 In any event, if we reject thin-truth-ism — i.e., if we accept premise (1) and the standard criterion of ontological commitment — then there are two general strategies that nominalists can adopt in giving a view of mathematical sentences like ‘3 is prime’. First, they can endorse a paraphrase view, and second, they can endorse a fictionalist view. Those who endorse paraphrase views claim that while sentences like ‘3 is prime’ are true, they should not be read as platonists read them, because we can paraphrase these sentences with other sentences that do not commit us to the existence of abstract objects. One view of this sort, known as if-thenism, holds that ‘3 is prime’ can be paraphrased by ‘If there were numbers, then 3 would be prime’ (for an early version of this sort of view, see the early Hilbert (1899 and his letters to Frege in Frege (1980)); for later versions, see Putnam (1967a and 1967b) and Hellman (1989)). A second version of the paraphrase strategy, which we can call metamathematical formalism (see Curry (1951)), is that ‘3 is prime’ can be paraphrased by “‘3 is prime’ follows from the axioms of  arithmetic”.[6]  A third version, developed by Chihara (1990), is that mathematical sentences that seem to make claims about what mathematical objects exist — e.g., ‘There is a prime number between 2 and 4’ — can be paraphrased into sentences about what it's possible for us to do (in particular, what it's possible for us to write down). Others to endorse paraphrase views include Hofweber (2005), Rayo (2008), Moltmann (2013), and Yi (2002).