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) Mandarin Chinese

  • a.

    liǎng *(zhāng) zhuō.zi

    two CL table

    ‘two tables’

  • 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 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.

(2) Chierchiastyle nominals (simplified)

  • a.

    zhuō—zi〛 = TABLE (i.e., the table-kind)

  • b.

    furniture〛 = FURNITURE (i.e., the furniture-kind)

  • 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 entities to the set of all sums that can be formed from those entities (Link 1983).2

(3) Chierchia-style numerals and classifiers (simplified)

  • a.

    liǎng〛 = λPP : ATOMIC(P).{x : *P(x) & μ#(x) = 2}

  • b.

    zhā—ng〛 = (i.e., the function from kinds to sets of atoms)

The 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).

(4)

  • Equivalences

  • zhāng〛(〚zhuōzi〛) = {x : ATOM(x) & TABLE(x)} = 〚table

2.2 Krifka 1995: Classifiers Are for Numerals

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).3

(5)

  • Mandarin nominals, equivalent to English count nouns

  • zhuōzi〛 = {x : ATOM(x) & TABLE(x)}

The 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.5

(6) Krifka-like numerals and classifiers (simplified)

  • a.

    two〛 = λPP : ATOMIC(P).{x : *P(x) & μ#(x) = 2}

  • b.

    liǎng〛 = λPmλP : ATOMIC(P).{x : *P(x) & m(x) = 2}

  • c.

    zhāng〛 = μ#

Under this account, a Mandarin numeral-plus-classifier is semantically equivalent to an English numeral, as shown in (7).

(7)

  • Equivalences

  • liǎng〛 (〚zhāng〛) = λP : ATOMIC(P).{x : *P(x) & μ#(x) = 2} = 〚two

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.7

2.3 Case Study: Western Armenian

In Western Armenian, the presence or absence of a classifier is completely optional, as shown in (8). (For similar examples and observations, see Donabédian 1993.)

(8)

  • yergu (had) dәgha

  • two CL boy

  • ‘two boys’

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).

(9)

  • a.

    dəgha1〛 = {x : BOY(x)}

  • b.

    dəgha2〛 = BOY

  • c.

    yergu〛 = λP : ATOMIC(P).{x : *P(x) & μ#(x) = 2}

  • d.

    had〛 =

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.

(10)

  • a.

    dəgha〛 = {x : BOY(x)}

  • b.

    yergu1〛 = λP : ATOMIC(P).{x : *P(x) & μ#(X) = 2}

  • c.

    yergu2〛 = λPmλP : ATOMIC(P).{x : *P(x) & m(x) = 2}

  • d.

    had〛 = μ#

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.

3 Idiosyncratic Numerals

3.1 Mi’gmaq and Chol

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).

(11)

  • a.

    na’n-ijig ji’nm-ug

    five-AGR man-PL

    ‘five men’

  • b.

    *na’n te’s-ijig ji’nm-ug

    five CL-AGR man-PL

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).9

(12)

  • a.

    *asugom-ijig ji’nm-ug

    six-AGR man-PL

  • b.

    asugom te’s-ijig ji’nm-ug

    six CL-AGR man-PL

    ‘six men’

Chol, 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.

(13)

  • a.

    ux-p’ej tyumuty

    three-CL egg

    ‘three eggs’

  • b.

    *ux tyumuty

    three egg

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.

(14)

  • a.

    *nuebe-p’ej tyumuty

    nine-CL egg

  • b.

    nuebe tyumuty

    nine egg

    ‘nine eggs’

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).10

(15)

  • a.

    Tyi k-mäñä ux-p’ej mansana.

    ASP 1ERG-buy three-CL apple

    ‘I bought three apples.’

  • b.

    Tyi k-mäñä nuebe mansana.

    ASP 1ERG-buy nine apple

    ‘I bought nine apples.’

3.2 Discussion

Both 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).

(16) 〚tyumuty〛 = {x : ATOM(x) & EGG(x)}

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).

(17)

  • Denotation of numeral that does not permit classifier

  • nuebe〛 = λP : ATOMIC(P).{x : *P(x) & μ#(x) = 9}

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).

(18)

  • a.

    Denotation of numeral that requires classifier

    ux〛 = λmλP : ATOMIC(P).{x : *P(x) & m(x) = 3}

  • b.

    Denotation of the classifier

    p’ej 〛 = μ#

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.

