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date: 16 October 2017

Number in Language

Summary and Keywords

Number is the category through which languages express information about the individuality, numerosity, and part structure of what we speak about. As a linguistic category it has a morphological, a morphosyntactic, and a semantic dimension, which are variously interrelated across language systems. Number marking can apply to a more or less restricted part of the lexicon of a language, being most likely on personal pronouns and human/animate nouns, and least on inanimate nouns. In the core contrast, number allows languages to refer to ‘many’ through the description of ‘one’; the sets referred to consist of tokens of the same type, but also of similar types, or of elements pragmatically associated with one named individual. In other cases, number opposes a reading of ‘one’ to a reading as ‘not one,’ which includes masses; when the ‘one’ reading is morphologically derived from the ‘not one,’ it is called a singulative. It is rare for a language to have no linguistic number at all, since a ‘one–many’ opposition is typically implied at least in pronouns, where the category of person discriminates the speaker as ‘one.’ Beyond pronouns, number is typically a property of nouns and/or determiners, although it can appear on other word classes by agreement. Verbs can also express part-structural properties of events, but this ‘verbal number’ is not isomorphic to nominal number marking. Many languages allow a variable proportion of their nominals to appear in a ‘general’ form, which expresses no number information. The main values of number-marked elements are singular and plural; dual and a much rarer trial also exist. Many languages also distinguish forms interpreted as paucals or as greater plurals, respectively, for small and usually cohesive groups and for generically large ones. A broad range of exponence patterns can express these contrasts, depending on the morphological profile of a language, from word inflections to freestanding or clitic forms; certain choices of classifiers also express readings that can be described as ‘plural,’ at least in certain interpretations. Classifiers can co-occur with other plurality markers, but not when these are obligatory as expressions of an inflectional paradigm, although this is debated, partly because the notion of classifier itself subsumes distinct phenomena. Many languages, especially those with classifiers, encode number not as an inflectional category, but through word-formation operations that express readings associated with plurality, including large size. Current research on number concerns all its morphological, morphosyntactic, and semantic dimensions, in particular the interrelations of them as part of the study of natural language typology and of the formal analysis of nominal phrases. The grammatical and semantic function of number and plurality are particularly prominent in formal semantics and in syntactic theory.

Keywords: atomicity, dual, features, general number, individuation, morphology, paucal, plural, semantics, singular

1 Defining the Category

When we say, in a suitably informal register, ‘nobody in their right mind would do that,’ is their singular or plural? The form contrasts minimally with his, her, its, in an opposition which usually expresses a semantic difference between individuals and pluralities of individuals. This difference is suspended in our example, however, which means ‘nobody in his or her right mind.’ This illustrates a general pattern, where a plural pronoun can express an individual variable bound by a quantified antecedent. The existence of this pattern means that, while in the English morphological system their unambiguously represents the plural member of a formal opposition, its function does not strictly coincide with the expression of plurality in the semantic sense. ‘Plural’ does not mean exactly the same thing at the two levels of analysis.

Consider now the phrase the deer. In isolation, it cannot be said to be singular or plural. But it has to take one or the other value, a fact that emerges in a syntactic context: the deer run or the deer runs. The word deer is special because, unlike most nouns (in English), it does not express the number contrast morphologically. However, a noun phrase like the rich has a number value too (plural, as in the rich are getting richer), even though the definite article and adjectives never distinguish number in their form, as a systematic fact of English grammar. Evidently, syntax references the number value of a constituent even when it is not morphologically realized (even in principle) by any one of its members. We should therefore recognize distinct dimensions for the category of number:

  • Morphologically, as a set of formal oppositions corresponding to alternative interpretations.

  • Morphosyntactically, a set of values defining distinct agreement patterns.

  • Semantically, a set of interpretations relative to the part structure of a reference domain, typically distinct in terms of numerosity.

What makes number a coherent grammatical notion is the mutual relation between these dimensions. It is only after delineating them that we can start asking questions about number as a linguistic category.

2 Functions

The nexus of morphological, morphosyntactic, and semantic properties which defines the category of number organizes the entities in the domain of discourse (including events) in terms of their internal structure. Collections have the structure of sums of individual atoms; correspondingly, the central function of number is to linguistically encapsulate the expression of collections, which can be established in various ways on the basis of the description of an entity type (many tokens of the type ‘book,’ for instance), or around a single pre-established referent: ‘me and others,’ ‘Tanaka and associates,’ ‘dresses and suchlike’ (these examples will be discussed directly below). A collection may be qualified as made up of elements scattered or grouped together, as with so-called distributive or collective markers in North American languages (Corbett, 2000, pp. 111–120). Certain number values discriminate sets based on their size (Section 4), not only in numerical terms but also as being ‘minimal’ or ‘augmented’ with respect to a fixed standard; duals and so-called ‘paucals’ often additionally require their referents to form a cohesive group. Through number, then, languages refer to entities characterized as having different types of internal structure. The labels ‘singular’ and ‘plural’ suggest that this reduces to the contrast between the quantities of one and more than one entity, formally modeled as a domain of atoms and a domain of their sums. But this is a serious oversimplication, and not just because number values go beyond singular and plural. First, mass nouns like water or courage tend to appear predominantly as singular across languages, but they are not interpreted as atoms in the same sense in which drop or crisis are. Second, the example of nobody in their right mind has shown that the plural can have an ‘inclusive’ interpretation, denoting not just sums but also atoms. In fact, the frequent acceptability of the plural in cases like zero calories or 0.5 units, and the mass reading of some plurals like brains or dregs suggest a different understanding of the function of plural, which points to a basic contrast between ‘one’ and ‘not-one.’

These general observations are prompted by a careful consideration of a few English examples; but clearly, any discussion of number in human language requires an examination of the whole typological spectrum. This broader perspective shows that number does not reduce to information about numerosity and to the contrast between one and more (or ‘non-one’) entities. Consider the following examples from Indonesian (Dalrymple & Mofu, 2012), where plural morphology is not inflectional and is realized by full reduplication:

(1)

Number in Language

While the reduplication of pulau ‘island’ simply results in the reading ‘islands’ in (1a), with minyak ‘oil’ it expresses ‘streams of oil’ in (1b), and with air ‘water’ it is probably related to the large quantity of material in (1c) while no particular semantic effect seems discernible in (1d). The ‘mass’ substance denotation of the nouns in (1b–d) is clearly responsible for these non-plural readings, but note that ‘mass’ and ‘count’ nouns do not have distinct morphosyntactic distribution in Indonesian, as in other languages that have numeral classifiers and measure nouns. In short, ‘plural’ is a determination not just for sums of individuals, but also for concrete extensions of atomless matter. The grammatical category that brings about these interpretations remains one and the same, however. A similar point emerges from the fact that in some languages, here illustrated by Japanese, the plural morpheme -tachi serves to denote both a group of entities described by the noun, and a group of entities related to the noun’s referent but not described:

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Number in Language

It should be added that the Japanese -tachi, like plural markers in several other languages, is typically if not invariably associated with a definite interpretation, a circumstance which sets it further apart from English-style number marking (see Nakanishi & Tomioka, 2004; Kurafuji, 2004, for competing views). Following Daniel and Moravcsik (2013), we can distinguish the ‘associative’ reading of the plural illustrated in (2b) from its ‘additive’ reading of (2a); they also add a ‘similative’ function, illustrated by the Telegu example in (3) (Kachru, Kachru, & Sridhar, 2008, p. 77, more precisely call ‘echo word’ this form of partial reduplication):

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Number in Language

Unlike in the associative example, here the head noun is itself interpreted as a collection, but the denotation to includes sums made up not just of dresses but also of unspecified similar items. There is a clear difference between pluralities described as multiple tokens of one type and pluralities constructed from one referent and a group of other unspecified entities related to it. What is noteworthy is that certain personal pronouns, even in English, regularly instantiate this second strategy, insofar as the first person ‘plural’ refers to a collection associated with the speaker (see Section 3.1).

3 Generality and Applicability

An important question is whether number is a necessary category in natural language. It is well known that many languages lack ‘grammatical’ number, but this can mean many things; for instance, that they have no inflectional paradigm expressing opposed number values; or that they grammaticalize individuation, collectivity, and distributivity, rather than singularity and plurality; or that that they encode information about the quantity of argument referents on verbal predicates (schematically, ‘he many-ate apple’), or on free-standing adverbials (‘he ate apple, repeatedly / a lot’). The Mohawk (Iroquian) example in (4) is from Corbett (2000, p. 113), who credits Marianne Mithun.

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Number in Language

Being neuter, the noun for ‘rock’ bears no plural marking, so it allows a singular or plural interpretation; with a distributive suffix, it means ‘different types of rocks’ (see also Mithun, 1988). In (5), from Karitiana (Tupi; from Müller & Sanchez-Mendes, 2008), the reduplicated verb expresses a plurality of giving events, independently of the interpretation of the nominals, which have no number marking (see Section 3.1):

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Number in Language

A precise characterization of number as a grammatical category partly depends on how one draws the line between inflection and derivation. In general, where number is clearly inflectional it characterizes several word classes, some as agreement targets rather than controllers (in the terminology of Corbett, 2000), it is obligatory, and it applies to all members of the word classes it can affect. Number-inflecting languages can have many invariable nouns (like deer), but the phrases they head have always a value for number. Many systems deviate from this picture, but they do not necessarily lack number: the category itself can still be linguistically relevant, as long as there are formal oppositions that express number-related content, even though it does not play a role in morphosyntax. We will consider two dimensions of variability across word classes and across the lexical items in any one class.

