Could you point out some theories on how the names for numbers developed?

Question

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.

Answer 1

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 *h_xok̂tṓ(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(h_a): "formed on the full-grade"
• 50: *penkʷe-k̂omt(h_a): id.
• 60: *kswek̂s-k̂omt(h_a): 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.

Answer 2

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/