Counting and Measuring: a theoretical and crosslinguistic account

Abstract

In this paper, I show that expressions like two glasses of wine are ambiguous between counting and measuring interpretations, and that each interpretation is associated with a different semantic representation. In each interpretation, glasses has a different function. In the counting interpretation, glasses is a relational noun, while in the measure interpretation, glasses is a measure head analogous to litre. This difference leads to a number of grammatical contrasts which can be explained by differences in the grammatical structure. I discuss whether these differences are only semantic or also expressed in the syntactic representation. The assumption that syntax directly reflects semantic interpretation leads to assigning counting NPs and measuring NPs two different syntactic structures: counting NPs are rightbranching with two modifying glasses of wine, while in measure expressions the numeral and the measure head form a measure predicate two glasses which modifies the N. I show that in Modern Hebrew and Mandarin counting structures and measuring structures clearly do have different syntactic structures, reflecting the semantic differences between counting and measuring. While the evidence in the case of English is less strong, the assumption that syntax directly reflects compositional syntactic structure results in the same basic syntactic contrasts in English as well. 1

New perspectives on the count–mass distinction: Understudied languages and psycholinguistics

“…Many studies have explored the semantics of container phrases, such as bags of in “three bags of rice” (Doetjes, ; Keizer, ; Khrizman, Landman, Lima, Rothstein, & Schvarcz, ; Landman, ; Landman, ; Lima, ; Partee & Borschev, ; Rothstein, , , , ; Scontras, ; Selkirk, ). As previously shown, in many languages described in the literature, container phrases are required in numeral constructions with substance and object mass nouns (16b).…”

“…One critical feature of container phrases is their ambiguity between what we will call here non‐measure (that include counting) and measure readings. Rothstein () points out three ways in which one could analyze the relationship between counting and measuring. One approach (cf.…”

“…One approach (cf. Lyons, ) would be to say that measuring is counting units rather than objects (“a mensural classifier is one which individuates in terms of quantity” [Lyons, , p. 463 apud Rothstein, , p. 4]). Another approach (cf.…”

“…As summarized by Rothstein (, p. 4–5), in this perspective, “ two kilos of flour gives the quantity of flour in terms of kilo units, two cats should be treated as giving the quantity of cat in terms of natural units.” These first two approaches make measuring equivalent to counting or vice versa. Finally, authors such as Rothstein (, ) and Scontras () argue that measuring and counting are distinct operations. Formal approaches that argue in favor of a distinction between counting and measuring found support in experimental studies and typological investigations of the grammatical and contextual factors that license the two operations.…”

“…These facts show that container nouns in constructions with numerals and mass nouns might give rise to other readings, such as locative, depending on their distribution and grammatical properties. Formal analyses of the interpretation of container phrases in a variety of languages (Dutch, Hungarian, Russian, Hebrew, and Yudja, among others) further expanded the typology of possible interpretations of container phrases (see also Khrizman et al, ; Lima, ; Rothstein, ), but more work on this topic needs to be done, particularly in languages where container phrases are optional in constructions with numerals and substance‐denoting nouns.…”