Nominalism

Abstract

‘Nominalism’ refers to a family of views about what there is. The objects we are familiar with (e.g. hands, laptops, cookies, and trees) can be characterized as concrete and particular. Nominalists agree that there are such things. But one group of nominalists denies that anything is nonparticular and another group denies that anything is nonconcrete. These two sorts of nominalism, referred to as ‘nominalism about universals’ and ‘nominalism about abstract objects’, have common motivations in contemporary philosophy. According to nominalists, universals and abstract objects are mysterious entities whose claim to existence is suspicious or ad hoc. This gives them reasons to want to reject universals and abstract objects but leads to an explanatory challenge: nominalists must explain away the appearance of the universal or the abstract. Varieties of nominalism differ with respect to how they address this challenge. Universals are sui generis entities that are typically thought to be what properties are. Nominalist theories about universals can thus be divided between those that admit that there are sui generis properties but maintain that they are particular instead of universal; those that use constructions out of concrete particular objects to play the role of properties, and those that reject properties altogether. Each of these nominalist strategies has its own merits and difficulties. Theories that seem to posit the existence of abstract objects, like mathematics and set theory, are successfully used in natural sciences. The utility of these theories challenges nominalism about abstract objects and has shaped the current debate about whether these objects exist. According to some nominalists, theories that posit abstract objects are useful but false. Other nominalists maintain that these theories are true but that their truth does not entail that abstract objects exist.