Nominalism

‘Nominalism’ refers to a reductionist approach to problems about the existence and nature of abstract entities; it thus stands opposed to Platonism and realism. Whereas the Platonist defends an ontological framework in which things like properties, kinds, relations, propositions, sets and states of affairs are taken to be primitive and irreducible, the nominalist denies the existence of abstract entities and typically seeks to show that discourse about abstract entities is analysable in terms of discourse about familiar concrete particulars.

In different periods, different issues have provided the focus for the debate between nominalists and Platonists. In the Middle Ages, the problem of universals was pivotal. Nominalists like Abelard and Ockham insisted that everything that exists is a particular. They argued that talk of universals is talk about certain linguistic expressions - those with generality of application - and they attempted to provide an account of the semantics of general terms rich enough to accommodate the view that universals are to be identified with them.

The classical empiricists followed medieval nominalists in being particularists, and they sought to identify the kinds of mental representations associated with general terms. Locke argued that these representations have a special content. He called them abstract ideas and claimed that they are formed by removing from ideas of particulars those features peculiar to the particulars in question. Berkeley and Hume, however, attacked Locke’s doctrine of abstraction and insisted that the ideas corresponding to general terms are ideas whose content is fully determinate and particular, but which the mind uses as proxies for other particular ideas of the same sort.

A wider range of issues has dominated recent ontological discussion, and concern over the existence and status of things like sets, propositions, events and states of affairs has come to be every bit as significant as concern over universals. Furthermore, the nature of the debate has changed. While there are philosophers who endorse a nominalist approach to all abstract entities, a more typical brand of nominalism is that which recognizes the existence of sets and attempts to reduce talk about other kinds of abstract entities to talk about set-theoretical structures whose ultimate constituents are concrete particulars.