A (de)numeral is adapted (i) if its form and/or structure is that of the corresponding (de)numeral in a foreign (source) language; and (ii) if it has been shaped to fit the (morpho)phonological requirements of the target language e.g. fra quadragénaire < lat quadragenarius ‘which contains 40 items; who is 40 years old’. Adapted denumerals are always adapted borrowings. These adapted words must be distinguished from words that are inherited, the form of which results from historical changes. In the website, ‘Adaptation <language>’ is a value of feature ‘Origin’, where ‘language’ indicates the name of the source language (when it is known).
Appellative denumeral
A crucial property of some entities is their being composed of n elements, repeated n times, etc. Appellative denumerals are nouns which denote entities exhibiting this numerical property, e.g. rus troj-ka ‘team of 3 (horses, people, airplanes, etc.) acting together’. Appellatif (appellative) is the denomination chosen by Tesnière for this type of denumerals (Tesnière 1934:73).
Approximative denumeral
Denumeral noun which denotes an approximate number of elements e.g. fra une vingt-aine de personnes 'about 20 people'.
Borrowing
A numeral or denumeral is borrowed if its form comes from a foreign language without any change or with a minimal phonological change imposed by the target language’s phonotactics e.g. fra quatuor ‘quartet’ < lat quattuor, rus sorok ‘forty’ (from Turkic through Old East Slavic), jap zero ‘zero’ < eng zero. In the present database, borrowed denumerals always correspond to borrowings in this strict sense. ‘Borrowing <language>’ is a value of feature ‘Origin’, where ‘language’ indicates the name of the source language (when it is known).
Cardinal number
In mathematics, cardinal numbers are a generalization of the natural numbers used to give the size (cardinality) of a set. The cardinality of a finite set is the number of elements in the set. Natural numbers are those used for counting (as in "there are 3 apples in the basket") and ordering (as in "the 11th page of the book"). In everyday language, cardinal numbers are the expressions used for counting and correspond to what we call here cardinal numerals (or simply Numbers, see Numeral below) here.
Collective denumeral
A collective numeral is a numerical expression used for denoting groupings of entities (Ojeda 1997, 1998). The term collective denumeral is relevant because collective numerals are denumeral in most languages e.g. isl tvennir sokkar ‘two pairs of socks’ compared to tveir sokkar ‘two socks’ (cardinal).
Counting vs. enumerating or reciting
“The numeral which is used to quantify a noun in an NP is not necessarily the same form as the corresponding numeral in the conventional recited counting sequence” (Hurford 2003 : 664). The distinction pinpointed by Hurford has been observed in few languages surveyed in the project.
The most basic use of numerals is counting. To know the number of apples that lie in a basket, one must count them. The outcome is a cardinal number, which indicates to the size of the set of apples (in the basket) e.g. ‘13’. To subsequently mention the number of apples, one can use an NP that includes a cardinal numeral quantifying the number of apples in question e.g. the 13 apples, these 13 apples. Hurford (2003 : 566) speaks of “attributive” use or form of numerals in this case. Insofar as the function of numerals in these constructions stems from a counting activity and expresses the cardinality of a set, these numerals will be included under the heading ‘counting (activity)’ or ‘counting numerals’ in the database. On the other hand, when numerals are enumerated or recited, in a way that follows the order of natural numbers and without the goal of counting anything, we will speak of the reciting use of numerals.
In several languages, numerals used in counting and reciting are not the same; the phenomenon is generally limited to the first numerals of the cardinal series. Here are a few examples for 1, 2, 3: rus counting = odin, dva, tri; reciting raz, dva, tri; deu counting ein, zwei, drei; reciting eins, zwei, drei; hun counting egy, két, három; reciting egy, kettő, három. Note that the reciting forms may also appear in specific constructions expressing counting in German and Hungarian (and other languages probably). It is important to keep in mind that there are languages (Thulung) where speakers are perfectly able to recite long lists of cardinal numerals even though these numerals are never, or very rarely, used in counting contexts.
Denumeral
A denumeral is a morphologically complex lexeme that is formed from a numeral e.g. fra quatr-ain ‘quatrain’ ← quatre ‘four’, eng ten-th ← ten.
Distributive denumeral
(see Gil (2013a)) Distributivity is a binary semantic relationship involving an expression denoting what is distributed (the distributed share), and another expression specifying the domain of elements affected by the distribution (the distributive key) (Cabredo-Hofherr & Etxeberria 2016). The range of meanings results from different choices of distributive key. Distributivity can be expressed syntactically e.g. ron copii au auscultate câte două cântece children:def have listened distr two songs ‘(the) children [key] listened (to) two songs [share] per child’ or morphologically e.g. eus umeek bi-na liburu irakurri zituzten children:def.erg two-distr books read aux ‘(the) children [key] read two books [share] each’ in accordance with the formula share per key. Only for the morphological expression of distributivity do we speak of distributive (de)numeral. Distributive denumerals embody morphological distributivity.
