"The Nature and Meaning of Numbers" (1888) by Dedekind. He proved that any set of mathematical objects conforming to the second order Peano axioms is isomorphic to the natural numbers. Peano axioms basically formalize the notion of well-behaved (that is practically useful) counting numbers.

If you were to dig deeper, you'd get to the murky philosophical depths of foundations of mathematics, but I prefer to not go there. Practically, if you want to reliably count something, you end up with the natural numbers (or, maybe, their subset that ultrafinitists are trying to formalize).