That's sounds a little absurd. A five year old child knows that 3 fingers is the same 3 as 3 ducks. Certainly 5000 years ago people understood 3 without ever kn

That's sounds a little absurd. A five year old child knows that 3 fingers is the same 3 as 3 ducks. Certainly 5000 years ago people understood 3 without ever knowing what an axiom is. The peano axioms didn't create arithmetic, arithmetic created the peano axioms. S(S(S(0))) follows | | |, not the other way around.