The inability to take mathematical discourse literally is indeed a problem for nominalists, who typically need to rewrite the relevant mathematical theories. As will become clear below, it is common that nominalization strategies for mathematics change either the syntax or the semantics of mathematical statements. For instance, in the case of modal structuralism, modal operators are introduced to preserve verbal agreement with the platonist (Hellman 1989). The proposal is that each mathematical statement S is translated into two modal statements: (i) if there were structures of the suitable kind, S would be true in these structures, and (ii) it's possible that there are such structures. As a result, both the syntax and the semantics of mathematics are changed. In the case of mathematical fictionalism, in order to preserve verbal agreement with the platonist despite the denial of the existence of mathematical objects, fiction operators (such as, ‘According to arithmetic…’) are introduced (Field 1989). Once again, the resulting proposal changes the syntax (and, hence, the semantics) of mathematical discourse. This is a significant cost for these views.