My dissertation has two aspects. On the one hand, it is a contribution to a first-order ontological dispute. I proceed by offering, over the course of four chapters, a sustained defense of nominalism (the view that there are no abstract objects). On the other hand, it is an exercise in metaontology. In particular, it is an attempt to undermine the framework for conducting ontological disputes handed down to us by Quine and his successors.
Neo-Quinean objectors to nominalism argue (to a first approximation) that we seem antecedently committed to endorsing various sentences that can be shown to imply that abstract objects exist. They further argue that there is no way that we can do without endorsing many of those sentences. We can’t, they argue, find workable, nominalistically friendly paraphrases for all of them; nor can we simply withdraw our assent (not without greatly impoverishing our ability to express various truths). It follows, they claim, that we are (on pain of logical inconsistency) “committed” to the existence of abstract objects.
I show how nominalists can successfully resist such arguments. I argue that we can consistently talk and reason as if there were abstract objects without believing in them, and that we can do so in the absence of a successful paraphrase strategy. Accordingly, the approach that I take could aptly be described as a “fictionalist” one.
In Chapter 1, I show how to resist empirical arguments against nominalism that are advanced on the part of some neo-Quineans. In Chapter 2, I consider and reject an argument put forward by Peter van Inwagen (a prominent neo-Quinean) for the conclusion that we are committed to believing in properties. In Chapter 3, I develop a novel, formal, nominalist account of the inferential utility of reasoning as if there are monadic, first-order properties. Finally, in Chapter 4, I argue that the considerations raised in the previous chapters generalize so as to encompass other domains of our discourse that neo-Quineans claim commit us to the existence of abstract objects.