David Armstrong in his A Combinatorial Theory of Possibility proposes that non-actual possibilities may be treated as fictions grounded in instantiated universals. In this paper, I first provide some objections to his theory. Then I make the case for Foundational Nominalism, the Armstrong inspired thesis that the whole of ontology supervenes on particulars described much as in the Quinean Nominalism that Armstrong rejected as an ontological ostrich. Finally, I argue that Foundational Nominalism permits a fictional theory of possibilities similar to (...) Brian Skyrms’ Tractarian Nominalism. (shrink)

Consider two similarity facts: a is similar to b with respect to G, and c is similar to d with respect to G. According to the Platonist approach to similarity, the analysis of such facts forces us to admit that similarity facts are to be analyzed into facts about universal similarities of the form: a is similar to b with respect to G, and c is similar to d with respect to G, where similarity is a universal. In this paper, (...) I defend Neutralism, a view according to which there are properties and similarities, but these are not universals, particulars, or of other categories. After presenting the Platonist analysis of similarity proposed by Russell and Grossmann, I examine the question of whether or not the Platonist analysis of similarity leads us inevitably to a conception of similarity as a universal. Then I offer a novel, alternative analysis of similarity free of commitment to universals. (shrink)

ABSTRACTBy the Many Categories problem, I mean the prima facie violation of Ockham’s Razor by realists about universals: there is, it might seem, just too much variety. Thus, David Armstrong posits both properties and relations. He also theorises about determinates of determinables. Another influential realist, E. J. Lowe distinguishes non-substantial from substantial universals. Yet again, both Armstrong and Lowe include in their ontology abstract particulars in addition to universals. My aim in this paper is to offer a unification of these (...) categories using an operator-theory. First, I show how operators provide a theory of abstract particulars of relations and of impure relational properties. Then, using impure relational properties I derive the Fregeanion Principle. After some metaphysics of mathematics, I provide a theory of determinables. Finally, I consider kinds and substances. (shrink)