Any known theory of the origin of numerals as a morphological category does not exist. But, obviously, there are some ideas in this regard. One of them occurred when studying the Nostratic languages and develops here in the sequel.
In ongoing studies we include to the Nostratic macrofamily the Indo-European, Finno-Ugric, Turkic, Semitic-Hamitic (Afroasian), Kartvelian and Dravidian languages. Maybe, it is possible that they include other languages, primarily North Caucasian (Northwest Caucasian and Nakh-Dagestani). However, we refer to the so-called "Altaic" languages only Turkic. In all things, total dissimilarity between the Turkic and Mongol numerals says against the genetic relation of Turkic and other Altaic, not to mention about similarity between Turkic and Tungus-Manchu, Korean and Japanese (see Table 1).
Table 1. The cardinal numbers of the ancient Turkic and the Mongolian languages.
The importance of similarity of numerical as anargument of genetic relationship between languages is confirmed by the semblance of numerals within particular language families of Nostratic phylum, and among the Turkic languages especially. Moreover, some similarities of numerals can be found also among the languages of different Nostratic families. For ease comparing of numerals up to ten of the particular Nostratic languages, they are summarized in Table 2. The Ingush and Kabardian numerals are assessed too for the estimation of their possible membership to the Nostratic languages.
Table 2. The cardinal numbers of the Nostratic languages.
Careful examination of the table makes it possible to detect some patterns that can be a starting point for finding the logic of formation of numerals in the Nostratic languages:
1. Turkic ikki “two” may be corresponded to some words of Finno-Ugric languages meaning "one" (Erzia vejke, Mari ik, Hung egy, Fin. yksi, Veps. üks'). They have also matches in some Indo-European languages such as O.I. éka “one” and many words of Iranian (Farsi, Tadjic, Kurdish jak, Baluchy, Gilani jek etc). Mayba Udm odez, Ivrit axat, Ar wāhid and Telugu okati “one” can be added here too.
2. Some Indo-European and Dravidian languages have similar words for the number one: Lat ūnus, (Gr οινοσ), Ger ein etc – Tulu onji, Tamil onru, Malayalam onnu, etc.
3. There is some similarity in even numerals: Indo-European *quetwor “four” (Latin quattuor, An. Ind. catvara, slav. četyre, etc.) – Hung. kettő, Khanty kät, Mansi kit, Erzia kavto “two", Komi kvajt, Udm kuat ', Khanty kut, Erzya kota, etc. "six"; PIE *seks “six" (Latin sex, Ger sechs, Slav. šestĭ, lit. šeši, etc.) – Turkic. sekiz “eight”, Hebrew šeš ”six”; Hebrew arba “six" – Georgian rva “eight” – Telugu aaru “six”. However, the most expressive is the likeness of Finno-Ugric and the Dravidian word for the number four: Fin. neljä, Erzia nile, Mansi nila, etc. – Malayalam nālu, Telugu naalugu, Tulu nāl etc.
4. Indo-European *deťm "ten" (Slav. desętĭ, O.Ind dáśa, lat. decem, etc.) corresponds to Udm., Komi das, hung. tiz „ten".
5. Neighboring numerals often rhyme: Russ sem’ „seven“ – vosem’ „eight“, dieviat’ „nine“ – desiat’ „ten“, Ger zwei "two" – drei "thre", Arm. yot' „seven“ – ut' „eight“, Türk. sekiz „nine“ – toquz „ten“, Fin. kahdeksan „eight“ – yhdeksän „nine“, Veps kahesa „eight“ – ühesa „nine“, Gondi sārūng “six’- ērūng “seven” etc.
6. Some facts evidence about cases of replacing old items by newer numbers. For example, the Chuvash pillĕk ”five” corresponds in the other Turkic languages bileg, bilezik ”carpus, wrist” which at first could also mean "five". However, at some time in all Turkic languages, Chuvash except, a new word beš spread for referring five.
The remaining cases of similarities will be considered during the process of further discussion. We begin our analysis by considering the origin of the name of a single object. Herewith we will bear in mind that the thinking of primitive man proceeded by their own laws, different from our formal-logical thinking. Before man came to the abstract understanding of numbers, the quantitative relationships between objects were joined with the objects themselves and could be used a variety of accounts for different categories of subjects. For example, while exchange equating of the two rams to one cow confused the difference between the numbers one and two.