3.1 Applicability Across Word Classes

The very nature of personal pronouns makes them the core grammatical locus for the expression of number distinctions. The reason is that person features oppose a single ‘speaker’ to one or potentially more than one ‘addressee’; third-person pronouns usually also involve number distinctions, but they are not so directly rooted in the content of person features. In the overwhelming majority of cases, the notion of ‘speaker’ is intrinsically singular, so that a first person plural pronoun denotes a collection that includes the speaker, not a collection of speakers (it follows that [speaker] and [addressee] as formal grammatical notions are best understood as meaning ‘includes the speaker’ and ‘includes the addressee’; see Harbour, 2014). Uses where ‘we’ refers to a genuinely plural speaker, like a committee expressing its collective view, are the exception rather than the rule. Person features, specifically [speaker], thus provide a primitive basis for a notional contrast between ‘one’ and ‘many’ (unsurprisingly, [speaker] also occupies the highest segment of the scale which defines applicability of number contrasts, followed by [addressee]; see Section 3.2).On this basis, some pronouns can refer to singleton referents and others to pairs, pluralities, or to sets that are minimally compatible with person specifications. These semantic distinctions do not always translate directly into formal ones, however. While the opposition between ‘I’ and ‘we’ seems absolutely fundamental, many languages express [1 person] and [plural] by distinct morphemes, like Mandarin Chinese ‘I’- wŏ-men ‘we’ (see Daniel, 2013, for a fuller typology, distinguishing plural affixes that are specific to pronouns or common to noun, as in Chinese). In such systems, pronouns distinguish singular from plural by adding a number morpheme to roots which are, in fact, number-neutral. But languages may well lack such a flexible number morpheme. When the two factors co-occur (pronominal root expressing person alone, and no available number morpheme for pronouns), this can lead to pronouns that truly do not express number contrasts.

In his description of the Amazonian language Pirahã, Everett (1986, pp. 280–282, 306) reports that pronouns only distinguish the three persons, and that plurality is conveyed in other ways: either by adding ‘a discourse particle marking secondary participant’ (roughly with the sense of ‘also,’ presupposing the participation of another referent or the repetition of the event described), or more commonly by conjoining pronouns for different persons, so that ti gixai means ‘me and you.’ Cysouw (2013) also reports Qawasqar, spoken in Chile, and Maricopa, spoken in Arizona, as having just one morpheme for both ‘I’ and ‘we.’

Aside from pronouns, typological variation mainly concerns the applicability of number to determiners and to the lexical classes of nouns, verbs, and adjectives (number-inflecting prepositions like the Irish duitduibh ‘to.2sg’-‘to.2pl’ are in fact prepositions fused with pronouns). Here we must clearly distinguish between number as agreement, where a value on the agreement ‘target’ is dictated by that of a ‘controller,’ and number as an intrinsic, not context-driven grammatical property. Agreement with the head noun family is what imposes the singular this in this family, for instance, even though the phrase denotes something which is at the same time one (as a group) and many (as its members), so that in several varieties of English it is compatible with the plural form of the verb (this family live in poverty).

The distribution of agreement across word classes is complicated by language-particular conditions. Even closely related languages can vary significantly in this respect; English, for instance, with its invariable definite article and adjectives, contrasts with many of its Germanic relatives.

When we consider instead the word classes that express number as controllers, the picture is much more uniform: apart from personal pronouns, when a language represents number oppositions at all they appear on elements like demonstratives, which can act as pronouns or as nominal determiners, on nominal determiners proper, and on nouns. Note that what counts as controller is the noun phrase as a whole; inside it, it is not obvious whether it is the noun or the determiner that sets the choice for a value. The importance of distinguishing abstract from morphological marking is highlighted by the familiar case of French, where nouns lack number-differentiated forms except for individual lexemes and affixes (like œilyeux ‘eye - eyes,’ or the suffix -al, plural -aux in nouns and adjectives). Here articles, along with other determiners and pronouns, have a paradigm that opposes singular and plural; but their value is keyed to that of lexical nouns, most of which are invariable. It would seem, therefore, that the agreement controller (the noun) lacks the morphological marking, which instead appears on the target (the article); unless, as some theories propose (see 8, end), the locus for grammatical number is at determiner level in the phrase, and what appears on lexical nouns is agreement morphology.

Verbs too can express number (generally plurality) as an intrinsic property. This is the value of pluractional verb forms, which denote a plurality of distinct events of the same type (iterated in time or multiply instantiated in space), or one event involving many participants. The Chechen examples in (6) (from Cabredo-Hofherr & Laca, 2012, p. 12, originally from Wood, 2007) show that the pluractional form of the verb stem (-ii’ira) triggers a multi-event interpretation independently of the number value of the object argument:

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Number in Language

The extent and generality of such formations vary significantly across languages (see Cabredo-Hofherr & Laca, 2012, for a recent overview), especially in the relative independence between the plurality of the event and the plurality of one or more arguments. As far as morphology is concerned, pluractional verbs can provide the only exponence for the plural interpretation of an argument, in languages that do not obligatorily express plurality on argument nominals. Veselinova (2013) (originally from Frajzyngier, 1993) provided an illustration from the Chadic language Mupun:

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Number in Language

Plural marking is not obligatory on the noun for ‘rat’ in (7b); it is the form of the verb that conveys the reading of multiple killings.

In many cases, a language has word-formation processes that build verbs with a pluractional value, also known as frequentative or iterative, like the Latin dormītāre ‘to be dozing’ from dormīre ‘to sleep.’ The label ‘verbal number’ usefully captures the content of such morphological patterns, but it should not be automatically construed as a grammatical category on a par with number on nouns and pronouns, unless the two have similar lexical distribution and parallel semantic function.

A related conclusion applies to those languages where number-related morphemes appear relatively freely as modifiers of arguments, predicates, or even question words, as illustrated by the following Korean examples (8), from Kwon & Zribi-Hertz (2004), and (9), via Acquaviva (2008), from Unterbeck (1993); the different transliterations are retained:

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Number in Language

(9)

Number in Language

What these examples show is that Korean has a pluralizing particle that can attach to hosts of various word classes, not that all these word classes ‘inflect’ (optionally) for number.

3.2 Applicability and Generality Across the Lexicon

In languages that distinguish number values on nouns, invariable nouns are not always the exception. In fact, it is very common for number marking to be restricted to a subset of the lexical items of the categories where it can apply—specifically, to those that occupy the highest segment on an ‘animacy hierarchy,’ an implicational scale which goes, at one extreme, from pronouns marked as [speaker] or [addressee], to nouns for inanimate entities at the other (see Corbett, 2000, pp. 54–94; his version of the scale is reproduced here).

speaker > addressee > 3 person > kin > human > animate > inanimate

The claim that number-differentiated nouns always occupy a continuous segment on the hierarchy identifies a single semantic basis for all instances where number marking selects a subset of the lexicon of nouns and pronouns. The result of this lexical differentiation can take various forms, as the items in the highest segment can contrast with the rest because their marking is obligatory, or because it is possible. Considering the exponence of plurality relative to a simpler distinction between human and inanimate nouns, Haspelmath (2013) accordingly distinguishes six classes: three where number marking is regularly present, absent, or optional, without semantic distinctions across the lexicon; and three where human nouns contrast with inanimate nouns. This can mean that human nouns are the only ones where a plural reading is morphologically expressed, in which case marking can be mandatory or optional; or they can be the only ones where it is obligatory rather than optional. Table 1, which summarizes the information contained in Haspelmath (2013), gives an idea of the numerical size of each type out of a sample of 291 languages.

Table 1 Plural Marking Across Segments of the Animacy Hierarchy

Difference Between Plural Marking on Human and on Inanimate Nouns

Example Language

Number of Languages in Sample of 291

All nouns without plural

Shigatse Tibetan

28

All nouns with plural, obligatory

West Greenlandic

133

All nouns with plural, optional

Baka (Niger-Congo, Cameroon)

55

Plural only for human nouns, optional

Hatam (West Papuan, Timor)

20

Plural only for human nouns, obligatory

Yamul Tiipay (Yuman, California)

40

Plural obligatory on humans and optional in inanimates

Arawak (Arawakan, Suriname)

15

Source: Haspelmath (2013).

The examination of specific systems motivates finer-grained semantic distinctions; animals, for instance, can straddle the plurality split, with pluralization applicable only to culturally salient animals (as is the case for dogs in the Athabaskan language Slave, which share with humans an optional plural morpheme; Corbett, 2000, p. 57, from Rice, 1989).

It is important to remember that ‘all nouns’ does not mean that there are no lexical exceptions, but that the distribution of plural marking is not governed by lexical semantic categories. In English, for example, plurality is marked on all nouns obligatorily; there are exceptions, like the invariable deer or aircraft, but the lack of marking remains a property of individual words (despite a semantic motivation) and does not systematically extend to whole semantic categories. Another aspect to bear in mind is that the typological distribution summarized in Table 1 concerns the morphological expression of plurality on nouns, not the range of nouns that can be semantically or morphosyntactically plural independently of their form. The basis for the restriction is semantic, but the restriction concerns morphology.

Similar semantic-based splits also emerge, in a different way, in languages where number marking is pervasive, obligatory where possible, and triggers agreement. A case in point are noun class languages like those in the Bantu family, which organize their nominal lexicon into several agreement classes, each defined by a specific choice of noun prefix and concord morphemes. In the clearest cases, a noun stem occurs in two classes, one with a singular and the other with a plural reading:

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Number in Language

The split consists in the fact that, of the variously estimated number of Swahili classes (18 for Crisma, Marten, & Sybesma, 2011, from which the examples are taken), only the first four (1–2 for humans, 3–4 for trees and plants) are so clearly organized in singular-plural pairs. The other classes, which are less coherent semantically, define such singular-plural pairings for many nouns, like ki-ti ‘chair’ (class 7)—vi-ti (class 8) ‘chairs’; but they also comprise many ‘one-class’ nouns, like ki-u ‘thirst’ (class 7), vi-dondo ‘small chips of wood,’ vi-rugu ‘anger’ (both class 8). In fact, also class 3 hosts unpaired nouns, like m-chana ‘daylight,’ so that the only classes regularly paired by number values are 1 and 2. All other classes not only host unpaired nouns but also serve to form words with distinct lexical content, corresponding to derivational functions rather than to number marking:

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Number in Language

Whether or not classes are best analyzed as paired singular-plural expressions of a single ‘gender’ (Carstens, 1993, 2008), the relation between number value and class assignment clearly decreases as we move away from the classes where semantic motivation is clearest. Lexical semantics, then, affects the organization of number marking across the lexicon.

