- Dual (grammatical number)
Dual (abbreviated du) is a grammatical number that some languages use in addition to singular and plural. When a noun or pronoun appears in dual form, it is interpreted as referring to precisely two of the entities (objects or persons) identified by the noun or pronoun. Verbs can also have dual agreement forms in these languages.
The dual number existed in Proto-Indo-European, persisted in many of the now extinct ancient Indo-European languages that descended from it—Sanskrit, Ancient Greek and Gothic for example—and can still be found in a few modern Indo-European languages such as Scottish Gaelic, Slovenian, Frisian, Chakavian and Sorbian. Many more modern Indo-European languages show residual traces of the dual, as in the English distinctions both vs. all, either vs. any, neither vs. none, and so on.
Many Semitic languages also have dual number. For instance, in Arabic all nouns can have singular, plural, or dual forms. For non-broken plurals, masculine plural nouns end with ون -ūn and feminine plural nouns end with ات -āt, whilst ان -ān, is added to the end of a noun to indicate that it is dual (even among nouns that have broken plurals).
- 1 Comparative characteristics
- 2 Use in modern languages
- 3 Hebrew
- 4 The dual in Indo-European languages
- 5 Languages with dual number
- 6 Notes
- 7 References
- 8 See also
Many languages make a distinction between singular and plural: English, for example, distinguishes between man and men, or house and houses. In some languages, in addition to such singular and plural forms, there is also a dual form, which is used when exactly two people or things are meant. In many languages with dual forms, use of the dual is mandatory, and the plural is used only for groups greater than two. However, use of the dual is optional in some languages such as many modern Arabic dialects including Egyptian Arabic. In other languages such as Hebrew, the dual exists only for words naming time spans (day, week, etc.), a few measure words, and for words that naturally come in pairs and are not used in the plural except in rhetoric: eyes, ears, and so forth. In Slovene the use of the dual is mandatory, except for nouns that are natural pairs, such as trousers, eyes, for which the plural form can be used.
Although relatively few languages have the dual number and most have no number or only singular and plural, using different words for groups of two and groups greater than two is not uncommon. English has words distinguishing dual vs. plural number, including: both/all, either/any, neither/none, between/among, former/first, and latter/last. Japanese, which has no grammatical number, also has words dochira (which of the two) and dore (which of the three or more), etc.
Use in modern languages
Among living languages, Modern Standard Arabic has a mandatory dual number, marked on nouns, verbs, adjectives and pronouns. (First-person dual forms, however, do not exist; compare this to the lack of third-person dual forms in the old Germanic languages.) Many of the spoken Arabic dialects have a dual marking for nouns (only), but its use is not mandatory. Likewise, Akkadian had a dual number, though its use was confined to standard phrases like "two hands", "two eyes", and "two arms". The dual in Hebrew has also atrophied, generally being used for only time, number, and natural pairs even in its most ancient form.
Austronesian languages, particularly Polynesian languages such as Hawaiian, Niuean and Tongan, possess a dual number for pronouns but not for nouns, as nouns are generally marked for plural syntactically and not morphologically. Other Austronesian languages, particularly those spoken in the Philippines, have a dual first-person pronoun; these languages include Ilokano (data), Tausug (kita), and Kapampangan (ikata). These forms mean we, but specifically you and I. This form once existed in Tagalog (kata or sometimes kita) but has disappeared from standard usage (save for certain dialects such as in Batangas) since the middle of the 20th century.
The dual was a standard feature of the Proto-Uralic language, and lives on in Sami languages and Samoyedic languages, while other branches like Finnish, Estonian and Hungarian have lost it. Sami also features dual pronouns, expressing the concept of "we two here" as contrasted to "we". Nenets, two closely related Samoyedic languages, features a complete set of dual possessive suffixes for two systems, the number of possessors and the number of possessed objects (for example, "two houses of us two" expressed in one word).
The dual form is also used in several modern Indo-European languages, such as Scottish Gaelic, Slovenian, Frisian and Sorbian (see below for details). The dual was a common feature of all early Slavic languages at the beginning of the second millennium CE.
