Not all philosophers of mathematics are convinced that Fieldian nominalizations are available to replace all scientific references to abstract mathematical objects. In particular, some have argued that certain explanations of nominalist facts make essential reference to abstract objects (Baker 2005, Batterman 2010). In response, others have sought to show that there are in fact good nominalist explanations of the facts in question (Daly and Langford 2009, Butterfield 2011, Menon and Callender 2013). In any case, it is not clear that Field’s metaphysical stance requires a full execution of his nominalizing programme, as opposed to a case for its cogency: difficulties in constructing nominalist theories can always be attributed to limitations of human ingenuity rather than the reality of abstract mathematical objects (Leng 2013).