 There is no consensus on whether the fictionalist responses to the Quine-Putnam argument are successful. But even if they are, there are other objections that platonists might raise against fictionalism. For instance, one might argue that fictionalists cannot account for the objectivity of mathematics (for responses to this, see Field (1980, 1989, 1998) and Balaguer (2009)). Or, second, one might argue that fictionalism is not a nominalistically acceptable view because formulations of it invariably involve tacit reference to various kinds of abstract objects, such as sentence types, or stories, or possible worlds (for responses to this, see Field (1989), Balaguer (1998a), and Rosen (2001)). For other objections to fictionalism, see, e.g., Malament (1982), Shapiro (1983a), Resnik (1985), Chihara (1990, chapter 8, section 5), Horwich (1991), O’Leary-Hawthorne (1997), Burgess and Rosen (1997), Katz (1998), Thomas (2000, 2002), Stanley (2002), Bueno (2003), Szabo (2003), Hoffman (2004), and Burgess (2004). For responses to these objections, see the various fictionalist works cited above, as well as Daly (2008) and Liggins (2010). And for a discussion of all these objections, as well as fictionalist responses to them, see the entry on  fictionalism in the philosophy of mathematics.)