Biblical and Mishnaic Hebrew
In Biblical, Mishnaic, and Medieval Hebrew, like Arabic and other Semitic languages, all nouns can have singular, plural or dual forms, and there is still a debate whether there are vestiges of dual verbal forms and pronouns. However, in practice, most nouns use only singular and plural forms. Usually ים -īm is added to masculine words to make them plural for example ספר/ספרים sēpher/səphārīm "book/books", whilst with feminine nouns the ה -ā is replaced with ות -ōṯ. For example פרה/פרות pārā/pārōṯ "cow/cows". An example of the dual form is יום/יומיים/ימים yōm/yomạyim/yāmīm "day/two days/[two or more] days". Some words occur so often in pairs that the form with the dual suffix -ạyim is used in practice for the general plural, such as עין/עינים ʻạyin/ʻēnạyim "eye/eyes", used even in a sentence like, "The spider has eight eyes." Thus words like ʻēnạyim only appear to be dual, but are in fact what is called "pseudo-dual", which is a way of making a plural. Sometimes, words can change meaning depending on whether the dual or plural form is used, for example; 'ayin can mean eye or water spring in the singular, but in the plural eyes will take the dual form of 'enayim whilst springs are 'eynot. Adjectives, verbs, and pronouns have only singular and plural, with the plural forms of these being used with dual nouns.
In Modern Hebrew as used in Israel, there is also a dual number, but its use is very restricted. The dual form is usually used in expressions of time and number. These nouns have plurals as well, which are used for numbers higher than two, for example:
Singular Double Triple פעם אחת páʻam aḥat (once) פעמיים paʻamáyim (twice) שלוש פעמים shalosh pəʻamim (thrice) שבוע אחד shavúaʻ eḥad (one week) שבועיים shəvuʻáyim (two weeks) שלושה שבועות shəlosha shəvuʻot (three weeks) מאה meʼa (one hundred) מאתיים matáyim (two hundred) שלוש מאות shalosh meʼot (three hundred)
The pseudo-dual is used to form the plural of some body parts, for instance:
- רגל régel (leg) → רגליים ragláyim (legs)
- אוזן ózen (ear) → אוזניים oznáyim (ears)
- עין ʻáyin (eye) → עיניים ʻeynáyim (eyes)
- יד yad (hand) → ידיים yadáyim (hands)
In this case, even if there are more than two, the dual is still used, for instance lə-kélev yesh arbaʻ ragláyim ("a dog has four legs").
The dual in Indo-European languages
The category of dual can doubtless be reconstructed for the Proto-Indo-European, the ancestor of all Indo-European languages, and it has been retained as a fully functioning category in the earliest attested daughter languages. The best evidence for the dual among ancient Indo-European languages can be found in Old Indo-Iranian (Vedic Sanskrit and Avestan), Homeric Greek and Old Church Slavonic, where its use was obligatory for all inflected categories including verbs, nouns, adjectives, pronouns and some numerals. Various traces of dual can also be found in Gothic and Old Irish (see below), and in some fossilized terms in Latin.
Due to the scarcity of evidence, the reconstruction of dual endings for Proto-Indo-European is difficult, but at least formally according the comparative method it can be ascertained that no more than three dual endings are reconstructible for nominal inflection. Mallory & Adams (2006) reconstruct the dual endings as:
- Nominative/Accusative/Vocative: *-h₁(e)
- Genitive/Ablative: *-h₁(e) / *-oHs
- Dative: *-me / *-OH
- Locative: *-h₁ow
- Instrumental: *-bʰih₁
Proto-Indo-European category of dual did not only denote two of something: it could also be used as an associative marker, the so-called elliptical dual. For example, the Vedic deity Mitrá, when appearing in dual form Mitrā́ it refers to both Mitra and his companion Varuṇa. Homeric dual Αἴαντε refers to Ajax the Greater and his fighting companion Teucer, and Latin plural Castorēs is used to denote both the semi-god Castor and his twin brother Pollux.