(19)

  • a.

    nuebe〛(〚tyumuty〛) = {x : x 1 *{x : ATOM(x) & EGG(x)} & μ#(x) = 9}

    nuebe〛(〚 p’ej 〛) → type mismatch

  • b.

    ux〛(〚tyumuty〛) → type mismatch

    (〚ux〛(〚 p’ej 〛))(〚tyumuty〛) = {x : x 1 *{x : ATOM(x) & EGG(x)} & μ#(x) = 3}

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).

(20) Chierchia-inspired interpretations of Chol

  • a.

    Nominal interpretations

    tyumuty1〛 = {x : ATOM(x) & EGG(x)},

    tyumuty2〛 = {arc face down}EGG

  • b.

    Numeral interpretations

    ux〛 = λP : ATOMIC(P).{x : *P(x) & μ#(x) = 3},

    nuebe〛 = λP : ATOMIC(P).{x : *P(x) & μ#(x) = 9}

  • c.

    Classifier interpretation

    p’ej 〛 = {arc face up}

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.

(21) False Predictions

  • a.

    ux〛(〚tyumuty1〛) = {x : x 1 *{x : ATOM(x) & EGG(x)} & μ#(x) = 3} → well-defined (cf. (13b))

  • b.

    (〚nuebe〛(〚 p’ej〛))(〚tyumuty2〛) = {x : x 1 *{arc face up and down}EGG & μ#(x) = 9} → well-defined (cf. (14a)), where *{arc face up and down}EGG = {x : ATOM(x) & EGG(x)}

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.

(22)

  • a.

    Etlenm-ultijig asugom te’s-ijig jinm-ug.

    laugh.PRES-PL six CL-AGR man-PL

    ‘Six men are laughing.’

  • b.

    Asugom te’s-ijig etlenm-ultijig jinm-ug.

    six CL-AGR laugh.PRES-PL man-PL

    ‘Six men are laughing.’

  • c.

    *Asugom etlenm-ultijig te’s-ijig jinm-ug.

    six laugh.PRES-PLCL-AGR man-PL

    ‘Six men are laughing.’

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.

(23) Chierchia’s predicted pattern

  • a.

    Numeral Noun1, *Numeral cl Noun1

  • b.

    *Numeral Noun2, Numeral cl Noun2

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).

(24)

  • a.

    one chair, *one item of chair(s)

  • b.

    *one furniture, one item of furniture

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.

4 Implications

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:

(25) Properties of ‘‘count languages’’

  • a.

    Plural marking (e.g., -s in English)

  • b.

    Direct numeral modification

  • c.

    Lack of a rich classifier system

  • d.

    Quantifier allomorphy (e.g., many vs. much)

  • e.

    Semantically singular denotations for lexical nouns

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.

Notes

Thanks to David Barner, Brendan Gillon, Peter Jenks, David Nicolas, the audience at NELS 43, and two anonymous reviewers for helpful discussion and feedback. We are especially grateful to Janine Metallic, Mary Ann Metallic, and Janice Vicaire for Mi’gmaq, and to Matilde Vázquez Vázquez, Juan Jesús Vázquez Á lvarez, and Nicolás Arcos López for Chol. Any errors in data or interpretation are of course our own.

1Chierchia’s (1998) actual proposal involves coercion operators that freely apply in any language. Critical to the present discussion, one conversion operator (π) maps kinds to Complete semilattices. The classifier then maps these complete semilattices to atomic predicates. Thus, 〚CL〛 ○ π = Note also that Chierchia interprets mass nouns in English as complete semilattices but has a conversion operator that maps such lattices into kinds. For the sake of exposition, we will ignore this subtlety.

2 The cardinality of a group is the number of minimal parts (also known as individuals) contained within the group. The number of minimal parts is always relative to a category or kind. We do not address how this relativization is implemented, but see Krifka 1995 and Bale and Barner 2009 for discussion.

3Krifka’s (1995) actual theory treats nouns in English and Mandarin as kinds. These kinds serve many purposes, including fixing how measure functions count. For simplicity, we have changed the kind denotations to atomic sets. What is critical to the present discussion is that Krifka makes distinctions in the numeral system rather than the nominal system.

4Krifka (1995) uses a different symbol to represent the measure function, namely, OU.

5 In our simplified version of Krifka’s (1995) theory, both types of numerals introduce a presupposition that their nominal arguments are atomic (i.e., they have atomic minimal parts, whether those minimal parts are inherent in the nominal denotation itself or induced by mensural classifiers). This requirement is represented by ATOMIC(P). Such presuppositions would predict the infelicity of DPs like *two firewood(s). The noun firewood does not have atomic minimal parts and hence fails to satisfy the presupposition.

