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

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.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.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 zhuō—zi ‘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.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 entities to the set of all sums that can be formed from those entities (Link 1983).2The numeral liǎng in (3a) is a function from atomic sets to sets of groups composed of two members from the atomic set. The classifier zhāng in (3b) is a function from kinds to predicates, represented as ∪.When a classifier like zhāng combines with a nominal like zhuōzi (as in (1a)), the result is denotationally equivalent to an English count noun. This is illustrated in (4).For Krifka (1995), denotations of nominals in Mandarin are comparable to those of nominals in English, shown in the simplified version of his theory in (5).3The difference lies in the numerals. Krifka (1995) hypothesizes that there are two different types of numeral interpretations crosslinguistically (see also Wilhelm 2008). On the one hand, there are numerals in nonclassifier languages like English. These have an incorporated measure function, μ#, and combine directly with nouns, as illustrated for English two in (6a).4 On the other hand, there are Mandarin-like numerals like liǎng in (6b). These do not have an incorporated measure function and thus require classifiers such as zhāng in (6c) to introduce a measure.5Under this account, a Mandarin numeral-plus-classifier is semantically equivalent to an English numeral, as shown in (7).As Krifka (1995) notes,6 there is very little evidence internal to English or Mandarin that would favor one proposal over the other. Both theories succeed in capturing the fact that Mandarin requires classifiers for counting, while English does not. For Chierchia, classifiers are necessary because of a deficiency of the nouns: they do not denote countable entities. For Krifka, classifiers are necessary because of a problem with the numerals: informally speaking, they do not come specified with information about which types of things they count.7In Western Armenian, the presence or absence of a classifier is completely optional, as shown in (8). (For similar examples and observations, see Donabédian 1993.)The two theories described above offer two possible explanations for this variation. Under Chierchia’s (1998) account, the noun dəgha ‘boy’ would be ambiguous, having one meaning that permits the noun to combine directly with numerals (a ‘‘count’’ denotation, as in (9a)) and another that requires a classifier (a ‘‘mass’’ denotation, as in (9b)). Numerals and classifiers have denotations as in (9c–d), similar to the denotations in (3).Krifka (1995), in contrast, could hypothesize that the noun dəgha ‘boy’ has a consistent count-type interpretation, but the numeral yergu is ambiguous. One meaning incorporates a measure function, as in (10b). The other meaning does not, as in (10c). See Borer 2005 for a similar proposal.There is no clear way to decide between the two theories language-internally in Western Armenian.8 However, this optionality raises an interesting consideration, namely, the possibility of variation within a single language. The two theories make different predictions with respect to crosslinguistic variation: Krifka’s numeral-based theory predicts the possibility of a language with idiosyncratic behavior among the numerals, whereas Chierchia’s theory is inconsistent with such a pattern. In section 3, we provide examples of languages that exhibit idiosyncratic patterns in the numeral domain, and we show that these data are uniquely compatible with Krifka’s account of classifiers.In Mi’gmaq, an Eastern Algonquian language, numerals 1–5 (along with numerals morphologically built from 1–5) do not appear with classifiers, while numerals 6 and higher must. In (11a), the numeral na’n ‘five’ combines directly with the noun; the classifier te’s is impossible, as shown in (11b).In contrast, the numeral asugom ‘six’ in (12a) cannot combine directly with a noun. It must instead appear with the classifier te’s, as shown in (12b).9Chol, a Mayan language of southern Mexico, also demonstrates idiosyncratic behavior in the numeral system. Mayan languages have a vigesimal (base 20) numeral system. Many speakers today, however, generally know and use Chol numerals only for numbers 1–6, 10, 20, 40, 60, 80, 100, and 400 (Vázquez Álvarez 2011:180); otherwise, they use number words borrowed from Spanish.As shown in (13), the traditional Mayan numerals, like ux ‘three’, require a classifier.In contrast, the Spanish-based numerals, like nuebe ‘nine’, cannot be used with classifiers, as shown in (14). This contrast is consistent across all Spanish- and Mayan-based numerals in the language and cannot be reduced to other factors like phonological size: multisyllabic Chol numerals like waxäk ‘eight’ still require classifiers, and Spanishbased numerals like ses ‘six’ still prohibit them.It should be noted that this is true not just of bilingual Spanish–Chol speakers, but also of speakers who are essentially monolingual in Chol. Regardless of degree of fluency, age, or level of bilingualism, speakers consistently find classifiers on Spanish-based numerals to be ungrammatical. Furthermore, this variation is not found within the nominal system. Nominals borrowed from Spanish require classifiers when they are used in conjunction with a Chol numeral, as shown with the Spanish loan mansana ‘apple’ in (15a). When such nominals appear with numerals of Spanish origin, no classifier is possible, as in (15b).10Both Mi’gmaq and Chol have some numerals that require classifiers, and some numerals that cannot appear with classifiers. This is consistent with an approach in which nominals have a consistent denotation and variation is found within the numerals themselves—that is, Krifka’s (1995) analysis. This is illustrated below with Chol lexical items, but is readily transportable to Mi’gmaq.Under Krifka’s analysis, nominals like tyumuty ‘egg’ have denotations equivalent to those of their English counterparts. The noun tyumuty is a predicate true of eggs, as in (16).The requirement for a classifier is dependent, not on the noun, but on the syntax and semantics of the numeral. In Chol, the interpretation of Spanish-origin nuebe ‘nine’ is a nominal modifier that has a cardinality measure (μ#) built into its meaning, as shown in (17).In contrast, the interpretation of ux (Chol ‘three’) is a function that takes a measure function as an argument, such as the cardinality measure p’ej, and yields a numeral modifier. This is illustrated in (18).As illustrated