 The easiest part of the fictionalist’s job here is arguing against the various anti-platonist views. All of these views—paraphrase nominalism, deflationary-truth nominalism, physicalism, and psychologism—can be understood (as fictionalism can) as reactions to platonism. Platonism is a very attractive view because it provides an extremely natural and pleasing account of mathematical practice and mathematical discourse. But despite this, many philosophers do not endorse platonism because they cannot bring themselves to accept its ontology. In other words, they simply don’t believe that there are any such things as abstract objects. Because of this, much of the work that’s been done in the philosophy of mathematics has been dedicated to attempts to avoid platonism. In particular, paraphrase nominalism, deflationary-truth nominalism, physicalism, and psychologism can all be understood in these terms. They all attempt to undermine the platonistic view of the truth conditions of mathematical sentences. But as will become clear below, there are serious problem with all of these views. And this is where fictionalism comes in: it grants the platonistic view of the truth conditions of mathematical sentences but still denies the platonist’s ontological thesis that there exist abstract objects. This makes fictionalism different from other anti-platonist views in an important way. We can appreciate this by noting that platonism involves two different theses, one semantic and the other ontological. The semantic thesis is an empirical hypothesis about the truth conditions of ordinary mathematical utterances, and the ontological thesis is a deeply metaphysical hypothesis about the existence of abstract objects. Every version of anti-platonism rejects the platonist’s ontological hypothesis, and all of the non-fictionalistic versions of anti-platonism reject the semantic thesis as well. Fictionalism is the only anti-platonistic view that doesn’t reject the semantic thesis. And this is why fictionalism can seem more attractive than the other versions of anti-platonism—because the platonist’s semantic hypothesis is extremely plausible and well-motivated. Thus, the versions of anti-platonism that reject this hypothesis can seem implausible and unmotivated.