Boolean semantics, mass-count properties, count nouns, mass nouns


The background for this paper is the framework of Boolean semantics for mass and count nouns, and singular and plural count nouns, as developed from the work of Godehard Link in Link 1983 (see e.g. the expositions in Landman 1991, 2010).

Link-style Boolean semantics for nouns (here called Mountain semantics) analyzes the oppositions mass-count and singular-plural in terms of the notion of atomicity: counting is in terms of singular objects, which are taken to be atoms. Consequently, Link bases his semantics on two separate Boolean domains: a non-atomic mass domain and an atomic count domain. Singular count nouns are interpreted as sets of atoms, and semantic plurality is closure under sum, so plural objects are sums of atoms.

In this, sorted setup portions - like two portions of soup - are a puzzle: they are mass stuff - soup -, but count - two. But in order to be count they must be atoms. But they are not, because they are just soup. Mountain semantics can deal with portions, but at a cost.

In the first part of this paper I outline Iceberg semantics, an alternative to Mountain semantics within the general framework of Boolean semantics.

Iceberg semantics specifies a compositional mechanism which associates with the standard denotation of any noun phrase (here called the body) a base set, a set that generates the body under the sum operation ⊔. For count nouns, the base is the set in terms of which the members of the body are counted and to which distribution takes place. In Iceberg semantics, what allows counting to be correct is the requirement on the interpretations of count nouns that the base of their interpretation is (contextually) disjoint.

Already at this level we see two salient properties of Iceberg semantics:

-Atoms and atomicity play no role in the theory, so we can assume an unsorted interpretation domain for mass nouns and count nouns. In Iceberg semantics, mass and count can be seen as different perspectives on the same stuff (different bases for the same body). This means that we can do away with the extreme body-sorting and body-gridding that atomicity entails.

With this we allow a simpler and more elegant analysis of mass-count interactions. For instance, portions can just be 'mass' stuff, evaluated relative to a count base.

-The mass-count distinction is formulated in terms of disjointness of the base. Iceberg semantics associates bases not just with the interpretations of lexical nouns, but with NPs in general and with DPs. This means that Iceberg semantics provides a compositional semantic theory of the mass-count distinction, and hence it provides a framework in which the mass-count nature of complex NPs and of DPs can be fruitfully studied.

It is the analysis of complex NPs and their mass-count properties that is the focus of the second part of this paper. There I develop an analysis of English and Dutch pseudo- partitives, in particular, measure phrases like three liters of wine and classifier phrases like three glasses of wine. We will study measure interpretations and classifier interpretations of measures and classifiers, and different types of classifier interpretations: container interpretations, contents interpretations, and - indeed - portion interpretations. Rothstein 2011 argues that classifier interpretations (including portion interpretations) of pseudo partitives pattern with count nouns, but that measure interpretations pattern with mass nouns. I will show that this distinction follows from the very basic architecture of Iceberg semantics.

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