In linguistics, a mass noun, uncountable noun, non-count noun, uncount noun, or just uncountable, is a noun with the syntactic property that any part and quantity of it is treated as an undifferentiated unit, rather than as something with discrete elements. Uncountable nouns are distinguished from count nouns. Given that different languages have different grammatical features, the actual test for which nouns are mass nouns may vary between languages. In English, mass nouns are characterized by the impossibility of being directly modified by a numeral without specifying a unit of measurement and by the impossibility of being combined with an indefinite article (a or an). Thus, the mass noun "water" is quantified as "20 litres of water" while the count noun "chair" is quantified as "20 chairs". However, both mass and count nouns can be quantified in relative terms without unit specification (e.g., "so much water", "so many chairs", though note the different quantifiers "much" and "many"). Mass nouns have no concept of singular and plural, although in English they take singular verb forms. However, many mass nouns in English can be converted to count nouns, which can then be used in the plural to denote (for instance) more than one instance or variety of a certain sort of entity – for example, "Many cleaning agents today are technically not soaps [i.e. types of soap], but detergents," or "I drank about three beers [i.e. bottles or glasses of beer]". Some nouns can be used indifferently as mass or count nouns, e.g., three cabbages or three heads of cabbage; three ropes or three lengths of rope. Some have different senses as mass and count nouns: paper is a mass noun as a material (three reams of paper, one sheet of paper), but a count noun as a unit of writing ("the students passed in their papers").
Grammatical number and physical discreteness In English (and in many other languages), there is a tendency for nouns referring to liquids (water, juice), powders (sugar, sand), or substances (metal, wood) to be used in mass syntax, and for nouns referring to objects or people to be count nouns. But there are many exceptions: the mass/count distinction is a property of the terms, not their referents. For example, the same set of chairs can be referred to as "seven chairs" (count) and as "furniture" (mass); the Middle English mass noun pease has become the count noun pea by morphological reanalysis; "vegetables" are a plural count form, while the British English slang synonym "veg" is a mass noun. In languages that have a partitive case, the distinction is explicit and mandatory. For example, in Finnish, join vettä, "I drank (some) water", the word vesi, "water", is in the partitive case. The related sentence join veden, "I drank (the) water", using the accusative case instead, assumes that there was a specific countable portion of water that was completely drunk. The work of logicians like Godehard Link and Manfred Krifka established that the mass/count distinction can be given a precise, mathematical definition in terms of quantization and cumulativity.
Cumulativity and mass nouns An expression P has cumulative reference if and only if for any X and Y:
If X can be described as P and Y can be described as P, as well, then the sum of X and Y can also be described as P. In more formal terms (Krifka 1998):
∀ X ⊆ U p [ C U M p ( X ) ⇔ ∃ x , y [ X ( x ) ∧ X ( y ) ∧ ¬ ( x = y ) ] ∧ ∀ x , y [ X ( x ) ∧ X ( y ) ⇒ X ( x ⊕ y ) ] ] {\displaystyle \forall X\subseteq U_{p}[\mathrm {CUM} _{p}(X)\Leftrightarrow \exists x,y[X(x)\,\wedge \,X(y)\,\wedge \,\neg (x=y)]\;\wedge \;\forall x,y[X(x)\,\wedge \,X(y)\Rightarrow X(x\,\oplus \,y)]]}
which may be read as: X is cumulative if there exists at least one pair x,y, where x and y are distinct, and both have the property X, and if for all possible pairs x and y fitting that description, X is a property of the sum of x and y. Consider, for example, cutlery: If one collection of cutlery is combined with another, we still have "cutlery". Similarly, if water is added to water, we still have "water". But if a chair is added to another, we do not have "a chair", but rather two chairs. Thus the nouns "cutlery" and "water" have cumulative reference, while the expression "a chair" does not. The expression "chairs", however, does, suggesting that the generalization is not actually specific to the mass-count distinction. As many have noted, it is possible to provide an alternative analysis, by which mass nouns and plural count nouns are assigned a similar semantics, as distinct from that of singular count nouns. An expression P has quantized reference if and only if, for any X:
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