ABSTRACT
Numbers (and indeed other far more esoteric mathematical entities) have proved to be a rich source of puzzlement for metaphysicians. Take the claim that there are at least five prime number bigger than 2. (Actually there are infinitely many of them.) This claim is clearly true, and, what is more, it would seem that we can know it a priori: we do not have to check any empirical facts about the world in order to satisfy ourselves that it is true. (This contrasts with, say, ‘there are at least five cities bigger than Birmingham’.) However, our claim, ‘there are at least five prime numbers bigger than 2’, asserts that there are (prime) numbers: in other words, that numbers exist (see existence). Hence, what kinds of things could numbers be, such that we can know a priori that they exist?
