quantifiers

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

xorxes on pc(>)
> For ro da poi broda cannot be Ax(x broda => if da poi broda is to
> be either the corresponding Ex( x broda & or (and this turns out to be
> equivalent) Ex st x broda
I never proposed that. I'm also not saying that {ro lo broda} should
be Ax(x broda => . That last thing is not a complete expression that
can function as a sumti, while {ro lo broda} is.
>  Unless, of course, poi is to take
> on fairly severe ambiguity (which gets worse if we bring in numerical and
> plurative quantifiers).
I'm afraid I don't see the ambiguity. I read {ro da poi broda cu brode}
as "every/each/all x which is a broda is also a brode". The only ambiguity
can be whether this is also saying that there is at least one x which is a
broda.
Just as a comment, you are taking {ci da} to mean "at least three x".
The canon is that bare numbers are exact, so that {ci da} would mean
"at least 3 and at most 3 x". I would prefer them to be of the "at least"
variety, but traditionally they are not.

pc:
Yes, I often put in just the focus parts of what I am talking about;
sorry if that misleads
you.  The interesting differences between ro da poi broda cu brode and
(su'o) da poi
broda cu brode  is not the x brode at the end but all that comes before,
what corresponds
to ro/su'o da poi broda (cu) and that is "for all x, if x broda then"
vs. "for some x, both x
broda and."  My point is that even "such that/ which is a" cannot cover
both of these
connectives, that  poi cannot be both conditional and conjunctive.  The
fact that the
English works I take to be evidence that the English expression, like the
Lojban, is
restrictive.
Similarly, I regularly don't mention the "at most n" clauses, since
nothing interesting for
our discussions goes on in them and they take up an awful lot of space.
They do,
however, move about freely in the contexts where that is important.
(I confess I am unclear what is the "that" xorxes never proposed, since I
had not said
hehad proposed anything and the rest of the paragraph was just stock
truisms.)

xorxes (>pc) :
>it comes as quite a shock to students that "All S is P" is true when there
> are no Ss (and a worse one if they hear that it is BECAUSE there are no
> Ss).
Actually, even children are well aware of that, even if it is hard to
recognize it in the logicians notation. Or do you think this dialogue
could not happen?
  child: Can I watch TV?
  parent: Did you put away all the toys you were playing with?
  child: Yes.
  parent: Ok, you can watch TV.
(later)
  parent: What's this? Your room is a mess, didn't you tell me that
          you had put away your toys?
  child: Yes, the toys that I was playing with, but I wasn't really
         playing with any.
Which means essentially that the child was taking "all" without
existential import when it was advantageous to do so. Of course, the
child will not understand that "All S is P" is true when there are no Ss
if you put it like that, but that doesn't mean that they don't in fact
understand the principle behind it. In fact, the child understood the
parent perfectly well, and yet uses this very technicality of the
quantifier to get away with it.

pc:
Sure, a kid can use this trick, it really is there among other meanings.
I think, however,
in this case this kid is using "must do all that F" in the available
"need not do any that
non-F" sense, then being casuistical on F (play with) for good measure.
The students'
shock is genuine too.

xorxes:
I'm sure that the natural interpretation is to assume existential import,
but I think that comes from another source, not from the natural meaning
of the quantifier.
If I say "Every person that I met this morning was wearing a blue hat", you
will naturally assume that I met at least one, and more likely more than
one person. But in my opinion this is not so much from what I said, but
from what I could have said instead but didn't. If I didn't meet anyone
this morning, then my sentence (even if taken as true) is not informative.
The talk of blue hats is even misleading. We tend to use language with some
purpose, not just to state irrelevant and misleading truths. If I met only
one person, then I would more likely have said "the person", instead of
"every person", so you will assume that I met more than one, since otherwise
there would be no reason to use "every" instead of "the". But when we
want to be misleading (as the child above), we are quite happy to take
recourse in the true deep meaning of quantifiers to state misleading truths.
And even children are very capable of doing this, it is not necessary
to have studied formal logic.