6 In his discussion of English, Krifka (1995) compares a theory where the measure function is incorporated into the noun with one where it is incorporated into the numeral. Thus, his comparison does not directly involve kinds and kind conversions, like Chierchia’s (1998). Rather, his alternative more resembles Cresswell’s (1976) theory, where count nouns have a built-in measure but mass nouns require a measure function as an argument. Still, the empirical consequences of Cresswell’s and Chierchia’s theories are rather similar: namely, the presence of measure terms is dependent on the noun rather than the numeral.

7 As an anonymous reviewer points out, both Cantonese and Mandarin have a broader range of patterns than what we present here (see Cheng and Sybesma 1999). For example, classifiers can be used without numerals to signal either singular definite interpretations in Cantonese or indefinite interpretations in Mandarin. On the surface, such facts seem to favor Chierchia’s (1998) account. According to Krifka (1995), classifiers serve as arguments to the numerals, and hence classifiers are not expected to appear without numerals. However, to account for the Cantonese and Mandarin data, Chierchia requires some kind of coercion operator to map the atomic set denotation to either a unique individual or an existential interpretation. A similar hypothesis could be maintained in Krifka’s system, except that the coercion operator would apply to measure functions rather than atomic sets. For example, a coercion function for the definite interpretation could be represented as follows: λmP. ι({x : P(x)& m(x)=1}). In the end, the broader pattern can be integrated into either account of classifiers.

8 The facts in Western Armenian have been simplified for expository purposes. As discussed in Donabédian 1993, there is a plural marker in Western Armenian that cannot cooccur with classifiers. However, numerals can combine directly with either bare nouns or plurals. Borer (2005) argues that this pattern is evidence that the plural marker and classifiers compete for the same syntactic head. However, Bale and Khanjian (2009) demonstrate that semantic factors alone can account for the lack of cooccurrence. Furthermore, Doetjes (2012) demonstrates that for some languages cooccurrence is possible, as exemplified by the plural marking in Mi’gmaq illustrated in section 3.

Note that Krifka’s theory can easily be adapted to account for the Western Armenian pattern. The bare noun would be interpreted as a complete semilattice, while the plural noun would be a strict plural without atomic parts (e.g., 〚dəgha〛={x : *BOY(x)} and 〚dəgha + PL〛 = 〚dəgha〛–BOY; see Bale, Gagnon, and Khanjian 2011). There would still be an ambiguity between the numeral modifiers such that one would take a measure function as an argument whereas the other would not. Also, one of the modifiers would presuppose that its nominal argument is a complete semilattice whereas the other would not (e.g., 〚yergu1〛 = λP.{x : P(x) &μ#(x) = 2}, 〚yergu2〛 = λmP : COMPLETE(P).{x : P(x) & m(x) = 2}, where COMPLETE is true only of predicates closed under join and meet). Thus, one type of numeral can combine with either plural or nonplural nouns but prohibits classifiers. The other type of numeral requires classifiers but can only combine with nonplural nouns. It is difficult for Chierchia’s theory to account for the Western Armenian plural pattern without hypothesizing either a phonologically null classifier (to convert plural nouns to singular denotations) or an ambiguity in the numeral system (one numeral applying to singular denotations, the other to plural denotations).

9 Since te’s cooccurs with what appears to be a plural marker (i.e., -ug), one might wonder about its status as a classifier (i.e., perhaps it patterns like English measure nouns). Two points are relevant. First, -ug only appears on animate nouns yet also appears on verbs and adjectives. It is questionable whether it has the same status as plural markers such as English -s. Second, Mi’gmaq has measure nouns, but they do not fit the same syntactic pattern as te’s. Furthermore, unlike measure nouns, te’s has no semantic content other than its measure function. In this respect, it behaves more like Mandarin default classifiers. See also footnote 8.

10 An anonymous reviewer suggests that this could be a problem with attaching Chol inflectional morphology to Spanish loans. This again cannot be right: Spanish loans appear with inflectional morphology (e.g., plural, possession) across the language. Even Spanish-based numerals may be inflected for person, as in (ia). Compare with the Chol numeral-plus-classifier in the same construction in (ib).

(i)

  • a.

    Nuebe-j-oñ-loñ.

    nine-EPEN-1ABS-PL.EXCL

    ‘We are nine.’ (i.e., a group of nine people)

  • b.

    Cha’-tyikil-oñ-loñ.

    two-CL.people-1ABS-PL.EXCL

    ‘We are two.’ (i.e., a group of two people)

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