If we must take mathematical statements to be true, must we also believe in the existence of abstract eternal invisible mathematical objects accessible only by the power of pure thought? Jody Azzouni says no, and he claims that the way to escape such commitments is to accept true statements which are about objects that don't exist in any sense at all. Azzouni illustrates what the metaphysical landscape looks like once we avoid a militant Realism which forces our commitment to anything (...) that our theories quantify. Escaping metaphysical straitjackets, while retaining the insight that some truths are about objects that do exist, Azzouni says that we can sort scientifically-given objects into two categories: ones which exist, and to which we forge instrumental access in order to learn their properties, and ones which do not, that is, which are made up in exactly the same sense that fictional objects are. He offers as a case study a small portion of Newtonian physics, and one result of his classification of its ontological commitments, is that it does not commit us to absolute space and time. (shrink)

∗ Apologies to Mark Hinchliff for stealing the title of his dissertation. (See Hinchliff, A Defense of Presentism. As it turns out, however, the version of Presentism defended here is different from the version defended by Hinchliff. See Section 3.1 below.).

The paper argues that the view that the particular quantifier is ‘existentially loaded’ is a relatively new one historically and that it has become entrenched in modern philosophical logic for less than happy reasons.

Metaontology – the study of the nature of ontological issues – has flourished in recent years. The focus of this summary will be on some views and arguments that are central to today’s debate. One theme will be that of how seriously to take ontology: whether there is reason to take a skeptical or deflationary attitude toward ontological claims, as theorists like Rudolf Carnap, Hilary Putnam, and Eli Hirsch in different ways have urged. The other theme will be that of (...) the viability of the Fregean and Quinean approaches to ontology that have been and still are central to analytic philosophy. (shrink)

This chapter discusses the obstacles faced by presentists after denying the existence of past and future individuals. Presentism must still account for the manifest facts about the past and the future, but problems may arise when the presentist attempts to provide an account of the past. There is nothing in the presentist’s ontology on which to base truths about the past. Also, there is a problem regarding singular truths about past individuals; if past individuals do not exist, then they do (...) not have properties or stand in relations. If they do not stand in relations, then there is no way to talk about them because reference is a relation. Even the thought of them cannot exist since singular propositions about them do not exist if they do not. This chapter shows the absurdity of these conclusions and endeavors to prove the existence of past individuals. (shrink)

I explicate and defend the claim that, fundamentally speaking, there are no numbers, sets, properties or relations. The clarification consists in some remarks on the relevant sense of ‘fundamentally speaking’ and the contrasting sense of ‘superficially speaking’. The defence consists in an attempt to rebut two arguments for the existence of such entities. The first is a version of the indispensability argument, which purports to show that certain mathematical entities are required for good scientific explanations. The second is a speculative (...) reconstruction of Armstrong's version of the One Over Many argument, which purports to show that properties and relations are required for good philosophical explanations, e.g. of what it is for one thing to be a duplicate of another. (shrink)

One puzzling feature of talk about properties, propositions and natural numbers is that statements that are explicitly about them can be introduced apparently without change of truth conditions from statements that don't mention them at all. Thus it seems that the existence of numbers, properties and propositions can be established`from nothing'. This metaphysical puzzle is tied to a series of syntactic and semantic puzzles about the relationship between ordinary, metaphysically innocent statements and their metaphysically loaded counterparts, statements that explicitly mention (...) numbers, properties and propositions, but nonetheless appear to be equivalent to the former. I argue that the standard solutions to the metaphysical puzzles make a mistaken assumption about the semantics of the loaded counterparts. Instead I propose a solution to the syntactic and semantic puzzles, and argue that this solution also gives us a new solution to the metaphysical puzzle. I argue that instead of containing more semantically singular terms that aim to refer to extra entities, the loaded counterparts are focus constructions. Their syntactic structure is in the service of presenting information with a focus, but not to refer to new entities. This will allow us to spell out Frege's metaphor of content carving. (shrink)

The dissertation is a defense of presentism, the thesis that only presently existing things exist. Many arguments against presentism, including those of McTaggart and Mellor, rely on the claim that the tenses are indexicals. In the first chapter I argue that which aspects of language are indexical depends on what there is. In particular, I argue that if presentism is true, the tenses are not indexicals. I base my response to McTaggart's argument for the unreality of tense on the claim (...) that the tenses are not indexicals. I include a modal analogue of McTaggart's argument, an argument for the unreality of the contingent, and respond to it in an analogous way. ;In the second chapter I discuss serious presentism, the thesis that objects have properties only when they exist. I discuss arguments by Plantinga and Prior and conclude that a presentist need not be a serious presentist and that serious presentism is false, false because present objects have properties when they do not exist, and false because past and future objects have properties now. I argue that a presentist, though not a serious presentist, can account for the independence of the past from the present without admitting the existence of past objects. ;One issue related to serious presentism is whether the presentist's quantifiers range over present objects only or over past and future objects as well. I argue that a presentist's quantifiers need not be existential and may range over past, present, and future objects. In the final chapter I develop a version of presentism I call unrestricted presentism. (shrink)