Number

Anna Kibort & Greville G. Corbett

1. What is 'number'
2. Expressions of 'number'
3. The status of 'number' as a feature
4. The values of 'number'
5. Oddly behaving number markers
6. Problem cases
7. Key literature

1. What is 'number'

'Number' is a grammatical category which encodes quantification over entities or events denoted by nouns or nominal elements. It derives from the ability to perceive something as a token, an instance of a class of referents, and the ability to differentiate between one and more than one (i.e. the 'plurality' of) instances of the referent. Since number can refer to entities or events, it has been suggested that in language we find both nominal number and verbal number, the latter phenomenon also being referred to as 'pluractionality'. However, on the alternative view, pluractionality is regarded as an expression of situaton type (see the entry on 'Aspect'), not number. The present entry will focus on nominal number.

In a language where nominal number is found, number-differentiability may not apply to all nouns. Traditionally, two types of noun are distinguished: 'count nouns' like the English cat, and 'mass nouns' like the English water. The count-mass distinction can be drawn from morphology - for example English count nouns usually have a singular and a plural form, while mass nouns are traditionally regarded as lacking the number distinction and having only the singular form (singularia tantum such as air) or only the plural form (pluralia tantum such as measles). This shows that for some nouns number may be lexically determined.

At the level of syntax, the count-mass distinction is drawn on the basis of the type of nominal phrase. In English, a very substantial proportion of nouns can be used both as count nouns and as mass nouns, and appear with the appropriate determiners, articles and quantifiers: Would you like a cake/some cake?, How many apples/How much apple have you had?, How many beers/How much beer have you had?, We need a new car / With a Lada you get a lot of car for your money (Cruse 1994:2860), We need a bigger table / There is not enough table for everyone to sit at (Allan 1980:547), Small farmers in Kenya grow corn rather than wheat / Triticum aestivum ssp. vulgare is a wheat suitable for high altitudes (Allan 1980:547). This ability of nouns to appear in either syntactic context is referred to as recategorisation (for a brief account of other terms see Corbett 2000:81). In his paper on the count-mass distinction in syntax, Allan (1980) claims that the traditional view labelling nouns as count or mass in the lexicon in inadequate, as the distinction relates to nominal phrases rather than to nouns. At the level of the lexicon, nouns show a countability preference, but countability is really a characteristic of nominal phrases. When both levels of analysis are taken into consideration, eight different classes of nouns can be distinguished in English, with the following examples running from the 'most count' to the 'least count' (Allan 1980:562): car, oak, cattle, scissors, mankind, admiration, equipment, Himalayas. Thus, 'count' and 'mass' are syntactic categories, and the meaning of a noun occurrence is a function of both its lexical meaning and the syntactic context in which it appears (Krifka 1994:2394).

At the level of semantics, Jackendoff's (1991) approach to the count-mass distinction captures a lot of the insights of the substantial literature on this subject (for references see Corbett 2000:78-82). He uses two semantic features, 'boundedness' and 'internal structure', to distinguish count from mass, while drawing a parallel between mass and bare plurals (both are treated as 'unbounded'), as well as between groups and bare plurals (both have 'internal structure', unlike substances which are made up of parts of themselves and unlike individuals which are treated as atomic). In this way, Jackendoff brings out the special position of committee-type nouns, and also points to the parallel analysis in verbal semantics of temporally bounded and temporally unbounded events. Corbett (2000:80) summarises Jackendoff's analysis in the following table of the semantic categories of the noun phrase:

Languages vary in how they classify their nouns with respect to the 'boundedness' and 'internal structure' of their referents, which reflects conceptual differences. For example, for most speakers of English a pea is large enough a component part of the substance peas to be considered an individual, but for speakers of Russian it isn't (cf. gorox 'peas' which does not distinguish singular and plural; Corbett 2000:80). In Arabic, the noun shajar 'tree' is a 'mass' noun denoting substance, i.e. an undifferentiated mass of 'tree-ness' (usually labelled a 'collective' in Arabic grammars). It is possible to express the meaning of an individual tree by adding an individuative suffix (shajar-a), and both the substance and the individual can be pluralised, (ashjār and shajarāt, respectively), the former denoting the plurality of tree-types (with a distributive interpretation), and the latter the plurality of tree-individuals (Cruse 1994:2858). For recent work on the compositionality of number and the morphosemantics of transnumeral nouns, from a typological perspective, see e.g. Acquaviva (2004; and forthcoming).

