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Okay... I was reading a book called "the 100 greatest philosophers" out
of boredom during my lunchbreak at my part time job, and I was reading
the section on Plato (I think), talking about archetypes etc, and I was
thinking about how this relates to qualifiers, quantifiers, plurality
etc. It seems to me... if a common noun represents an archetype, say
"man", then we can get from that:
the archetype itself (perhaps "maleness"?)
the set of instantiations of the architype ("all men")
a subset of the complete set
an individual member of the set ("a/the man")

 And then I started wondering if any languages "number" system actually
makes this four way distinction... and from that I got onto the problem
of the definition of subset, since a subset can contain only one
element, or, in set theory at least, no elements at all (the null set is
a subset of all sets including itself), so the distinctions above don't
necessarily make any distinction between singular and plural (and how do
you handle mass nouns? Count the whole set as the set every single
"atom", "molecule", "point", whatever of the substance and then use
subsets but not individual members? Or some other approach?), and
started thinking about making other distinctions such as plurality or
specificality (if we distinguish specificality in this system then it
seems to me that taken as a whole we mostly do away with the need for
qualifying words such as "any" etc).
 I was also thinking about what it means to have a plural argument to a
verb... take for instance "The men went to the supermarket". This
amounts to feeding each member of the group "the men" to the verb, with
(often) the added implication that each of them went in a way somehow
related to the others going. If I said "John went to the supermarket,
and Fred went to the supermarket, and..." then I am not necessarily
implying that they did it together or that each of them going is related
in any way. Most languages have an easy way of giving the first meaning,
but the second seems to me more tricky. In English we'd usually use
"each" I think, as for example in: "Each man went to the supermarket" or
"Each of the men went to the supermarket". This removes the implication
that the events are related, or at least makes them more distantly
related. How do other languages handle this? How do your conlangs handle
this?
 This has mostly been a ramble... there wasn't any objective really,
except that I thought someone else might have ideas on this topic. :) I
hope someone finds it interesting.... or has some added thoughts. :)
I've always found the examples of logical languages I've seen... less
than exciting to be honest, but thoughts linking maths/logic and
language are interesting me tonight.