Beside nominal (nouns, adjectives and pronouns), the dual was also present in verbal inflection where the syncretism was much lower.
Of living Indo-European languages, the dual can be found in Scottish Gaelic dialects, Welsh, Breton, but fully functioning as a paradigmatic category only in Sorbian, Chakavian and Slovene. Remnants of the dual can be found in many of the remaining daughter languages, where certain forms of the noun are used with the number two (see below for examples).
The dual in Greek
The dual can be found in Ancient Greek Homeric texts such as the Iliad and the Odyssey, although its use is only sporadic, owing as much to artistic prerogatives as dictional and metrical requirements within the hexametric meter. There were only two distinct forms of the dual in Ancient Greek.
In classical Greek, the dual was all but lost, except in the Attic dialect of Athens, where it persisted until the fifth century B.C. Even in this case, its use depended on the author and certain stock expressions.
In Koine Greek and Modern Greek the only remnant of the dual is the numeral for "two", δύο, dýo, which has lost its Genitive and Dative cases (both δυοῖν, dyoĩn) and retains its nominative/accusative form. Thus it appears to be undeclined in all cases.
The dual in Latin
The dual was lost in Latin and its sister Italic languages. However, certain fossilized forms remained, for example, diviginti (twenty), but triginta (thirty), the words ambo (both, compare Slavic oba), duo/duae with a dual declension.
The dual in the Celtic languages
Reconstructed Common Celtic nominal and adjectival declensions contain distinct dual forms; pronouns and verbs do not. In Old Irish, nouns and the definite article still have dual forms, but only when accompanied by the numeral da "two". Traces of the dual remain in Middle Welsh, in nouns denoting pairs of body parts that incorporate the numeral two: e.g. deulin (from glin "knee"), dwyglust (from clust "ear").
In the modern languages, there are still significant remnants of dual number in Scottish Gaelic in nominal phrases containing the numeral dà (including the higher numerals 12, 22, etc.) As the following table shows, dà combines with a singular noun, which is lenited. Masculine nouns take no special inflection, but feminine nouns have a slenderized dual form, which is in fact identical to the dative singular.
Singular Dual Plural cù ("a dog", masculine) dà chù ("two dogs") trì coin ("three dogs") clach ("a stone", feminine) dà chloich ("two stones") trì clachan ("three stones")
Languages of the Brythonic branch do not have dual number. As mentioned above for Middle Welsh, some nouns can be said to have dual forms, prefixed with a form of the numeral "two" (Breton daou-/div-, Welsh dau-/deu-/dwy-, Cornish dew-/diw-). This process is not fully productive, however, and the prefixed forms are semantically restricted. For example, Breton daouarn (< dorn "hand") can only refer to one person's pair of hands, not any two hands from two different people. Welsh deufis must refer to a period of two consecutive months, whereas dau fis can be any two months.
The dual in the Germanic languages
The dual was present in all the early Germanic languages, as well as in Proto-Germanic. However, the dual had been entirely lost in nouns by that time, and since verbs agreed with nouns in number, so had the third-person dual form of verbs as a result. The dual therefore remained only in the first and second person pronouns and their accompanying verb forms.
Gothic retained this situation more or less unchanged. It had markings for the first and second person for both the verbs and pronouns, for example wit "we two" as compared to weis "we, more than two". Old English, Old Norse and the other old Germanic languages had dual marking only in the personal pronouns, but not in the verbs.
The dual has disappeared as a productive form in all the living languages, with loss of the dual occurring in North Frisian dialects only quite recently.[when?] The dual survives very marginally in some Limburgish dialects as weet (we two) and jee (you two), but is archaic and no longer in common use. In Austro-Bavarian, the old dual pronouns have replaced the standard plural pronouns, for example, accusative enk, you plural (from Proto-Germanic *inkw, *inkwiz). A similar development in the pronoun system can be seen in Icelandic and Faroese. Another remnant of the dual can be found in the use of the pronoun begge ("both") in the Scandinavian languages of Norwegian and Danish, bägge in Swedish and báðir/báðar/bæði in Faroese and Icelandic. In these languages, in order to state "all + number", the constructions are begge to/báðir tveir/báðar tvær/bæði tvey ("all two") but alle tre/allir tríggir/allar tríggjar/øll trý ("all three"), while the form *alle to is unattested.
