I don’t know if this is agreement, but the way I have thought about it for a while now is that mathematics, including arithmetic, is more like a game than anything else. Rules like the Peano Postulates exist simply because those are rules that we think are appropriate to the game—they handle cases like accumulating bottlecaps in an elegant fashion—not because they have a seperate, Platonic reality.
I don’t know if this is agreement, but the way I have thought about it for a while now is that mathematics, including arithmetic, is more like a game than anything else. Rules like the Peano Postulates exist simply because those are rules that we think are appropriate to the game—they handle cases like accumulating bottlecaps in an elegant fashion—not because they have a seperate, Platonic reality.