A modal fictionalist may be driven to accept that the fiction is a collection of propositions in response to any of several objections: the worry about artificiality, the worry about incompleteness, or alternatively on more general grounds (given that taking fictions to be collections of propositions is attractive quite apart from considerations about modal fictionalism).
As the label suggests, they do not regard their view as a species of non-cognitivism, but like fictionalism the view does accept one of non-cognitivism's two constitutive negative theses while rejecting the other.
And Rosen (2001) argues that fictionalism is epistemically permissible because another community of scientists could accept the very same theories that we do while endorsing or, more to the point, rationally endorsing a fictionalist attitude toward the mathematical components of their theories.
Fictionalism is an approach to theoretical matters in a given area which treats the claims in that area as being in some sense analogous to fictional claims: claims we do not literally accept at face value, but which we nevertheless think serve some useful function.
It is possible to accept the conceptual thesis but deny the metaphysical thesis (e.g., those who hold a version of color fictionalism or a projectivist theory or the Illusory theory).
Together with fictionalism it illustrates a position which accepts only one of the two negative theses constitutive of standard non-cognitivism.
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.
It should be noted, though, that several different defenders of fictionalism have responded to worries about the nominalistic status of their own particular versions of fictionalism.
The argument can be put like this: Fictionalists face a dilemma: they have to endorse either hermeneutic fictionalism or revolutionary fictionalism, but neither is plausible.
Consult Daniel Nolan's entry on modal fictionalism for what criticisms have been leveled specifically against modal fictionalism.
