My primary point is actually that I don't care if math is useful. Math is awesome. This is obviously an extremely rare viewpoint, but very common among.

But I do agree with that quote, more or less. I think that potentially some models are true, but those models are almost certainly less useful for most purposes than the crude and easy to work with approximations.

I agree that second-order logic is not necessary to work with the integers. Second-order logic is necessary to work with the integers and only the integers, however. Somewhat problematically, it's not actually possible to work with second-order logic.

What sort of practical tasks are you thinking of?