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2. Expressions of 'number'

Nominal number can be found expressed on the noun/nominal element, on or in the noun phrase, or on the verb. When it is found on the noun/nominal element or the noun phrase as such, it can be thought of as 'inherent', and when it is found on other elements of the noun phrase or the clause, for example as a result of agreement with the noun, it can be thought of as 'contextual' (for a discussion of inherent versus contextual features see Corbett 2006a:123-124; Anderson 1982; Booij 1994, 1996; and the 'Feature Inventory' page). In both types of loci, the actual expressions of number can involve: special number words (whose syntactic status may vary considerably depending on the language), syntactic means (i.e. agreement, found most commonly on demonstratives and verbs, but also on articles, adjectives, pronouns, nouns especially in possessive constructions, adverbs, adpositions, and complementisers), a variety of morphological means (inflections, various types of stem change, zero expressions, clitics), and lexical means (such as suppletion, or - if occurring within one language - a wide variety of number expressions which means that the number-marked forms of nouns must be remembered by the speaker rather than derived from a single underlying representation). Furthermore, number is often marked in more than one way within one language. It may be marked by two different means, for example by morphological means and by syntactic means (this is very common), or by morphological means and by a number word (as in Dogon, a group of ten related Voltaic languages within Niger-Congo, spoken in Mali), or very commonly by two or more morphological means (e.g. a stem change together with inflection). Some languages use several means of marking number on a single item - in Seri (a Hokan language spoken in Mexico) and Chontal (a Mayan language of Mexico) some nouns show four means of marking number at once (Turner 1976). See Corbett (2000:133-177) for detailed discussion of all the expressions of number, and Dryer (2005:138-141) for a discussion of six different ways of indicating plurality morphologically on the noun, and their distribution among the world's languages, based on a sample of 957 languages.

Looking at the nominal phrase, it is common for number marking to appear on the head noun, e.g. English cat ∼ cats, French cheval 'horse' ∼ chevaux 'horses'. The locus of number information can also be the determiner, as in the (spoken) French le livre (|lə livr|) 'book' ∼ les livres (|le livr|) 'books'; in English, in addition to number marking on nouns, certain determiners also have different forms depending on the number of their head noun: this cat ∼ these cats. An example of another agreeing element within the noun phrase is the adjective, as in the Russian staraja kniga 'old book' ∼ staryje knigi 'old books'. The number marker may also be attached to the nominal phrase as such, rather than to one specific constituent, as in Farsi (Persian), where it is attached to the final element in the noun phrase: ketāb 'the book' ∼ ketāb-hā 'the books', ketāb-e bozorg 'the large book' ∼ ketāb-e bozorg-hā 'the large books' (Cruse 1994:2859).

It is also possible, although relatively uncommon, for nominal number to be marked exclusively on the verb. This is the case in Meriam (or, Miriam, a language of the Trans-Fly family, spoken in Eastern Torres Strait Islands, Australia), where the verb encodes the number of its subject (a four-way distinction between singular, dual, paucal, or plural) and its object (singular or plural only), so e.g. irmile means 'one follows one', irmirdare 'a few follow one', and dirmiriei 'two follow many', etc. (Cruse 1994:2859, Corbett 2000:23, data from Piper 1989). In Amele (a Trans-New Guinea language spoken in Papua New Guinea) nominal number must be indicated on the verb and may optionally be indicated on the noun or by pronominal copy, but this marking is restricted to kinship terms (Corbett 2000:137, after Roberts 1987:162, 201, 203; Haspelmath 2005:142, after Roberts 1987:171). In Arafundi (a Sepik-Ramu language spoken in Papua New Guinea), the speakers do not seem to opt for marking number on the noun at all, though it is marked on the pronoun. However, the main locus of number marking in Arafundi is the verb (Corbett 2000:137, after Nichols 1992:148-149 and personal communication with William Foley).

