Underquantification: an application to mass terms

Mass terms are linguistically defined according to the following features: they do not occur with cardinals (*six rices), they are not pluralisable (*rices), they are quantified over using classifiers (six grains of rice), they accept determiners that do not occur with count nouns and, conversely, do not combine with some count noun articles (much rice/*many rices). The particularities of mass terms with regard to quantification gives them an ontological status that also differentiates them from count nouns. In particular, the notion of individuation is not straightforward: we cannot retrieve the minimal constituents of an instance of water as we do for an instance of cats (by counting the number of individual cats in the group under consideration). Still, it is desirable to consider count and mass nouns in the same framework. That is, given the phrases two kilograms of rice and two kilograms of apples, we would expect the ‘two kilograms’ to have the same formal representation, i.e. to behave in a unique way whether quantifying over rice or over apples. This paper claims that all subject noun phrases can be given a unique underspecified formalisation in terms of quantification (which we term underquantification). The claim has consequences for our ontological and linguistic understanding of mass terms. We suggest that it is possible to categorise mass terms in relation to divisibility: whether we can find elementary parts for them which are the same nature as their whole (a drop of water is water, so water is divisible; it is perhaps less clear what a part of progress is). We argue for an underspecified logical form which can be applied to both divisible and indivisible noun phrases (although the domain of quantification is not the same in both cases), satisfying our requirement for a unique quantificational formalisation of count nouns and mass terms.