Numeral (linguistics): Difference between revisions

In linguistics, a '''numeral''' in the broadest sense is a [[word]] or [[phrase]] that describes a numerical [[quantity]]. Some theories of [[grammar]] use the word "numeral" to refer to [[cardinal number]]s that act as a [[determiner]] that specify the quantity of a [[noun]], for example the "two" in "two hats". Some theories of grammar do not include determiners as a part of speech and consider "two" in this example to be an [[adjective]]. Some theories consider "numeral" to be a [[synonym]] for "number" and assign all numbers (including [[Ordinal numeral|ordinal numbers]] like the [[compound word]] "seventy-fifthfirst") to a [[part of speech]] called "numerals".<ref>Charles Follen: ''A Practical Grammar of the German Language''. Boston, 1828, p.&nbsp;9, p.&nbsp;44 and 48. Quote: "PARTS OF SPEECH. There are ten parts of speech, viz. Article, Substantive or Noun, Adjective, Numeral, Pronoun, Verb, Adverb, Preposition, Conjunction, and Interjection.", "NUMERALS. The numbers are divided into cardinal, ordinal, proportional, distributive, and collective. [...] Numerals of proportion and distribution are [...] &c. ''Observation.'' The above numerals, in fach or fäl´tig, are regularly declined, like other adjectives."</ref><ref>Horace Dalmolin: ''The New English Grammar: With Phonetics, Morphology and Syntax'', Tate Publishing & Enterprises, 2009, p.&nbsp;175 & p.&nbsp;177. Quote: "76. The different types of words used to compose a sentence, in order to relate an idea or to convey a thought, are known as parts of speech. [...] The parts of speech, with a brief definition, will follow. [...] 87. Numeral: Numerals are words that express the idea of number. There are two types of numerals: ''cardinal'' and ''ordinal''. The cardinal numbers (''one, two, three...'') are used for counting people, objects, etc. Ordinal numbers (''first, second, third...'') can indicate ''order, placement'' in ''rank'', etc."</ref> Numerals in the broad sense can also be analyzed as a noun ("three is a small number"), as a [[pronoun]] ("the two went to town"), or for a small number of words as an [[adverb]] ("I rode the slide twice").

Numerals can express relationships like quantity (cardinal numbers), [[sequence]] (ordinal numbers), [[frequency]] (once, twice), and part ([[fraction]]).<ref name=GloL>{{Cite web|url=http://www-01.sil.org/linguistics/glossaryoflinguisticterms/WhatIsANumeral.htm|title=What is a numeral?|access-date=2017-03-06|archive-date=2016-11-25|archive-url=https://web.archive.org/web/20161125083926/http://www-01.sil.org/Linguistics/GlossaryofLinguisticTerms/WhatIsANumeral.htm|url-status=live}}</ref>

{{Redirect-distinguish|collective numeral|collective number|collective noun}}

Numerals may be [[attributive]], as in '''''two''' dogs'', or [[pronominal]], as in ''I saw '''two''' (of them)''.

Many words of different parts of speech indicate number or quantity. Such words are called [[quantifier (linguistics)|quantifier]]s. Examples are words such as ''every'', ''most'', ''least'', ''some'', etc. Numerals are distinguished from other quantifiers by the fact that they designate a specific number.<ref name=GloL/> Examples are words such as ''five, ten, fifty, one hundred, etc.'' They may or may not be treated as a distinct part of speech; this may vary, not only with the language, but with the choice of word. For example, "dozen" serves the function of a [[noun]], "first" serves the function of an [[adjective]], and "twice" serves the function of an [[adverb]]. In [[Old Church Slavonic]], the cardinal numbers 5 to 10 were feminine nouns; when quantifying a noun, that noun was [[Declension|declined]] in the genitive plural like other nouns that followed a noun of quantity (one would say the equivalent of "five '''of''' people"). In English grammar, the classification "''numeral''" (viewed as a [[part of speech]]) is reserved for those words which have distinct grammatical behavior: when a numeral modifies a noun, it may replace the [[article (grammar)|article]]: '''''the/some''' dogs played in the park'' → '''''twelve''' dogs played in the park''. (*'''''dozen''' dogs played in the park'' is not grammatical, so "dozen" is not a numeral in this sense.) English numerals indicate [[cardinal number (linguistics)|cardinal numbers]]. However, not all words for cardinal numbers are necessarily numerals. For example, ''million'' is grammatically a noun, and must be preceded by an article or numeral itself.

In linguistics, however, numerals are classified according to purpose: examples are [[ordinal number (linguistics)|ordinal number]]s (''first'', ''second'', ''third'', etc.; from 'third' up, these are also used for fractions), [[Adverbial number|multiplicative (adverbial) numbers]] (''once'', ''twice'', and ''thrice''), [[multiplier (linguistics)|multipliers]] (''single'', ''double'', and ''triple''), and [[distributive number]]s (''singly'', ''doubly'', and ''triply''). [[Georgian language|Georgian]],<ref>{{cite web| url = http://wals.info/feature/description/| title = Walsinfo.com}}{{DlinkDead link|date=August 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> LandLatin, and Romanian (see [[Romanian numbers#Distributive numbers|Romanian distributive numbers]]) have regular [[distributive number]]s, such as Latin ''singuli'' "one-by-one", ''kbini'' "in pairs, two-by-two", ''terni'' "three each", etc. In languages other than English, there may be other kinds of number words. For example, in Slavic languages there are [[English numerals#Collective numbers|collective numbers]] (monad, pair/dyad, triad) which describe sets, such as ''pair'' or ''dozen'' in English (see [[Russian numerals]], [[Polish numerals]]).