Among the different expressions of nominal number, three less common systems have been found. One has been referred to as inverse number, where the number marker changes the basic number meaning of the stem to which it is attached, in either direction, indicating the less expected number. This has been observed in Kiowa (or, Kiowa Apache, Athapaskan), Maasai (Nilotic), and several Oceanic languages. Inverse number expressed through agreement may lead to the phenomenon of polarity, which occurs when two markers are exponents of two features (gender and number). When the value of one feature is changed the marker changes, but if both values are changed the form stays the same, resulting in the polar opposites being identical. This is the case for some nouns in Somali (Cushitic). For details of these phenomena and references, see Corbett (2000:159-166). The second type of a less common number marking system has been referred to as minimal-augmented system (and another variant: minimal/ unit-augmented/ augmented system). This happens when a marker does not express number in an absolute sense, but when it expresses relative number, as is the case in several Australian languages. For example, in Rembarrnga the marker -bbarrah is used when there is one entity more than the logical minimum. This relative view of number only makes a difference in the expression of pronominal forms, and so it represents a different organisation of the morphology of person and number, not an alternative set of semantic distinctions for number (see Corbett 2000:166-169 and references therein). Finally, the third less common means of number expression has been referred to as constructed numbers. These occur where there is a mismatch between number marking of different elements which produces additional number values, for example the combination of a plural pronoun and singular verb gives a dual interpretation. Such a dual is 'constructed' from the number on the pronoun and the number on the verb, and the three-value number system (singular, dual, plural) is 'constructed' from the two parts. This is the case in Hopi (Uto-Aztecan), where the pronoun distinguishes singular from dual/plural and the verb distinguishes singular/dual from plural, but where animate nouns have a straightforward three-way distinction, indicated by three distinct markers. For other examples and references see Corbett (2000:169-171).

Apart from using different methods of expressing number, languages vary with regard to which of the number-differentiable nominals are involved in the number system. In English and similar languages, the majority of nominals mark number, from the personal pronouns and nouns denoting humans (e.g. teachers), through nouns denoting animates (e.g. pigs), nouns denoting inanimate objects (e.g. books), to some nouns denoting abstract entities (e.g. weeks). However, many languages restrict the expression of number to only a subset of their nominals. It has been observed that the sets of nominals involved in number distinctions in different languages relate to the animacy hierarchy. Smith-Stark (1974) proposed the first version of the animacy hierarchy relevant to number marking, having considered the marking of nominal phrases for plural number and agreement in plural number (mainly verbal agreement, but with some instances of agreement within the noun phrase). The following, updated version of the hierarchy is essentially Smith-Stark's, with the additional distinction of the third person pronouns:

Thus, if plurality is a significant opposition for some nominals but irrelevant for others, it 'splits' the language at some point of the animacy hierarchy (Smith-Stark 1974:657). For example, in Bengali the split is between pronouns and nouns: number is obligatory for pronouns, while other plural suffixes are optional (Masica 1991:225-226, cited in Corbett 2006b:726). Similarly, Quechua (a language of Peru) and Korean mark number only in the pronoun system (Cruse 1994:2859). In Bininj Gun-Wok (a large group of related dialects spoken in Western Arnhem Land, Australia), pronominal affixes on the verb mark number for humans but not normally for nonhumans (Evans 2003:234-235, 417-418, cited in Corbett 2006b:726). In Warrgamay (Australian, spoken in Queensland), number is not marked on the verb. Number marking of nominals is obligatory only in pronouns referring to humans (and occasionally tame dogs). First and second person pronouns can only refer to humans and have to be specified for number (singular, dual, or plural). The third person pronoun's dual and plural forms are also reserved for humans, and the number is expressed obligatorily. The form used as the third person singular pronoun is unmarked for number and can refer to all persons and all numbers, humans an non-humans (Dixon 1980:266-268, Dixon 1981:39-40, cited in Corbett 2006b:725). In Mundari (Afro-Asiatic, spoken in east India), verbs agree in number with all nominals on the hierarchy down to animates, but not with inanimates (Bhattacharya 1976:191-192, cited in Corbett 2006b:726). More examples of languages chosing different points on the hierarchy for the number-marking split can be found in Corbett (2000:54-66). Haspelmath (2005:142-145) provides information on the occurrence and obligatoriness of plural marking on nouns in 290 languages, all in accord with the animacy hierarchy. He suggests a possible further distinction within animates between 'higher' and 'lower' animals, in those languages where nouns referring to some animals pattern with humans and others with inanimates. Alternatively, this pattern of marking could be seen as extending 'personal' status to some, usually domesticated, animals. Finally, Haspelmath's suggestion of a possible further division within the category of 'Inanimate', into 'Discrete inanimates' and 'Nondiscrete inanimates', can be seen as corresponding to the 'count-mass' distinction discussed above in §1 which is responsible for the number differentiability of nouns in the first place.

