THEORY: Kinds of Plurals, and Methods of Indicating Them

Hello, the list.

I have been looking around on Google for a little while, and have
found a few different terms used to indicate different kinds of
plurals.
Among these terms are "distributive plural", "aggregate
plural", "collective plural", "cumulative plural", and others, not
all of which I understand, and some of which don't seem to be
distinct, as far as I can tell, although the writers seem to think
they may be.

I have also found mentions of various languages --- Serbian is one,
and American Sign Language is another --- that distinguish either
more precisely or more explicitly than English does.  Some of these
seem to mark the difference on the pluralized nominal itself; some of
them seem to mark it in the agreement marking on the verb.

My questions are;
How many different kinds of plural are there?
What are they called?
Can the list give me a complete list of terms, even if no-one can say
that it is a complete list of the kinds of plural?
What do the terms mean, roughly?  How do they differ?
Are some terms synonymous with others?  And which with which, if so?
What are the various ways natlangs distinguish between the various
kinds of plurals?
Which natlangs require such disambiguity?  Which merely allow it?
Which cannot disambiguate easily?
I know various auxlangs/engelangs/loglangs handle these problems
various ways, but --- does anyone's artlang or fictlang conlang
handle this in a way they are particularly proud of or think is
particularly interesting?
-----
For anyone who doesn't understand what I'm talking about, I offer the
following prototypical example from English, which seems to be
popular when the author is writing in English.
Consider the ditransitive sentence:
"Two students gave three teachers four books."
The subject, "two students", can be interpreted two different ways:
either as "a duet of students" (which I here call "aggregate",
although that may not be what I should be calling it); or as "each of
two students", which I am pretty sure is what is meant
by "distributive plural".
Similarly, the indirect (or primary) object, "three teachers", can be
interpreted either as "a trio of teachers" (aggregate?) or as "each
of three teachers" (distributive!).
If both subject and indirect/primary object are aggregates, only four
books get given in total; but if both subject and indirect/primary
object are meant as distributive plurals, a total of twenty-four
books get given.
If the subject is distributive but the indirect/primary object is
aggregate, a total of eight books are given; if the subject is
aggregate and the indirect/primary object is distributive, a total of
twelve books are given.
A mixed case is also possible; the teachers might be an aggregate for
one student but distributive for the other, or, the students might be
an aggregate for some teacher(s) but distributive for some other(s).
I don't think this particular sentence varies much in meaning
depending on whether the direct/secondary object is meant aggregately
or distributively.
-----
Thanks for writing.
Tom H.C., in MI



		
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