In this paper I argue that presentism has a problem accounting forthe truth of statements whose truth conditions seem to require therebe relations that hold between present and non-present objects. Imotivate the problem and then examine several strategies for dealingwith the problem. I argue that no solution is forthcoming, and thispresents a prima facie problem for presentism.

A singular thought can be characterized as a thought which is directed at just one object. The term ‘thought’ can apply to episodes of thinking, or to the content of the episode (what is thought). This paper argues that episodes of thinking can be just as singular, in the above sense, when they are directed at things that do not exist as when they are directed at things that do exist. In this sense, then, singular thoughts are not object-dependent.

Nominalism is the view that abstract mathematical objects like numbers, functions, and sets do not exist. The chapter articulates and defends a variety of nominalism, based on a reading of mathematical statements in terms of possible linguistic constructions. The chapter responds directly to a recent study of nominalism by Gideon Rosen and John Burgess, and develops a reply to the Quine-Putnam indispensability argument for the existence of mathematical objects.

The article first rehearses three deflationary theories of reference, (1) disquotationalism, (2) propositionalism (Horwich), and (3) the anaphoric theory (Brandom), and raises a number of objections against them. It turns out that each corresponds to a closely related theory of truth, and that these are subject to analogous criticisms to a surprisingly high extent. I then present a theory of my own, according to which the schema “That S(t) is about t” and the biconditional “S refers to x iff S (...) says something about x” are exhaustive of the notions of aboutness and reference. An account of the usefulness of “about” is then given, which, I argue, is superior to that of Horwich. I close with a few considerations about how the advertised theory relates to well-known issues of reference, the conclusions of which is (1) that the issues concern reference and aboutness only insofar as the words “about” and “refer” serve to generalise over the claims that are really at issue, (2) that the theory of reference will not settle the issues, and (3) that it follows from (2) that the issues do not concern the nature of aboutness or reference. (shrink)

Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's (...) arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose. (shrink)

The form of nominalism known as 'mathematical fictionalism' is examined and found wanting, mainly on grounds that go back to an early antinominalist work of Rudolf Carnap that has unfortunately not been paid sufficient attention by more recent writers.

This paper develops a novel version of mathematical fictionalism and defends it against three objections or worries, viz., (i) an objection based on the fact that there are obvious disanalogies between mathematics and fiction; (ii) a worry about whether fictionalism is consistent with the fact that certain mathematical sentences are objectively correct whereas others are incorrect; and (iii) a recent objection due to John Burgess concerning “hermeneuticism” and “revolutionism”.

A theory of objective mathematical correctness is developed. The theory is consistent with both mathematical realism and mathematical anti-realism, and versions of realism and anti-realism are developed that dovetail with the theory of correctness. It is argued that these are the best versions of realism and anti-realism and that the theory of correctness behind them is true. Along the way, it is shown that, contrary to the traditional wisdom, the question of whether undecidable sentences like the continuum hypothesis have objectively (...) determinate truth values is independent of the question of whether mathematical realism is true. (shrink)

I defend my nominalist account of mathematics from objections that have been raised to it by Mark Colyvan.

Tim Crane (2011) characterizes the cognitive role of singular thought via singular mental files: the application of such files to more than one object is senseless. As many do, he thus stresses the contrast between ‘singular’ and ‘general’. I give a counterexample, plurally-directed singular thought, and I offer alternative characterizations of singular thought—better described as ‘objects-directed thought’—initially in terms of the defeasibility of the descriptions associated with one's thinking of an object, and then more broadly in terms of whether descriptions (...) of the object or description-independent epistemic routes to the object are primarily operative in an agent's thinking. (shrink)

Metaphysicians are among the very wiliest of philosophers. This means that an attack on a metaphysical position will fail if it only proceeds by showing that the posited objects are odd in some metaphysically significant way. To choose a pertinent example, if one wants to oppose the fictional realist, it isn’t enough to show that fictional entities have arbitrary individuation conditions, that they flit in and out of existence, or that they are far more numerous and varied than one imagines. (...) As Eaker (2012) and Effingham (2012) remind us, the fictional realist and the metaphysical fundamentalist can agree that this is what fictional objects are like. It’s even insufficient to claim that such objects are mind- and language dependent, utterly dependent on our thinking of them (or on our coining terms that stipulatively ‘refer’ to them). Fictional realists and metaphysical fundamentalists can agree with this too, but deny these are sufficient conditions for non-existence. (shrink)

A distinction between the epistemic practices in mathematics and in the empirical sciences is rehearsed to motivate the epistemic role puzzle. This is distinguished both from Benacerraf's 1973 epistemic puzzle and from sceptical arguments against our knowledge of an external world. The stipulationist position is described, a position which can address this puzzle. Methods of avoiding the stipulationist position by using pure logic to provide knowledge of mathematical abstracta are discussed and criticized.