The animacy hierarchy makes several correct predictions about number marking. The first one, discussed so far in this section, has been formulated as a constraint by Corbett (2000:56): 'The singular-plural distinction in a given language must affect a top segment of the animacy hierarchy'. Indeed, so far no languages have been found where number distinction would be relevant for a non-top segment of the animacy hierarchy, or where it would be additionally relevant for another segment of the hierarchy non-adjacent to the top segment. The second prediction concerns the relation of number marking on nouns and number agreement to the animacy hierarchy: 'Lexical items may be irregular in terms of number marking with respect to the animacy hierarchy and regular in terms of agreement, but not vice versa' (Corbett 2000:67). This means that syntactic tests (i.e. agreement) are found to match the hierarchy as well as or better than the morphological test (i.e. a marker, typically on the noun itself). Thus, the English noun sheep is not a counter-example to the hierarchy, since the agreement it triggers is regular (this sheep has..., these sheep have...). Furthermore, moving rightwards along the hierarchy, the different positions give increasingly regular results. The third prediction, formulated as a general constraint of the animacy hierarchy on number differentiation, is the following (Corbett 2000:70): 'As we move rightwards along the animacy hierarchy, the likelihood of number being distinguished will decrease monotonically (that is, with no intervening increase)'. This prediction is borne out in two different situations. First, it is true of languages where there is a sharp cut-off point between cases where number must be distinguished and those where it cannot; and second, it is true of languages where the difference is a matter of optional marking as opposed to no marking. So far, no languages have been found where number is optionally distinguished at a high point of the hierarchy and obligatorily distinguished at a lower point of the hierarchy (for the same type of marking). For detailed discussion of all the morphological effects of the animacy hierarchy, and examples, see Corbett (2000:54-78).

The animacy hierarchy also helps explain recategorisation effects (the ability of the noun to appear in either a 'count' or a 'mass' syntactic context, see §1). Generally, the lower the position on the hierarchy, the more readily available are recategorisation readings (since the 'normal' singular-plural opposition is typically not required). This means that recategorisation is the easiest with inanimates, and as we move up the hierarchy, it becomes progressively more difficult, requiring more and more special circumstances. This is true both of the recategorisation from mass to count (two coffees please, she offered three wonderful wines during dinner, small kindnesses), and of the recategorisation from count to mass (there was not enough table for everyone to sit at, there was dog all over the road) (Corbett 2000:78-87).

The committee-type nouns (i.e. the semantic category of nominal phrases referred to as 'groups' in §1) are singular morphologically and typically have a normal plural. However, when singular, they may take plural agreement (as in British English: the committee have decided). The fact that there is choice of agreement and a possible mismatch between the number marking on the noun and the marking on the verb (agreement) is due to the semantics of the noun. The pattern of agreement conforms to the agreement hierarchy (attributive < predicate < relative pronoun < personal pronoun): 'For any controller that permits alternative agreement forms, as we move rightwards along the agreement hierarchy, the likelihood of agreement with greater semantic justification will increase monotonically (that is, with no intervening decrease) (Corbett 2006a:207). For discussion of 'group' nouns in English and examples from other languages see Corbett (2000:187-191; 2006a:158-165, 206-237; 2006b:728-729).

