 Field’s alternative proposal to platonic realism (1980, 1989) is that although mathematical sentences such as ‘7 is prime’ are false, the utility of mathematical theories can be explained otherwise than in terms of their truth. For Field, the utility of mathematical theories resides not in their truth but in their conservativeness, where a mathematical theory S is conservative if and only if for any nominalistically respectable statement A (i.e. a statement whose truth does not imply the existence of abstract objects) and any body of such statements N, A is not a consequence of the conjunction of N and S unless A is a consequence of N alone (Field 1989: 125). In short, mathematics is useful, not because it allows you to derive conclusions that you couldn’t have derived from nominalistically respectable premises alone, but rather because it makes the derivation of those (nominalistically respectable) conclusions easier than it might otherwise have been. Whether or not Field’s particular brand of error-theory about arithmetic is plausible is a topic of some debate, which unfortunately cannot be pursued further here (see Hale and Wright 2001).