In a series of works, Jody Azzouni has defended deflationary nominalism, the view that certain sentences quantifying over mathematical objects are literally true, although such objects do not exist. One alleged attraction of this view is that it avoids various philosophical puzzles about mathematical objects. I argue that this thought is misguided. I first develop an ontologically neutral counterpart of Field’s reliability challenge and argue that deflationary nominalism offers no distinctive answer to it. I then show how this reasoning generalizes (...) to other philosophically problematic entities. The moral is that puzzle avoidance fails to motivate deflationary nominalism. (shrink)

An extensive exploration of the special properties of ‘exist’ is here undertaken. Two of several results are: Denying that `exist’ has associated with it a set of necessary and sufficient conditions has seemed to a number of philosophers to imply metaphysical nihilism . This is because it has seemed that without such conditions the target domain of `existence’ is arbitrarily open. I show this is wrong. Second, my analysis sheds light on the puzzling question of what we are asking when (...) we ask of something, `Does it exist?’ and mean that question in an ontically relevant way. (shrink)

According to the familiar Quinean understanding of ontological commitment, (1) one undertakes ontological commitments only via theoretical regimentations, and (2) ontological commitments are to be identified with the domain of a theory’s quantifiers. Jody Azzouni accepts (1), but rejects (2). Azzouni accepts (1) because he believes that no vernacular expression carries ontological commitments. He rejects (2) by locating a theory’s commitments with the extension of an existence predicate. I argue that Azzouni’s two theses undermine each other. If ontological commitments follow (...) from predications of existence, then ontological commitments can be expressed in the vernacular via negative existential sentences. (shrink)

Jody Azzouni argues that whilst it is indeterminate what the criteria for existence are, there is a criterion that has been collectively adopted to use ‘exist’ that we can employ to argue for positions in ontology. I raise and defend a novel objection to Azzouni: his view has the counterintuitive consequence that the facts regarding what exists can and will change when users of the word ‘exist’ change what criteria they associate with its usage. Considering three responses, I argue Azzouni (...) has best reason to take one that ultimately renders unsuccessful his arguments against mathematical abstracta. (shrink)