Finally, there are also instances of the so-called verbal number (or, 'pluractionality') which relate to the semantics of the verb, and which occur when a concept akin to number is expressed by the verb to indicate (a difference in) the number of events or the number of participants. An example of event number can be found in Rapa Nui (Oceanic, spoken on Easter Island): ruku means 'dive', while ruku ruku 'go diving' expresses more than one dive, though not necessarily more than one diver, so it is the event which is 'plural'. An example of verbal number relating to the number of participants is found in Hiuchol (Uto-Aztecan, spoken in west-central Mexico), where a transitive verb has pronominal affixes according to subject and object, and the stem of the verb (typically glossed as 'singular' or 'plural') depends on participant number, that of the object of the transitive verb (the absolutive argument). Both event number and participant number have recently been reported for Itonama (a nearly extinct language isolate spoken in lowland Amazonian Bolivia), which is the first attested case of verbal number in South America (Crevels 2006). Verbal number of the participant type depends on the entity most directly affected by the event, and it may contrast with the nominal number marking on the verb. So far, no examples have been found of verbal number being expressed other than on the verb. Verbal number is usually restricted to relatively small numbers of verbs, and the most common means of its expression are the use of separate verbs (similar in meaning to the English kill versus exterminate), stem modification (usually reduplication or gemination), and derivational morphology. For details and references, see Corbett (2000:243-264), also Newman (2006:640-641).

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3. The status of 'number' as a feature

In order for a language to be considered to have the grammatical feature of number, it has to be possible for number to be recognised in the absence of numerals or other quantifiers. Therefore, the number system should not be confused with the numeral system in a language.

We will now consider nominal number. It is a morphosyntactic feature if it participates in agreement in the language, regardless of whether it is expressed on the controller (the noun/nominal element, or the noun phrase as such) or not. If number is expressed on the noun/nominal element or the noun phrase, but is not found affecting other elements of the clause, it is normally regarded a morphosemantic feature in the language.

Nominal number is inherent to nouns, and contextual to all other elements in the clause which express number due to agreement. On some nouns, number is lexically supplied - this is the case with nouns which have one lexically determined number value that they impose on the agreeing elements (e.g. English health, trousers). In other cases, where the nouns of a given language can be associated with different number values available in this language, number is semantically selected. In such languages, number (both inherent and contextual) is typically regarded as an inflectional feature if it is obligatory. However, in number systems with general number (see §4), number can be seen as derivational (Corbett 1999). Alternatively, all inherent number (i.e. number marked on nouns themselves, and on the nominal phrases as such) could be regarded as derivational, while all contextual number (i.e. number marked on other elements of the clause, through agreement) - as inflectional.

In those cases where verbal number is derivational (Corbett 1999:3, Durie 1986; Mithun 1988a, 1988b), and where two values can be distinguished, it is an inherent feature of the verb and may be regarded a morphosemantic feature. It is not a morphosyntactic feature, as no agreement effects of verbal number have yet been found.

One contemporary language has been reported not to have the category of number at all. It is Pirahã (the only remaining member of the Mura family; spoken along the Maici River in Amazonas, Brazil), which does not appear to have any plural forms, even in the pronouns. The ways of expressing the notion of plurality are by conjoining, the associative/comitative postposition, and various quantifiers. But there does not seem to be a grammatical feature of number (Corbett 2000:50-51, after Everett 1986, 1997). A similar situation has been reported for two ancient languages: Kawi (Old Javanese), and Classical Chinese.

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4. The values of 'number'

In order for a language to be considered to have a value of grammatical number, it has to be possible for that value to be recognised, either on nominal elements or through agreement, in the absence of a numeral or other quantifier. The following number values have been found (based on Corbett 2000; with thanks to Dunstan Brown for discussion of the definitions):