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

xorxes (>pc):
>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 (ro, su'o and no
> -- ? has that last one changed again?).
I'm not sure I follow. {ro} is A, {su'o} is E, what is I, {pa}?
And what is O, is that {no}?

pc:
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?)

sos:
>         Incidentally, ro lo broda always was ro lo su'o broda, since ro
> ALWAYS implies su'o -- it is the "if" that gets the empty set in,
> remember.
That's not what the grammar papers say. They have inner {su'o} for {le},
which makes a lot of sense to me, because there I do want existential
import. But it has the innocuous {ro} as the inner for {lo}.
pc:
Well, neither John's nor lojbab's grades in logic were all that good and,
worse, I often
gave snap answers to questions I got in the middle of long conversations
in the middle of
the night and then did not proof-read.  In short, the grammar book is
wrong, if Lojban is
meant to have any significant connection with logic.

sos:
>         But, if you want the modern reading, Lojban has it and exactly the
> way modern logic does, so there is no loss.
You said modern logic takes "All S is P" to have no existential import.
pc:
Yup!  It translates  "All S is P" as "for every x, if x is S, then x is
P," i.e.,
exactly Lojban ro da zo'u [whatever disjunction with the first disjunct
negated is] x broda
[relevent inter-sentential comma] x brode  (I like Polish notation for
these things).  This
guarantees there is something in the universe of discourse but does not
guarernatee any S
(broda).

sos:
>  I would urge that for 4 is
> represented in Lojban with something in the general area: re prenu, re
> gerku zo'u py pencu gy.  That would then settle the whole mess in a
> systematic way (and, of course, could be reached as afterthought using
> leapers).
I think that still gets you the nested form. {re prenu re gerku cu pencu}
should be equivalent to the prenexed {re prenu re gerku zo'u py pencu gy}.
For the other I propose {re prenu e re gerku zo'u py pencu gy}. The {e}
forces the two persons and two dogs to be at the same level.
pc:
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.  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.  This
leaves at least one of gy and py without an antecedent referent and so
does not say what
is wanted:  For two men, they pat gy and for two dogs (py/the men) pat
them (depending
on how we interpret the scope of re prenu). The two are on the same
level,perhaps, but
not in the same sentences anymore.  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 (I suggested
using explicit
universals in the logical forms at some point to emphasize the dependency
relation of
some quantifiers on others -- or we could do away with some quantifiers
altogether and
go with Skolem functions, essentially what I would like lo to do. But
that is another
story.)

sos:
>         What is abstruse about version 4?  It is different and more narrow
> than 3 but hardly difficult to understand, since it is almost as often
> what one means or understands by the English version "Two men patted two
> dogs."
Not really. When you say that in English, you don't usually mean to describe
exactly four relationships. It usually means {lu'o re nanmu cu pencu lu'o
re gerku}, a single relationship between a mass of two men and a mass of
two dogs. This allows for one man touching both dogs and the other touching
only one of them, for instance, which would be covered by the English
version.

The English version would be unlikely if the exact claim was wanted. A much
longer paraphrase like "there were two dogs and two men, and each man
touched each dog" would probably be used.
pc:
Yes, the English could mean this more fuzzy thing, and often does.  It
also could  and
often does version 4  or version 3-- and probably most of the other
however many of
those things we said there were.  We do have rather different experiences
-- or senses at
least -- of what English sentences mean.  I suppose we ought to fill our
our cases more,
but, happily, nothing hangs on this pseudo-empirical point, since we
agree (I think) that
the English MIGHT mean any of these in certain lights.  So, we want to be
more precise
but not significantly more wordy in Lojban.

sos:
>le broda seems to force us to think
> (incorrectly) that we are talking about non-brodas.
It doesn't force me to think that. I always assume that {le broda} means
we are talking about a broda. {lo vi broda } is still legal also
pc:
I think it is the cases that xorxes is about the only one in this
conversation who has
consistently remembered that le broda is usually a broda (strictly, I
would say, members
of a set of brodas).  Still, lovi (etc.) broda has some advantages -- and
one major
disadvantage: the fact that lo is quantified su'o.  We need some
experimentation, for
theory work it saves a lot of space and conceptual turmoil, getting
almost as good as a
referring expression for convenience.

>djer then xorxes:
> I believe that
> lojban should always mirror the best in logic, and accept whatever
> changes that implies.
I agree.
pc:
Me, too.  So let us get on with it.  Although I think we have some
fundamental
disagreements about what is good and  maybe even some about how close we
are to logic
at the moment.

pc>|83