ABSTRACT
Peter van Inwagen’s meticulously crafted opening statement is a welcome clarification and development of his views on ontological commitment and goes a considerable distance, I think, toward closing the gap between us. The heart of his essay is to be found in his Sections 5–7 in Chapter 1. But before we look more closely at those sections, it deserves to be mentioned at the outset that van Inwagen has said almost nothing in his Opening Statement by way of answer to the question under debate, namely, do abstract objects, in particular numbers, exist? His essay focuses almost entirely on the articulation and defense of a neo-Quinean criterion of ontological commitment, which, as we have seen, serves as premiss (I) of some sort of Indispensability Argument for Platonism. 1 But he says very little about the various responses to premiss (II) of the Indispensability Argument, such as absolute creationism, conceptualism, arealism, fictionalism, ultima facie strategies, and pretense theory. 2 Since these alternatives to Platonism are consistent with van Inwagen’s proffered criterion of ontological commitment, he has yet to offer a prima facie case for the reality of abstract objects. Since he will doubtless address these alternatives in his Reply to my Opening Statement (which I have, of course, not yet read), I shall not say anything further about them at this juncture.
