Property dualists shouldn’t be nominalists about properties

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.