3.3 General Number

In languages that can otherwise morphologically distinguish alternative number values, a noun form compatible with interpretations corresponding to distinct values can instantiate ‘general number’ (cf. the related concept of ‘set noun’ in Rijkhoff, 2002). The in-depth discussion in Corbett (2000, pp. 9–19) made precise this traditional notion and defined it not as a form that happens to be underspecified for number value but as an underspecified interpretation. This may have a special form, distinct from those of singular and plural; more usually it is expressed by the same form also used for singular or plural. The examples in (12) reproduce those given by Corbett (2000, p. 11) for the Cushitic language Bayso (which also has a distinct paucal form; see Section 4.1):

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Number in Language

The term ‘general number,’ however, is sometimes used more loosely to refer to forms that do not express a value by themselves. In such cases, the question arises whether such nouns are also numberless in a morphosyntactic and semantic sense. In fact, this question conceals unexpected difficulties. It seems intuitive that when a noun occurs in a noun phrase that is unambiguously singular or plural, in a morphosyntactic and semantic sense, it must be at least compatible with these values. So, in Malagasy the noun boky, in itself neither singular nor plural, must be compatible with the values of the demonstratives itsy and iretsy, unambiguously singular and plural, respectively (Paul, 2012, p. 101):

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Number in Language

This raises the question whether what is singular or plural is the noun or the noun phrase. An answer depends on a specific analysis of the language in question and must rest on theoretical assumptions about the representation of number in nominal structures. Empirical evidence is available, however. For Malagasy, Paul (2012) makes a strong case that the interpretation of bare nouns is genuinely indeterminate. The key observation is that, in (14), boky can mean ‘one book’ or ‘books’ not just in the first conjunct but in both; this means that the sentence is true in a situation where Soa read one book and Be several, or vice versa—the interpretation does not co-vary, as would be expected if the first occurrence set one of the values:

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Number in Language

In a different sense, nouns not formally marked for number can be analyzed as semantically numberless in phrases that refer generically to a whole species, like the dodo; see Section 7.3.

4 Values

Although singular and plural do not correspond to specific interpretations in a simple one-to-one fashion, they remain grammatical specifications with distinct semantic content. They are not the only ones, however. Beside them, the main additional values for number are:

  • dual and trial, which restrict the denotation to sets of a certain (low) cardinality

  • paucal, which does not identify a cardinality but rather applies to collections that are ‘small’ in number, often also sharing a cohesive property

  • ‘greater’ and ‘maximal’ plural, for collections that are, respectively, too big to be easily enumerated, and equated with the totality of objects matching the description

Not included in this list are so-called collective and distributive markers which in American languages like Mohawk (Iroquian), Nahuatl, and Kwak’wala (Wakashan) qualify a nominal’s denotation as cohesive or scattered (in different locations or subcategories), since these characterize types of plurality instead of establishing distinct number values. Also disregarded are singulatives (see Section 5.4), which derive an individual-denoting noun from a basic term that can have plural or ‘general’ interpretation; as can be seen, these too are not separate number values as much as ways to realize them.

4.1 Cardinality-Based and Approximative Values

The dual, familiar from various ancient Indo-European languages and a few modern ones (Lithuanian, some Slavonic languages like Slovene and Upper Sorbian, Breton), is also found in families as diverse as Afro-Asiatic (Arabic), Uralic (Nenets), Kiowa-Tanoan (Kiowa), Micronesian (Mokilese), and in several Australian languages. Much rarer is the trial, attested in some Austronesian languages (Larike) and in the Daly family of Australian languages (Ngan’gityemerri). A quadral is sometimes reported, but Corbett’s (2000, pp. 26–30) assessment concludes that these forms never strictly refer to four-membered collections; rather, they apply to small-sized groups and can provide a distinct expression for special not number-related senses (in Sursurunga Corbett reports reference to multiple kinship pairs and collective addresses in speeches).

The restriction based on cardinality distinguishes duals and trials from paucals, which more generally apply to small collections and thus discriminate between types of pluralities on the basis of perceptually relevant size (‘small’ versus ‘big,’ in an indeterminate sense influenced by cultural and contextual factors). Many languages express this distinction through special nominal or pronominal forms, which contrast with a non-paucal plural (Bayso; Cushitic) and, not infrequently, with a dual (Fijian; Oceanic), or in isolated cases even with a dual and a trial (Lihir; Oceanic). In fact, all of these values represent ways to morphologize the same psychologically real notion of collections that stand out from larger pluralities. From available descriptions, it is rare to find the dual and the trial employed strictly for all and only two- and three-membered collections, without any qualifications; thus Slovene and Larike (Austronesian) both have a dual that strictly applies to pairs (Larike has a trial too, strictly for three-membered collections), but both can also refer to the same collections with the plural. The picture is complicated by the frequent occurrence of duals that no longer represent a genuine value for number but survive only for a subset of nouns, as is the case for modern Hebrew, some Arabic dialects, and Breton. In Hebrew, dual morphology can apply to a few nouns (mostly units of time) to express a dual interpretation, even though the nouns so marked count as syntactically plural for agreement purposes. However, morphological dual marking can also replace the function of the plural, typically for nouns for natural pairs, but also for natural collections like ‘teeth’ (Schwarzwald, 1991, cited in Acquaviva, 2008, pp. 31–32):

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Number in Language

Similar uses of dual morphology to denote natural collections with more than two members are also attested in biblical Hebrew, Maltese, Arabic, and Akkadian (Acquaviva, 2008, pp. 102, 252, and literature cited there). While these types of ‘dual’ do not illustrate a number value in the strict sense, they show the intimate relation between dual (and trial) and the paucal.

Symmetrically to paucals, ‘greater’ plurals, or plurals of abundance, are special forms that discriminate those types of pluralities whose size is conceptualized as too large for individual enumeration; for example, Miya (Chadic) opposes sə̀bə ‘people’ and kùtə ‘things’ to sə̀babáw ‘a large number of people’ and kùtatáw ‘a large number of things’ (Harbour, 2014, p. 199, from Schuh, 1998, p. 199). Again, the semantic contrast is not a matter of sheer size, but ultimately of accessibility of individuals. Corbett (2000, p. 31) cites two examples from Banyun and Fula (both Niger-Kordofanian), where a special noun class assignment for nouns signals that the referents cannot be counted because the sum is indefinitely large or because the speaker ‘does not feel it necessary.’ There is a connection between the idea of indefinite size and genericity. Consider the pronominal system of Mokilese, which distinguishes a greater plural (Table 2).

Table 2 Mokilese Pronouns

Person

Singular

Dual

Plural

Greater Plural

1 inclusive

//

kisa

kisai

kihs

1 exclusive

ngoah(i)

kama

kamai

kimi

2

koah/koawoa

kamwa

kamwai

kimwi

3

ih

ara/ira

arai/irai

ihr

Source: Corbett (2000, p. 35).

Harrison (1976; cited by Corbett, 2000, p. 34) calls the second set of plural forms ‘remote plural’ and describes them as referring to ‘groups of people, usually large, and most of which are probably not directly present when being discussed.’ Greater plurals that express this generic interpretation approach a global reading, as ‘indefinitely many X’ shades into ‘X in general’ and ‘all X’ in a generic sense. Details, of course, depend on individual descriptions and may vary across languages. In particular, some languages seem to distinguish not one but two ‘greater’ plurals (Harbour, 2014, p. 202 cites Banyun and the Arawakan language Warekena).

4.2 ‘Minimal-Augmented’ Values

A final type of value does not arise from a finer articulation of plurality into distinct subvalues, but from a different conceptualization of what counts as a minimal element in the denotation. Some languages organize the paradigm of personal pronouns by opposing not singular to plural, but the smallest collection compatible with the person features to larger collections. An example is Ilokano (Austronesian), here discussed on the basis of Nevins (2011); see also Noyer (1997), and for other such cases Corbett (2000, pp. 166–168) and especially Harbour (2011a) on Winnebago (Siouan). The personal pronouns of this language distinguish singular and plural, and the first-person plural further distinguishes an inclusive form tayo, interpreted as ‘we including you (addressee),’ from an exclusive form mi interpreted as ‘we not including you (addressee).’ In addition, there exists a separate form ta interpreted as ‘we two (speaker plus addressee).’ It would seem appropriate, then, to classify the first-person forms on the basis of two clusivity values (inclusive and exclusive) and three, not two, number values: a singular ‘me,’ which is by its own meaning cannot denote any other individual apart from the speaker, a plural ‘we,’ which distinguishes the inclusive tayo ‘me, you, and others’ from the exclusive mi ‘me and others but not you,’ and dual ta, meaning ‘me and you alone.’ But positing a dual number value just for this latter form distorts the logic of this paradigm. There are no dual second- or third-person forms, only a first-person one. The crucial observation is that the dual reading ‘me and you alone’ denotes the smallest collection of individuals compatible with the characterization ‘first person inclusive,’ and it is only in this function that a putative dual emerges; elsewhere, the number opposition simply distinguishes a singular from a plural, not only in the second and third persons but also in the first exclusive (ko ‘me alone’ vs. mi ‘me and others but not you’).

Instead of positing a strange three-value number system in which dual forms are missing precisely in all persons that have a singular, it is much more revealing to think of just two number values for each person feature: one for forms denoting the smallest set compatible with a given person characterization, and one for forms denoting larger collections. If the latter can be intuitively seen as ‘plural,’ the former is not ‘singular’ but rather ‘minimal’: it denotes a single individual in most values, but a pair in the one person value that must denote at least a pair, namely the one characterized as inclusive. Formally, a feature [± augmented] makes this intuition precise: given a person feature, it defines elements of the denotation that have (or lack) a subelement, which also satisfies that feature. Nevins (2011, p. 422) can thus re-interpret Ilokano personal pronouns as providing the [–augmented] and [+augmented] values for the four person characterizations defined by the features [±speaker, ±hearer]: first person inclusive and exclusive, with a positive value for [+speaker], and second and third person, marked [–speaker]. The pair ‘you and I’ satisfies the property of including both speaker and hearer, but neither of the two subelements of this pair does.

