 Peano’s axioms for arithmetic, e.g., yield an infinite regress. We are told that zero is a natural number, that every natural number has a natural number as a successor, that zero is not the successor of any natural number, and that if \(x\) and \(y\) are natural numbers with the same successor, then \(x = y\). This yields an infinite regress. Zero has a successor. It cannot be zero, since zero is not any natural number’s successor, so it must be a new natural number: one. One must have a successor. It cannot be zero, as before, nor can it be one itself, since then zero and one would have the same successor and hence be identical, and we have already said they must be distinct. So there must be a new natural number that is the successor of one: two. Two must have a successor: three. And so on … And this infinite regress entails that there are infinitely many things of a certain kind: natural numbers. But few have found this worrying. After all, there is no independent reason to think that the domain of natural numbers is finite—quite the opposite.