On the Inflection of Numbers

[alice]

In PIE, the numbers up to "four" inflected for gender, "one" inflected like a singular adjective, and the others inflected like plurals.

Are there languages in which numbers greater than one inflect as singulars? Or in which the inflection of numbers is more complicated?

Arabic is interesting in this regard, I know; are there others?

[Miekko]

In Finnish, numbers normally inflect as singulars, and take singular nouns - although under some circumstances, they can go plural. These include:

- with plurale tantum nouns (nouns that lack singular forms)
- some combinations of determiners where one of them is a number can cause the number and noun and all to be plural if they occur in some orders.

[Basilius]

In PIE, the numbers up to "four" inflected for gender, "one" inflected like a singular adjective, and the others inflected like plurals.

'Two' (and 'both'), as well as 'twenty', were declined as duals. (In some descendant languages, this treatment was also applied to 'twelve', 'twenty two', 'thirty two' etc., but these can be secondary formations.)

Higher numbers, 'hundred' and 'thousand', were regular (collective) nouns; so, 'one hundred' was declined as a singular noun, 'two hundreds' as a dual, etc.

Are there languages in which numbers greater than one inflect as singulars? Or in which the inflection of numbers is more complicated?

In most Slavic languages the numbers 5-10 look like i-stem singular nouns (and appear to be derived from the ordinals). E. g. in Russian (стать 'stature' being a historical i-stem; the difference in stress position depends on a characteristic of the stem rather than of the endings):

Code: Select all

     пять 'five'    стать 'stature'

Nom.   пять            стать
Gen.   пяти́            ста́ти
Dat.   пяти́            ста́ти
Acc.   пять            стать
Inst.  пятью́           ста́тью
Loc.   пяти́            ста́ти

Russian numbers from 5 to 90 may also fit your demand about something more complicated if you consider their combinations with nouns: the numeral is construed like the head of the NP in Nom. and Acc. (with the noun in Gen. Pl.) but looks like an attribute in the other cases (so the numeral and the noun are in the same case). Compounds 50-90 were historically some similar types of NP's, so their declension is rather bizarre, e. g. for '50':

Code: Select all

Nom.   пятьдеся́т
Gen.   пяти́десяти
Dat.   пяти́десяти
Acc.   пятьдеся́т
Inst.  пятью́десятью
Loc.   пяти́десяти 

(The -деся́т in Nom. and Acc. being historically a Gen. Pl. of the substantive 'ten'; the other cases incorporate the regular, singular-like case forms of десять '10'.)

[Soap]

It's often assumed that the PIE word for hundred is derived from the word for ten, since they have two consonants in common. Not much of a commonality, but similar things exist ... e.g. the Germanic word for thousand is derived from the Germanic word for hundred. If this were true it wouldnt be a normal number.

[Yng]

For the benefit of those who don't know about the hellishly complicated classical Arabic numeral system:

The numbers 'one' and 'two' act entirely regularly as adjectives and are usually only added to a noun inflected for singular or dual respectively for emphasis:

رجل واحد
rajulun [wāħidun]
man-NOM.INDEF one-NOM.INDEF
one man

رجلان إثنان
rajulān [it̠nān]
man-DUAL.NOM.INDEF two-DUAL.NOM.INDEF
two men (note that it̠nān is itself a root it̠n- with standard dual suffix -ān; the feminine has an -at- inserted regularly between the stem and the suffix, just like normal dual adjectives)

The remainder of the numbers up to ten form a possessive or construct phrase with a plural noun in the genitive; as a slightly confusing addition, they agree in number and the feminine forms look like masculine forms and the masculine forms look like feminine forms (i.e. have the standard feminine ending ة -ah 'taa marbuuta'). The numbers themselves take case depending on the syntactic context, as expected.

ثلاثة رجال
t̠alāt̠atu rijālin
three-MASC-NOM.CONST man.PLU-GEN.INDEF
three men

ثلاث نساء
t̠alāt̠u nisāˀin
three.FEM-NOM.CONST woman.PLU-GEN.INDEF
three women

11-19 demand the accusative indefinite singular on a following noun and are themselves always likewise in the accusative indefinite, irrespective of syntactic context; 12 is an exception and has case agreement in the ones because of its typical dual ending. The 'ten' element in all of the teens, ˁašar, has what is usually termed 'gender agreement' as opposed to 'gender polarity': unlike its counterpart outside -teen compounds, its feminine form takes the typical feminine ending, and its masculine form no ending. The units, on the other hand, act as expected - one and two have gender agreement, 3-9 do not:

ثلاثة عشر رجلا
t̠alāt̠ata ˁašara rajulan
three-MASC-ACC.INDEF ten-ACC.INDEF man-ACC.INDEF
thirteen men