• Singular - quantifies the denotation of the nominal element by specifying that there is exactly 'one'. Additionally, but not necessarily, this value may be assigned on the basis of the formal properties of the nominal element (as in singularia tantum, e.g. health/*healths). Furthermore, if singular number functions as general number (see below), it may specify a lack of commitment with regard to quantification (e.g. in Japanese, see Corbett 2000:14, citing Bernard Comrie personal communication). The term 'singulative' is sometimes used for the concept 'singular', especially when the singular is overtly expressed; 'singulative' has also been used sometimes for 'singular' in systems where the singular is distinct from general number.
• Plural - quantifies the denotation of the nominal element by specifying that there are 'more than one'. Additionally, but not necessarily, this value may be assigned on the basis of the formal properties of the nominal element (as in pluralia tantum, e.g. *measle/measles). Furthermore, if plural number functions as general number (see below), it may specify a lack of commitment with regard to quantification. Corbett (2000:17) notes, however, that this system does not exist in pure form, that is, no language employs it as the normal case. For example, in Cushitic languages, general number can be the same as singular number for some nouns, but the same as plural number for other nouns (e.g. in Arbore, a Cushitic language spoken in Ethiopia, general number may contrast with the singular in the absence of a distinct plural form; see Corbett 2000:17-18 for examples and discussion). Finally, it is important to note that the meaning of plural number naturally varies according to the system in which it is embedded. That is, the term is used irrespective of whether a dual, trial or paucal is also present in the number system, and no terminological distinction is made to differentiate 'more than one', 'more than two', or 'more than three'. However, in languages which have a paucal, the number value expressing 'many entities', i.e. the concept 'plural', is sometimes called a 'multiple' (as has been the case e.g. in Fijian).
• Greater plural - this value is only found in languages which also have the value 'plural' (e.g. Arabic), hence it may be considered a further distinction within the plural. Greater plural expresses the fact that there is an excessive number of entities or events denoted by the nominal element (in which case it is sometimes called the 'plural of abundance'), or the fact or that the nominal element denotes all possible instances of the referent (in which case it is sometimes called the 'global plural').
• Dual - quantifies the denotation of the nominal element by specifying that there are exactly 'two' (as in Upper Sorbian, see Corbett 2000:20 for examples and discussion). Additionally, but not necessarily, this value may be assigned on the basis of the formal properties of the nominal element (as in dualia tantum, e.g. mangautek 'scissors' in the Yukon dialect of Central Alaskan Yupik; Jacobson 1984:226). The use of the dial varies across languages which have this value. In some languages, dual may be used to refer to any two entities, but in others it must refer to a natural pair such as eyes, and still in others it must refer to two items unless they are a natural pair (Corbett 2000).
• Trial - quantifies the denotation of the nominal element by specifying that there are exactly 'three' (e.g. Larike, see Corbett 2000:21 for examples and discussion).
• Paucal - quantifies the denotation of the nominal element by specifying that there is a 'small number' of distinct entities (i.e. the semantics of the paucal is similar to that of the English quantifier 'a few'). There is no specific upper bound in terms of numerosity that can be put on the use of the paucal, while its lower bound depends on whether there is a dual and trial in the system. In languages which make a further distinction within this category, the values have been referred to as 'paucal' and 'greater paucal'. Note also that what some linguistic traditions might call a 'quadral', is better analysed as paucal or greater paucal (see a brief discussion of quadrals in §6 below, 'Problem cases').
• Greater paucal - this value is only found in languages which also have the value 'paucal' (e.g. Sursurunga), hence it may be considered a further distinction within the paucal. The greater paucal quantifies the denotation of the nominal element by specifying that there is a 'small number' of distinct entities, greater than that expressed by the paucal, but smaller than that expressed by the plural (i.e. the semantics of the greater paucal is similar to that of the English quantifier 'several'). Note also that what some linguistic traditions might call a 'quadral', is better analysed as paucal or greater paucal (see also a discussion of quadrals in §6 below, 'Problem cases').
• General number - specifies a lack of commitment with regard to quantification over the denotation of nominal elements (Corbett 2000:9-19). There is a theoretical issue whether general number is a value of the number feature, or whether it is outside the number system and specifies that the number feature is not realised (i.e. the whole category of number is optional in such languages). On Corbett's (2000) analysis, since in many languages the absence of plural marking does not necessarily imply the singular, the form for 'general number' may express the meaning of the noun without reference to number (as in Cushitic) and may therefore be outside the number system. In some languages (e.g. Baiso, Cushitic), the general number may have a unique form. However, separate coding for general number is very rare, as it is normally realised by one of the other feature values (usually the singular).

The minimal number system consists of two values: singular and plural. All other number systems are built on this primary opposition.

A common system is one in which these two values are supplemented by a dual - for example, in Upper Sorbian (West Slavonic) or Central Yupik (spoken in Alaska). It is important to note that the addition of any other value to the system has an effect on the plural - it gives the plural a different meaning. Thus, if the system is singular-dual-plural, the plural is used to express 'three or more'. Furthermore, the use of a dual may be non-obligatory or subject to restrictions. For example, the dual in Kxoe (Central Khoisan, spoken in Namibia), when used with reference to a man and his wife, is an insult as it implies that they are together by chance; instead, the plural is used in this situation.

