Truth in PW and the solution of Hale's dilemma for modal fictionalism

In explaining their modal views modal fictionalists hope to be able to talk about possible worlds without making a commitment, in any sense, to the existence of worlds. Bob Hale (1995a), however, has constructed a "simple" dilemma argument against the fictionalist view. In his reply to Hale, Gideon Rosen (1995) tried to take the first horn of the dilemma, but his reply was, as I show, ineffective if not confused. John Diver (1999), on the other hand, has sought to revise the original realist translation scheme to meet the dilemma, but his effort was both implausible and unnecessary. Both Rosen and Diver assume that Hale's dilemma is detrimental to modal fictionalism as formulated in Rosen's (1990) and (1993). But I argue in this paper that Rosen's formulation, and so the modal realist view, is not threatened by Hale's dilemma at all. I also axiomatize the fictionalist's favorite modal operator "according to the hypothesis of a plurality of worlds," so that Rosen's optimism can be justified.