  Our default view is that mathematical standards decide questions in mathematics proper, for example questions such as whether Fermat's Last Theorem or the Axiom of Choice is true. Scientific standards are thought not to affect this: when Andrew Wiles proved Fermat's Last Theorem in the mid-1990s, he was not particularly concerned with how his proof would go down in physics departments, or more generally its impact on empirical science. Similarly, the claim that if some large cardinal axiom is not scientifically sanctioned (perhaps because it leads to no new empirical consequences) then there is no good reason to accept it is, as Maddy points out, ‘out of step with the actual practice of set theory’ (1997, 132), and indeed out of step with the actual practice of much philosophy. We usually do not judge large cardinal axioms by scientific standards; we judge them by mathematical standards. Quine was self-consciously going against the grain when he rejected the higher flights of set theory on scientific grounds (1986, 400).