The trial occurs in systems with the number values: singular, dual, trial, plural - for example, in Larike (Malayo-Polynesian, spoken in Indonesia), Ngan'gityemerri (a dialect of Nangikurrunggur, Australian) and some other Australian languages. The dual and trial forms in Austronesian can frequently be traced back to the numerals 'two' and 'three', and the plural to the numeral 'four'. However, in many of those languages the connections are only diachronic, and the 'trial' form synchronically has the function of a paucal. However, in Larike it is strictly a trial.

The paucal has been found in the following systems: singular, paucal, plural - though such systems are rare, one has been found in Baiso (Cushitic, spoken in Ethiopia); singular, dual, paucal, plural - this widespread system is found, for example, in Fijian and many other Oceanic languages, in some Australian languages, in Yimas (Sepik-Ramu, Papua New Guinea), Murik (Malayo-Polynesian), and Meriam (or, Miriam, Trans-Fly family, spoken in Eastern Torres Strait Islands, Australia) mentioned earlier in §2; singular, dual, trial, paucal, plural - this system is found in Lihir (Oceanic, spoken in Papua New Guinea), although the status of the trial in this language is uncertain; if it is not a strict trial, then the system may be the following: singular, dual, paucal, greater paucal, plural; this system is also found in Sursurunga and Tangga (both Oceanic, Papua New Guinea), and Marshallese (also Oceanic, spoken on Marshall Islands) (see §6 'Problem cases' below for a discussion of the question of the quadrals). The five-value systems listed above are the largest number systems that have been documented.

In many number systems, certain numbers are facultative - that is, their choice is optional and, when it is not taken, the plural is used in its place (for detailed discussion of facultative number see Corbett 2000:42-50).

Finally, in minimal-augmented systems (and minimal/ unit-augmented/ augmented systems), which have an inclusive/exclusive distinction in the first person, the number values dual and trial are expressed only on the first person inclusive by using the morphology otherwise associated with the singular and the dual, respectively (even though the semantics of first person inclusive entail that it cannot be singular). There is an analysis of this (mentioned in §2 above) in which the morphology is seen as representing the minimal number associated with the particular person value. Under such a system, the label 'minimal' can be seen as corresponding to the concept 'singular', except if one is dealing with first person inclusive minimal, which would be corresponding to the concept 'dual' (Corbett 2000:166-169). Therefore, it is possible to specify a mapping from a minimal-augmented system (or a minimal/ unit-augmented/ augmented system) to a regular number system such as the one outlined above, and avoid postulating additional number values (again, thanks to Dunstan Brown for discussion of this issue).

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5. Oddly behaving number markers

Korean has a very interesting plural marker, -tul, which may have additional meanings depending on where it occurs (Corbett 2000:137-138, after Song 1975, and Lee 1991). It may be found on the noun, where it is not obligatory and its presence depends on definiteness (definite noun phrases are likely to have the head noun marked for number) and on the animacy hierarchy (nouns denoting humans and other animates are much more likely to be marked for number than inanimates). It may also occur in the predicate, where it may appear on almost any element of the clause (for example, apart from the subject, it may appear on the verb, the object, the indirect object, and even separately on the modifier or quantifier of the object). The occurrence of the plural marker in the predicate is not obligatory, but it is not redundant. It indicates that the constituent to which it is attached expresses new information (Lee 1991:83), and it imposes a distributive reading (Song 1997), while the lack of the marker means that the clause is ambiguous with respect to the distributive/collective distinction. For more references of the literature on this construction and on number in Korean, see Corbett (2000:138).

Other uses of number. The regular expression of number may be taken over for purposes other than its normal meaning. There are three broad grups of these other uses: honorific uses (to indicate respect), unexpected uses in the general area of conjoining, and various affective uses (such as the exaggerative, the intensificative, the approximative, the evasive, and the anti-associative) (Corbett 2000:219-242).

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6. Problem cases

Interrelation between number and person: the question of the associative. When we consider the meaning of the pronouns I versus we, it is clear that here we have an associative use of the plural, as we is most often used for 'I and other(s) associated with me' (Moravcsik 2003, Corbett 2005). In English, the associative use is available only for the items at the very top of the animacy hierarchy. The associative is best considered a separate category (see Corbett 2000:101-111; also the entry on 'Associativity' in this Inventory).