Another example of a lost dual exists in the Faroese ordinals 1st and 2nd, which can be translated two ways: First there is fyrri and seinni, which mean the 1st and 2nd of two respectively, while fyrsti and annar mean 1st and 2nd of more than two.
The dual in the Baltic Languages
Among the Baltic languages, the dual form existed but is now nearly obsolete in standard Lithuanian. It can be occasionally found in poetic contexts and some dialects. The dual form Du litu was still used on two litas coins issued in 1925, but the plural form (2 litai) is used on modern two litas coins.
Singular Dual Plural vyras ("a man") vyru ("two men") vyrai ("men") mergina ("a girl") mergini ("two girls") merginos ("girls") einu ("I go") einava ("We two go") einame ("We (more than two) go")
The dual in the Slavic languages
Common Slavic had a complete singular-dual-plural number system, although the nominal dual paradigms showed considerable syncretism, just as they did in Proto-Indo-European. Dual was fully operable at the time of Old Church Slavonic manuscript writings, and it has been subsequently lost in most Slavic dialects in the historical period.
Of the living languages, only Slovene, Chakavian and Sorbian have preserved the dual number as a productive form. In all of the remaining languages, its influence is still found in the declension of nouns of which there are commonly only two: eyes, ears, shoulders, in certain fixed expressions, and the agreement of nouns when used with numbers.
In all the languages, the declension of the "two" maintains most of its dual characteristics, which can be verified from the table below.
language nom.-acc.-voc. gen.-loc. dat. instr. Common Slavic *dъva (masc.) / *dъvě (fem./nt.) *dъvoju *dъvěma *dъvěma Belarusian два (masc./nt.) дзве (fem.) двух (masc./nt.)
Croatian dva/dvoje (masc./nt.) dvije (fem.) dva/dvoje (masc./nt.) dviju (fem.) dvama (masc./nt.) dvima/dvjema (fem.) dvama (masc./nt.) dvima/dvjema (fem.) Czech dva (masc.) / dvě (fem./nt.) dvou dvěma dvěma Polish dwa (masc./nt.) / dwie (fem.)1 dwu / dwóch dwu / dwóm dwoma / dwiema Russian два (masc./nt.) / две (fem.) двух двум двумя Slovak dva (masc. inanim.), dvaja-dvoch (masc. anim.) / dve (fem., nt.) dvoch dvom dvoma/dvomi Serbian два/dva (masc./nt.)
двају/dvaju (masc. Gen only; Loc = Instr)
двеју/dveju (fem. Gen only; Loc = Instr)
Slovene dva (masc.) dve (fem./nt.) dveh dvema dvema Sorbian dwaj (masc.) dwě (fem./nt.) dweju² dwěmaj dwěmaj Ukrainian два (masc./nt.) дві (fem.) двох двом двома
- In some Slavic languages, there is a further distinction between animate and inanimate masculine nouns. In Polish, for animate masculine nouns the possible nominative forms are dwaj, or dwóch.
- In Sorbian, the form given is for the genitive, since the locative form is the same as the dative and instrumental forms.
Furthermore, it should be noted that the words oba and obidva (obydwa in Polish), which both mean "both", are declined similarly to the numeral "two."
In Common Slavic, the rules were relatively simple for determining the appropriate case and number form of the noun, when it was used with a numeral. The following rules apply:
- With the numeral "one", both the noun, adjective, and numeral were in the same singular case, with the numeral being declined as an adjective.
- With the numeral "two", both the noun, adjective, and numeral were in the same dual case. There were separate forms for the masculine and neuter-feminine nouns.
- With the numerals "three" and "four," the noun, adjective, and numeral were in the same plural case.
- With any numeral above "four", in the nominative case, the numeral was followed by the noun and adjective in the genitive plural case. For all other cases, both the noun, adjective, and numeral were in the same plural case.