Some languages have a very limited set of numerals, and in some cases they arguably do not have any numerals at all, but instead use more generic quantifiers, such as 'pair' or 'many'. However, by now most such languages have borrowed the numeral system or part of the numeral system of a national or colonial language, though in a few cases (such as [[Guarani language|Guarani]]<ref>{{Cite web|title=Numbers in Guaraní (Papapy Avañe'ême)|url=https://omniglot.com/language/numbers/guarani.htm|access-date=2021-06-11|website=omniglot.com|archive-date=2021-06-11|archive-url=https://web.archive.org/web/20210611191500/https://omniglot.com/language/numbers/guarani.htm|url-status=live}}</ref>), a numeral system has been invented internally rather than borrowed. Other languages had an indigenous system but borrowed a second set of numerals anyway. An example is [[Japanese numerals|Japanese]], which uses either native or Chinese-derived numerals depending on what is being counted.

In many languages, such as [[Chinese numerals|Chinese]], numerals require the use of [[numeral classifier]]s. Many [[sign language]]s, such as [L[American Sign Language|ASL]], [[Incorporation (linguistics)|incorporate]] numerals.

In many languages, numerals up to the base are a distinct [[part of speech]], while the words for powers of the base belong to one of the other word classes. In English, these higher words are [[hundred (word)|hundred]] 10², [[thousand]] 10³, [[million]] 10⁶, and higher powers of a thousand ([[short scale]]) or of a million ([[long scale]]—see [[names of large numbers]]). These words cannot modify a noun without being preceded by an article or numeral (*''hundred dogs played in the park''), and so are nouns.

| align="right" | 0 ||[[Names for the number 0|Zero]]|| aught, cipher, cypher, donut, dot, duck, goose egg, [[Tennis score#Scoring a game|love]], nada, naught, nil, none, nought, nowt, null, ought, oh, squat, zed, zilch, zip, zippo, Sunya ([[Sanskrit]])

| align="right" | 1 || One || ace, individual, single, singleton, unary, unit, unity, Pratham ([[Sanskrit]])

| align="right" | 100 || One hundred || centred, century, ton, [[long hundred|short hundred]]

| align="right" | 120 || One hundred [and] twenty || [[long hundred]],<ref name="ShipAssistant" /> great hundred, ''(obsolete)'' hundred

The following table details the myriad, octad, Ancient Greek Archimedes's notation, Chinese myriad, Chinese long and -yllion names for powers of 10.

There is also a [[Donald E. Knuth|Knuth]]-proposed system notation of numbers, named the -yllion system.<ref>{{Cite web|title=Large Numbers (page 2) at MROB|url=http://mrob.com/pub/math/largenum-2.html#yllion|access-date=2020-12-23|website=mrob.com|archive-date=2012-02-13|archive-url=https://web.archive.org/web/20120213070143/http://mrob.com/pub/math/largenum-2.html#yllion|url-status=live}}</ref> In this system, a new word is invented for every ''2ⁿ''-th power of ten. <!-- This Anchor tag serves to provide a permanent target for incoming section links. Please do not modify it, even if you modify the section title. -->

! Value !! Myriad System Name !! Octad System Name !! Ancient Greek Myriad Scale !! [[Chinese numerals#Large numbers|Chinese Myriad Scale]]!! Chinese Long Scale !!Knuth-[[-yllion|proposed]]<br>System Name

| align="center" | Second Myriadmyriad

| align="center" | Myriad Octadoctad

| 萬億 (万亿)