in (19a), nuebe can combine directly with nouns like tyumuty to yield a set of groups where each group consists of 9 individual items (eggs, in the case of tyumuty). However, the combination of nuebe with a classifier leads to a type mismatch and presupposition failure.The opposite pattern holds for ux, as illustrated in (19b). Combining ux directly with tyumuty leads to a type mismatch, whereas combining it with the classifier p’ej and then tyumuty yields a set of groups where each group consists of 3 individual eggs.Unlike Krifka’s theory, Chierchia’s cannot account for the patterns illustrated in (19). To account for acceptable forms where numerals combine directly with nouns, such as nuebe tyumuty, as well as forms where classifiers intervene, such as ux-p’ejtyumuty, Chierchia would need to hypothesize that nouns in Mi’gmaq and Chol are ambiguous. Under this account, all nouns would have two interpretations: one interpretation that requires classifiers, and another that does not, as shown in (20a). The numerals would have interpretations that were independent of the classifier, whereas the classifier would be a function from kinds to sets, as shown in (20b–c).Critically, if nouns like tyumuty in (20a) are ambiguous in this respect, then the ungrammatical forms are unexpected. Nothing would prevent a classifier-less Mayan numeral from combining with the interpretation of tyumuty ‘egg’ that denotes an atomic set. Similarly, nothing would rule out the possibility that the kind-denoting variant of tyumuty could combine with the Spanish-based numeral nuebe, requiring a classifier.However, these combinations of numerals and classifiers are not acceptable.Syntactic facts also favor Krifka’s analysis. In Chol, classifiers morphologically attach as suffixes to numerals. Although Mi’gmaq classifiers are separate words, word order effects provide similar evidence that numerals and classifiers form a constituent independent of the noun. As shown in (22a–b), the numeral and classifier can be separated as a unit from the noun. However, as shown in (22c), the classifier and noun cannot be separated from the numeral. This suggests that there is a tighter connection between the numeral and classifier than between the classifier and noun.Li and Thompson (1981) propose that the numeral and classifier form a constituent in Mandarin Chinese, although see Zhang 2011 for a more nuanced discussion of classifier-noun constituency.Note that the evidence above only demonstrates that classifier systems in some languages are uniquely compatible with Krifka’s theory. It has not been demonstrated that all languages have the same kind of classifier system. It is possible that there are two types, one like Krifka’s and another that patterns as Chierchia’s theory would predict. Indeed, the investigation of Mi’gmaq and Chol provides a template for the kind of pattern one would need to find to establish the existence of this other classifier system. Unlike Krifka’s theory, Chierchia’s predicts that it should be possible to have a lexical numeral that requires a classifier when modifying one noun, yet prohibits a classifier when modifying another.Such a pattern would demonstrate that the presence or absence of a classifier depends on the noun that is being modified rather than on the numeral. On the surface, one might think that English has such patterns, as shown in (24).However, the status of this as an example of Chierchia’s predicted pattern rests on the classification of item and the use of the partitive preposition of. Are measure words like item and kilo classifiers? Unlike classifiers in other languages, these words have the same distributions as regular nouns and take nominal morphology such as plural marking. In other words, the surface evidence suggests that these words do not belong to the same type of category as classifiers (for discussion, see Cheng and Sybesma 1999).Whether Chierchia’s predicted pattern exists or not is an empirical matter, one that will not be resolved here. However, the mere existence of Krifka-style classifiers, even if they are not universal, has some consequences for the study of syntax and semantics crosslinguistically.Mi’gmaq and Chol demonstrate that, at least in some languages, the factors governing the appearance of classifiers are independent of the existence of a syntactic distinction between mass and count nouns (for discussion, see Wilhelm 2008). A weak implication of this finding is that the presence or absence of a rich classifier system is not a reliable diagnostic for whether a language has count nouns or not. However, this separation of classifier systems from nominal distinctions calls into question whether it is useful to classify languages in terms of mass/count. As Bloomfield (1933) discusses, what makes the mass/count distinction interesting are the corresponding semantic and syntactic patterns that are, in principle, separable from the ontological divide between ‘‘countable things’’ and ‘‘uncountable stuff ’’ (see also Bunt 1985, Gillon 1992, Chierchia 1998, Bale and Barner 2009). For example, consider the following grammatical properties associated with count syntax:Mandarin does not allow numerals to combine directly with nouns, has a rich classifier system, does not have a productive plural marker, and lacks allomorphy among its quantifiers. English, in contrast, has two lexical noun categories (mass and count), has no classifier system, has a productive plural, allows numerals to combine directly with nouns, and permits quantifier allomorphy. Linguists influenced by Bloomfield (1933) have explored the hypothesis that this clustering of properties is in some way connected: that noncount languages pattern like Mandarin, whereas count languages pattern like English.However, previous work has shown that plural marking does not always cluster with the other properties (Borer 2005, Bale and Barner 2012). Mi’gmaq and Chol demonstrate further that classifiers are independent of the nominal distinction in some languages. The fact that the first three properties in (25) do not reliably cluster together weakens the utility of classifying languages in terms of whether they have a mass/count distinction or not. Since the only correlation remaining is the relatively minor connection between quantifier allomorphy and singular denotations, one wonders whether it is better for investigative purposes to give up on the term mass/count language, which carries with it the burden of being defined with respect to all of the properties in (25), and instead concentrate on the individual properties independent of whether they correlate or not in any given language.

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