Quantifiers and negation with unusual grammatical number

As some of you may remember, I have given Índumom Tovlaugadóis no less than
four grammatical numbers.  In the process, I have given myself no less than
a logical headache.  I am confident, however, that listmembers are schooled
enough in logic to provide some me some pain relief :-)  (I *should* be
able to figure this out myself since I passed two semesters of formal
logic, but that was over ten years ago, and I started running into problems
as soon as we started working with quantifiers.)

Tovlaugadóis has: singular (1), paucal (2-7 or so), plural (more than 7 or
so), and multal (a great many) as its four grammatical numbers.  (Paucal
and multal can also be used to convey that the number was lesser or greater
than expected or sufficient, and other fun constructions can be made with
the multal, but that is beside the point at the moment.)  I can deal with
the idea of four categories for number, or I wouldn't have put it into the
language, but my brain starts running in logical circles as soon as I try
to use quantifiers or negation with Tovlaugadóis nouns.

As soon as I start using negation, things can start going a little
loopy.  "I don't have plural.flute" could still be construed to mean that I
have five of them, since five falls under the language's threshold for
plural.  "I don't have multal.cooking-pot" would probably be construed to
mean that I don't have a greater than average number of cooking pots.  How
a speaker would interpret "I don't have paucal.flute" is beyond my guess,
unless it means that I don't have fewer flutes than you would expect me to
have.  "I don't have singular.flute" would just about have to be construed
as meaning that I don't have any flutes at all.  Which brings me to my next
point.

What is the proper grammatical number to use when asking "Do you have any
flutes?"  Do I use the plural as I do in English?  The problem is that
Tovlaugadóis has three separate number categories that all correspond to
the English plural.

What do I do when I want to negate existence and say "There weren't any
skirts"?  "There weren't any skirts" (i.e. skirts didn't exist then) means
something different than the singular "There wasn't any skirt," so that
must indicate that I need to use one of the other three numbers.  Some
instinct tells me that the paucal will not work here.  That leaves the
plural and the multal.  Where plural ends and multal begins is a fluid
boundary, but if the number is difficult to count (e.g. the number of
leaves on a tree), then it is multal.  The multal is also used to create
some things that we would consider to be collective nouns.  An example of
this is the name Tovláugad that you see me use to refer to the people who
speak Tovlaugadóis.  The -ad at the end is the multal affix.  "Tovláugad"
means "The Instructed Ones," and using the multal like that refers to all
of the people together.

Let's see if I can figure out the semantics of a non-negated "any" with
each of the four numbers.  "Any singular.man" should mean exactly what it
does in English.  (e.g. "Any man found breaking curfew will be
arrested."  Ok, not a concept that fits into Tovlaugadóis culture, but it
was the first example of the use of "any" that sprang to mind.)  "Any
paucal.man" would end up meaning any small party of men, and "any
plural.man" might end up being interpretable as "any non-small party of
men."  "Any multal.man" could end up meaning more than one thing.  It could
mean "any very large group of men," and it could also mean "any men at
all," since the multal can be used to refer to a collective group of every
instance of a thing.

I can figure out that "every" should be paired with a singular noun, as it
is in English, and that "all" should be paired with the paucal, plural, or
multal, depending on which range the total number of items in question
falls into.  The same goes for "Which of the men spoke?" where the number
given to "men" should depend on how many there were total.  The same goes
for the use of "none."

I'm not certain that I'm up to trying to tackle the semantics of "some" in
Tovlaugadóis; I think it could get real complicated real fast.  How would I
say, for instance "Some men hunt with spears, others use bows"?  What
number should "men" be in?  Can I further twist the semantics by using
different numbers for "men"?

If I want to say, "People have always wondered if the moon is made out of
green cheese," do I use the plural or the multal?  My instincts (and not my
English-speaking ones) are telling me that "people" in that sentence should
be in the multal rather than in the plural.  Something is telling me that
what I have labled as the "plural" is not a true plural in this scheme but
is merely an intermediate range spanning the gap between "few" and "many"
and that the true plural is the mutal.  "Plural.person have always
wondered..." would end up meaning "There have always been some people who
have wondered..." wouldn't it?  Of course "Multal.person have always
wondered..." could also be interpreted to mean "A great many people have
always wondered..." or even "Most people..."  Upon further reflection, I am
begining to think that if you mean "all," then it is going to be neccessary
to *specify* "all" in Tovlaugadóis.  Otherwise, there is an unacceptable
level of ambiguity.  (Or does anyone want to vote that the speakers might
find this level of ambiguity to be acceptable?  After all, there are
langages where "yes" doesn't necessarily mean "yes," and the speakers find
that level of ambiguity acceptable.)

I'm not sure that this is going anywhere but towards more
confusion.  Anyone care to help me out?  Has anyone ever come up with any
scheme of grammatical number similar to this?  Does any natlang do anything
like this?  When I set up this number scheme in an inflected language, I
knew that I was going to complicate things for myself by multiplying the
number of inflections necessary, but I had no idea that it would do
anything this strange to the semantic space.  Wheeee!

Isidora
confused as usual
perhaps more so than usual

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