The problem with this move is that, even if mathematical fictionalists formulate the statement of the completeness theorem without referring to mathematical entities, the proof of this theorem assumes set theory (see, for instance, Boolos and Jeffrey 1989, pp. 131–140). Therefore, fictionalists cannot use the theorem without undermining their nominalism. After all, the point of providing a nominalistic proof of the conservativeness of set theory is to show that, without recourse to platonist mathematics, the mathematical fictionalist is able to establish that mathematics is conservative. Field has offered a platonist argument for the conservativeness result (Field 1980)—an argument that explicitly invoked properties of set theory. The idea was to provide a reductio of platonism: by using platonist mathematics, Field attempted to establish that mathematics was conservative and, thus, ultimately dispensable. In contrast with the earlier strategy, the goal was to provide a proof of the conservativeness of set theory that a nominalist could accept. But since the nominalistic proof relies on the completeness theorem, it is not at all clear that it is in fact nominalist. Mathematical fictionalists should first be able to prove the completeness result without assuming set theory. Alternatively, they should provide a nominalization strategy for set theory itself, which will then entitle them to use metalogical results.