 Balaguer’s non-formalistic version of fictionalism retains Field’s thesis that mathematical “correctness” has to do with being true in the story of mathematics, but it abandons the Fieldian view that the story of mathematics consists in currently accepted axioms. According to Balaguer, the so-called “story of mathematics” consists in the thesis that there actually exist abstract mathematical objects of the kinds that platonists have in mind, i.e., the kinds that our mathematical theories purport to be about. Thus, on this view, a mathematical sentence is fictionalistically correct if and only if it would have been true if there had actually existed abstract mathematical objects of the kinds that platonists have in mind. Balaguer argues that if fictionalists adopt this view, they can avoid the above problem with Field’s view and, more generally, they can completely solve the problem of objectivity because they can mimic everything platonists say about objectivity. 