| align="center" | Eleventh Octadoctad

Not all peoples use [[Counting|counting]], at least not verbally. Specifically, there is not much need for counting among hunter-gatherers who do not engage in commerce. Many languages around the world have no numerals above two to four (if they are actually numerals at all, and not some other part of speech)—or at least did not before contact with the colonial societies—and speakers of these languages may have no tradition of using the numerals they did have for counting. Indeed, several languages from the Amazon have been independently reported to have no specific number words other than 'one'. These include [[Nadahup languages|Nadëb]], pre-contact [[Mocoví language|Mocoví]] and [[Pilagá language|Pilagá]], [[Culina-Madijá language|Culina]] and pre-contact [[Jarawara language|Jarawara]], [[Jabutí language|Jabutí]], [[Canela language|Canela-Krahô]], [[Botocudo|Botocudo (Krenák)]], [[Chiquitano language|Chiquitano]], the [[Campa languages]], [[Arabela language|Arabela]], and [[Jivaroan languages|Achuar]].<ref>{{Cite web |url=http://www2.gslt.hum.gu.se/dissertations/hammarstrom.pdf |title=Hammarström (2009, page 197) "Rarities in numeral systems" |access-date=2010-06-16 |archive-url=https://web.archive.org/web/20120308070048/http://www2.gslt.hum.gu.se/dissertations/hammarstrom.pdf |archive-date=2012-03-08 |url-status=dead }}</ref> Some languages of Australia, such as [[Warlpiri language|Warlpiri]], do not have words for quantities above two,<ref>UCL Media Relations, [http://www.ucl.ac.uk/media/library/aboriginal "Aboriginal kids can count without numbers"] {{Webarchive|url=https://web.archive.org/web/20180620234700/http://www.ucl.ac.uk/media/library/aboriginal |date=2018-06-20 }}</ref><ref>{{cite journal |last1=Butterworth |first1=Brian |last2=Reeve |first2=Robert |last3=Reynolds |first3=Fiona |last4=Lloyd |first4=Delyth |title=Numerical thought with and without words: Evidence from indigenous Australian children |journal=PNAS |date=2 September 2008 |volume=105 |issue=35 |pages=13179–13184 |doi=10.1073/pnas.0806045105 |pmid=18757729 |pmc=2527348 |bibcode=2008PNAS..10513179B |quote=[Warlpiri] has three generic types of number words: singular, dual plural, and greater than dual plural. |doi-access=free }}</ref><ref>The Science Show, [http://www.abc.net.au/rn/scienceshow/stories/2008/2375526.htm Genetic anomaly could explain severe difficulty with arithmetic] {{Webarchive|url=https://web.archive.org/web/20100301113203/http://www.abc.net.au/rn/scienceshow/stories/2008/2375526.htm |date=2010-03-01 }}, Australian Broadcasting Corporation</ref> and neither did many [[Khoisan languages]] at the time of European contact. Such languages do not have a word class of 'numeral'.

Many languages of [[Melanesia]] have (or once had) counting systems based on parts of the body which do not have a numeric base; there are (or were) no numerals, but rather nouns for relevant parts of the body—or simply pointing to the relevant spots—were used for quantities. For example, 1–4 may be the fingers, 5 'thumb', 6 'wrist', 7 'elbow', 8 'shoulder', etc., across the body and down the other arm, so that the opposite little finger represents a number between 17 ([[Torres Strait Island languages|Torres Islands]]) to 23 ([[Eleman language|Eleman]]). For numbers beyond this, the torso, legs and toes may be used, or one might count back up the other arm and back down the first, depending on the people.{{cn|date=August 2024}}

Quaternary systems are based on the number 4. Some [[Austronesian peoples|Austronesian]], [[Melanesians|Melanesian]], [[Sulawesi]], and [[Papua New Guinea]] ethnic groups, count with the base number four, using the term ''asu'' or ''aso'', the word for [[dog]], as the ubiquitous village dog has four legs.<ref name="Ryan, Peter p&nbsp;219">Ryan, Peter. ''Encyclopaedia of Papua and New Guinea''. Melbourne University Press & University of Papua and New Guinea,:1972 {{isbn|0-522-84025-6}}.: 3 pages p&nbsp;219.</ref> This is argued by anthropologists to be also based on early humans noting the human and animal shared body feature of two arms and two legs as well as its ease in simple arithmetic and counting. As an example of the system's ease a realistic scenario could include a farmer returning from the market with fifty ''asu'' heads of pig (200), less 30 ''asu'' (120) of pig bartered for 10 ''asu'' (40) of goats noting his new pig count total as twenty ''asu'': 80 pigs remaining. The system has a correlation to the [[dozen]] counting system and is still in common use in these areas as a natural and easy method of simple arithmetic.<ref name="Ryan, Peter p&nbsp;219"/><ref>Aleksandr Romanovich Luriicac, Lev Semenovich Vygotskiĭ, Evelyn Rossiter. ''Ape, primitive man, and child: essays in the history of behavior''. CRC Press: 1992: {{isbn|1-878205-43-9}}.</ref>

The traditional [[Chinese units of measurement]] were base-16. For example, one jīn&nbsp;(斤) in the old system equals sixteen [[tael]]s. The [[suanpan]] (Chinese [[abacus]]) can be used to perform hexadecimal calculations such as additions and subtractions.<ref>{{Cite web|url=http://totton.idirect.com/soroban/Hex_as/|title=算盤 Hexadecimal Addition & Subtraction on a Chinese Abacus|website=totton.idirect.com|access-date=2019-06-26|archive-date=2019-07-06|archive-url=https://web.archive.org/web/20190706221609/http://totton.idirect.com/soroban/Hex_as/|url-status=live}}</ref>

* Crespo Cantalapiedra, I. (2023). ''[https://zenodo.org/records/10225997 La diversidad en las lenguas: los numerales] {{Webarchive|url=https://web.archive.org/web/20240224123657/https://zenodo.org/records/10225997 |date=2024-02-24 }}''. Online book (in Spanish).