If the arguments given so far are correct, then the only remaining views—the only philosophies of mathematics that haven’t been ruled out—are platonism and fictionalism. Thus, to complete their argument, fictionalists need merely to provide an argument for premise (5); in other words, they just need to argue against platonism. But this turns out to be a lot harder than arguing against the various non-fictionalistic versions of anti-platonism considered above. As we’ve seen, fictionalists can arg