As one can see from the table, the words, using for the number one in the languages of considered family derive from different roots, except that the Old Indian éka can be likened to the Finno-Ugric words having the root *ek/ik. After further searches, similar numbers were found in several Iranian languages, in particular Farsi – jak, Kurdish – ēk, and Gilaki – jek “one”. Obviously, words of Finno-Ugric languages (Komi, Udm kyk) meaning “two” derived from the same root by reduplication (ik-ik). Number two was seen initially as a couple, a sort of a unit of the pair of objects – two eyes, ears, hands. The emergence of the dual grammatical number would be meaningless if the two pairs of items were not opposed to the large set of items which had a separate category of number. Taking into account the possible similarities in the names of neighboring numbers and initially unconscious quantitative difference between the numbers 1 and 2, we assume that the Turk ikki “two” has the same origin and look for the original word which according its meaning could suit for the start of counting. After a short search we can stop at the Indo-European pronoun *eĝ.
It is quite logical for man to begin counting from himself therefore the same word might well be used to characterize myself and the number 1. Analysis of the symbolic meanings of numbers in the folklore led ethnographers to the conclusion that the symbolism of the one claimed the symbolism of the center too, and the number 1 become meaning the "divine" or "royal" number and a person which it defines (NOVIKOVA Ě.Î. 1993, 278). The primitive man looked at the world from self-serving positions which led him to the identification of himself with the unit, symbolizing the center.
The assumption that the primary identity of the numeral "one" and the pronoun "I" is also supported by the fact that other Indo-European word *sem meaning "one" corresponds to the pronoun “myself” in the Slavic languages. Derived words from this root in some Indo-European languages kept sense "one" or mean "same", "equal", "similar" (Latin similis, Eng same, etc.) Obviously, this numeral is the most ancient in the human language as similar words meaning "one" can be found in many languages, in particular, in Daghestan (Andi, Godoberi, Tabasaran. – seb, sab)? Korean hana, Ainu šine etc.
Further confirmation of the identity of the numeral "one" and the pronoun "I" is the fact that some Indo-European words having meaning “one” (Latin ūnus, Gr οινοσ, Goth ains, Eng one, Old-Irish oen) are similar to the words meaning "I" in the Semitic languages (Hebrew, ani, Ar ana) and in Hungarian èn. The similarity of the first-person pronoun singular and the numeral "one" can be observed in Kabardian: se “I” – zy “one", Ingush: so «I», sa «my» – caI «one" (besides saI “man"). If the pronouns were used for counting, it should exist examples of using for accounting also the second person pronouns. At least one such example is present – PIE *dvou ”two" in sounding is like the PIE *tu “you” (singular). It would be logical to assume that the third person pronoun was used with the meaning "three", but such match is not found. Obviously, this is due to the fact that at first the count was continued only up to two, followed by uncertainty "a lot".
Thus, we can assume that using third person pronouns to refer to three items was not necessary at the time of birth of the count. Nevertheless, its tracks are found in the names of numbers. Indo-European and Dravidian words meaning "one" (Latin ūnus etc. – Tulu onji, etc., see above) correspond to the Indo-European words meaning "he, that, this" (Russian on, Lit. añs, Old Ind anyas, N Germ enn, Hittite anni). It is interesting that similar words in Semitic languages belong to the first person pronoun, just as Hung. én “I” does. Obviously, this is because the same word for the speaker means "I", and for the listener – "he".
Overcoming uncertainty "a lot" was happened by dividing large number of subjects in pairs and further counting occurred already by pairs, and this explain similarity of even numbers can be observed even within the same language: Hebrew šnaim «two» – šmone “eight", Hung. négy (in other Finno-Ugric neljä, nyl, nila a.o.) – Hung nyolc “eight”, Mansi nila “four”- n'ololov “eight” Pair counting also explains the similarity in the names of numbers "one" and "two", another example of which can be a match: Lat. par “equal”, paria “couple" – Chuv pěr “one" (in other Turkic – bir). It is possible that word cam to the ancient Italics from the Bulgars.
Of course, while paired counting the first two pairs were very clearly were aware therefore the number 4 became particular importance. It was the last "small" number, after which large numbers followed and all numbers from 1 to 4 acquired a special meaning in human consciousness, what is evidenced, for example, by all genres of Ukrainian folklore: riddles, proverbs, beliefs, etc (Ibid, 276). Special significance of the number 4 is confirmed by the Indo-European *octou “eight" in the form of dual number i. e. basically means two fours.
In addition, we note the striking similarity of the Finno-Ugric and the Dravidian word meaning "four", while the names of the remaining numbers are totally dissimilar (see Table 2). The number 4 corresponds to the directions of natural human spatial orientation (left-right, front-back) and, most importantly, the number of fingers on one hand without the large one, so the binary counting system easily transferred in the quaternary one. However there arose confusion in the numbers of pairs, as uncertainty "a lot" was felt for a long time. Also intertribal trade assisted confusion when the names of numbers were no longer aligned with the pronouns of an unknown language for one of the contractors, but took a specific value of a number. Besides, due to the local character of trade relations, local countable nomenclature took place and the standardization of number names was not occurred for a long time. In such circumstances it is possible that similar words were used for different numbers (Tulu enma "eight", Gondi anma "nine "), and different words for the same number were used as it is confirmed by the examples of even more recent times ("two" and "pair", "twelve" and "a dozen").