Distributives and collectives are sometimes listed as additional values along the same dimension as singulars and plurals, but the evidence suggests that they should not be considered additional values comparable with the basic number values, nor subdivisions of these. Rather, they are different categories, like associatives (Corbett 2000:111-120).

Acehnese (Malayo-Polynesian, spoken on Sumatra, Indonesia) has been suggested as a language lacking the category of number, but it has number just in the first person (Corbett 2000:§3.2.4.3).

No clear case of a quadral has been found (Corbett 2000:26-30), meaning a value of grammatical number that quantifies the denotation of the nominal element by specifying that there are exactly 'four'. The quadral has been used in the description of at least three languages from the Austronesian family. A well-documented suggested case is Sursurunga (Oceanic, Papua New Guinea; Hutchisson 1986, and personal communications). The forms labelled quadral are restricted to the personal pronouns, but are found with all of them: the first person (inclusive and exclusive), the second and the third. However, besides being used of four, the quadral has two other uses which account for most of its instances. First, plural pronouns are never used with terms for dyads (kinship pairs like uncle-nephew/niece) and the quadral is then used instead for a minimum of four, and not just for exactly four. The second additional use is in hortatory discourse; the speaker may use the first person inclusive quadral, suggesting joint action including the speaker, even though more than four persons are involved. Thus, if the values of number are based on meaning, the quadral forms should be considered paucal rather than quadral.

Similarly, the suggested trial in Sursurunga is also used for small groups, typically around three or four, and for nuclear families of any size. It is therefore not strictly a trial - rather, it could be glossed as 'a few' and also qualify as a paucal. The traditional quadral, then, which is frequently used with larger groups of four or more, and could be glossed as 'several', is in fact a greater paucal, and the traditional trial is a (normal/lesser) paucal. The plural, as we would expect, is for numbers of entities larger than are covered by the quadral (though there is no strict dividing line at any particular number), and the number system of Sursurunga can be represented as: singular, dual, paucal, greater paucal, and plural.

The other two languages for which the quadral has been claimed can be analysed along the same lines. Tangga, closely related to Sursurunga, (Capell 1971:260-262; Beaumont 1976:390; confirmed by Malcolm Ross, personal communication) also has five number forms, and it seems clear that the forms which have the numeral 'four' as their source are not quadrals but rather paucals (Malcolm Ross, personal communication citing Maurer 1966; this is also Schmidt's view given in Capell 1971:261). Unfortunately, we have no information on whether Tangga has a genuine trial or whether it has two paucals. Marshallese, more distantly related to Sursurunga, with five number forms for the first, second and third person pronouns (Bender 1969:8-9), also has an additional use of the quadral form: it is often used rhetorically with groups of more than four to give an illusion of intimacy (Bender 1969:159). Again, then, this may not be strictly a quadral.

Finally, there are several false trails in the literature regarding quadrals - that is, suggestions of other Austronesian languages with quadrals - which turn out in fact to have four number values not five. In such cases, the plural may have a form in which the numeral four can be reconstructed. Thus, we have found no clear case of a quadral, by which we mean a grammatical form for referring to four distinct entities in the way that trials refer to three.

Can number be a feature of government? As with gender, we have not found instances of number as a feature of government. And similarly, there are instances of a number value found on elements which normally have to agree in number with a controller, but the controller is absent. The example that is cited for gender (see the entry on 'Gender' in this Inventory) also illustrates the assignment of a default number value. In Polish, when a predicate adjective is used in nominalisation (as in 'being happy') or a predicate adjective is a complement of an infinitive, it has to appear in instrumental case, singular number, and masculine/neuter gender:

Since the adjective has to express gender and number, in a situation where there is no controller that could dictate its gender and number, it shows 'default agreement', which is typically 'third person singular neuter'. Hence, instances of adjectives expressing number, which have no controller for number, are not instances of government but of default agreement in number.

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7. Key literature

• Corbett, Greville G. 2000. Number. Cambridge: CUP.
• Corbett, Greville G. 2006. Number. In: Brown, Keith (ed.) The Encyclopedia of Language and Linguistics. 2nd Edition. Oxford: Elsevier. 724-731.
• Newman, Paul. 2006. Pluractionals (Distributives). In: Brown, Keith (ed.) The Encyclopedia of Language and Linguistics. 2nd Edition. Oxford: Elsevier. 640-641.

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