Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...) facts about that function and facts about some sound logics for those languages. In doing so, I prove that, given some plausible metaphysical assumptions, a large class of sentences about properties of concrete objects are “safe” on nominalistic grounds. Whenever some true sentences about concrete objects and some sentences belonging to this class that are true according to platonists collectively entail a conclusion about concrete objects, some nominalistically acceptable sentences are true and entail the same conclusion. Because the proof can itself be formulated without abstract objects, it provides a nominalistic explanation of the success of theories that invoke properties of concrete objects. (shrink)

Substance dualism is the view that there are two fundamentally different kinds of substances: physical and mental. By contrast, according to property dualism there is only one kind of substance (physical) but two fundamentally different kinds of properties: physical and mental. Property nominalism is the view that there are neither repeatable nor non-repeatable fundamentally predicable entities (i.e. neither universals nor tropes) and that things being a certain way or being related in a certain way must ultimately be accounted for in (...) terms of concrete particulars. In this paper, we consider a number of different kinds of property nominalism and argue that none of them sits well with property dualism. We pay special attention to the question of what it could mean for a property to count as mental given different nominalistic accounts of properties. Our conclusion is that property nominalism and property dualism are not a stable match. This is surprising, since property dualism has usually been understood as a thesis that is neutral about the nature of fundamental ontological categories and the relation between them. (shrink)