pa remna, quantifiers

[Logical Language Group <lojbab@access.digex.net>]

>> Well, you *can* say that pa remna has one head, two arms, two legs.
>
>You can say anything you want, but if you say that you are saying
>something that is not true, since more than exactly one human have that
>number of members.  (Unless you want to argue that you mean at a certain
>time, in a certain place, but I don't think that's fair.)

This bothers me.  I haven't thought it out thoroughly, but perhaps it is
desireable to have "pa remna" = "pa lo remna" be a subselection from
remna which makes no claim about other members of remna.  This would be
a distinct difference from having "lo remna" = "da poi remna".

I'm not capable at the moment of thinking through the implications of
this on actual usage, logic, the "any" issue, labels like (-specific,
-definite) etc., and someone would probably correctly disagree with me
on whatever I said anyway since logical implications are slippery to me
(logical soap, right? zo'o).  So I'll let you guys tell me why I'm wrong
before I try to defend it.

Or have you guys gotten to the same point as me?
>In any case, I have reconsidered the case of general quantifiers and I'm
>now inclined to take your view, which really does seem much more
>intuitive.  Some examples:
>
>(1)     so'i prenu cu klama so'i da
>        Many people go to many places.
>
>(2)     so'i da se klama so'i prenu
>        Many places are gone to by many people.

I think these would have more clearly showed your issue if you had said
"so'i stuzi" instead of "so'i da".  Otherwise, I get distracted by the
issues of quantificational logic.  Do you intend that your conclusion be
the same for "so'i stizu" in the above.

>In English, those two mean different things.  The most natural meaning
>(I think) is:  for (1) that each of many people goes to many places, but
>since everybody can go to different places, each place might be gone to
>by very few people; and for (2) that each of many places are gone to by
>many people, but each person maybe goes to one place only.
>
>What do they mean in Lojban?  That depends on how are general
>quantifiers to be interpreted.
>
>I thought {re prenu} was to be interpreted as:  "There exists an x that
>is a person and there exists a y that is a person and x is not equal to
>y:"  and whatever was claimed was claimed for x and for y.
>
>But I think And's interpretation is better:  "There is a set of two
>persons, such that for every x of that set:"  whatever.

This sounds exactly like "ro lo re prenu".  And yet, somehow I think you
are intending to say what I said above.  That "re prenu" identifies a
set of two people out of all who are people, and makes a claim only
about those two.  Maybe "re prenu" = "ro le re lo ro prenu" which
preserves the veridicality and non-specificity of lo at the time of
selection but then seems to make the two people definite thereafter.

>(Actually, it has to be supplemented by "and no set of more than two
>persons", if the exactness of numbers is to be preserved.)
>
>This would mean that general quantifiers (almost anything except {ro}
>and {su'opa}), really hide one existential and one universal quantifier,
>rather than some indefinite number of existential ones.  This causes (1)
>and (2) to mean different things.  But if they were to mean the same
>thing, it would be that each of the many persons goes to each of many
>places, which is not the most useful meaning.
>
>I couldn't find a single example with more than one general quantifier
>in the reference grammar, so I don't know if there really is a policy on
>this.  My impresion was that they were supposed to be generalized
>existentials, but I may well be wrong.  I better let John answer.

Even if we had a policy, it would have had to be rethought in the face
of the "any" issue and the issue quantification scope of implicit
"su'opa", since I suspect the quantification issues of those you call
the non-general ones impact those of the general ones.  If order does
not matter for su'o and ro quantifiers on "lo" then order doesn't matter
for the general quantifiers either.

I wonder if the question you raise is made fuzzy by the use of
fuzzy numbers.  How do we compare:

               ci remna cu se tuple re tuple
               3 people have 2 legs?

vs.

               re tuple cu tuple ci remna
               2 legs are legs for 3 people?

Are the English sentences similar in meaning (I think both have typical
meanings that differ, but they are sufficiently ambiguous that in some
cases the meanings could reverse; e.g. replacing "2" with "6" in the
above - especially the first one.)

And:
>I of course agree. BUT we must make sure we won't be lacking a simple
>grammatical means to say:
>
>   There is a set, X, and there is a set, Y, such that for
>     every V, V in X, and for every W, W in Y, V goes to W.
>
>(= your "each of many people goes to each of many places").
>
>I tentatively propose that, slightly contrary to what you suggest, this
>should be the meaning of
>
>> (1)     so'i prenu cu klama so'i da
>> (2)     so'i da se klama so'i prenu
>
>While "For each of many people there are many places that they go to"
>should be:
>
>    sohi lo prenu cu klama sohi da
>    (= ro lo sohi lo prenu)
>
>That is, {lo broda} is equivalent not to {suho lo [suho] broda} (or to
>{da poi broda}) but to {ro lo suho lo [suho] broda}, while {suho broda}
>is still equivalent to {suho da poi broda}.
>
>What do people reckon to this?

Sounds like you ended up where I did, but backwards (and you have "lo"
instead of "le", which may be not much more than aesthetics).  I am of
the opinion that "quantifier broda" should be the same as "quantifier lo
broda" as it is now, but expanding as you suggest; if you want a "da
poi" you say "da poi".

Note that something is inherently wrong with your formulation, since it
is infinitely recursive:  every instance of "lo" expands into a nested
pair of "lo" which in turn expands into 4 nested "lo", ad nauseum.

lojbab