Abstract
Mathematical fictionalism is the view according to which mathematical objects are ultimately fictions, and, thus, need not be taken to exist. This includes fictional objects, whose existence is typically not assumed to be the case. There are different versions of this view, depending on the status of fictions and on how they are connected to the world. In this paper, I critically examine the various kinds of fictionalism that Roberto Torretti identifies, determining to what extent they provide independent, defensible conceptions of mathematical ontology and how they differ from platonism (the view according to which mathematical objects and structures exist and are abstract, that is, they are neither causally active nor are located in spacetime). I then contrast Torretti’s forms of fictionalism with a version of the view that, I argue, is clearly non-platonist and provides a deflationary account of mathematical ontology, while still accommodating the attractive features of the view that Torretti identified.