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Modal fictionalists face a problem that arises due to their possible-world story being incomplete in the sense that certain relevant claims are neither true nor false according to it. It has recently been suggested that this incompleteness problem generalises to other brands of fictionalism, such as fictionalism about composite or mathematical objects. In this paper, I argue that these fictionalist positions are particularly threatened by a generalised incompleteness problem since they cannot emulate the modal fictionalists’ most attractive response. I then defend mathematical and compositional fictionalism by showing that the reasons for which the incompleteness problem has been thought to affect them are mistaken. This leads to the question of whether there are other fictionalist positions to which the problem does in fact generalise. I give a general account of the features of a fictionalist position that generate the incompleteness problem and argue that whenever a fictionalist position does exemplify these features then the problem can be addressed in analogy to the modal fictionalists’ preferred response.

DOI: 10.1007/s11229-015-1000-1

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