 Aside from this, the only argument against platonism that has received much attention in the philosophy of mathematics is an Ockham’s-razor-based argument. We will return to this argument (very briefly) in section 3; for now, we can simply note that, like the epistemological argument and the multiple-reductions argument, the Ockham’s-razor-based argument is very controversial, and the claim that this argument refutes platonism is (at the very least) tendentious. Thus, the overall conclusion that we seem led to here is this: even if fictionalists can motivate the platonist/fictionalist semantics of mathematical discourse and, thus, eliminate all of the anti-platonistic alternatives to fictionalism, they do not have any really compelling argument against platonism, or for the conclusion that fictionalism is superior to platonism. In other words, fictionalists don’t have any compelling argument for premise (5), and so the positive argument for their view is, at best, incomplete.