As a result, ta ‘you and I alone’ and individual-denoting forms (the traditional ‘singular’ ones) can be grouped together as [–augmented], as they denote the minimal size that satisfies the person features; all ‘plurals’ are instead [+augmented].

This analysis posits a number feature with a very precise interpretation evaluated relative to another grammatical feature (person). In doing so, it moves the typology of number values to a different, more theoretical level. In fact, it calls into question the validity of notions like ‘singular,’ ‘dual,’ and ‘plural’ as more than convenient descriptive devices (Harbour, 2011a,b, 2014), because a dual interpretation, applied to person features, is an epiphenomenon resulting from the feature [± augmented]. This is an aspect of the normal tension between description and analytical interpretation; we can add that, first, a typology of number must reflect the specificity of Ilokano or Winnebago, and second, that this specificity concerns pronouns, which often differ from nouns in their system of number values.

4.3 Relations Between Values and ‘Constructed Number’

The systems of values are very often subject to limitations both in terms of the category and, for nouns, of the lexical items they apply to (see Section 3). A typical illustration is provided by the Australian language Guugu Yimidhirr (Haviland, 1979, pp. 55, 66–67), where pronouns distinguish singular, dual, and plural, while nouns only signal number-related information through derivational suffixes that express a plural or, for some kin terms, a collective interpretation (for people related to a single person). Importantly, ‘approximative’ values are not limited to lexical nouns; the paucal applies to pronouns in languages such as Sursurunga (Australian), Longgu (Austronesian), Mele-Fila, Lihir, and Fijian (Oceanic) (Corbett, 2000, p. 22 also mentions the Yuman language Walapai, spoken in Arizona); while Mokilese, as we have seen, displays a greater plural value for pronouns. It remains to be seen whether all possible values can equally apply to nouns and pronouns.

When the value systems of different word classes are misaligned, one notable consequence that can arise is the phenomenon known as ‘constructed number’ (Corbett, 2000, pp. 169–170). In this scenario, an interpretation corresponding to a specific value arises when two elements of a syntactic phrase are marked for two different values; this differs from the common scenario in which one of the two has a default unmarked form. Hopi (Uto-Aztecan), the most discussed example (Corbett, 2000, p. 169; Cowper, 2005; Harbour, 2014, p. 215), overtly distinguishes two values on verbs and pronouns, but the two align in different ways with semantic interpretations. The ‘singular’ verbal form applies to arguments that are either singular or dual, while the ‘singular’ pronoun strictly applies to individuals, leaving the ‘plural’ for pairs and greater sums. The result is that a dual reading for ‘we two ran’ arises by combining a dual/plural pronoun with a singular/dual verb:

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This may be viewed as an instance of ‘construction’ of a dual value out of a ‘plural’ pronouns and a ‘singular’ verb; but given that a dual value is elsewhere attested in Hopi (on nouns), it seems better to analyze the pronominal and verbal forms as expressing also a dual reading, but through different members of the two-way formal opposition. In a different type of ‘construction,’ the formal expression of one value is built on that of another value, so that two markers co-occur on the same word. One of Harbour’s (2014, p. 217) illustrations is Bonan (or Bao’an; Mongolic), which opposes a singular (bare stem, more ‘horse’), a plural (more-la ‘horses’), and a paucal; this is expressed by the suffix -ghu- in tandem with the plural suffix, resulting in more-ghu-la ‘a few horses.’ Evidently, a proper account of these cases requires a precise analysis of the morphosyntactic value of each form and of its semantic content.

An important component of any typology of number values is the recognition of implicational patterns between the various systems. Greenberg’s (1966) Universal 34 famously states that ‘no language has a trial unless it has a dual’ and ‘no language has a dual unless it has a plural.’ Typological research has sharpened these results, which must now take into account a fuller range of values including the ‘approximative’ ones (non–cardinal-based), as well as the role of optionality for certain values and the presence of ‘general’ number (see Corbett, 2000, pp. 38–50). The theory of number features developed by Harbour (2011a,b, 2014) has recently argued for a unified and formally precise account for a full set of such implications (see Section 8).

5 Morphology and the Paradigmatic Axis

The exponence of number takes place through the most diverse strategies, across the entire typological spectrum. The claim that a language has no number means that no such category is referenced at any level as part of the grammatical system (this has been claimed about Pirahã, cf. 2.2.1), and that other means like conjunction are used to express information about numerosity, quantity, and the internal structure of the elements in the discourse domain. Other systems express this type of information by means of a small set of affixes or morphological operations (like reduplication), which can modify words of various categories. The Korean examples in 2.2.1 provide an illustration; Halkomelem (Salish) provides another (from Wiltschko, 2008, pp. 642, 679–680; see also Wiltschko, 2012):

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The intensive reading ‘very fast’ of the reduplicated plural in (17c) highlights the lack of isomorphism between the traditional notion of ‘plural’ and the content of this modification pattern in Salish, which is polysemous when compared to what plural means in Indo-European or Semitic. When non-inflectional modification of this sort is simply opposed to number-neutral forms (general number, as opposed to unmarked singular), it may be better seen as expressing plurality as a facet of a broader semantic characterization which includes intensive degree or large size, rather than plural as one of the values of number. This is not the case where plural marking is part of the exponence of number as an inflectional category.

5.1 Varieties of Number Morphology

Setting aside the question of whether ‘plural’ marking always realizes number as a grammatical category (a question the answer to which turns on the precise understanding of ‘grammatical’), the exponence itself can take a great variety of forms, dependent on the morphological profile of single languages. We can distinguish the following exponence strategies for plurality (see also Dryer, 2013):

  • as word morphology: affixes, stem changes (including tone), reduplication

  • as free form or clitic

  • classifier choice

Examples for the first type are provided in (18); it should perhaps be added that these examples do not necessarily represent the only type of plural morphology on the respective languages.

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As for plural words, the Tongan example of free form in (19a) is one of the many provided by Dryer (1989); while (19b) shows how the plural morpheme attaches to the last element of the noun phrase in Basque:

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Any one language can (and typically does) display more than one pattern, across different lexical items, and also, subject to language-particular constraints, on the same word, as shown by familiar examples like the German Büch-er ‘books’ from the singular Buch.

Where number is an inflectional category, agglutinating languages typically realize it through affixes that remain invariant across morphosyntactic contexts and may display clitic-like properties like the Turkish -ler in (20), from Acquaviva (2008, p. 59), which modifies both conjuncts but attaches to the phrase-final one:

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Fusional languages instead typically express number through portmanteau morphemes that cumulate the exponence of other categories. The inflectional endings of languages like Latin typically express number and case; they do not realize gender directly but through default gender values for a choice of declensional class. Correspondingly, in the genitive plurals verb-ōrum ‘of words’ (neuter) and pir- ōrum ‘of pear-trees’ (feminine), the ending -ōrum fuses information about declensional class, case, and number.

5.2 Number and Noun Classification

Of particular importance is the relation of number morphology with systems of noun classification: noun classes, genders, and classifiers. The first type was exemplified with Swahili in Section 2.2. above, and we saw there that what expresses a choice of number value (for the class pairings that can be interpreted in this way) is not a particular prefix, but the assignment to a class, which determines not just a noun prefix but a choice of agreement morphemes as well. Number oppositions are not the only function of such pairings, as we saw, nor are pairings always one-to-one, so that the Swahili singular simba ‘lion’ (class 9) corresponds not just to simba (class 10) ‘lions’ (both without prefix), but also to ma-simba (class 6), glossed with collective interpretation as ‘pride (that is, group) of lions.’ Crisma, Marten, & Sybesma (2011, p. 272) note that, where gender value and class assignment systematically coincide in this way, there is no direct evidence for number as a morphosyntactic feature distinct from gender (or class assignment); this contrasts with the situation in languages like Italian, where verbal agreement, for instance, is in number only.

Number value coincides with class assignments also in languages that distinguish a small number of genders, each marked by a variety of exponents, rather than numerous noun classes identified by a specific choice of prefixes and agreeing morphemes. This is the case for languages of the Cushitic family of Afroasiatic, like Rendile (Oomen, 1981) and Somali (Lecarme, 2002), where certain nouns form the plural by moving into the same agreement class of the singular of the opposite gender; for instance, the Rendile masculine arab ‘elephant’ has the plural arabe, which triggers feminine concord on agreeing verbs and is marked by a stem-final -e like other feminine singular nouns ending in consonant. According to Mathieu (2012), reassignment of a noun to a different gender has a similar function in the Algonquian language Ojibwe, where it turns nouns into singulatives (see Section 5.4) and thus into countable nouns that allow for number marking.

5.3 Inverse Number

The relevant Somali pattern has been described as in terms of ‘polarity,’ because the same exponence expresses two ‘polar’ opposites in the intersection of gender and number features (masculine plural and feminine singular). More generally, without reference to two distinct feature values, we speak of ‘inverse’ number marking when the same morphology marks opposed values on different lexical items. The following example is from Grimm’s (2012) study of Dagaare (Niger-Congo), where -ri (itself unmarked for tone) realizes the plural of words like ‘child’ but the singular of nouns for less individuated notions like ‘seed’:

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Such ‘inverted’ patterns, where a morpheme expresses a value that is not absolute but relative to the type of noun stem it modifies, typically accompanies a division between nominal stems: some of them are intrinsically singular, and need some marking to express plurality, while others are intrinsically plural, and need some marking to express singularity. Both Dagaare nouns in (21) require a suffix, but many languages, especially in the Nilo-Saharian family, systematically feature nouns of the three types: with distinct suffixes for singular and plural, bare for singular and suffixed for plural, or bare for plural and suffixed for singular. Baale, cited from Dimmendaal (2000, pp. 224–228), is an example:

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5.4 Singulative

The formation of a singular like dʊrsa-jí, based on an unmarked plural, exemplifies what is generally called called a singulative (the corresponding derived plural is sometimes called ‘plurative’). This category of singular nouns is well represented in languages like Breton, Welsh, and Arabic (including Maltese), which have many ‘collective’ underived plural nouns. For example, dail and del, morphosyntactically plural, express ‘foliage’ respectively in Welsh and Breton; the singular ‘leaf’ are the singulatives dailen and delenn. In Arabic the picture is more complex, because the ‘base’ and the singulative forms do not just express the plural and the singular value in an inflectional opposition, but represent two derived nouns which in turn can be inflected for number. The singulative, and in many cases the unsuffixed plural too, has therefore a separate plural, as in this paradigm from the Damascus dialect described by Cowell (1964, pp. 297, 369); see Mifsud (1996) for similar Maltese data:

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The interest of such paradigms lies in showing what cells morphology makes available in systems where singulative and plural formation exist side by side, but they should not be taken to suggest that all forms have comparable diffusion (the form derived from collectives, in particular, can be quite rare and restricted in usage), nor that the morphological oppositions correspond to uniform, clear-cut semantic oppositions across languages.

