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Full Idea
To begin with, in Mesopotamia, counting systems applied to specific commodities (so the symbol for 'three sheep' applied only to sheep, and 'three cows' applied only to cows), but later words for abstract qualities emerged.
Gist of Idea
Mesopotamian numbers applied to specific things, and then became abstract
Source
Peter Watson (Ideas [2005], Ch.04)
Book Ref
Watson,Peter: 'Ideas: from fire to Freud' [Phoenix 2006], p.129
A Reaction
It seems from this that we actually have a record of the discovery of true numbers. Delightful. I think the best way to describe what happened is that they began to spot patterns.