Element counting denumerals (subpartitive denumerals)
These denumerals are adjectives which indicate the number of units that make up the referent of the N they modify e.g. codage bin\aire coding two\sfx ‘binary coding’ (= code with 2 elements), cycle duodénaire ‘cycle of twelve years’.
Exhibitive denumerals
These are nouns denoting an entity which is explicitly correlated with a particular Number e.g. bul dvoj-ka karo ‘2 (of) diamonds’. They can be considered as an extreme variety of appellative denumerals.
Factorization of numerals
(see Comrie (2013)) Factorization is the decomposition of linguistic expressions for numerals according to the (arithmetic) base that is used in constructing numeral expressions on the one hand, and of the simple names for Numbers that are available in the language on the other. The base is the value n in the pattern ‘xn + y’: numeral x is multiplied by n before the addition of some other numeral. The order of elements varies from language to language and according to practices of multiplication and addition (and very rarely substraction). For instance, numeral 100,085 is decomposed differently in French and Japanese: fra cent mille quatre-vingt-cinq 100 × 103 + ((4 × 20) + 5), jap juu-man-hachi-juu-go 10 × 104 + ((8 × 10) + 5) (man = 10,000).
Fractional numerals
Fractional numerals are two-part expressions involving a numerator and a denominator. While the numerator is always a cardinal numeral, the denominator is generally a denumeral constructed either from a cardinal or an ordinal e.g. ces jedna sedm-ina ‘1/7’ ← sedm ‘7’.
A lexeme formation system is homolexical if the units used as inputs belong to the native lexicon. If these units are borrowed or adapted from a foreign language in a massive and systematic way, the system is said to be heterolexical. This is the case in languages such a Burmese, Korean and Japanese, which exhibit two series of (de)numerals for some intervals. By default, languages are assumed to be homolexical, something denoted in the database by the value ‘indigenous’ for the feature ‘Origin’. For heterolexical languages, the value of this feature is the name of the language that is the source of the borrowed units.
Multiplicative denumeral
These denumerals denote the number of times something happens e.g. ndl vier-maal / vier-voud ‘4 times’.
Naming series of numerals
The following denominations have been chosen for each series of numerals / numbers that corresponds to the relevant intervals:
(i) 1-9 (one digit): expressions denoting numerals with one digit (including zero). In most languages, these are simple lexical numerals (Hurford 2003). They have been called simple numerals here.
(ii) 10-90 (two digits): series of tens (série des dizaines) = series (i) with each figure multiplied by 10 and to which simple numerals (addends) have been added. These numerals constitute serialized augends (Greenberg 2000), as do all series from (iii) to (v) mentioned below.
(iii) 100-900 (three digits): series of hundreds (série des centaines) = series (i) with each figure multiplied by 100 and to which simple numerals or (numerals from the series of) tens have been added.
(iv) 1000-9000 (four digits): series of thousands (série des mille) = series (i) with each figure multiplied by 1000 and to which simple numeral, tens and/or hundreds have been added.
(v) 10,000-90,000… (five to n digits): series of ten (hundred…) thousands = series (i) with each figure multiplied by 10,000, 100,000, etc. and to which simple numerals, tens, hundreds, and/or thousands, etc. have been added.
There is a sub-series that needs to be distinguished because some languages deal with it in a specific way (nêlêmwa), although they generally lack an appropriate term to refer to it: this is the initial sub-part of series (ii), that will be called ‘first series of tens’ in the present database.
The series of tens includes not only round Numbers, which are serialized augends such as 10, 20, 30, 40, 50, etc., but also these Numbers with an addend, such as 21, 33, 35, 42, etc. The same holds for hundreds, thousands and larger numbers. To name Numbers of this latter type, we use ‘numerals of the second tens’ (e.g. 21), ‘numerals of the third hundred’ (e.g. 349), ‘numerals of the fifth hundred’ (e.g. 537), and so on.
Numeral / number
Following Huddleston & Pullum (2002), the term numeral is used for linguistic expressions (five) and number for meanings (‘5’). However, for reasons of convenience, the term Number is sometimes used for cardinal numbers and ‘numeral n’ abbreviates ‘numeral denoting Number n’ (Number 12 denotes ‘12’).
Numeration base
This is the numerical base used for counting in a given language. A language may have several numerical bases, with typical bases being 5, 10, 20, although most languages have only one.