5.5 Plural Classifiers

A typical classifier ensures the combinability of a noun in a set of contexts (not just after numerals) and its choice is keyed to the interpretation of the noun stem and determines that of the noun phrase. The best-known variety is the ‘unitizing’ classifier, which accompanies a numeral or another expression of quantity and makes a noun countable in structures of the form ‘so-many [unit] noun.’ A different choice of classifier, however, can impose a ‘plural’ reading; the two are contrasted in (24a-b), from Crisma, Martens, & Sybesma (2011, pp. 287–288):

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One crucial property distinguishes a classifier like xiē from a number morpheme: it can never be used for counting, as in three books. The same běn of (24a) must be used instead (san běn shū ‘three clf book,’ and not *san xiē shū ‘three clf.pl book’). This means that the opposition is not one between singular- and plural-marking, the first restricting the denotation to singletons and the second to sums; rather, as Borer (2005, p. 184) discusses, both classifiers divide the nominal’s reference, the ‘plural’ restricting the denotation to indefinitely membered sums (like several in English), while the ‘non-plural’ lacks this specification and defaults to a singular reading in the absence of indications to the contrary.

Plural classifiers have different properties in different languages. Aikhenvald (2003, pp. 189, 235) mentions Tariana (Arawakan) and in Akatek (Mayan), where plural classifiers are restricted respectively to animate and to human beings. Akatek has both noun classifiers (keyed to choices of lexical stem) and numeral classifiers (which depend on syntactic context, like in Chinese), which can co-occur; the form of interest is eb’, a plural numeral classifier for human referents, as in xaʔ eb’ nax winax ‘here are the men,’ with an ‘actualizing’ morpheme xaʔ followed by the two classifiers eb’ (plural), nax, and the stem for ‘man’ (Aikhenvald, 2003, p. 188). In Tariana, classifiers occur only on some head nouns, with the function of derivational affixes (for example, heku-da ‘fruit,’ with the classifier glossed as ‘round object,’ and heku-na ‘tree,’ where -na is labeled ‘long vertical’); apart from these cases, classifiers in this language (and in North Arawakan in general) function as noun class agreement markers, appearing on adjectives, demonstratives, numerals, and other modifiers, in forms that are keyed to the choice of the head noun. The point of interest is that the plural human classifier -peni co-occurs with nouns that are already plural in their form, like ãtʃa ‘men’ in (25) which is reported to contrast with tʃãɾi ‘man’:

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As is clear from the use of such forms on modifiers, sensitive to and coexisting with the plural value of the head noun, we are at the boundary between classifiers and noun class morphemes.

Some languages in North America, especially in the Athabaskan family, categorize the entities in the domain of discourse through distinct classifying verbs. They should also be mentioned in this connection, since some choices for these classificatory verbs apply to pluralities. For example, Bearlake Athabaskan distinguishes forms for ‘hand me the tea’ referring to one box/bag or several boxes/bags by the alternation of the suffixes in the imperative séghanį-chu and séghanį-wa (Mithun, 1999, p. 107). However, the relation with number is quite indirect: the property of being manifold, holding of a verb’s argument, is on a par with categories like being animate, or having a certain shape, or being a container (empty or full), in the overview of Mithun (1999, pp. 106–110). The non-deterministic nature of such determinations and the systematic lack of agreement further distinguish this encoding of numerosity from number as a grammatical category.

6 Morphosyntax and the Syntagmatic Axis

Number morphology is subject to considerable variation across syntactic contexts. Without attempting to cover the countless language-particular facts, we can distinguish the issues raised by classifiers and by numerals; the variable expression of plural according to the structure of the noun phrase adds a further aspect to morphosyntactic variability.

6.1 Plural and Classifiers

Usually number and classifiers are seen as mutually exclusive, as most languages with a developed system of classifiers (whether or not restricted to numerical contexts) lack a grammatical number category on nouns. More precisely, Greenberg (1990 [1972]) stated that languages with numeral classifiers have no obligatory number marking on nouns. In effect, numeral classifiers can co-occur with plurally marked nouns, but when they do, plurality is generally non-obligatory; this is the case for Yucatec Maya (Butler, 2011):

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There are claims, however, that some languages with classifiers have an obligatory expression of nominal plural (see Bisang, 2012, on Ejagham, Niger-Congo, and the remarks in Aikhenvald, 2003, p. 249).

6.2 Numerals and Other Quantity Expressions

The difference between languages that demand, allow, or forbid the expression of plurality on nouns governed by numerals higher than one is a familiar one: to express ‘five cars,’ Spanish has ‘cars’ in the plural (cinco coches), Finnish in the singular (viisi autoa), and Armenian allows either (hing avtomeqena/hing avtomeqena-ner). In fact, the variation patterns are much more complex. First, we must clearly separate the use of singular proper from the use of an unmarked form which is better analyzed as expressing general number (Section 3.3.). Second, in cases like Armenian, the picture is complicated by the existence of numeral classifiers, which may be associated with numerals (and in that case prevent plural marking on the noun). Third, languages can vary in the range of numerals that constrain number marking on the noun they modify: in Arabic, for instance, the singular is necessary after numerals up to 10, and the plural is used above (even for values ending in unit digits; 14 patterns with 20, not with 4). Russian, which requires a singular after 1–4, is a well-known example of an intricate cluster of conditions, which determine distinct choices for number and case on the head noun and its modifiers, distinguishing nominative/accusative from oblique environments and requiring a special case and number combination for the head noun after 2-3-4 (the genitive singular, or a form nearly identical with it). But there is another dimension of variability, not cross- but intra-linguistic. In many languages, certain nouns (typically but not exclusively units of measure or of value) deviate from the usual pattern after numerals and display either an irregular number value or special forms only used with numerals and some quantifiers. Among the irregular singulars are the German nouns in drei Sack/Mann/Fass ‘three sacks / men / barrels’ or the Scottish Gaelic in trì là/bliadhna ‘three days / years’; we may add the English three stone/fathom/pound, in the dialects that use these nouns as units of measure. The Irish nouns in trí cinn/troigthe ‘three heads [as ‘items’]/foot’ are instead irregularly plural, as 3–10 usually govern the singular in that variety; other nouns appear in this context not only as plurals, but also with a special form (trí bliana ‘three years,’ instead of the regular plural blianta). A special ‘counting’ form is also the Dutch stuks ‘pieces,’ which replaces the regular stukken to express the reading ‘items’ in quantifying contexts (see Acquaviva, 2008, for more examples and discussion). Although not all such ‘special’ nouns are units of measure in the strict sense, the central role of this category and the restriction to quantifying contexts clearly suggest a relation with numeral classifiers (see Acquaviva, 2008).

6.3 Variable Expression of Number in the Noun Phrase

A different sort of morphosyntactic variability arises when the morphology of number depends on the structure of the extended noun phrase (or determiner phrase). Schematically, this happens when the exponence of plural on the noun or a modifier depends on their order inside the phrase, as can be seen with the feminine plural suffix -ja in these examples from an Italoromance (not Italian) variety from Lunigiana:

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Several instances of such ‘floating’ plural in the noun phrase are known from the Romance domain, including Catalan, Friulian, Occitan, and Walloon (see Pomino, 2013). Something similar happens in colloquial French, where a plural [z] can emerge in liaison contexts before nouns, after elements that do not inflect for number: comme[z]études ‘as studies.’

In other languages, the variable positioning of plural morpheme suggests that it marks the highest determiner in the phrase, akin to a phrasal clitic; this is Baker’s (2008) analysis of Basque, similar to what Butler (2011) argues for Yucatec Maya (see Section 6.1). Substantial differences in the morphology of number separate the various cases, and within Romance the phenomena are not all amenable to the same analysis; but they all bring to the fore the importance of morphosyntactic conditions on number morphology, which are easily sidelined in accounts based on isolated examples.

7 Semantics

Our overview has considered the semantic import of number in its various grammatical expressions. It is also possible to examine the semantic dimension of number on its own terms. This perspective allows a global language-independent account of the range of interpretations associated with number-marked expressions of natural language, but it requires a rigorous analytical vocabulary and must be grounded in notions such as individuation and atomicity.

7.1 Formal Approaches to Number and Plurality

As we saw in the example nobody in their right mind (Section 1), a notion of semantic number can be distinguished that does not coincide with the normal value of a morphosyntactic category. More such mismatches can be listed between content and form, such as the plural marking of nouns describing countable atoms like scissors, or the dual in function of plural for Hebrew nouns like šinayim or even (as a duale tantum) for mayim ‘water,’ or the widespread use of dual morphology to express a paucal and/or collective reading. Notions like ‘individual object’ or ‘collection’ or ‘atomless mass’ must therefore be definable independently of characterizations that themselves rely on number, like ‘singular’ or ‘plural.’

