  There are two versions of mathematical structuralism: a realist view according to which mathematical structures exist independently of their concrete instantiations; and an eliminativist position according to which statements about mathematical structures are disguised generalisations about their instantiations that exemplify them (see Shapiro 1997, 149–50.) For an excellent survey see Reck and Price (2000). The most well known advocates of realist structuralism in the philosophy of mathematics are Parsons (1990), Resnik (1997) and Shapiro (1997). Recent critiques include Hellman (2005) and MacBride (2005). The relationship between ontic structural realism and ante rem structuralism has been explored by Psillos (2006a), Busch (2003), French (2006), Pooley (2006a), Leitgeb and Ladyman (2008), Ladyman (2007)