Obviously, while paired counting numerals one and two and 2 could easily turn in synonymous what we observe in the likeness of the Turkic and Finno-Ugric numerals of such value. In connection with this hypothesis, Indo-European *quetwor can mean "two pairs", arising from composing two synonyms *(i)ki and *dvou. It is also logical to assume that by pair counting odd numbers were not originally perceived and appeared later. No wonder they are considered as "bad" or strange numbers (cf. the means of English odd). This is explained by the fact that archaic world tended to identify every odd thing and surpluses with disordered, unstable, dynamic and therefore dangerous, bad element (Ibid, 278). Therefore, the similarity of odd numbers in the Nostratic languages is expressed very unclearly and can be simply accidental, or be the result of later borrowings.
However, despite some confusion in the names of even numbers less than ten, ten items have already determined more or less clearly, helped by the number of fingers on both hands. Apparently, this happened at a time when the northern Nostratic tribes migrated to Eastern Europe, as the languages of their descendants have nothing mutual with Semitic-Hamitic, Kartvelian and Dravidian names for the ten subjects. But Hebrew and Arabic words teša / tis`ah “nine” are somewhat like this numeral in some modern Indo-European languages. Is it random coincidence or whether this phenomenon has some explanation, yet to be determined. Some Dravidian languages (Kurukh, Malto, Peng, Kui, Kuvi) have the form das for the number ten, close to the word of Indo-European languages, but they can be later borrowed from Hindi, Bengali, and other Indian languages, as the most widened Dravidian languages Telugu, Tamil, Tulu have nothing like. The rate of development of counting systems was very slow. People have learned to count after ten quite late and the formation of the numerals went different ways at people even speaking closely related languages. For example, the duodecimal system of accounts among the Germans said that the account after ten began after the split of the Indo-European community (3rd thousand BC). The advantage of duodecimal system was the fact that 12 is divisible by two, three and four, while 10 could be divided only by two and five (HIRT HERMAN. 1940). However, this advantage is not used by all peoples of the word.
The common Indo-European original form of the numeral ten is restored as *deťm (Latin děcěm, Germ tehun, Slav desętĭ, Let desmit, etc.) and interpreted as "two five" while Gmc *handu “hand”, which has no counterparts in other Indo-European languages, was compounded inone word with late word-formation di-/de- “two" originated from Gr dis (VASMER MAX. 1964: 507-508). This is very doubtful interpretation, despite the fact that we can find a more transparent etymology of the European word. It may have the same origin as the Old Turkic *dekim “a lot”, "set", which is restored according to the word recorded in ancient Turkic writing takım “many, set" (NADELIAYEV V.M., NASILOV D.M., TENISHEV E.R., SHCHERBAK A.M. 1969) wich has the match in Turkish takım "group, team". Obviously, while intertribal trade, the general praform used by the Türk in general terms took on a more specific meaning at the Indo-Europeans. That this could just happen, is confirmed by Tat. tugyz meaning both "nine" and "a lot". We can assume that the words like tekim also meant "ten" in the Turkic languages but only later were replaced by on, un which can be compared with the Indo-European words having meaning “one” (Lat unus, Eng one etc), as ten subjects can be one unity counting by tens.
It is more difficult with the number 10 in the Finno-Ugric languages where different words are used for it. However, the most spread primordial form can be restored as *deksan presented as partial word in the Finnish numerals "eight" (kahdeksan) and “nine” (yhdeksän). These numbers, as well as in other Finno-Ugric languages, are formed by a form of "ten minus two” (kah has the same origin as kaksi “two") and ten without one (yh as yksi “one”). This assumption is known thinking that the Finnish word is supposedly borrowed from some Indo-European. It is considered unacceptable and is disputed for other reasons. Instead, it is proposed that the second part of the Finnish words be considered not -deksan, but -eksan out of Fin. eksy "to be lost". Then "eight" should mean "without missing two" (out of ten), and "nine" – "without missing one" (HÄKKINEN KAISA. 2007: 315-316). However FU *deksan, IE *deťm, as Old Turkic tekim can be a common Nostratic heritage. The form *deksan was something simplified in other Finno-Ugric languages (Upper-Mari – dakšy, Low-Mari – daše, Vepsian – esa, Erzya and Moksha – ksa/kse). The simplified form das means ten in the Komi and Udmurt languages, but it is loan-word from Iranian where similar words also ten. The numerals eight and nine in the Komi and Udmurt languages contain formant mys but its meaning remains unknown. When this question becomes clearer, then it will be possible to speak more confidently about the origin of the numerals "eight" and "nine" in the Finno-Ugric languages.