Ordinal numeral
(see Stolz & Urdze 2005; Stump 2010) An ordinal numeral is a numerical expression used for ordering (as in "the second page of the book"). Ordinal numerals correspond to what is called ordinal numbers in everyday language. In most languages, ordinal numerals are denumeral.
Simple / complex numeral
Simple numerals are those that cannot be formed by the productive morphological patterns that are used to create complex numerals in the language in question. This view leads us to consider as simple both forms that have been inherited e.g. fra cinquante ‘fifty’ and former derivations from older stages of the language which are no longer transparent e.g. eng twelve, thrice. Complex numerals are those that are not simple e.g. eus hiru-garren three-ord 'third'.
Syntatics
(see Dryer (2013), Gil (2013b)) Syntactics is the set of syntactic (and more generally combinatorial Mel'čuk (1993: 117) structures permitted by the grammar of a given language. For (de)numerals, syntactics specifies the syntactic patterns a given (type of) (de)numeral occurs in.
Age specifying denumeral
Adjectival denumerals specially used to indicate the number of years that the modified N’s referent has been lasting or existing, e.g. fra concession trentenaire ‘concession that lasts 30 years’, maison centenaire ‘100-year-old house’, vieillard septuagénaire ‘seventy-year-old man’. In some languages, these denumerals have may a nominal use e.g. fra club de dix-septenaires ‘club for seventeen-year-old people’, in others a specific nominal denumeral is used for this purpose e.g. ita Un undic-enne cinese ‘an eleven-year old Chinese (boy)’.
References
Cabredo Hofherr Patricia & Urtzi Etxeberria. 2016. Distributive numerals in Basque. In Cremers Alexandre, Thom van Gessel & Floris Roelofsen (eds), Proceeding of the 21st Amsterdam Colloquium, 185-194. Amsterdam: University of Amsterdam. (http://events.illc.uva.nl/AC/AC2017/Proceedings/) (July 2018.)
Comrie Bernard. 2013. Numeral Bases. In Dryer Matthew S. & Martin Haspelmath (eds), The World Atlas of Language Structures Online, Available online athttp://wals.info/chapter/131, Accessed on 2019-02-08. Leipzig: Max Planck Institute for Evolutionary Anthropology.
Dryer Matthew S. 2013. Order of Numeral and Noun. In Dryer Matthew S. & Martin Haspelmath (eds), The World Atlas of Language Structures Online, Available online at http://wals.info/chapter/54, Accessed on 2019-02-08. Leipzig: Max Planck Institute for Evolutionary Anthropology.
Fradin Bernard. 2015. Denumeral categories. In Muller Peter O., Ingeborg Ohnheiser, Susan Olsen & Franz Rainer (eds), Handbook of Word-Formation, Vol. 2, 1515-1528. Berlin / New York: Mouton de Gruyter.
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Gil David. 2013b. Numeral Classifiers. In Dryer Matthew S. & Martin Haspelmath (eds), The World Atlas of Language Structures Online, Available online at //wals.info/chapter/55,Accessed on 2015-03-23.: Leipzig: Max Planck Institute for Evolutionary Anthropology.
Greenberg Joseph H. 2000. Numeral. In Booij Geert, Christian Lehmann & Joachim Mugdan (eds), Morphologie Morphology. Ein internationales Handbuch zur Flexion und Wortbildung An International Handbook on Inflection and Word-Formation, Vol. 1, 771-783. Berlin / New York: Walter de Gruyter.
Huddleston Rodney & Geoffrey K. Pullum (eds) 2002. The Grammar of the English Language. Cambridge: Cambridge University Press.
Hurford James R. 2003. The interaction between numerals and nouns. In Plank Frans (ed), Noun Phrase Structures in the Languages of Europe, 561-620. Berlin / New-York: Mouton de Gruyter.
Mel'čuk Igor A. 1993. Cours de morphologie générale. Première partie: le mot. 5 vols. (Vol. 1. Montréal: Presses de l'Université de Montréal - CNRS Editions.
Ojeda Almerindo E. 1997. A Semantics for the Counting Numerals of Latin. Journal of Semantics 14 (2):143-171.
Ojeda Almerindo E. 1998. The semantics of collectives and distributives in Papago. Natural Language Semantics 6 (3):245-270.
Stolz Thomas & Aina Urdze. 2005. Ordinal numerals. In Haspelmath Martin, Matthew S. Dryer, David Gil & Bernard Comrie (eds), The World Atlas of Language Structures. Oxford: Oxford University Press. (http://wals.info/chapter/53)
Stump Gregory T. 2010. The derivation of compound ordinal numerals: Implications for morphological theory. Word Structure 3 (2):205-233.
Tesnière Lucien. 1934. Petite grammaire russe. Edition 1964. Paris: Didier.