Nominalism and Ideological Parsimony

Dan Marshall (the University of Hong Kong)

Nominalists deny that there are any abstract objects, such as properties, sets or numbers. Realists about abstract objects, on the other hand, hold that there areabstract objects. It is widely thought that i) nominalism is less ideologically parsimonious than realism since nominalists must regard as primitive many notions realists can analyse, and that ii) this provides grounds for rejecting nominalism and endorsing realism. Realists, for example, have claimed that, while they can analyse ‘might have been more massive than...actually is’ and ‘there are as many...as’, nominalists must regard these predicates as primitive. This paper argues that this is not the case: nominalists can provide analyses of both these predicates that are just as good as the analyses realists provide. It also argues that the manner in which nominalists can provide these analyses suggests that nominalism isn't less ideologically parsimonious than realism afterall. If this is correct, then one major reason for rejecting nominalism fails.