 Paraphrase nominalists might try to respond to this argument by denying that they are committed to the thesis that their paraphrases fit with the intentions of ordinary mathematicians and ordinary folk. Indeed, claims of this sort have been made by both Chihara (1990, 2004) and Hellman (1998). But paraphrase nominalists cannot endorse this stance, for if they do, their view will collapse into a version of fictionalism. If paraphrase nominalists admit that platonists and fictionalists are right about the meanings of real mathematical utterances—i.e., the utterances of actual mathematicians—then (since they also want to maintain that there are no such things as abstract objects) they will be committed to the claim that the utterances of actual mathematicians are untrue. Thus, if paraphrase nominalists don’t claim that their paraphrases capture the actual meanings of ordinary mathematical sentences, then their view won’t provide a genuine alternative to fictionalism. It will collapse into a version of fictionalism. More specifically, a paraphrase nominalist would just be a fictionalist who thinks that we ought to alter our mathematical language, or what we mean by our mathematical utterances; or perhaps the claim would simply be that we could alter our mathematical language if we wanted to and that this fact provides fictionalists with a way of responding to certain objections.