 Field’s hard-road response is based on the rejection of premise (i). He argues that mathematics is, in fact, not indispensable to empirical science. Field tries to establish this thesis by arguing that our empirical theories can be nominalized, i.e., reformulated in a way that avoids reference to, and existential quantification over, abstract objects. This is an extremely controversial claim, and it is very difficult to establish, for presumably, one would have to actually carry out the nominalization for every one of our empirical theories—thus, the name hard-road fictionalism. Field did not try to do this for all of our empirical theories. Rather, he tried to motivate his position by explaining how the nominalization would go for one empirical theory, namely, Newtonian Gravitation Theory. Now, some people have complained that even if Field’s strategy could work for this one theory, it might not work for other theories, and in particular, Malament (1982) has argued that his strategy would not work in connection with Quantum Mechanics (but see Balaguer (1996b and 1998a) for an argument that Field’s strategy can be extended to the case of quantum mechanics, and see Bueno (2003) for a response). Moreover, there are several other objections that have been raised against Field’s program—see, e.g., Malament (1982), Shapiro (1983), Resnik (1985), and Chihara (1990, chapter 8, section 5). On the other hand, there are other works that develop, or provide motivation for, hard-road nominalist views; e.g., Arntzenius and Dorr (2012) develop a way to nominalize the theory of differentiable manifolds. At present, the status of the Fieldian hard-road response to the Quine-Putnam argument remains controversial.