Editing Mass noun (section)

==Cumulativity and mass nouns==
An expression ''P'' has [[cumulativity|cumulative reference]] if and only if<ref>Krifka, Manfred 1989. Nominal reference, temporal constitution and quantification in event semantics. In [[Renate Bartsch]], Johan van Benthem and Peter van Emde Boas (eds.), Semantics and Contextual Expressions 75-115. Dordrecht: Foris.</ref><ref>{{cite journal |last=Nicolas|first=David |date=2008 |title=Mass nouns and plural logic |journal=Linguistics and Philosophy |volume=31 |issue=2 |pages=211–244 |doi=10.1007/s10988-008-9033-2 |s2cid=13755223 |url=http://d.a.nicolas.free.fr/Nicolas-Mass-nouns-and-plural-logic-Revised-2.pdf |access-date=2012-02-19 |url-status=dead |archive-url=https://web.archive.org/web/20120219021719/http://d.a.nicolas.free.fr/Nicolas-Mass-nouns-and-plural-logic-Revised-2.pdf |archive-date=2012-02-19 }}</ref> 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):

:<math>\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)]]</math>

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''.<ref>Borer, Hagit. (2005) ''Structuring Sense: In Name Only''. Volume 1. Oxford: OUP. (p. 124)</ref>

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.<ref name=Gillon>Brendan S. Gillon (1992) Towards a common semantics for English count and mass nouns. Linguistics and Philosophy 15: 597–639</ref>

An expression ''P'' has [[quantization (linguistics)|quantized reference]] if and only if, for any X:
*If ''X'' can be described as ''P'', then no proper part of ''X'' can be described as ''P''.
This can be seen to hold in the case of the noun ''house'': no proper part of ''a house'', for example the bathroom, or the entrance door, is itself a house. Similarly, no proper part of ''a man'', say his index finger, or his knee, can be described as ''a man''. Hence, ''house'' and ''man'' have quantized reference.  However, collections of ''cutlery'' do have proper parts that can themselves be described as ''cutlery''. Hence ''cutlery'' does not have quantized reference. Notice again that this is probably not a fact about mass-count syntax, but about prototypical examples, since many singular count nouns have referents whose proper parts can be described by the same term. Examples include divisible count nouns like "rope", "string", "stone", "tile", etc.<ref name=Gillon/>

Some expressions are neither quantized nor cumulative. Examples of this include  [[collective noun]]s like ''committee''. A committee may well contain a proper part which is itself a committee.  Hence this expression is not quantized.  It is not cumulative, either: the sum of two separate committees is not necessarily a ''committee''.  In terms of the mass/count distinction, ''committee'' behaves like a count noun. By some accounts, these examples are taken to indicate that the best characterization of mass nouns is that they are ''cumulative nouns''. On such accounts, count nouns should then be characterized as ''non-cumulative'' nouns: this characterization correctly groups ''committee'' together with the count nouns. If, instead, we had chosen to characterize count nouns as ''quantized nouns'', and mass nouns as ''non-quantized'' ones, then we would (incorrectly) be led to expect ''committee'' to be a mass noun. However, as noted above, such a characterization fails to explain many central phenomena of the mass-count distinction.