Re: THEORY: Kinds of Plurals, and Methods of Indicating Them

Hello, Chris, and thanks for writing.

[WHAT DISTRIBUTIVITY MEANS]
Greville Corbett's "NUMBER" gives Amerindian-language examples
where "distributive" means different /types/; this is another
possibility besides different times and/or different places.

[SPECIFIC AMERINDIAN LANGUAGES]
I used my Google-Print account to look at some of the pages of
Greville Corbett's "NUMBER" that discuss distributives and
collectives.  Like you, he mentions mostly the Amerindian languages;
and he gives specific examples.  Of course I can't print them off; I
have to wait until my library locates an out-of-state university that
is willing to loan us their copy.

[DISTRIBUTIVE/COLLECTIVE NOMINAL? OR MARKED ON VERB?]
In the appropriate chapter (approximately pages 110-120), Corbett
discusses /only/ /NOMINAL/ marking of Distributive vs. Collective.
But he does mention the existence of Verbal markings; perhaps he
takes it up later in the book, or elsewhere.  (Obviously, /you/ have
run across /someone's/ treatment of it.)

[HOW THIS TOPIC CAME UP]
In a personal e-mail "trialog" with Ray Brown and Joseph Bridwell, I
mentioned a situation in which a person holds each member of a set of
beliefs in high confidence, but seriously doubts that every last one
of them can be true.  As an example; suppose I have a booklet from
the U.S. Government containing 10,000 statements, and I am 99.95%
confident that each one of them is true.  Distributively, then, I
have high confidence that all of them are true.  But, there is a
quite low probability that not even one of the 10,000 statements is
false.  Collectively, then, I seriously doubt that all of them are
true.

[PARALLELS WITH OMEGA-CONSISTENCY]
It struck me that if a predicate P is provably distributively-false
for all natural numbers, but provably not collectively-false, then
this is just exactly omega-inconsistency.

A model of "arithmetic" (number theory) is "omega-consistent" if
there is no predicate P for which it is possible to prove "for some n
P(n)" while, at the same time, it is possible to prove for each
particular natural number k, "not P(k)".  A model that is not omega-
consistent is omega-inconsistent (bet that caught everyone by
surprise!).

What really is surprising, is that, there are plenty of consistent
models that are omega-inconsistent.

(A model is "consistent" if there is no statement q for which it is
possible to prove both "q" and "not q".)

-----

Thanks for writing, everyone.  Any and all replies will be welcomed
and read.

Thanks for writing, Chris.

Looking forward to reading your next post,

Tom H.C. in MI.

 --- In conlang@yahoogroups.com, Chris Bates
> <chris.maths_student@N...> wrote:
> Distributive in many languages typically implies (as the name
suggests)
> that the events (or entities) are distributed over space and/or
time.
> Many amerindian languages mark distributivity on the verb.
Collectivity
> implies that the events (or entities) are all in one place. I've
mostly
> heard of these terms with reference to events and verbal marking
though,
> and I can't say I'm familiar with nominal plural marking labelled
> distributive or collective.
>
> > 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.