 Paraphrase nominalism is the view that ordinary mathematical sentences like ‘3 is prime’ should not be read at face value—or more specifically, that they should not be read as being of the form ‘Fa’ and making claims about mathematical objects. There are a few different versions of this view. Perhaps the most famous is if-thenism. On this view, ‘3 is prime’ is best interpreted as expressing a conditional claim, such as ‘If there were numbers, then 3 would be prime’, or perhaps ‘Necessarily, if there are numbers, then 3 is prime.’ (Versions of if-thenism have been developed by Putnam (1967a,b), Horgan (1984), Hellman (1989), Dorr (2008), and Yablo (2017); moreover, a precursor to this view was endorsed by the early Hilbert (see his 1899 and his letters to Frege in Frege 1980). Finally, other versions of paraphrase nominalism have been endorsed by Chihara (1990), Yi (2002), Hofweber (2005), Rayo (2008, 2013), and Moltmann (2013); and one might also interpret Curry (1951) and Wittgenstein (1956) in this way.) 