  Field (1980) presents a case for denying the second premise of the Quine-Putnam argument. That is, he suggests that despite appearances mathematics is not indispensable to science. There are two parts to Field’s project. The first is to argue that mathematical theories don’t have to be true to be useful in applications, they need merely to be conservative. (This is, roughly, that if a mathematical theory is added to a nominalist scientific theory, no nominalist consequences follow that wouldn’t follow from the nominalist scientific theory alone.) This explains why mathematics can be used in science but it does not explain why it is used. The latter is due to the fact that mathematics makes calculation and statement of various theories much simpler. Thus, for Field, the utility of mathematics is merely pragmatic — mathematics is not indispensable after all.