Numeral (linguistics)

To view Spanish numerals, see Annex:Name of Spanish Numbers

A numeral is a proper name for a number. Natural languages, as languages that allow statements about physical realities, have linguistic-cognitive subsystems capable of naming numbers and counting.

Natural language numbering systems are based on finger counting. That is why practically all the numbering systems of the languages of the earth use numbering systems based on base 10 or base 20.

Number base

Vigesimal and Decimal Systems

Most Indo-European languages use a decimal number system, which means that number names are grouped in series of ten, and that there are roots for numbers one through nine, ten, one hundred, the thousand and the other names are derived from the roots for the cited numerals. Other families of languages also use the decimal system and there are families of languages where vigesimal systems are used (Basque, Mayan languages, Utoaztec languages, etc.). Some languages have base five subsystems, within a decimal or vigesimal system.

However, there are no known comprehensive counting systems that are not based on base 10 or base 20. This restriction seems related to the fact that the original idea of counting was associated with the fingers of the hands or the set of fingers of the hands and feet. Systems not based on base 10 or 20 are scarce, although they appear in Australian languages in a general way and —in a marginal way— in some American languages, such as Waimiri and Arará (two Carib languages), Resiguaro (an Arawakan language), Harakmbet and Andoque (language isolates), which tend to use quasi-binary systems.

They are words that express order or quantity in a precise way.

Other bases

Quaternary (4)

Some Austronesian and Melanesian, including Māori, some languages of Sulawesi, and some of Papua New Guinea, use counting systems based on 'four'. In these languages the term asu or aso (derived from Javanese asu, 'dog'), is used for &# 39;four' since dogs in these cultures are the most abundant quadruped. It has been proposed that this system could have arisen in the context of farmers trading animals at a market, thus fifty asu would represent a set of 200 things, if 30 asu (120) are subtracted from that amount, it would quickly lead to the inference that only 20 asu (80) remain, and the generalization of the idea of counting things as forming complete asu would have given rise to this curious system of counting. Note that this system could be cognitively related to the use of dozens as an extended counting system because the arithmetic of division is simple in dozens.

Quinary (5)

Quinary systems using base 5 are also attested. Obviously, these systems, as well as the decimal and vigesimal systems, derive from counting fingers (a hand has five fingers). An example of this type of system is found in the api language, a language of Vanuatu, where 'five' #39; and 'hand' they simply say luna 'five, hand', 'ten' we say lua-luna 'two-five', 'fifteen' it is said tolu-luna 'three-five', etc. The number 'eleven' It is called lua-luna tai 'two-five one' and 'seventeen' tolu-luna lua 'three-five two'. A basically identical system is found in the Emberá-Catio (Choco family).

Although purely quinary systems are not frequent, the use of base five as "auxiliary base" or "sub-base" used for some numbers, so in many languages of the world it is common for 6 to be called 'five/hand and one', 7 'five/hand and two', etc. For example, Nahuatl has a vigesimal base (base, 20) but uses 5 as a sub-base: 6 chik^wasē, 7 chikōme, 8 chik^wēi and 9 chiknāwi.

Sextal (6)

Kanum is an exotic example of a language with a base 6 counting system. The Sko languages, however, use base 24, where sub-base 6 is used.

Octal (8)

The octal system uses the number 8 as the base. This system is attested in the Yuki language of California and in the Pame languages of central Mexico. This is because both human groups use the gaps between their fingers to count more than the fingers themselves.

Twenty-quarter (24)

The Sko languages use a base 24 counting system, where 6 is used as a sub-base.

Thirtieth-dual (32)

Ngiti uses base 32.

Sexagesimal (60)

The ekari uses base 60 to count. In Sumer the base 60 seems to have been used for certain uses, although always with 10 as a sub-base, perhaps a mixed system between decimal and duodecimal systems. The use of this curious system in Sumer is behind the modern use of the sexagesimal degrees of the measure of angles in degrees, minutes and seconds. Use from which also derives the measurement of time in minutes and seconds, as well as the division of the circumference in 360º.

Octogesimal (80)

It has been published that the Supyire language has a base 80 counting system, in this language you count in scores (using 5 and 10 as sub-bases) up to 80 and then in eighties up to 400, and from there from 400 to 400.

kàmpó	Русский	sicy transformation	♪	bé-tànre	♪	k signal	♪	báár-ìcy transformation
400	80	4	and	23	and	10	and	5+4

799 [i.e. 400 + (4 x 80) + (3 x 20) + {10 + (5 + 4)}]’

Systems without base

Many Melanesian languages use (or used) counting systems based on body parts rather than on a numerical basis. This system does not have exclusive words for numbers, but rather the names of certain parts of the body are used to count. For example between 1 and 4 the fingers are used, 5 is called 'thumb', 6 'wrist [of the hand]', 7 'elbow', 8 'shoulder' etc. So across the body and then down the other arm, so the opposite little finger represents 17 (Islas Torres) or 23 (Eleman languages). For numbers beyond these values, the torso, legs, and toes are used, or one can count backwards to the other arm and back to the first.

"Arithmetic" numeral

It is also a well-studied topic, what arithmetic principles are used by the number systems of the world's languages. For example, the sum is universal in all languages (eighteen = ten and eight = 10 + 8), to express a number that can expressed by a certain number of times the base plus a number less than the base. Multiplication is also very common to express certain numbers above the base (two hundred = 2 x 100). In some languages, subtraction to form numbers appears implicitly (Latin duōdēvigintī '18' = 2 before 20 = 20 - 2). Instead, division is totally marginal in numeral formation and is generally restricted to fractions like 1/2.

Ordinal, partitive and multiplicative numerals

In many languages, in addition to the cardinal numerals or common numerals used to count, there are other additional types of numerals: ordinal, partitive, distributive, multiplicative, etc. Latin is an example of languages with all these types of numerals:

In inflectional languages these ordinal numerals are forms derived from the lexemes that are used to form common numerals.

Comparison of numerals

The numerals reconstructed for the mother protolanguage of various language families. Among the languages of Eurasia are:

For the languages of Africa we have:

For the languages of America we have:

And for the languages of Oceania:

Ordinal Indicator

An ordinal indicator is a symbol to indicate an ordinal number. In Spanish two types are used: "º" and "ª" according to grammatical gender, either "ᵒˢ", "ᵃˢ" and "ᵉʳ").