First, I discuss the older “theory-centered” and the more recent semantic conception of scientific theories. I argue that these two perspectives are nothing more than terminological variants of one another. I then offer a new theory-centered view of scientific theories. I argue that this new view captures the insights had by each of these earlier views, that it’s closer to how scientists think about their own theories, and that it better accommodates the phenomenon of inconsistent scientific theories.

This paper responds to John Burgess's ‘Mathematics and _Bleak House_’. While Burgess's rejection of hermeneutic fictionalism is accepted, it is argued that his two main attacks on revolutionary fictionalism fail to meet their target. Firstly, ‘philosophical modesty’ should not prevent philosophers from questioning the truth of claims made within successful practices, provided that the utility of those practices as they stand can be explained. Secondly, Carnapian scepticism concerning the meaningfulness of _metaphysical_ existence claims has no force against a _naturalized_ version (...) of fictionalism, according to which our ordinary standards of scientific evidence may show that we have no reason to believe the mathematical existence claims made within the context of our mathematical and scientific theories. (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.).

Our aim in this paper is to bring to light two sources of tension for Christian theists who endorse the principle of unrestricted composition, that necessarily, for any objects, the xs, there exists an object, y, such that the xs compose y. In Value, we argue that a composite object made of wholly valuable parts is at least as valuable as its most valuable part, and so the mereological sum of God and a wholly valuable part would be at least (...) as valuable as God; but Christian theism arguably demands that no concrete object other than God can be as valuable as God. And in Creation, we argue that the conjunction of theism and unrestricted composition, together with the claim that every concrete entity that is numerically distinct from God is created by God, implies that God is created by God. We conclude by examining the prospects of restricting the thesis of unrestricted composition to the domain of material or spatiotemporal objects as a way to sidestep the above arguments against the conjunction of Christian theism and unrestricted composition. (shrink)

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.

Sherlock Holmes is a fictional individual. So is his favorite pipe. Our pre-theoretical intuition says that neither of them is real. It says that neither of them really, or actually, exists. It also says that there is a sense in which they do exist, namely, a sense in which they exist “in the world of” the Sherlock Holmes stories. Our pre-theoretical intuition says in general of any fictional individual that it does not actually exist but exists “in the world of” (...) the relevant fiction. I wish to defend this pretheoretical intuition. To do so, I need to defend two claims: that fictional individuals do not actually exist, and that they exist “in the world of” the relevant fiction. The aim of this paper is to defend the first claim. (shrink)

Parmenides didn't mention reference as such, but if he had he would have undoubtedly agreed with the philosophers who nowadays hold what is called "the axiom of existence": that one can only refer to what exists. The sources of possible support for this view are examined and rejected. Primary support for the axiom is given by two sorts of argument; one concerning quantification, the other summarizing a standard Parmenidean puzzle. Weaknesses in both are exposed. Finally, the relations between the axiom (...) and connected claims about predication and truth are probed, and an attempt is made to determine the limits of the mutual support these claims give one another. (shrink)

