If Q2 is {su'o}, then (ii) and (iii) are the same. And so if
both Q1 and Q2 are {su'o}, then all (i), (ii) and (iii) are
the same.
pc:
What is the other quantifier in each case?  the other of _ro_ - _su'o_? Or
might it be a numeric?  I take it that "subordinate" here means that the
choice of the instantiations of the subordinate is a function of/depends
on the choice for the superordinate.  I guess my problem is what does
"the same" mean?   While AxAyFxy is equivalent to AyAxFxy (case iii
with _ro_?)  AxEyFxy does not entail (and so is not equivalent to)
EyAxFxy, so the two do not seem to be coordinate.  Similarly, ExAyFxy
is not entailed by AyExFxy and so they are not equivalent nor
coordinate. Or do you have some other sense of coordinate in mind?  I
do not understand this passage at all.
After a day of (occasional) mulling what I come up with is that this is
another way of saying that (where "affect" is about allowing different
choices with different instances)
        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.
pc>|83