Relations and Nominalism

The Limits of Class-Theoretic Approaches

Abstract

In this paper, I shall discuss a problem for nominalist theories: What is the ontological status of relations? Since nominalists reject universals, they must reduce relations to particulars. Some theories, such as Class Nominalism and Resemblance Nominalism, postulate classes to reduce relations. I examine two classical criticisms against the analysis of relations in Nominalism: the problem of order and the issues involving the Wiener-Kuratowski procedure. Even though the claim that relations are not classes is a well-established thesis, I introduce two additional arguments against it. First, determining which class corresponds to a relation is arbitrary. Second, I argue that nominalist theories fail to provide an adequate hierarchical structure of reality. While previous objections focus primarily on technical issues in the reduction of relations to classes, my critique challenges the metaphysical coherence of such reductions.