NOMINALISM Ghislain Guigon Final draft of the article summary of a thematic entry on Nominalism for the Routledge Encyclopedia of Philosophy https://www.rep.routledge.com/articles/thematic/nominalism/v-2 'Nominalism' refers to a family of answers to the central question of ontology: 'what is there?'. Nominalists agree that there are concrete particulars. But one group of nominalists denies that anything is non-particular and another group denies that anything is non-concrete. These two sorts of nominalism, about universals and about abstract objects, have common origins in the Middle Ages and 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 wish 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 genuine properties are. Nominalist theories about universals can thus be divided between those that take sui generis properties to be particular instead of universal; those that take properties to be constructions out of (classes of) concrete particulars, and those that reject properties altogether. Each of these nominalist strategies has its own merits and difficulties. The central question to decide whether abstract objects exist is whether their existence is indispensable to our best scientific theories. Nominalists about abstract objects contend that they are not indispensable. Some of them argue that, although theories like mathematics that posit abstract objects are useful in natural sciences, they are false. Other nominalists maintain that mathematics is true but deny that its truth entails that mathematical entities exist. 1 Introduction 2 Common difficulties with universals and abstract objects 3 Nominalism about universals 4 Nominalism about abstract objects