Peter van Inwagen has long claimed that he doesn’t understand substitutional quantification and that the notion is, in fact, meaningless. Van Inwagen identifies the source of his bewilderment as an inability to understand the proposition expressed by a simple sentence like “,” where “$\Sigma$” is the existential quantifier understood substitutionally. I should think that the proposition expressed by this sentence is the same as that expressed by “.” So what’s the problem? The problem, I suggest, is that van Inwagen takes (...) traditional existential quantification to be ontologically committing and substitutional quantification to be ontologically noncommitting, which requires that the two quantifiers have different meanings—but no different meaning for the substitutional quantifier is forthcoming. What van Inwagen fails to appreciate is that substitutional quantification is directed at a criterion of ontological commitment, namely, W. V. O. Quine’s, which is quite different from van Inwagen’s criterion. Substitutional quantification successfully avoids the commitments Quine’s criterion would engender but has the same commitments as existential quantification given van Inwagen’s criterion. The question, then, is whether the existential quantifier is ontologically committing, as van Inwagen believes. The answer to that question will depend on whether the ordinary language “there is/are,” which is codified by the existential quantifier, is ontologically committing. There are good reasons to doubt that it is. (shrink)

This book is an exploration and defense of the coherence of classical theism’s doctrine of divine aseity in the face of the challenge posed by Platonism with respect to abstract objects. A synoptic work in analytic philosophy of religion, the book engages discussions in philosophy of mathematics, philosophy of language, metaphysics, and metaontology. It addresses absolute creationism, non-Platonic realism, fictionalism, neutralism, and alternative logics and semantics, among other topics. The book offers a helpful taxonomy of the wide range of options (...) available to the classical theist for dealing with the challenge of Platonism. It probes in detail the diverse views on the reality of abstract objects and their compatibility with classical theism. It contains a most thorough discussion, rooted in careful exegesis, of the biblical and patristic basis of the doctrine of divine aseity. Finally, it challenges the influential Quinean metaontological theses concerning the way in which we make ontological commitments. (shrink)