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)

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of (...) nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (shrink)

Modern philosophy of mathematics has been dominated by Platonism and nominalism, to the neglect of the Aristotelian realist option. Aristotelianism holds that mathematics studies certain real properties of the world – mathematics is neither about a disembodied world of “abstract objects”, as Platonism holds, nor it is merely a language of science, as nominalism holds. Aristotle’s theory that mathematics is the “science of quantity” is a good account of at least elementary mathematics: the ratio of two heights, for example, is (...) a perceivable and measurable real relation between properties of physical things, a relation that can be shared by the ratio of two weights or two time intervals. Ratios are an example of continuous quantity; discrete quantities, such as whole numbers, are also realised as relations between a heap and a unit-making universal. For example, the relation between foliage and being-a-leaf is the number of leaves on a tree,a relation that may equal the relation between a heap of shoes and being-a-shoe. Modern higher mathematics, however, deals with some real properties that are not naturally seen as quantity, so that the “science of quantity” theory of mathematics needs supplementation. Symmetry, topology and similar structural properties are studied by mathematics, but are about pattern, structure or arrangement rather than quantity. (shrink)

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.

The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of an apparently different kind, and what, if any, intrinsic properties mathematical objects possess. According to one influential interpretation of mathematical discourse, this is because the objects under study are themselves incomplete; they are positions or akin to positions in patterns or structures. Two versions of this idea are examined. It is argued (...) that the evidence adduced in favor of the incompleteness of mathematical objects underdetermines whether it is the objects themselves or our knowledge of them that is incomplete. Also, holding that mathematical objects are incomplete conflicts with the practice of mathematics. The objection that structuralism is committed to the identity of indiscernibles is evaluated and it is also argued that the identification of objects with positions is metaphysically suspect. (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)

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)

SOME MODERN THOMISTS claiming to follow the lead of Thomas Aquinas, hold that the objects of the types of mathematics known in the thirteenth century, such as the arithmetic of whole numbers and Euclidean geometry, are real entities. In scholastic terms they are not beings of reason but real beings. In his once-popular scholastic manual, Elementa Philosophiae Aristotelico-Thomisticae, Joseph Gredt maintains that, according to Aristotle and Thomas Aquinas, the object of mathematics is real quantity, either discrete quantity in arithmetic or (...) continuous quantity in geometry. The mathematician considers the essence of quantity in abstraction from its relation to real existence in bodily substance. "When quantity is considered in this way," he writes, "it is not a being of reason but a real being. Nevertheless it is so abstractly considered that it leaves out of account both real and conceptual existence." Recent mathematicians, Gredt continues, extend their speculation to fictitious quantity, which has conceptual but not real being; for example, the fourth dimension, which by its essence positively excludes a relation to real existence. According to Gredt this is a special, transcendental mathematics essentially distinct from "real mathematics," and belonging to it only by reduction. (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)

Aristotelian, or non-Platonist, realism holds that mathematics is a science of the real world, just as much as biology or sociology are. Where biology studies living things and sociology studies human social relations, mathematics studies the quantitative or structural aspects of things, such as ratios, or patterns, or complexity, or numerosity, or symmetry. Let us start with an example, as Aristotelians always prefer, an example that introduces the essential themes of the Aristotelian view of mathematics. A typical mathematical truth is (...) that there are six different pairs in four objects: Figure 1. There are 6 different pairs in 4 objects The objects may be of any kind, physical, mental or abstract. The mathematical statement does not refer to any properties of the objects, but only to patterning of the parts in the complex of the four objects. If that seems to us less a solid truth about the real world than the causation of flu by viruses, that may be simply due to our blindness about relations, or tendency to regard them as somehow less real than things and properties. But relations (for example, relations of equality between parts of a structure) are as real as colours or causes. (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.

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)

This book expounds a system of ideas about the nature of mathematics which Michael Resnik has been elaborating for a number of years. In calling mathematics a science he implies that it has a factual subject-matter and that mathematical knowledge is on a par with other scientific knowledge; in calling it a science of patterns he expresses his commitment to a structuralist philosophy of mathematics. He links this to a defense of realism about the metaphysics of mathematics--the view that mathematics (...) is about things that really exist. (shrink)

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)

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)

A lot of work in metaphysics relies on linguistic analysis and intuitions. Do we want to know what sort of things there are or could be? Then let’s see what sort of things there must be in order for what we truthfully say to be true. Do we want to see whether x is distinct from y? Then let’s see whether there is any statement that is true of x but not of y. And so on. In this paper I (...) argue that this way of proceeding is full of traps and is bound to be pretty useless unless we already have a good idea of what sort of things there are, and of how we are going to count them. (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.).

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of (...) nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second. (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)

Essays on a wide range of areas and topics in Asian studies for scholars looking to incorporate Asia into their worldview and teaching. Contributors give contemporary presence to Asian studies through a variety of themes and topics in this multidisciplined and interdisciplinary volume. In an era of globalization, scholars trained in Western traditions increasingly see the need to add materials and perspectives that have been lacking in the past. Accessibly written and void of jargon, this work provides an adaptable entrée (...) to Asia for the integration of topics into courses in the humanities, social sciences, cultural studies, and global studies. Guiding principles, developed at the East-West Center, include noting uncommon differences, the interplay among Asian societies and traditions, the erosion of authenticity and cultural tradition as an Asian phenomenon as well as a Western one, and the possibilities Asian concepts offer for conceiving culture outside Asian contexts. The work ranges from South to Southeast to East Asia. Essays deal with art, aesthetics, popular culture, religion, geopolitical realities, geography, history, and contemporary times. “This volume truly lies at the intersection of scholarship and teaching. Each essay has the potential to help rethink approaches to scholarly issues, and there is a great deal of material for classroom discussion and examples. The book’s breadth—covering India, China, Korea, the Sea of Malay, Bhutan, and other locations—is impressive.” — Robert André LaFleur, Beloit College. (shrink)

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.

Presentism is the doctrine that only the present is real. Since ordinary talk and thought are full of quantification over non-present objects, presentists are in a familiar predicament: in their unreflective moments they apparently commit themselves to far more than their ontological scruples allow. A familiar response is to begin a project of paraphrase. Truths appearing to quantify over problematic entities are shown, on analysis, to not involve quantification over those entities after all. But I think that we might be (...) better off abandoning paraphrase altogether. I suggest a project of discovering “underlying truths” rather than paraphrases. I will explore this strategy as applied to defending presentism, but my hope is that lovers of desert landscapes everywhere will herein find words of comfort. (shrink)

Before Duns Scotus, most philosophers agreed that God is identical with His necessary intrinsic attributes--omnipotence, omniscience, etc. This Identity Thesis was a component of widely held doctrines of divine simplicity, which stated that God exemplifies no metaphysical distinctions, including that between subject and attribute. The Identity Thesis seems to render God an attribute, an abstract object. This paper shows that the Identity Thesis follows from a basic theistic belief and does not render God abstract. If also discusses how one might (...) move from the Identity Thesis to the full doctrine of divine simplicity and shows that the Identity Thesis generates a new ontological argument. (shrink)

The main goal of this paper is to urge that the normal platonistic account of mathematical truth is unsatisfactory even if pure abstract entities are assumed to exist (in a non-Question-Begging way). It is argued that the task of delineating an interpretation of a formal mathematical theory among pure abstract entities is not one that can be accomplished. An important effect of this conclusion on the question of the ontological commitments of informal mathematical theories is discussed. The paper concludes with (...) a sketch of a non-Platonistic theory of mathematical truth which utilizes an unanalyzed notion of logical possibility. (shrink)

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, (...) I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant. (shrink)