Classifiers Are for Numerals, Not for Nouns: Consequences for the Mass/ Count Distinction

1 Introduction

In languages with numeral classifier systems, nouns must generally appear with one of a series of classifiers in order to be modified by a numeral. This squib presents new data from Mi’gmaq (Algonquian) and Chol (Mayan), arguing that numeral classifiers are required because of the syntactic and semantic properties of the numeral (as in Krifka 1995), rather than the noun (as in Chierchia 1998). The results are shown to have important consequences for the mass/count distinction.

Mandarin Chinese is a frequently cited example of a language with numeral classifiers. As shown in (1), classifiers cannot be dropped in the presence of numerals.

1. (1). Mandarin Chinese

   1. a. liǎng *(zhāng) zhuōzi

      two    cl    table

      ‘two tables’

   2. b. liǎng *(píng)        jiǔ

      two    cl.bottle wine

      ‘two bottles of wine’

Krifka (1995) and Chierchia (1998) provide two very different accounts of the theoretical distinction between languages with classifiers (like Mandarin) and those without (like English). Chierchia links the distinction to the nominal system, arguing that nonclassifier languages have a mass/count distinction among nouns, while classifier languages do not. All nouns in Mandarin are likened to mass nouns in English. Krifka, on the other hand, proposes that the difference lies in the numeral system. He argues that classifier languages morphologically separate the semantic measure function (i.e., the classifier) from the numerals, whereas nonclassifier languages have a measure function incorporated into the numerals.

Here we bring in new data from Mi’gmaq and Chol to distinguish between the two theories. In both languages, certain numerals obligatorily appear with classifiers, while others never do. We show that these idiosyncratic numeral systems cannot be accounted for under Chierchia’s influential (1998) proposal. Furthermore, we show that these results have consequences for the mass/count distinction. Krifka’s theory, unlike Chierchia’s, treats the classifier/nonclassifier distinction as being theoretically independent of the syntactic mass/count distinction (see Wilhelm 2008). We question whether it is meaningful, or even empirically justified, to maintain a mass/count distinction once classifier systems are treated in this way.

2 Theoretical Background and Previous Work

2.1 Chierchia 1998: Classifiers Are for Nouns

Chierchia (1998) argues that numerals have a uniform interpretation in both classifier and nonclassifier languages, but hypothesizes a difference in the nominal systems. In English, there are two categories of nouns: one consisting of nouns that are directly compatible with numeral modification (so-called count nouns, like table and girl), and another consisting of nouns that are not (so-called mass nouns, like furniture and water). Chierchia proposes that in a classifier language like Mandarin there is only one category of noun, and, much like the English category of mass nouns, this category is not directly compatible with numeral modification. A simplified version of Cherchia’s nominal interpretations is shown in (2), where ^∩ is a function from predicates to kinds.¹ Here the Mandarin noun zhuōzi ‘table’ in (2a) denotes a kind, like the English mass noun furniture in (2b), but unlike the English count noun table in (2c), which denotes a set of atoms.

1. (2). Chierchia-style nominals (simplified)

   1. a. 〚zhuōzi〛 = ^∩table (i.e., the table-kind)

   2. b. 〚furniture〛 = ^∩furniture (i.e., the furniture-kind)

   3. c. 〚table〛 = {x : atom(x) & table(x)} (i.e., set of individual tables)

According to Chierchia (1998), numeral modification relies on measure functions that count (stable) atoms. The kinds in (2a) and (2b), in contrast to the set in (2c), contain no such atoms. As a result, they must be converted into atomic sets before combining with numerals. Thus, just as English mass nouns require measure words to combine with numerals (e.g., ‘two pieces of furniture’), so all nouns in Mandarin require classifiers that convert kinds into atomic sets.

Chierchia-style denotations for numerals and classifiers are provided in (3), where atomic is a function true of predicates with atomic minimal parts (i.e., atoms); µ_# is a measure function from a group to the cardinality of that group; and * is a closure operator from a set of...