Quine has called the question, ‘What is there?’ the “ontological question.” But if we call this question by that name, what name shall we use for the question, ‘What are we asking when we ask “What is there?”’? I shall call it ‘the meta-ontological question’. I shall call the attempt to answer the meta-ontological question ‘meta-ontology’ and any proposed answer to it ‘a meta-ontology’. In this essay, I shall briefly sketch a meta-ontology. The meta-ontology I shall present is broadly Quinean. (...) I am, in fact, willing to call it an exposition of Quine’s meta-ontology. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Peter van Inwagen FICTION AND METAPHYSICS Many works of fiction address themselves directly to metaphysiced issues. One thinks of the stories of Olaf Stapledon, Charles Williams, or Jorge Luis Borges. Other fiction is more subtly and indirectly related to metaphysics — A la recherche du temps perdu, for exeimple, or, in a radier different way, some science fiction. The relations that various novels and stories bear to the questions (...) ofmetaphysics would be an interesting topic, but it is not the topic of the present article, which is the relevance to metaphysics not of this or that work, but ramer of the very existence of such a thing as fiction. We shall see mat philosophical reflection on fiction can lead one to certain remarkable metaphysical conclusions. Not surprisingly, the area of metaphysics to which these conclusions pertain is ontology. The word, though not the study it represents, is a new one — it is probably a seventeenth-century coinage. In the present century, the word "ontology" is associated mainly with the names of Heidegger and Quine. I shall be using the word in Quine's sense: as a name for the study that attempts to answer the question, What is there? Quine's contributions to this study are of central importance for the thesis of this article. These contributions may be divided into two parts: those that belong to ontology proper and those that belong to what we may call meta-ontology. By Quine's "ontology proper," I mean his actual attempt to answer the question, What is there? This attempt is of great intrinsic interest, but it is not relevetnt to my topic. By Quine's meta-ontology, I mean his feunous discussion of what it is to ask what there is emd his famous dieses about how to approach mis question.1 These theses are the product of a really remarkable effort to think clearly about questions almost no one had thought cleeirly about, and a proper appreciation of them will liberate one from some very old and very strong illusions about being emd existence. Or so many philosophers, including the present author, would say. And yet Quine's meta-ontology, when it is combined with what seem to be some very simple emd obvious facts about fiction, yields a result mat seems just obviously wrong: that names drawn from works of fiction ("Mr. Pickwick" emd "Tom Sawyer," for example, as well as proper names of odier sorts, such as "Dotheboys Hall" and "Barchester") denote existent objects. The thesis of this 67 68PHILOSOPHY AND LITERATURE article is mat this consequence of Quine's meta-ontology does not constitute a reductio ad absurdum; radier, Quine's meta-ontology should be retained and mis consequence accepted. I shall first examine Quine's meta-ontology in the abstract, and then in application to fiction. In the abstract, Quine's meta-ontology may be viewed as comprising four propositions. (1)Being is die seune as existence. That is, to say mat things of a certain sort exist emd to say mat there être things of diat sort is to say pretty much the same diing. For example, to say diat horses exist is to say mere are horses, and to say mat diere was such a person as Homer is to say that Homer existed. This might seem obvious, but on reflection it can seem less obvious. Suppose I am discussing someone's delusions and I say, "There are a lot of diings he believes in that do not exist." On die face of it, I appear to be saying diat diere are diings — the poison in his drink, his uncle's medice, emd so on — that do not exist. To tedce a radier more metaphysical example, I have read a letter to the editor of a newspaper, the audior of which argues diat contraception is a sin since it prevents people who would omerwise exist from doing so. This may be a bad argument on meiny grounds that have nothing to do with metaphysics, but it is certainly clear diat its propounder believes diat diere are unconceived people, people who might have existed but who, owing to certain acts of contraception, do not exist... (shrink)

Inwagen, Peter van_Dispensing with Ontological Levels.

I defend the thesis that at least some abstract objects are uncreated. I choose to discuss a rather neglected category of abstract object, shapes. I choose to discuss shapes because I think the members of my audience may have fewer metaphysical preconceptions about shapes than about, e.g., numbers or propositions or attributes.

In “God and Other Uncreated Things,” I defended the position that at least some properties are uncreated. I argued that this thesis does not contradict the creedal statement that God is the creator of all things, visible and invisible, because that statement presupposes a domain of quantification that does not include properties. William Lane Craig has contended that this defense of the consistency of my position with the Nicene Creed fails, owing to the fact that there are clear patristic statements (...) to the effect that the domain of quantification presupposed in the Nicene Creed must be understood as absolutely unrestricted. In this paper, I grant his premise but present reasons for doubting whether his conclusion—that the proposition that there are uncreated properties contradicts the Nicene Creed—follows from it. (shrink)

NeoFregeanism is an intriguing but elusive philosophy of mathematical existence. At crucial points, it goes cryptic and metaphorical. I want to put forward an interpretation of neoFregeanism—perhaps not one that actual neoFregeans will embrace—that makes sense of much of what they say. NeoFregeans should embrace quantifier variance.

By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...) three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain. (shrink)

Van Fraassen defines constructive empiricism as the view that science aims to produce empirically adequate theories. But this account has been misunderstood. Constructive empiricism in not, as it seems, a description of the intentional features of scientific practice, nor is it a normative prescription for their revision. It is rather a fiction about the practice of science that van Fraassen displays in the interests of a broader empiricism. The paper concludes with a series of arguments designed to show that constructive (...) empiricism so understood is self-undermining. (shrink)