ثلاث عشرة نساء
t̠alāt̠a ˁašaratan nisāˀan
three.FEM-ACC.INDEF ten-FEM-ACC.INDEF woman-ACC.INDEF
thirteen women

إثنتا عشرة نساء
it̠natā ˁašaratan nisāˀan
two-FEM-NOM.DUAL.CONST ten-FEM-ACC.INDEF woman-ACC.INDEF
twelve women

20-99 work comparatively predictably. They govern a following noun in the accusative indefinite singular. 1 and 2 have gender agreement; 3-10 have gender polarity. Units are connected to ten with wa- 'and' and the numerals inflect for case as demanded by their role in the sentence. Tens are formed from their equivalent units by the addition of the masculine plural suffix -ūn/-īn (variant depending on case); the only exception is twenty, which is formed (slightly irregularly) from the root of ten and is thus ˁišrūn.

خمس وخمسوى مرأة
xamsun wa-xamsūn maraˀatan
five-NOM.SING.INDEF and-fifty.NOM woman-ACC.INDEF
fifty-five women (NOM)

خمسا وخمسين مرأة
xamsan wa-xamsīn maraˀatan
five-ACC.SING.INDEF and-fifty.ACC woman-ACC.INDEF
fifty-five women (ACC)

خمسة وخمسين رجلا
xamsatan wa-xamsīn rajulan
five-MASC-ACC.SING.INDEF and-fifty.ACC man-ACC.INDEF
fifty-five men (ACC)

100s, 1000s etc demand a genitive singular:

ألف رجل
ˀalfun rijalin
thousand-NOM.INDEF man-GEN.INDEF
a thousand men

[Miekko]

It's often assumed that the PIE word for hundred is derived from the word for ten, since they have two consonants in common. Not much of a commonality, but similar things exist ... e.g. the Germanic word for thousand is derived from the Germanic word for hundred. If this were true it wouldnt be a normal number.

From the IE word, not from the Germanic word.

[Ser]

To make things shorter about Arabic (case and number of modified noun not included):

1-2: behave like adjectives, full case and state inflection, agreeing in case and gender with their nouns
(From now on, everything behaves like normal quantifiers/determiners, and they're always in the construct state if modifying a noun or in the indefinite if they're not, except for 10-11 and 13-19 which are always in the construct no matter what.)
3-10: full case inflection according to the syntactic environment, agree in gender with their nouns (though with gender polarity)
11: no case inflection (always in the accusative), agrees in gender with its noun
12: full case inflection according to the syntactic environment, agrees in gender with its noun
13-19: no case inflection (always in the accusative), agree in gender with their nouns (though with gender polarity)
20-99: full case inflection according to the syntactic environment, agree in gender with their nouns (though with gender polarity)
100, 200, 300...: full case inflection according to the syntactic environment, no agreement with their noun.
101-102, 201-202...: use of the construction "a thousand X and X.SG" and "a thousand X and X.DUAL", e.g. كتاب ألف ليلة وليلة "book.NOM.CONS thousand.OBL.CONS night.OBL.INDEF and_night.OBL.INDEF '[book of the] 1001 nights', full case inflection according to the syntactic environment (for both the word for "hundred/thousand/million/billion..." and the second instance of "X")
103-199, 203-299...: behave in whatever way the number of the last two digits behaves, so 112 and 212 behave just like 12, etc.

And to answer the question of OP: Arabic doesn't have any inflections that are specific to singulars. Some declensions occur in singular and plurals, and others occur only in plurals. It's perfectly normal for a noun or adjective to have a singular in one declension and the plural in another declension, e.g. مطبخ maṭbax 'kitchen' (triptote declension) > مطابخ maṭābix 'kitchens' (diptote declension). Plurality is generally marked through change in the stem (the "broken" plurals with "transfixes"), sometimes combined with a change in declension as above, or through some of said plural suffixes that are their own declension. So we can't say the numbers "inflect like plurals" or "like singulars".

(note that it̠nān is itself a root it̠n- with standard dual suffix -ān; the feminine has an -at- inserted regularly between the stem and the suffix, just like normal dual adjectives)

i-? I don't think it's normal to consider /i/ a root at all, for any word. The root is ṯ-n-y anyway, related to ثنى ṯannä "to double (sth) up", مثنى muṯannan "dual" (adj.), etc.

Also, if you wanna be über-traditional, it's اثنان (ʾi)ṯnāni, with an initial همزة الوصل.

11-19 demand the accusative indefinite singular on a following noun and are themselves always likewise in the accusative indefinite, irrespective of syntactic context;

The numbers go in the accusative construct (except for twelve), the nouns go as you say.

12 is an exception and has case agreement in the ones because of its typical dual ending.

