  To explain how this bivalent attitude might work in practice, take Maddy's favourite example: set theory. Suppose that ZFC + LCA is our current accepted set theory, where LCA is some collection of large cardinal axioms. Given mathematical naturalism about mathematics proper, there is no question of rejecting ZFC + LCA in favour of, say, ZFC + the axiom that there are no inaccessibles, or some other set theory, say Quine's New Foundations. Mathematical standards sanction ZFC + LCA, so that is the set theory we must accept. But how should we interpret ZFC + LCA? Platonistically, structurally or in some other way? That is a philosophical question, so given scientific naturalism about the philosophy of mathematics (and philosophy more generally) its correct answer is that sanctioned by scientific standards. For example, if an overriding scientific criterion of simplicity favours platonism over all other interpretations, that must be the correct interpretation of ZFC+LCA.