With the loss of the dual in most of the Slavic languages, the above pattern now is only seen in the forms of the numbers for the tens, hundreds, and rarely thousands. This can be seen by examining the following table:
Language 10 20 30 50 100 200 300 500 Common Slavic *desętь *dъva desęti *trije desęte *pętь desętь *sъto *dъvě sъtě *tri sъta *pętь sъtь Belarusian дзесяць дваццаць трыццаць пяцьдзесят сто дзвесце трыста пяцьсот Bulgarian десет двадесет тридесет петдесет сто двеста триста петстотин Croatian deset dvadeset trideset pedeset sto dvjesto tristo petsto Czech deset dvacet třicet padesát sto dvě stě tři sta pět set Polish dziesięć dwadzieścia trzydzieści pięćdziesiąt sto dwieście trzysta pięćset Russian десять двадцать тридцать пятьдесят сто двести триста пятьсот Serbian десет двадесет тридесет педесет сто двеста триста петсто Upper Sorbian dźesać dwaceći třiceći pjećdźesat sto dwě sćě tři sta pjeć stow Slovak desať dvadsať tridsať päťdesiat sto dvesto tristo päťsto Slovene deset dvajset trideset petdeset sto dvesto tristo petsto Ukrainian десять двадцять тридцять п'ятдесят сто двісті триста п'ятсот
The Common Slavic rules governing the declension of nouns after numerals, which were described above, have been preserved in Slovene. In those Slavic languages that have lost the dual, the system has been simplified and changed in various ways, but many languages have kept traces of the dual in it. In general, Czech, Slovak, Polish and Ukrainian have extended the pattern of "three/four" to "two"; Russian, Belarusian, Croatian and Serbian have, on the contrary, extended the pattern of "two" to "three/four"; and Bulgarian and Macedonian have extended the pattern of "two" to all numerals. The resulting systems are as follows:
- In Czech, Slovak, Polish and Ukrainian, numerals from "two" to "four" are always followed by a noun in the same plural case, but higher numerals (if in the nominative) are followed by a noun in the genitive plural.
- In Russian, Belarusian, Croatian and Serbian, numerals from "two" to "four" (if in the nominative) are followed by a noun in a form originating from the Common Slavic nominative dual, which has now completely or almost completely merged with the genitive singular. Higher numerals (if in the nominative) are followed by a noun in the genitive plural.
- In Bulgarian and Macedonian, all numerals are followed by a noun in a form originating from the Common Slavic nominative dual, which has now been re-interpreted as a special so-called "count form" or "quantitative plural".
These different systems are exemplified in the table below where the word "wolf" is used to form nominative noun phrases with various numerals. The dual and forms originating from it are underlined.
"wolf" "wolves" "two wolves" "three wolves" "five wolves" noun form nom. sing. nom. plur. varies Common Slavic *vьlkъ vьlci dъva vьlka (nom. dual) tri vьlci (nom. pl.) pętь vьlkъ (gen. pl.) Slovene volk volkovi dva volkova (nom. dual) trije volkovi (nom. pl.) pet volkov (gen. pl.) Czech vlk vlci dva/tři vlci (nom. pl.) pět vlků (gen. pl.) Polish wilk wilki
dwa/trzy wilki (nom. pl.)
dwaj/trzej wilcy (nom. pl.)
pięć wilków (gen. pl.) Slovak
dva/tri vlky (nom. pl.)
dvaja/traja vlci (nom. pl.)
päť vlkov (gen. pl.)
piati vlci (nom. pl.)
Ukrainian вовк вовки́ два/три во́вки (nom. pl.) п'ять вовків (gen. pl.) Belarusian воўк ваўкі два/тры ваўкі (nom. pl.) пяць ваўкоў (gen. pl.) Russian волк волки два/три волкa (gen. sg.) пять волков (gen. pl.) Serbian and Croatian вук/vuk вукови/vukovi (concrete)
два/три вука/dva/tri vuka (gen. sg.) пет вукова/pet vukova (gen. pl.) Bulgarian вълк вълци два/три/пет вълка (count form)
The dual has also left traces in the declension of nouns describing body parts that humans customarily had two of, for example: eyes, ears, legs, breasts, and hands. Often the plural declension is used to give a figurative meaning. The table below summarizes the key such points.