No case agreement, it takes the case of its syntactic environment...

[Yng]

i-? I don't think it's normal to consider /i/ a root at all, for any word. The root is ṯ-n-y anyway, related to ثنى ṯannä "to double (sth) up", مثنى muṯannan "dual" (adj.), etc.

I meant 'stem' rather than root, I guess, as in 'form that affixes are added to'. Not that it's important.

Also, if you wanna be über-traditional, it's اثنان (ʾi)ṯnāni, with an initial همزة الوصل.

Aha! This is what I thought, but when I checked Wikipedia it seemed to say otherwise.

[Declan]

In Irish, certain types of words always are in singular when being counted (aon bhád amháin, dhá bhád, trí bhád, ...), others have a historical dual form (aon mhuc amháin, dhá mhuic, trí mhuc), others have a special form that's used with more than three (so aon bhliain amháin, dhá bhliain, trí bliana but bliana isn't the normal plural of bliain). There are then another set of numbers for people, which also are, or sometimes aren't, used with nouns referring to people. That system has also changed enormously over time and in each dialect, lots of the dual forms are totally ignored now for example, and lots in Connemara would use the plural with numbers, but I think that everyone uses either singular or dual plural (which ever exists) after two always.

You also get eclipsis and lentition after numbers, so, 1-6 is normally lentition and 7-9 eclipsis, eclipsed after 10, but nothing after any other multiple of ten. Words like bliain which have a special plural change at 3 and aren't lenited (is that a word? I'd normally say don't take a séimhiú) from 3-6, but are eclipsed from 7-10.

[linguoboy]

There are then another set of numbers for people, which also are, or sometimes aren't, used with nouns referring to people.

Historically these are compounds with fear "man" (PIE *wih₁rós), e.g. trí fhear > tríúr, cúig fhear > cúigear, etc. (See also aon fhear > aonar "alone".)

Words like bliain which have a special plural change at 3 and aren't lenited (is that a word?)

It is.

[Yng]

Welsh shows a vaguely similar system, although considerably more simplistic. Generally speaking nouns are found in the singular after numbers. The different decimal numbers trigger different mutations following nouns, and some of them agree in gender with the following noun. One of the numbers (un 'one') agrees for gender but not in form, only in the mutation it causes. I'll illustrate the forms with car ('car', masc) and cadair ('chair', fem):

un car, un gadair
dau gar, dwy gadair
tri char, tri chadair
pedwar car, pedair cadair
pum car, pum cadair (note pum < pump in isolation)
chwe char, chwe chadair (note chwe < chwech in isolation. chwech is usually found in all positions in colloquial Welsh)
saith car, saith cadair
naw car, naw cadair
deg car, deg cadair

So far this is relatively simple. However, some nouns have special 'counted' forms which are different from both their singular and plural: blwyddyn 'year', blwydd 'years' but dwy flynedd 'two years'. Some nouns also take the nasal mutation after certain numbers (by comparison with Irish I would guess that these numbers originally caused mutation in all nouns): dwy flynedd but can mlynedd (compare can cadair, 'a hundred cars'), saith mlynedd, wyth mlynedd, naw mlynedd, deng mlynedd (again these are usually levelled in spoken Welsh). Unlike Irish no dual forms are retained, although there are some historical duals which are now used as plurals (dwylo 'hands < llaw, dwyfron 'breasts' < bron). Another construction is also possible with o and a plural noun: dau o geir, dwy o gadeiriau.

[Declan]

(See also aon fhear > aonar "alone".)

I'd heard the cúig fhear -> cúigear but never thought of aonar as being derived from aon fhear even though it's considerably more obvious!

By the way, when did those two branches (Brythonic and Goidelic?) split, or is this a sort of contested issue? Also, is there a good description of how mutations arose with examples? I only ever seem to find detailed explanations of how they work now and really vague descriptions of how they arose that I don't fully understand. Furthermore, when did they start becoming grammatical?

[alice]

By the way, when did those two branches (Brythonic and Goidelic?) split, or is this a sort of contested issue?

In prehistory, i.e. we don't know. The prehistory of Celtic is notoriously hazy, even more so when you take Continental Celtic into account.

Also, is there a good description of how mutations arose with examples? I only ever seem to find detailed explanations of how they work now and really vague descriptions of how they arose that I don't fully understand. Furthermore, when did they start becoming grammatical?

You might want to try Paul Russell's A History of the Celtic Languages, which has a chapter about this. Unless Dewrad, for one, knows of anything better, that is

[Yng]

Also, is there a good description of how mutations arose with examples? I only ever seem to find detailed explanations of how they work now and really vague descriptions of how they arose that I don't fully understand. Furthermore, when did they start becoming grammatical?

