A mass noun has none of these properties: It cannot be modified by a number, cannot occur in plural, and cannot co-occur with quantificational determiners.
However, some abstract phenomena like "fun" and "hope" have properties which make it difficult to refer to them with a count noun.
Following the work of logicians like Godehard Link and linguists like Manfred Krifka, we know that the mass/count distinction can be given a precise mathematical definition in terms of notions like cumulativity and quantization.
The following examples are of nouns which, while seemingly innately countable, are still treated as mass nouns: A classifier, therefore, implies that the object(s) referred to are countable in the sense that the speaker intends them to be enumerated, rather than considered as a unit (regardless of quantity).
The use of a classifier is similar to, but not identical with, the use of units of measurement to count groups of objects in English.