Language Examples Czech certain body parts and their modifying adjectives require in the instrumental and genitive plural cases dual forms : se svýma očima (instrumental dual: "with one's own (two) eyes") or u nohou (genitive dual: "at the (two) feet"). Colloquial Czech will often substitute the dual instrumental for the literary plural instrumental case. Polish Oko ("eye") and ucho ("ear") have plural stems deriving from old dual forms, and alternative instrumental and genitive plural forms with archaic dual endings: gen. pl. oczu/ócz/oczów, uszu/uszów; instr. pl. oczami/oczyma, uszami/uszyma). The declension of ręka ("hand, arm") also contains old dual forms (nom./acc./voc. pl ręce, instr. pl. rękami/rękoma, loc. sg./pl. rękach/ręku). The historically dual forms are usually used to refer a person's two hands (dziecko na ręku "child-in-arms"), while the regularized plural forms are used elsewhere. Other archaic dual forms, including dual verbs, can be encountered in older literature and in dialects: Jak nie chceta, to nie musita "If you don't want to, you don't have to". Slovak In Slovak, the genitive plural and instrumental plural for the words "eyes" and "ears" has also retained its dual forms: očú/očí and ušú/uší. Ukrainian The words eyes and shoulders had dual forms in the instrumental plural case: очима ("eyes") and плечима ("shoulders"). Furthermore, the nominative plural word "вуса", which is the dual of "вус" ("whisker"), refers to the moustache, while the true nominative plural word "вуси" refers to whiskers. Bulgarian Some words such as ръка "hand" use the originally dual form as a plural (ръце). Russian In Russian the world колено ("knee", "tribe (Israelites)") has different plurals: колена ("Israelites") is pure plural and колени (body part) is a dual form. Some cases are different as well: коленами vs. коленями (instr.pl.).
Beside Sorbian languages, Chakavian dialect and the extinct Old Church Slavonic, the Slovene is the only Slavic language that retains full grammatical use of the dual, including distinct dual forms for both nouns and verbs. The dual declension merges with the plural in certain nominal cases (e.g., genitive). Note that dual number is compatible with use of the pronoun oba(dva) or obe(dve) ("both").
Nominative case of noun "wolf", with and without numerals:
without numerals nom. sg. (wolf) nom. dual (2 wolves) nom. pl. (wolves) Slovene volk volkova volkovi with numerals wolf 2 wolves 3 (or 4) wolves 5 (+) wolves (gen. pl.) Slovene en volk dva volkova trije volkovi pet volkov
The dual is recognised by many Slovene speakers as one of the most distinctive features of the language and a mark of recognition, and is often mentioned in tourist brochures.
For verbs, the endings in the present tense are given as -va, -ta, -ta. The table below shows a comparison of the conjugation of the verb oddati, which means to give away and belongs to Class I in the singular, dual, and plural.
Singular Dual Plural First Person oddam oddava oddamo Second Person oddaš oddata oddate Third Person odda oddata oddajo
In the imperative the endings are given as -iva for the first person dual and -ita for the second person dual. The table below shows the imperative forms for the verb hoditi (to walk) in the first and second persons of the imperative (the imperative does not exist for 1st person singular).
Singular Dual Plural First Person hodiva hodimo Second Person hodi hodita hodite
As in Slovenian, the Sorbian language (both dialects Upper and Lower Sorbian) have preserved the dual. For nouns, the following endings are used:
Masculine Feminine/Neuter Nominative, Accusative, Vocative -aj/-ej -e (2) /-y/-i Genitive (1) -ow -ow Dative, Instrumental, Locative -omaj -omaj
(1) The genitive form is based on the plural form of the noun. (2) The -e ending causes various softening changes to occur to the preceding constant, for further information see the article on Sorbian.
