 The formalistic view has been developed by Field (1980, 1989, 1998). On his view, the difference between ‘3 is prime’ and ‘3 is composite’ is analogous to the difference between, say, ‘Santa Claus wears a red suit’ and ‘Santa Claus wears a green suit’. More specifically, Field’s idea is that the difference between sentences like ‘3 is prime’ and ‘3 is composite’ is that the former (but not the latter) are part of a certain well-known “story”, namely, the story of mathematics. Field puts this point by saying that while ‘3 is prime’ and ‘3 is composite’ are both strictly untrue, the former is true in the story of mathematics, whereas the latter is not. Now, most of Field’s view here is consistent with both formalistic fictionalism and non-formalistic fictionalism. The difference between these two views has to do with what fictionalists take the story of mathematics to consist in. For Field, the story of mathematics consists essentially in a bunch of formal systems, namely, the ones that we currently accept. More precisely, he says (1998, p. 391) that a mathematical sentence is fictionalistically correct if and only if it is “a consequence of accepted axioms [in a]…sense of consequence that goes a bit beyond first-order consequence in including the logic of the quantifier ‘only finitely many’”. So on this view, the difference between sentences like ‘3 is prime’ and ‘3 is composite’—the reason the former are “correct” and the latter are not—is that the former follow from accepted mathematical axioms. (This view has also been endorsed by Leng (2010); she says that mathematical acceptability comes down to following from accepted axioms.)