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At this point I don't want to explain my personal crackpot theories on how names for numbers emerged and I assume that anything remotely connected with the origin of language is highly speculative and hard if not impossible being researched empirically. Nethertheless, centuries of speculation might have culminated into a few theories which might be considered an educated guess or even more.

Here I limit the theories onto the origin of the names for numerals, what probably doesn't make it much easier.

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    Numbers are a fairly late invention to languages, and there are many different ways of organizing the system, if that's what you mean. As to where the actual words come from, they come from the words of the previous generations, all mingled together and mushed up. With little things like Latin quinque next to pinque in Oscan or Umbrian, because it comes after quattuor in counting. The same thing happened in reverse with English four, five. We kept the /f/ in five_but changed the initial consonant of _four to anticipate five. But that's just English and Latin. – jlawler Mar 13 '17 at 23:53
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    We have evidence of number words going back perhaps 10,000 years at maximum. We have evidence of languages still spoken today that don't have number words. We have evidence of language use going back a million years at minimum, but no evidence of what the languages were like. Obviously it's possible to have a language without numbers, so they have to be posited as a later development, not an essential part like verbs. – jlawler Mar 14 '17 at 14:23
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    We only know about evidence-based theories here, sorry. – jlawler Mar 14 '17 at 15:20
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    @AbdulAlHazred But modern studies in the origin of life aren't non-evidence-based - they perform experiments in labs to see how plausible their theories are, and so far it's optimistic. And evolutionary linguists have done similar things about the evolution of language. – WavesWashSands Mar 15 '17 at 12:26
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    @AbdulAlHazred Actually, they can use creolisation as a possible way to test theories of language emergence; Bickerton and Givón are both famous proponents of that. And yes, we have observed language emerging ex nihilo. – WavesWashSands Mar 19 '17 at 2:36
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The following theories that try to explain the origin of Proto-Indo-European numerals are mentioned in J. P. Mallory, D. Q. Adams, The Oxford Introduction to Proto-Indo-European and the Proto-Indo-European World:

  • 1 *h₁oi-no-s: from the anaphoric pronoun *h₁ei- (i.e. English one)
  • 1 *sem-s: originally "one united together"
  • 2 *dweh₃(u), *dwoh₃(u): originally a demonstrative pronoun 'that one further away'
  • 3 *tréyes: from a root meaning "further" or a root meaning "middle, top, protuding" (referring to the middle finger)
  • 4 *kʷetóres: may have a relationship to idea of a span of four fingers or the little finger, or from the enclitic for "and" + the root of "three"
  • 4 *mei-wos: from a root meaning "be small", referring to the little finger or expressing "five minus one"; alternatively, from a root meaning "large", referring to a "large span" (of fingers)
  • 5 *pénkʷe: from a root meaning "fist"; less likely, from a root meaning "all, totality"
  • 6 *kswek̂s: from a root meaning "hand" + a root meaning "increase", or maybe borrowed from another language
  • 7 *septḿ̥: borrowed from another language
  • 8 *hxok̂tṓ(u): dual form of an uncertain root; the root may have meant "sharp, pointed", maybe referring to a set of pointing fingers; alternatively, the root may have been borrowed from Proto-Kartvelian
  • 9 *h₁newh₁m̥ (*h₁newh₁n̥): from a root meaning "new" (expressing "new number after eight"), or one meaning "without" (expressing "ten without one")
  • 10 *dék̂m̥(t): from roots meaning "two" and "hand", or from roots meaning "right" and "hand", or having a root that means "reach"
  • 12 *dwō dek̂m̥(t): "two-ten"
  • 15 *penkʷe dek̂m̥(t): "five-ten"
  • 20 *wīkitih₁: "two-tens"
  • 30 *trī-k̂omt(ha): "formed on the full-grade"
  • 50: *penkʷe-k̂omt(ha): id.
  • 60: *kswek̂s-k̂omt(ha): id.
  • 100: *k̂m̥tóm: shortening of a root meaning "ten tens" or "tenth ten"

But these are just speculation. When mentioning the etymology of *h₁oi-no-s, the authors write that

Although there are a number of other theories, this etymology is one of the few thought up for any of the numbers that is at all likely to be correct.

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This might not be directly what you were looking for, but if you're interested in the "names" for numerals, one thing I think might be valid is the point of "discrimination", i.e. because the numbers are all quite frequently used in daily conversations, people need to discriminate them as distinctly as possible. This is similar to the role played by genders in gendered languages.

Thus you might observe that the pronunciations of the basic number words from 1 to 10 are mostly very distinct in most languages and they're not easy to be confused together. Maybe the true "origin" of those names can be a bit random, but the point is, through the evolution they must be as distinct from each other as possible.

This was the theory of one of our professors anyways and you may go to his blog for detailed expositions. https://michaelramscar.wordpress.com/ https://ramscar.wordpress.com/

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    Interestingly, there also seems to be an opposing tendency to make adjacent numerals more similar to one another; see my post and the comments below it here: linguistics.stackexchange.com/questions/15674/… – ewawe Mar 18 '17 at 21:47
  • Can put up a deep link to the relevant blog entries? – jknappen - Reinstate Monica Mar 20 '17 at 10:31
  • @jknappen Actually I believe that was from one of his lectures, and I'm not sure I'm allowed to reproduce lecture slides online directly, or whether he directly put that in some slides at all. But if you read through his blogs you'll see similar ideas, e.g. on the distribution of names. – xji Mar 20 '17 at 18:39
  • Could the downvoter explain the reason? Is it because the link is considered to be not specific enough? As I said, I just heard that through one of his lectures so I'm not sure I can put up any direct reference here. The links contain related ideas. – xji Mar 20 '17 at 18:43

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