However, it is contentious whether our best-supported empirical theories do commit us to abstract mathematical entities. The most prominent version of naturalist irrealism about mathematics, Hartry Field’s fictionalism, disputes precisely this claim. According to Field, we can construct “nominalist” versions of scientific theories that avoid commitment to abstract mathematical objects yet are explanatorily superior to the “platonist” alternatives. Field argues that we do not have to regard mathematics itself as literally true in order to understand its use in science and other applications. Rather it can be viewed as a “useful fiction” which facilitates inferences between nominalistic scientific claims, but is not itself implicated in our most serious beliefs about the world (Field 1980, 1989).