 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 zero in on arithmetic, there are still many different ways to formulate the argument. One way to do this is as follows: (A) if there are any sequences of abstract objects that satisfy our arithmetical theories, then there are infinitely many, and there is nothing “metaphysically special” about any of these sequences that makes it stand out as the sequence of natural numbers; but (B) platonism is committed to the thesis that there is a unique sequence of abstract objects that is the natural numbers. Therefore, (C) platonism is false.