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This chapter concerns the proportional readings of many and most, for example, where many/most students are smart means ‘the ratio of smart students to non-smart students is high/greater than 1:1’. The authors argue for a GQ analysis of proportional most over Hackl’s adjectival analysis based on distributional differences between relative most (the most P) and proportional most (most P). This GQ analysis is also shown to be supported by morpho-syntactically complex realizations of proportional most, such as the Romanian cei mai mulţi ‘the.MPL more many.MPL’ and cele mai multe ‘the.FPL more many.FPL’. Turning to proportional many, they argue that it shares a syntactic position with cardinal many, namely, SpecMeasP below Det. For the semantics of proportional many, building on Solt’s degree-theoretic approach based on measure functions with a cardinality dimension, the authors propose that measure functions themselves can have a proportional interpretation, based on proportional scales, in which the measure of the entity across a certain dimension is evaluated with respect to the measure of a ‘whole’ in which that entity is included.
Object mass nouns, such as furniture, are mass, but they allow quantity evaluations and comparisons in terms of a cardinal scale. This paper addresses the vexing question of how such cardinal comparisons are possible for object mass nouns, given that, as mass nouns, these expressions are not countable. Building upon her theory of count nouns based on semantic atomicity (entities that are indexed to counting contexts), and on her work on the distinction between counting and measuring and the semantics of measure functions, Rothstein proposes a treatment of quantity evaluations for object mass nouns based on measure comparisons using values on a cardinality scale which, unlike counting does not require access to a set of semantic atoms. Rothstein then extends this analysis and argues that two types of estimation operations have grammatical properties associated with measuring: Russian approximative inversion, and cardinality estimation in Mandarin.
In this chapter, Krifka proposes a mereotopological formal semantic theory, enriched with a temporal dimension (a spatiotemporal haptomereology) that can account for the individuation of objects and (portions of) substances over time in terms of an ontology that underlies our use of natural language in the sense of Bach’s (1981) natural language metaphysics. Krifka’s spatiotemporal haptomereology can model not only how entities in space are connected but also how entities in time are connected. This, in turn, allows for the definition of solids, liquids, gases, grains, and individuals. For example, a solid in an interval t, t’ is an entity whose interior parts touch the same parts between t and t′. With these theoretical developments, Krifka proposes an account of different types of individuation over time. For example, he proposes that material identity over time can be established via matter individuals: individuals that are understood as identifying the same matter over time. The re-identification of matter over time, it is proposed, is based on the mereotopological notion of maximally self-connected entities described by Grimm, and a haptomereological modeling of change over time.
Granular mass nouns, such as rice, have conceptually, and perceptually, salient entities in their denotations (i.e., individual rice grains). However, these entities are not directly accessible to semantic counting operations, nor can granular mass nouns be coerced into a count interpretation involving such entities. In this paper, Sutton and Filip address why this should be the case. Their analysis is based on the proposal that there are two key ingredients in lexical entries for grammatical counting: the object identifying function, which identifies perceptually or functionally salient entities in a noun’s denotation, and the schema of individuation, which concerns a perspective on these entities relative to a context of utterance. Based on these parameters, as well as on the mereotopological differences between concepts denoting granulars (rice, lentil), as opposed to other Spelke objects (cat, chair), Sutton and Filip show how we can explain why granular nouns exhibit count/mass variation within and between languages. Finally, they outline why the grammatical reflexes of granular nouns is central to understanding countability from a cross-linguistic perspective.