Since Link (1983), formal semantic approaches use lattices, mathematical constructs with precise algebraic properties, to model the denotation of natural language expressions in ways that make precise the value of number. On the basis of the algebraic operation of join, sums (and sums of sums) can be defined from a domain of atoms, and plural noun phrases denote over a domain formed by the set made up by these atoms and all their sums. In the ‘inclusive’ reading of plural, where a plurally marked expression can be true of individuals as well as sums, the denotation includes atoms along with their sums; a ‘strict’ reading excludes the atoms. The inclusive reading appears, for example, in interrogative contexts: if one has exactly one child, the question do you have children? can receive a truthful answer in the affirmative, showing that children in this case does not denote just pluralities. ‘Inclusive’ and ‘exclusive’ are descriptive terms, which capture observational properties of the interpretation of plural nouns; it is matter of debate whether plurals are best analyzed as ambiguous between these two readings, or whether the use of singular and plural in cases like do you have children, but also do you have a broom (as opposed to do you sell brooms?) depends on a pragmatically determined default (see Farkas, 2006). Denotations can be further restricted to sums with a certain number of atomic members, or to sums that include as subelements sums that satisfy certain predicates. Both atoms and sums are individuals in this perspective, with the difference that sums are ‘plural’ individuals. The structures so modeled apply to any domain built on atomic individuals and their sums, be they entities like objects or persons, or events. The latter case is illustrated mainly by pluractional verbs, but may also arise in examples like 4,000 ships passed through the lock (Krifka, 1990), where what is counted are ship-passing events and not ships.

Analyses of the different possible readings of plural, in particular, represent a major research strand in formal semantics. This work has firmly established a distinction between distributive readings, where a predicate applies individually to every single element in the argument’s denotation, as in the boys laughed, and collective ones, where it applies to a sum as a whole, as in the boys met. There is evidence that natural language interpretation involves the use of a distinct type of plural entity beside sums, namely groups, which unlike sums have the status of atomic individuals in their own right (see Landman, 1989; Schwarzschild, 1996 for diverging views). To see the rationale for such higher-order individuals, consider the two sentences in (28):

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The two sentences have different truth conditions, but if only atoms and sums existed, the coordinated subjects would have the same denotation in both examples, namely the totality of the cards (the sum denoted by the conjoined noun phrases in both cases). Not so if each conjunct refers to a distinct abstract individual, whose identity is preserved in the conjunction.

7.2 ‘Oneness’ and Countability

Formal models presuppose the existence of a domain of entities, which they represent in ways conducive to revealing semantic explanations. But what it means to be ‘one’ for semantic purposes, and specifically in connection with linguistic number, is not a trivial question. Even for count nouns, an example like two books in one illustrates the flexibility that natural language can display in defining what counts as ‘one,’ and correspondingly as ‘non-one.’ There are several ways in which the linguistic encapsulation of criteria of ‘oneness’ have a direct impact on the use of grammatical number. As we saw (Section 6.2), nouns used as units of measure often display an irregular number marking in quantificational contexts. Duals and paucals can express a collective interpretation for items that, though distinct at one level, form a cohesive unity (Section 4.1). And at one remove from grammatical number, but still relevant, is the ‘oneness’ that underlies the choice between collective and distributive marking in North American languages like Papago (Tohono O’odham), which Ojeda (1998) analyzed in terms of oppositions between singular and plural ‘locus’ (see Section 4 for references).

The semantic property of defining atomic units is paramount for formal analyses of the mass/count distinction. The classic approach, from Link (1983), models individuals in the discourse domain as atoms, pluralities as their sums (and sums of sums), and masses as atomless sums, that is sums without minimal atomic parts. This formalizes the intuition that count nouns define standards of wholeness, while mass nouns denote entities that can be divided in infinitely many ways without losing their essential properties. Of course this is only an approximation, not only because, in fact, mass nouns come in different types and even prototypical substances are not in fact infinitely divisible (water is not), even though they may be so conceptualized, but also because count nouns like twig, branch, or line, denote entities that can be subdivided into parts which still fall under the same predicate (a subpart of a line is still a line), unlike canonical count nouns like cat, car, or indeed atom (Rothstein, 2010, and subsequent literature have brought into focus the distinction between countability and atomicity, and the need for a sharper understanding of atomicity). Nouns like furniture or footwear (often called ‘fake’ mass nouns) represent another empirical domain that calls for a refinement, since they share the syntactic properties of mass nouns like water but are true of well-defined individual atoms (see again Rothstein, 2010; Barner & Snedeker, 2005, for experimental results on quantity judgments involving this type of noun).

The importance of the linguistic encoding of ‘oneness’ for the use of number emerges especially in connection with countability. Mass nouns would seem to be generally singular, and semantic analyses usually reflect this by positing for them an atomless domain without minimal parts, rather than one formed on the basis of atomic individuals. Only atom-denoting singulars can be pluralized, in this classic view (Chierchia, 1998b); but recent research has shown that mass plurals are well attested, and that even for countable nouns, plurality does not just denote sums of individuals (see examples like 0.5 units in Section 2 and Section 8). Coercing a mass noun into a number opposition often results in a recategorization as a count noun, as in familiar examples like one beer/three beers (this can be grammaticalized as a singulative-forming strategy, as argued by Mathieu, 2012, for Ojibwe; see Section 5.2); but coercion has its limits and seems systematically unavailable with ‘fake’ mass nouns like furniture(De Belder, 2013). In particular this last class of nouns, singular and syntactically mass but denoting collections of discrete entities, brings to the fore the tension between semantic interpretation as sums of individuals and grammatical characterization through singular number and countability. It must be noted that these forms are ‘collective’ in that they typically presuppose that the individuals they denote share a place or a function; in this case too, an interpretation as ‘one’ has non-trivial effects on the grammatical encoding of entities and on the use of number in particular.

7.3 Number and Genericity

The interplay between number and determiners is a crucial ingredient in generic reference. With the appropriate predicates, the plural conveys a distinctly generic interpretation in structures like whales will soon be extinct, where the determinerless noun whales does not apply to any collection of whales (not even to the total collection: all whales will soon be extinct is not equivalent) but to an abstract ‘kind.’ Such bare plurals, as they are known in the literature, characteristically express generic interpretations in languages like English, but the singular also allows a generic reading, with the right choice of determiner and in the right context:

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In fact, this type of variability derives from the fact that genericity covers distinct readings: the whale will soon be extinct is acceptable, but not a whale will soon be extinct, nor the average whale will soon be extinct. Countability adds a further dimension, because the mass counterpart of a bare plural like whales is a bare singular, as in gold is rare; and in this case there are much stricter constraints on using the definite article for reference to a kind (*the gold is widespread). The English pattern represents, however, only one example of how languages crucially use the number category to express genericity. From the rich literature on the subject, we can point out that Romance languages, for instance, typically require a definite article for plural nouns interpreted generically (French les dinosaures ont disparu, Romanian dinozaurii [def.] au dispărut, ‘dinosaurs disappeared’), but Brazilian Portuguese also allows a bare singular in this function: pedreiro é preguiçoso ‘bricklayers are lazy’ (lit. ‘bricklayer is lazy’; Dobrovie Sorin & Pires de Oliveira, 2010). Most importantly, the ‘optional’ plural of Korean (which in fact is mandatory in certain interpretations) is reported to be incompatible with a generic reading by Kwon & Zribi-Hertz (2005):

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Number in Language

Evidently, the element glossed ‘pl’ in Korean differs from English plural not just distributionally but also semantically. This shows that a correct understanding of the role of number in the expression of genericity must take into account the different values that number morphology can have across languages.

8 Theories of Linguistic Number

Number is a pervasive category in language, involved in fundamental aspects of linguistic conceptualization (individuation, countability, distributive and collective predication, genericity), and instantiated in the most diverse ways across the typological spectrum. Therefore, a very large body of work touches on it, especially in semantics, morphology, and linguistic typology. Scholarship focusing specifically on number in language has not been very prominent until recent decades, although Quine (1960) and already Frege (1884) had framed their discussion on the conceptualization of unity and counting in terms of elucidations of natural language expressions. On the other hand, the relation between number and countability, and the analysis of the manifold interpretations expressed by plurality, have been central concerns for the rich tradition of studies in formal semantics which developed especially (but not only) after Link (1983), but much of this work only considered English and closely related languages, and tended to treat the singular-plural divide, in form and function(s), as a linguistic given. Things have changed in more recent times, with a surge in interest for the phenomenology of number across languages and for the place of number in the grammatical make-up of nominal and also verbal expressions. Much of the impetus for this development has been provided by Corbett’s (2000) monograph, which made accessible an impressive amount of material organized in a unified analytic perspective. Simplifying a very complex picture, three leading strands can be identified in contemporary scholarship on number, centered, respectively, on its typology across language systems, on its grammatical representation in the noun phrase, and on its semantic typology.

The first strand capitalizes on the results of broad-ranging surveys that cover familiar and especially less familiar systems, in which a substantial role is played by the work of Corbett himself and of the Surrey Morphology Group (the Slavonic number bibliography being an example of the resources made available on its website). Along with many other contributions, we should note in particular the relevant chapters in the World Atlas of Language Structures (Daniel & Moravcsik, 2013; Dryer, 2013; Haspelmath, 2013). The facts and especially the generalizations uncovered in this direction have considerably sharpened our view of the grammatical encoding of number, especially concerning noun class or classifier systems.

The second strand groups together a large and diverse body of work addressing the fundamental question of what number is in a theory of grammar, particularly as a key component of noun phrases. Rijkhoff (2002) stands out as a broad-ranging typology from a functional-cognitive perspective, but the structure of the noun phrase has especially been a classic theme in formal generative syntax, with the representation of number taking center stage since the early 1990s. A renewed impulse was given by Borer (2005), which has shaped later research with the proposal to analyze number as a divider of reference, a function distinct from that of conveying quantity. This reinterpretation has provided a unified analytic framework for the study of number and classifier systems as grammatical variants, a move that introduces a much broader typological perspective and relates naturally to current developments in semantics (see the papers in Massam, 2012).