Another variant of the numeral "ten" is spread in the Baltic-Finnish and Mordvin languages: Finnish. kymmenen, Est. kümme, Erzya kemen 'etc. Obviously, it is based on the name of the palm (Finnish kämmen, Est. kämmal, Veps. kämen', Khant. kömõn). The languages Mari, Mansi and Sami have for "ten" the words lu, lov, love, logi, Hungarian has tíz. It is believed that they are based on the ancient Finno-Ugric word presented in Fin. lukea "to read" (HÄKKINEN KAISA. 2007: 532).
Since an odd number of objects were not perceived by people for a long time, "extra" item was joined to a greater or lesser number. However, it is rightly to assumed that the number 3 appeared earlier other odd numbers and the relevant words could originate from the nearest even number 4 (as opposed to two, four subjects could be sooner perceived as three). Therefore, we consider forms of the numerals "three" and "four" in the Nostratic languages. We can see that Indo-European *treis “three”, Turkic tort “four "and Semitic-Hamitic *talat “three” (Class. Ar. rhalatah, Syrian-Ar. tlāte, Hebrew šaloš, etc.) have remote similarity. This let to assume their common origin from the word meaning "wrong, bad." Traces of it have been preserved in many Turkic languages as ters "wrong, perverse, complex, reverse, opposite”. Such traces are less distinct in Indo-European languages, but still visible: lat. trīstus "bad," Old Eng. dryslic “awful”. Following the same way, we can take to examination of the Fin. kummalinen, Est. kummaline “strange” and others similar ones for the number 3 (Finnish kolme, Erzya kolmo). While metathesis of consonants, such words might mean "three", but similar words are not found yet in other Finno-Ugric languages. If this assumption about the origin of the numeral 3 is true, then the Tur tört "four"should be a secondary name, produced from the names of three, as four originally was not "bad" number. This change seems unlikely because of the special values of the number 4 however can have explanation. On early stage of development accounts, the number 3 because of its “incorrectness” seemed to be incomprehensible for man and become mystical connotation in accordance with the three coordinates of the universe by vertical (the upper, middle and lower worlds). Since the number 4 is consistent with the coordinates in the horizontal plane, both the numbers have equally great importance in the human psychology. Such phenomenon is reflected, for example, in the form of religious buildings – churches in Ukraine have since long were "built with four angles and three tops". Another example could be a characteristic alternation of "three or four" in the Ukrainian archaic poetics: "Poles came by three ways, and the Tatars by four ones did” and many others (Popovich M.V. 1985: 82).
The Indo-Europeans in general and, in particular, the Celts lent a form of the triad, trinity to all what was supernatural and sacred . Taking into account the possibility of tabooed substitutions in the religious sphere, changing the names of the numbers becomes quite understandable, moreover, that the three could mean "the opposite" in accordance with the value of Turkic ters. Again Chuv tăvattă "four" also evidences that the Trc tört / dört “four" are secondary names. The ancestors of the Chuvash, the Bulgars, had been early separated from the other Turkic community, and therefore kept the old name, not knowing about the new word-formation. We can assume that this rather complicated word was a reduplication of the Nostratic numeral "two", derivative of which was preserved in Indo-European – *dvou, ie four could exist in Turkic in the form *dvadva which from Chuv tăvattă evolved, and from it later and Latin quattuor did.
It is difficult to assume the origin of numerals meaning “five”. On the one hand, it could be like to the nearest even number, on the other hand to take the name of the hand as adequacy to five fingers. In this case, five objects could be the unit of account and hence the names "one" and "five" may be similar, as we see when comparing Komi öti “one" and the Hungarian öt “five", which has parallels in other Finno-Ugric languages.
It is even more difficult to judge about the origin of numerals meaning "Seven" and "Nine." Ways of their creation in different languages were different, but it is obvious that the number "Nine" got its name later than "Seven". With the score up to eight and a good imagination of all the previous ones, as well seven had to have its own name. Number more than eight or received a sense "a lot" or combined in pairs, ie, "nine" and "ten" could be called by the same word. However, over time "nine" owed its name while in Indo-European languages, it meant in the sense of "new", judging by the fact that in these languages the word "new" and "nine" are similar.
A certain connection between numerals and pronouns have already attracted the attention of linguists. For example, it is believed that the numeral two in many languages of the world is used to form the dual personal pronoun "we two", "two of you" (BABAYEV K.V. 2009: 132-134). In principle, such a transformation is logical if the numeral "two" originated before the pronoun. However, it is believed that originally pronouns were absent in languages and evolved from other lexical or morphological units of language later (ibid, 119), that is, they can also develop from numerals. Although in certain cases, a reverse process could be occurred.
I look for the book of László Honti "Die Grundzahlwörter der uralischen Sprachen"