Both me and Dewrad have explained this before elsewhere with examples, but I'll give you a brief explanation: allophonic sound change across word boundaries. Sometimes this was caused by a cluster (/t/ + /k/ > /x/): ni chenaist 'you did not sing' comes from older nit cenaist or something older. Sometimes it was just intervocalic lenition: the mutation on adjectives following a feminine noun comes from a historic feminine noun (almost all of which ended in a vowel) plus an adjective beginning with a consonant. In most of these cases, the original environment causing the allophonic 'mutated' form to exist disappeared because of sound change - e.g. loss of final vowels on feminine nouns - and the change was grammaticalised.

[Mecislau]

If you want complex numbers, go look at Slavic. What Basilius said about Russian doesn't even delve into some of the crazier stuff.

In general, the loss of the Proto-Slavic dual wrecked havoc on most of the Slavic languages' numeral systems each language attempted to come up with a different system to replace the lost number, while at the same time chopping up and parcelling out lots of little remnants of the old dual into all sorts of different functions.

I actually just finished writing a paper on the subject (as in, literally an hour ago). I'll revise it a bit and post it to my website at some point.

[Declan]

Both me and Dewrad have explained this before elsewhere with examples, but I'll give you a brief explanation: allophonic sound change across word boundaries. Sometimes this was caused by a cluster (/t/ + /k/ > /x/): ni chenaist 'you did not sing' comes from older nit cenaist or something older. Sometimes it was just intervocalic lenition: the mutation on adjectives following a feminine noun comes from a historic feminine noun (almost all of which ended in a vowel) plus an adjective beginning with a consonant. In most of these cases, the original environment causing the allophonic 'mutated' form to exist disappeared because of sound change - e.g. loss of final vowels on feminine nouns - and the change was grammaticalised.

Hmm, that seems to make absolutely perfect sense, I'm now not entirely sure what confused me in the first place.

[Salmoneus]

By the way, when did those two branches (Brythonic and Goidelic?) split, or is this a sort of contested issue? Also, is there a good description of how mutations arose with examples? I only ever seem to find detailed explanations of how they work now and really vague descriptions of how they arose that I don't fully understand. Furthermore, when did they start becoming grammatical?

Nobody knows.
If you believe in Gallo-Brittonic, that gives you a vaguely interesting date, in that there are Gaulish and Lepontic inscriptions from the 7th or 6th centuries BC, by which time (if you treat these as proper Gaulish and not some pre-split language that happens to look vaguely like gaulish) Goidelic would have had to have split off by then. If you believe in Insular Celtic, on the other hand, the Brythonic/Goidelic split could have happened later (theoretically up until the 4th century, when Old Irish appears, although of course in practical terms you'ld expect there to have been some time between the split and OI suddenly appearing full-formed).

My vague impression from The Internet is that celtic is believed to have broken up by at least 800BC - although the specific B/G could have happened later, or indeed much earlier (since Proto-Celtic may just have been a group of dialects, in which proto-Brythonic and proto-Goidelic were already recognisable strains - though that's just me speculating there).

[hwhatting]

Nobody knows.
If you believe in Gallo-Brittonic, that gives you a vaguely interesting date, in that there are Gaulish and Lepontic inscriptions from the 7th or 6th centuries BC, by which time (if you treat these as proper Gaulish and not some pre-split language that happens to look vaguely like gaulish) Goidelic would have had to have split off by then. If you believe in Insular Celtic, on the other hand, the Brythonic/Goidelic split could have happened later (theoretically up until the 4th century, when Old Irish appears, although of course in practical terms you'ld expect there to have been some time between the split and OI suddenly appearing full-formed).

I don't think any serious Celticist nowadays thinks of Insular Celtic as a genetic unit any more - as we have come to know more both about Continental Celtic and about the history of Goidelic and Brythonic sound changes, it has become quite clear that any shared features of Goidelic and Brythonic (e.g. lenition, initial mutations) are areal features and not genetically inherited. The Britonnic onomastic and inscriptional material of the Roman times is indistinguishable from the equivalent Gaulish material, while Goidelic shows divergent developments, e.g. of the syllabic resonants, that must be very old, as they aren't shared by any of the continental languages.
So the old division of Celtic into Insular and Continental is not a valid genetic classification - it's more of a division between "became extinct" (Continental) and "survived and shared some areal developments" (Insular). The genetic taxa of Celtic are Goidelic, Gallo-Britannic, Celtiberian, with Lepontic (as you mentioned) being disputed between being a more archaic form of what later became Gallo-Britonnic or an own taxon; some other languages that have been postulated as Celtic (Ligurian, Pictish, Tartessian) might form additional taxa if confirmed as Celtic.