Given that the epistemological argument does not succeed in refuting platonism, fictionalists might attempt to provide some other argument against platonism. One such argument that has received considerable attention is the multiple-reductions argument. The classical statement of this argument is given, once again, by Benacerraf (1965). The argument can be run in connection with any of our mathematical theories, but the point is usually made in connection with arithmetic. Moreover, even when we