In many languages, we find two distinct sets of nouns, viz. count nouns and mass nouns, that behave in slightly different ways: count nouns permit singular and plural forms (and so on), whereas mass nouns do not. Sometimes, the lines between the two can be crossed, and a mass noun can be turned into a count noun or vice versa. However, let's consider a different way of giving mass nouns something number-like.
A very simple, but subtle and tricky thing one could do is just to introduce mandatory marking of volume or size for mass nouns. Simply put, sometimes, water takes a marker that indicates lots of water, but this marker is mandatory under some circumstances.
Now, the interesting - and probably unformalizable - bit is when that marker is supposed to be used. Whoever authors such a conlang would need to provide some kind of guidelines, probably with individual guidelines for different types of mass nouns, that also are somewhat vague - i.e. there's probably a set of contexts or amounts for which both forms would be permissible.
One could imaginably also permit for ways of making count nouns out of both of the forms, and vice versa, turn count nouns into mass nouns of either form. (And maybe even cross-pollination: {plur, sing} * {small, large} and {small, large} * {plur, sing}. Duly note that these cartesian products are ordered pairs, so the operations are not commutative - [plur, small] may not be the same thing as [small, plur].
One could imaginably also permit for ways of making count nouns out of both of the forms, and vice versa, turn count nouns into mass nouns of either form. (And maybe even cross-pollination: {plur, sing} * {small, large} and {small, large} * {plur, sing}. Duly note that these cartesian products are ordered pairs, so the operations are not commutative - [plur, small] may not be the same thing as [small, plur].
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