For example, the declension of sin (masculine) and crow (feminine) in the dual in Upper Sorbian would be given as
hrěch (sin) wróna (crow) Nominative, Accusative, Vocative hrěchaj wrónje Genitive hrěchow wrónow Dative, Instrumental, Locative hrěchomaj wrónomaj
For verbs, the endings in the present tense are given as -moj, -tej/-taj, -tej/-taj. The table below shows a comparison of the conjugation of the verb pisać, which means to write and belongs to Class I in the singular, dual, and plural.
Singular Dual Plural First Person pisam pisamoj pisaamy Second Person pisaš pisatej pisaće Third Person pisa pisaatej pisaja
Languages with dual number
- Austronesian languages
- Indo-European languages
- Ancient Greek
- Germanic languages (only first and second person pronouns and verb forms)
- Insular Celtic languages:
- Old Church Slavonic
- Old East Slavic
- Sorbian languages:
- Uralic languages
- Afroasiatic languages
- Other languages
- ^ Dual Personal Pronouns and Dual Verbs in Hebrew Gary Rendsburg The Jewish Quarterly Review, New Ser., Vol. 73, No. 1 (Jul., 1982), pp. 38-58 doi:10.2307/1454459
- ^ E.g. ambō "both", and duo "two", the latter with Iambic shortening.
- ^ Ringe (2006, pp. 42)
- ^ Clackson (2007, p. 101)
- ^ Lewis, Henry; Holger Pedersen (1989). A Concise Comparative Celtic Grammar (3rd ed.). Göttingen: Vandenhoeck & Ruprecht. pp. §§246, 468. ISBN 3-525-26102-0. Thurneysen, Rudolf (1993) . A Grammar of Old Irish. Trans. by D. A. Binchy and Osborn Bergin. Dublin Institute for Advanced Studies. ISBN 1-85500-161-6. Evans, D. Simon (1989) . A Grammar of Middle Welsh. Dublin Institute for Advanced Studies. pp. §§30, 33. ISBN 1-85500-000-8.
- ^ Ó Maolalaigh, Roibeard; Iain MacAonghuis (1997). Scottish Gaelic in Three Months. Hugo's Language Books. ISBN 978-0-85285-234-7.
- ^ Heinecke, Johannes (2002). "Is there a Category of Dual in Breton or Welsh?". Journal of Celtic Linguistics 7: 85–101.
- ^ Howe, Stephen. The Personal Pronouns in the Germanic Languages. A study of personal pronoun morphology and change in the Germanic languages from the first records to the present day. [Studia Linguistica Germanica, 43]. Berlin: de Gruyter, 1996. (xxii + 390 pp.) pp. 193-195.
- ^ Mayer, Gerald L. (1973) "Common Tendencies in the Syntactic Development of 'Two', 'Three,' and 'Four' in Slavic." The Slavic and East European Journal 17.3:308–314.
- ^ These forms are taken from De Bray, R. G. A. Guide to the Slavonic Languages. London, 1951.
- ^ However, Ukrainian is special in that the form used with "two", "three" and "form" has the stress pattern of the genitive singular and thus of the old dual.
- ^ Paul V. Cubberley (2002) Russian: a linguistic introduction. p.141
- ^ Browne, Wayles and Theresa Alt (2004) A Handbook of Bosnian, Serbian and Croatian.  P.21
- ^ Friedman, Victor (2001) Macedonian.  P.19
- ^ Swan, Oscar E. (2002). A Grammar of Contemporary Polish. Bloomington, IN: Slavica. pp. 57, 199, 216. ISBN 0-89357-296-9.
The Dual can also be found in the native Korean counting system: 둘 (dul), meaning 2.
- Ringe, Donald (2006). From Proto-Indo-European to Proto-Germanic. New York: Oxford University Press
- Mallory, James Patrick; Adams, Douglas Q. (2006). The Oxford Introduction to Proto-Indo-European and the Proto-Indo-European World. New York: Oxford University Press
- Clackson, James (2007). Indo-European Linguistics, An Introduction. New York: Cambridge University Press
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