NOMINALISM AND ABSTRACT REFERENCE

The Realist argues that there are states of affairs that obtain in the world which are accurately described by (la)-(3a). This point can be made more linguisti? cally by claiming that these sentences incorporate terms which refer to universals and, further, that these terms play essential roles in these sentences and cannot be eliminated through paraphrase. Thus, the truth of these sentences presupposes the exis? tence of universals.2 The terms that allegedly refer to universals in sentences (la)-(3a) are called abstract singular terms, e.g., redness, orangeness, blue? ness, and mankind. The Realist, then, challenges those who deny the existence of universals to account for sentences (1) (3) in such a way that they still make plausible claims about the world without entailing the exis? tence of universals. Now it is generally agreed that there are three major schools of thought regarding the nature of properties?Extreme Nominalism (properties do not exist), Nominalism (properties exist and are themselves particulars), and Realism (properties exist and are universals). Further, it is generally agreed that, whereas sentences which ex hibit abstract reference like (l)-(3) are problematic for Extreme Nominalism, they can be adequately handled by Nominalism and, thus, abstract reference cannot be used as an argument for or against Nomi? nalism vis a vis Realism. The purpose of this article is to refute that claim. Specifically, I will show that sentences like (l)-(3) are equally troublesome for Nominalism and Ex? treme Nominalism, and that the phenomenon of ab? stract reference does lend support to a Realist interpretation of properties. First, a brief sketch of Extreme Nominalism, Nominalism, and Realism will be given. Second, we will investigate Extreme Nominalist and Nominalist arguments which seek to show that abstract singular terms refer to sets of concrete or abstract particulars. Finally, we will con? sider Extreme Nominalist and Nominalist attempts to offer reductive paraphrases of sentences which incorporate abstract singular terms.