The third strand is associated with the proposal advanced by Chierchia (1998a,b, 2010) and amply developed in the response it has generated, that cross-linguistic variation in the encoding of number and individuation has a semantic basis in the different ways languages use nouns and determiners to express kinds and properties. This line of study developed from an already extensive literature on the expression of kinds, which incorporated a comparative dimension. At the intersection of formal syntax and semantics, but addressing language variation across the whole typological spectrum, the work of Chierchia and that inspired by it has greatly enlarged the empirical scope of formal semantic investigations, but more importantly it has made it directly relevant for syntactic analyses, and conversely. In effect, over and above the question whether the fundamental parametrization is syntactic or semantic (see Deprez, 2005), the overlap between this strand and the second one is so significant that in many cases the distinction is one of emphasis on the semantic or morphosyntactic aspects, or is simply not there at all (for illustration, see again Massam, 2012; Bale & Coon, 2014).

These three strands, of course, do not cover the whole range of recent advances in the analysis of number. A few more specific themes can be highlighted, variously related to the broad approaches just outlined, and straddling the boundaries between morphology, syntax, and semantics.

Elucidating the difference between inflectional and non-inflectional number was already an important goal in typology and comparative morphology, but it has acquired an even greater urgency in the context of theories that aim to be couched in language-invariant terms. The structural analysis by Wiltschko (2008, 2012), in particular, derives a cluster of grammatical and semantic properties that differ according to whether plurality is a modifier or rather the value of a projecting syntactic head. Kwon and Zribi-Hertz (2004, 2005) reach a similar conclusion, but on different empirical bases (Korean instead of Halkomelem Salish). Their syntactic approaches complement in an interesting fashion the semantic analysis of Indonesian plural by Dalrymple & Mofu (2012), who clarify the function of another such ‘optional’ plural.

The precise definition of the features involved in grammatical number represents another important theme, which again is not new but has received a new powerful impulse by the recent advances in the three strands listed above. The most developed proposal is due to Harbour (2011a, 2014), who has articulated a theory that defines number values in rigorous set-theoretic terms, and derives a large body of cross-linguistic data from a very small set of assumptions. A key aspect of this approach is that it takes features as primitives, which underlie not just number but other grammatical determinations too (crucially, the analysis of number values rests on the same [+cumulative] feature at the basis of the formal analysis of countability and verbal aspect). This necessitates an in-depth discussion of markedness, in its semantic and morphological facets (Bale, Gagnon, & Khanjian, 2011; Harbour, 2011b; Nevins, 2011).

Finally, the distribution of exclusive and inclusive readings for plural noun phrases (sums only or atoms and sums; see Section 7.1) is one of the main empirical motivations for the view, first spelled out in Sauerland (2003), that number is a property not of nouns but of noun phrases, and that plural, under the inclusive reading, is in fact the semantically unmarked value, whose use is constrained by pragmatic principles. Later work has individuated important cross- and intra-linguistic constraints on the distribution of inclusive and exclusive plural reading, which have become a significant empirical line of inquiry in the growing body of comparative analyses of number that merge morphology, syntax, and semantics (Bale, Gagnon, & Khanjian, 2010; Mathieu, 2014).

Further Reading

Acquaviva, P. (2013). Number. In M. Aronoff (Ed.), Oxford bibliographies in linguistics. New York: Oxford University Press.Find this resource:

Aikhenvald, A. (2003). Classifiers. Cambridge, U.K.: Cambridge University Press.Find this resource:

Aikhenvald, A. (2011). Classifiers. In M. Aronoff (Ed.), Oxford bibliographies in linguistics. New York: Oxford University Press.Find this resource:

Bale, A., & Barner, D. (2011). Mass-count distinction. In M. Aronoff (Ed.), Oxford bibliographies in linguistics. New York: Oxford University Press.Find this resource:

Borer, H. (2005). In name only. Oxford: Oxford University Press.Find this resource:

Cabredo Hofherr, P., & Laca, B. (Eds.). (2012). Verbal plurality and distributivity. Berlin: De Gruyter.Find this resource:

Chierchia, G. (1998a). Plurality of mass nouns and the notion of semantic parameter. In S. Rothstein (Ed.), Events and grammar (pp. 53–103). Dordrecht, The Netherlands: Kluwer.Find this resource:

Chierchia, G. (1998b). Reference to kinds across languages. Natural Language Semantics, 6, 339–405.Find this resource:

Chierchia, G. (2010). Mass nouns, vagueness and semantic variation. Synthese, 174, 99–149.Find this resource:

Corbett, G. (2000). Number. Cambridge, U.K.: Cambridge University Press.Find this resource:

Dayal, V. (2004). Number marking and (in)definiteness in kind terms. Linguistics and Philosophy, 27, 393–450.Find this resource:

Dryer, M. S., & Haspelmath, M. (Eds.). (2013). The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology.Find this resource:

Harbour, D. (2014). Paucity, abundance, and the theory of number. Language, 90, 185–229.Find this resource:

Ionin, T., & Matushansky, O. (2006). The composition of complex cardinals. Journal of Semantics, 23, 315–360.Find this resource:

Ionin, T, &. Matushansky, O. (2013). Numerals. In M. Aronoff (Ed.), Oxford bibliographies in linguistics. New York: Oxford University Press.Find this resource:

Krifka, M., Pelletier, F.-J., Carlson, G., ter Meulen, A., Chierchia, G. C., & Link, G. (1995). Genericity: An introduction. In G. Carlson & F. J. Pelletier (Eds.), The generic book (pp. 1–124). Chicago: University of Chicago Press.Find this resource:

Kwon, S. N., & Zribi-Hertz, A. (2004). Number from a syntactic perspective: Why plural marking looks truer in French than in Korean. In O. Bonami & P. Cabredo-Hofherr (Eds.), Empirical issues in syntax and semantics (Vol. 5, pp. 133–158). Paris: CNRS.Find this resource:

Link, G. (1998a). Plural. In G. Link, Algebraic Semantics in Language and Philosophy (pp. 35–75). Stanford, CA: Center for the Study of Language and Information.Find this resource:

Link, G. (1998b). Quantity and number. In G. Link (Ed.), Algebraic Semantics in Language and Philosophy (pp. 213–229). Stanford, CA: Center for the Study of Language and Information.Find this resource:

Massam, D. (Ed.). (2012). Count and mass across languages. Oxford: Oxford University Press.Find this resource:

Rothstein, S. (2010). Counting and the mass-count distinction. Journal of Semantics, 27(3), 343–397.Find this resource:

Schwarzschild, R. (1996). Pluralities. Dordrecht, The Netherlands: Kluwer.Find this resource:

Song, J. J. (Ed.). (2011). The Oxford handbook of linguistic typology. Oxford: Oxford University Press.Find this resource:

Wilhelm, A. (2008). Bare nouns and number in Dëne Sųliné. Natural Language Semantics, 16(1), 39–68.Find this resource:

References

Acquaviva, P. (2008). Lexical plurals. Oxford: Oxford University Press.Find this resource:

Aikhenvald, A. (2003). Classifiers. Cambridge, U.K.: Cambridge University Press.Find this resource:

Baker, M. (2008). The syntax of agreement and concord. Cambridge, U.K.: Cambridge University Press.Find this resource:

Bale, A., & Coon, J. (2014). Classifiers are for numerals, not for nouns: consequences for the mass/count distinction. Linguistic Inquiry, 45, 695–707.Find this resource:

Bale, A., Gagnon, M., & Khanjian, H. (2010). Cross-linguistic representations of numerals and number marking. Proceedings of Semantics and Linguistic Theory (SALT), 20, 582–598.Find this resource:

Bale, A., Gagnon, M., & Khanjian, H. (2011). On the relationship between morphological and semantic markedness: The case of plural morphology. Morphology, 21, 197–221.Find this resource:

Barner, D., & Snedeker, J. (2005). Quantity judgments and individuation: Evidence that mass nouns count. Cognition, 97, 41–66.Find this resource:

Bisang, W. (2012). Numeral classifiers with plural marking. A challenge to Greenberg. In D. Xu (Ed.), Plurality and classifiers across languages in China (pp. 23–42). Berlin: De Gruyter.Find this resource:

Borer, H. (2005). In name only. Oxford: Oxford University Press.Find this resource:

Butler, L. K. (2011). When number doesn’t Agree: Evidence from Yucatec Maya. LSA Annual Meeting, Pittsburgh.Find this resource:

Cabredo-Hofherr, P., & Laca, P. (Eds.). (2012). Verbal plurality and distributivity. Berlin: De Gruyter.Find this resource:

Carstens V. (1993). On nominal morphology and DP structure. In S. A. Mchombo (Ed.), Theoretical aspects of Bantu grammar (pp. 151–180). Stanford, CA: Center for the Study of Language and Information.Find this resource:

Carstens, V. (2008). DP in Bantu and romance. In C. De Cath & K. Demuth (Eds.), The Romance-Bantu connection (pp. 131–165). Amsterdam: Benjamins.Find this resource:

Chierchia, G. (1998a). Plurality of mass nouns and the notion of semantic parameter. In S. Rothstein (Ed.), Events and grammar (pp. 53–103). Dordrecht, The Netherlands: Kluwer.Find this resource:

Chierchia, G. (1998b). Reference to kinds across languages. Natural Language Semantics, 6, 339–405.Find this resource:

Chierchia, G. (2010). Mass nouns, vagueness and semantic variation. Synthese, 174, 99–149.Find this resource:

Corbett, G. (2000). Number. Cambridge, U.K.: Cambridge University Press.Find this resource:

Cowell, M. (1964). A reference grammar of Syrian Arabic (based on the dialect of Damascus). Washington, DC: Georgetown University Press.Find this resource:

Cowper, E. (2005). A note on number. Linguistic Inquiry, 36, 441–455.Find this resource:

Crisma, P., Marten, L., & Sybesma, R. (2011). The point of Bantu, Chinese and romance nominal classification. Rivista di Linguistica, 23, 251–299.Find this resource:

Cysouw, M. (2013). Inclusive/Exclusive distinction in independent pronouns. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/39, Accessed on 2016-04-12.)Find this resource:

Dalrymple, M., & Mofu, S. (2012). Plural semantics, reduplication and numeral modification in Indonesian. Journal of Semantics, 29, 229–260.Find this resource:

Daniel, M. (2013). Plurality in independent personal pronouns. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/35, Accessed on 2016-04-12.)Find this resource:

Daniel, M., & Moravcsik, E. (2013). The associative plural. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/36, Accessed on 2016-04-12.)Find this resource:

De Belder, M. (2013). Collective mass affixes: When derivation restricts functional structure. Lingua, 126, 32–50.Find this resource:

Déprez, V. (2005). Morphological number, semantic number and bare nouns. Lingua, 115, 857–883.Find this resource:

Dimmendaal, G. (2000). Number marking and noun categorization. Anthropological Linguistics, 42, 214–261.Find this resource:

Dobrovie Sorin, C., & Pires de Oliveira, R. (2010). Generic bare singulars in Brazilian Portuguese. In K. Arregi, Z. Fagyal, S. A. Montrul, & A. Trembley (Eds.), Romance linguistics 2008: Interactions in romance (pp. 203–215). Amsterdam: John Benjamins.Find this resource:

Dryer, M. S. (1989). Plural words. Linguistics, 27, 865–895.Find this resource:

Dryer, M. S. (2013). Coding of nominal plurality. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/33, Accessed on 2016-04-12.)Find this resource:

Everett, D. (1986). Pirahã. In D. Derbishire & G. Pullum (Eds.), Handbook of Amazonian languages (Vol. 1, pp. 280–325). Berlin: De Gruyter.Find this resource:

Farkas, D. (2006). The unmarked determiner. In S. Vogeleer & L. Tasmowski (Eds.), Definiteness and plurality (pp. 81–105). Amsterdam: John Benjamins.Find this resource:

Frajzyngier, Z. (1993). A grammar of Mupun. Berlin: Dietrich Reimer.Find this resource:

Frege, G. (1884). Die Grundlagen der Arithmetik. Eine logisch-mathematische Untersuchung über den Begriff der Zahl. Breslau: Wilhelm Köbner.Find this resource:

Greenberg, J. (1966). Language Universals: with Special Reference to feature Hierarchies. The Hague: Mouton.Find this resource:

Greenberg, J. (1990) [1972]. Numeral classifiers and substantival number: Problems in the genesis of a linguistic type. In K. Denning & S. Kemmer (Eds.), On : Selected writings of Joseph Greenberg (pp. 166–193). Stanford, CA: Stanford University Press.Find this resource:

Grimm, S. (2012). Individuation and inverse number marking in Dagaare. In D. Massam (Ed.), Count and mass across languages (pp. 75–98). Oxford: Oxford University Press.Find this resource:

Harbour, D. (2011a). Valence and atomic number. Linguistic Inquiry, 42, 561–594.Find this resource:

Harbour, D. (2011b). Descriptive and explanatory markedness. Morphology, 21, 223–245.Find this resource:

Harbour, D. (2014). Paucity, abundance, and the theory of number. Language, 90, 185–229.Find this resource:

Harrison, S. (1976). Mokilese reference grammar. Honolulu: University Press of Hawaii.Find this resource:

Haspelmath, M. (2013). Occurrence of nominal plurality. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/34, Accessed on 2016-04-11.)Find this resource:

Haviland, J. (1979). Guugu Yimidhirr. In R. M. W. Dixon & B. Blake (Eds.), Handbook of Australian languages (pp. 27–180). Amsterdam: John Benjamins.Find this resource:

Idrissi, A. (2000). On Berber plurals. In J. Lecarme, J. Lowenstamm, & U. Shlonsky (Eds.), Research in Afroasiatic grammar (pp. 101–124). New York: John Benjamins.Find this resource:

Kachru, B., Kachru, Y., & Sridhar, S. N. (Eds.). (2008). Language in South Asia. Cambridge, U.K.: Cambridge University Press.Find this resource:

Krifka, M. (1990). Four thousand ships passed through the lock. Linguistics and Philosophy, 13, 487–520.Find this resource:

Kurafuji, T. (2004). Plural morphemes, definiteness, and the notion of semantic parameter. Language and Linguistics, 5, 211–242.Find this resource:

Kwon, S. N., & Zribi-Hertz, A. (2004). Number from a syntactic perspective: Why plural marking looks truer in French than in Korean. In O. Bonami & P. Cabredo-Hofherr (Eds.), Empirical issues in syntax and semantics (Vol. 5, pp. 133–158). Paris: CNRS.Find this resource:

Kwon, S. N., & Zribi-Hertz, A. (2005). Pluriels et généricité nominale: les enseignements du coréen. In C. Dobrovie-Sorin (Ed.), Noms nus et généricité (pp. 159–195). Paris: Presses Univeristaires de Vincennes.Find this resource:

Landman, F. (1989). Groups I. Linguistics and Philosophy, 12, 559–605.Find this resource:

Lecarme, J. (2002). Gender “polarity”: Theoretical aspects of Somali nominal morphology. In P. Boucher & M. Plénat (Eds.), Many morphologies (pp. 109–141). Somerville, MA: Cascadilla Press.Find this resource:

Link, G. (1983). The logical analysis of plurals and mass nouns: A lattice-theoretical approach. In R. Bäuerle, C. Schwarze, & A. von Stechow (Eds.), Meaning, use, and interpretation of language (pp. 303–323). Berlin: De Gruyter.Find this resource:

Loporcaro, M. (1994). Sull’analisi del plurale femminile la donia “le donne” nei dialetti della Lunigiana. L’Italia dialettale, 57, 35–42.Find this resource:

Lynch, J. (1998). Pacific languages: An introduction. Honolulu: University of Hawaii Press.Find this resource:

Massam, D. (Ed.). (2012). Count and mass across languages. Oxford: Oxford University Press.Find this resource:

Mathieu, E. (2012). On the mass/count distinction in Ojibwe. In D. Massam (Ed.), Count and mass across languages (pp. 172–198). Oxford: Oxford University Press.Find this resource:

Mathieu, E. (2014). Many a plural. In A. Aguilar-Guevara, B. Le Bruyn, & J. Zwarts (Eds.), Weak referentiality (pp. 157–181). Amsterdam: John Benjamins.Find this resource:

Mifsud, M. (1996). The collective in Maltese, Rivista di Linguistica, 8, 29–51.Find this resource:

Mithun, M. (1988). Lexical categories and the evolution of number marking. In M. Hammond & M. Noonan (Eds.), Theoretical morphology: Approaches in modern linguistics (pp. 211–234). New York: Academic Press.Find this resource:

Mithun, M. (1999). The languages of Native North America. Cambridge, U.K.: Cambridge University Press.Find this resource:

Müller, A., & Sanchez-Mendes, L. (2008). The meaning of pluractionality in Karitiana. In A. R. Deal (Ed.), Proceedings of SULA 4 (Semantics of Under-Represented Languages in the Americas), University of Massachusetts Occasional Papers in Linguistics 35 (pp. 247–258). Amherst, MA: Graduate Linguistics Students Association.Find this resource:

Nakanishi, K., & Tomioka, S. (2004). Japanese plurals are exceptional. Journal of East Asian Linguistics, 13, 113–140.Find this resource:

Nevins, A. (2011). Marked triggers vs. marked targets and impoverishment of the dual. Linguistic Inquiry, 42, 413–444.Find this resource:

Noyer, R. (1997). Features, positions and affixes in autonomous morphological structure (PhD Diss.). MIT, Cambridge, MA.Find this resource:

Ojeda, A. (1998. The semantics of collectives and distributives in Papago. Natural Language Semantics, 6, 245–270.Find this resource:

Oomen, U. (1981). Gender and plurality in Rendille. Afroasiatic Linguistics, 8, 35–75.Find this resource:

Paul, I. (2012). General number and the structure of DP. In D. Massam (Ed.), Count and mass across languages (pp. 99–111). Oxford: Oxford University Press.Find this resource:

Pomino, N. (2013). Partial or complete lack of plural agreement: The role of morphology. In S. Gaglia & M.-O. Hinzelin (Eds.), Inflection and word formation in the Romance languages (pp. 201–230). Amsterdam: John Benjamins.Find this resource:

Quine, W. van O. (1960). Word and object. Cambridge, MA: MIT Press.Find this resource:

Rice, K. (1989). A grammar of slave. Berlin: De Gruyter.Find this resource:

Rijkhoff, J. (2002). The noun phrase. Oxford: Oxford University Press.Find this resource:

Rothstein, S. (2010). Counting and the mass-count distinction. Journal of Semantics, 27, 343–397.Find this resource:

Saeed, J. (1999). Somali. London Oriental and African Language Library 10. Amsterdam: John Benjamins.Find this resource:

Salminen, T. (1997). Tundra Nenets Inflection. Helsinki: Suomalais-Ugrilainen Seura.Find this resource:

Sauerland, U. (2003). A new semantics for number. Proceedings of Semantics and Linguistic Theory (SALT), 13, 258–275.Find this resource:

Schuh, R. (1998). A grammar of Miya. Berkeley: University of California Press.Find this resource:

Schwarzwald, O. (1991). Grammatical vs. lexical plural formation in Hebrew. Folia Linguistica, 25, 577–608.Find this resource:

Schwarzschild, R. (1996). Pluralities. Dordrecht, The Netherlands: Kluwer Academic Publishers.Find this resource:

Surrey Morphology Group. Slavonic number bibliography.

Unterbeck, B. (1993). Kollektion, Klassifikation und Transnumerus. Eine typologische Studie zum Koreanischen. Frankfurt: Peter Lang.Find this resource:

Veselinova, L. (2013). Verbal number and suppletion. In M. S. Dryer & M. Haspelmath (Eds.), The world atlas of language structures online. Leipzig: Max Planck Institute for Evolutionary Anthropology. (Available online at http://wals.info/chapter/80, Accessed on 2016-04-11.)Find this resource:

Wiltschko, M. (2008). The syntax of non-inflectional plural marking. Natural Language and Linguistic Theory, 26, 639–694.Find this resource:

Wiltschko, M. (2012). Decomposing the mass/count distinction: Evidence from languages that lack it. In D. Massam (Ed.), Count and mass across languages (pp. 146–171). Oxford: Oxford University Press.Find this resource:

Wood, E. (2007). The semantic typology of pluractionality (PhD Diss.). University of California, Berkeley.Find this resource: