"Paraphrasing Away Properties of Concrete Objects"
Austere nominalists hold that there are no abstract objects whatsoever. One particularly difficult problem austere nominalists confront is that we say things all the time that seemingly entail that there are abstract objects and that, in combination with claims about concrete objects and logical principles, enable us to come to specific conclusions about concrete objects in ways essential for nearly every domain of inquiry. Austere nominalists seem forced to either give up on doing any serious investigation by disavowing abstract discourse or else contradict themselves by exclaiming their nominalism. In response to this problem, I will present a strategy nominalists can use to get by without saying things that entail that there are properties of concrete objects, relying only on a small number of additional ideological primitives and truth-preserving principles. This strategy lays the foundation for a more general strategy for avoiding commitment to several kinds of abstract object.