We assume that you are sitting, alone, in a chair. Peter Unger has recently argued that this mundane scenario is incompatible with the orthodox view that you are a material object. If Materialism is true, he argues, then many experiencing, thinking subjects are in your chair, each reading this article. Since you are in fact alone, Materialism must therefore be rejected. Unger concludes that the only view compatible with your solitude is a form of Substance Dualism. We show that Unger (...) overstates and thereby undermines his case. Careful attention to his Dualism suggests a version of Materialism more sophisticated than those Unger considers and that is immune to his arguments. This is because the essence of Unger's Dualist strategy is available to his Materialist opponent. This raises the prospect of resolving the dispute between Materialists and Dualists. To avoid Unger's argument, Materialists and Dualists must both endorse analogous principles without independent motivation. We should believe whichever theory provides the most satisfying account of why those principles hold. (shrink)

This is an essay for advanced undergraduates and graduates. I present the problem of the many in detail.

In §2-4, I survey three extant ways of making sense of indeterminate truth and find each of them wanting. All the later sections of the paper are concerned with showing that the most promising way of making sense of indeterminate truth is via either a theory of truthmaker gaps or via a theory of truthmaking gaps. The first intimations of a truthmaker–truthmaking gap theory of indeterminacy are to be found in Quine (1981). In §5, we see how Quine proposes to (...) solve Unger’s problem of the many via positing the possibility of groundless truth. In §6, I elaborate the truthmaker gap model of indeterminacy first sketched by Sorensen (2001, ch.11) and use it to give a reductive analysis of indeterminate truth. In §7, I briefly assess what kind of formal framework can best express the possibility of truthmaker gaps. In §8, I contrast what I dub ‘the ordinary conception of worldly indeterminacy’ with Williamson’s conception of worldly indeterminacy. In §9, I show how one can distinguish linguistic from worldly indeterminacy on a truthmaker gap conception. In §10, I briefly sketch the relationship between truthmaker gaps and ignorance. In §11, I assess whether a truthmaker gap conception of vagueness is really just a form of epistemicism. In §12, I propose that truthmaker gaps can yield a plausible model of (semantic) presupposition failure. In §13, in response to the worry that a truthmaker gap conception of indeterminacy is both parochial and controversial—since it commits us to an implausibly strong theory of truthmaking—I set forth a truthmaking gap conception of indeterminacy. In §14, I answer the worry that groundless truths, of whatever species, are just unacceptably queer. A key part of this answer is that a truthmaker–truthmaking gap model of indeterminacy turns out to be considerably less queer than any model of indeterminacy which gives up on Tarski’s T-schema for truth (and cognate schemas). (shrink)

Although the predominant view is that vagueness is due to our language being imprecise, the alternative idea that objects themselves do not have determinate borders has received an occasional hearing. But what has failed to be appreciated is how this idea can avoid a puzzle Peter Unger named “The Problem of the Many.”[i].

Introduction In the first four chapters of this book, I develop and defend a monistic account of human persons according to which human persons are highly ...

Anyone who endorses Universalism and Four Dimensionalism owes us an argument for those controversial mereological theses. One may put forth David Lewis's and Ted Sider's arguments from vagueness. However, the success of those arguments depends on the rejection of the epistemic view of vagueness, and thus opens the door to a fatal confrontation with one particularly troubling version of The Problem of the Many. The alternative for friends of Universalism and Four Dimensionalism is to abandon those currently fashionable arguments in (...) favor of others which are consistent with the epistemic view of vagueness and with the elegant solution it furnishes to that problem. (shrink)

Consider a cat on a mat. On the one hand, there seem to be just one cat, but on the other there seem to be many things with as good a claim to being a cat, and there seems to be nothing in the vicinity with a better claim. Hence, the problem of the many. In his ‘Many, but Almost One,’ David Lewis offered two solutions. According to the first, only one of the many is indeed a cat, although it (...) is indeterminate exactly which one. According to the second, the many are all cats, but they are almost identical to each other, and hence they are almost one. For Lewis, the two solutions do not compete with each other but are mutually complementary, as each can assist the other. This paper has two aims: first to argue against the first of these two solutions, and then to defend the second as a self-standing solution from Lewis’s considerations to the contrary. In both parts I will assume the certainly plausible but also controversial view on the nature of vagueness, having it that vagueness is a kind of semantic indecision—of which Lewis himself is one of the main defenders. (shrink)

Kilimanjaro is a paradigmatic mountain, if any is. Consider atom Sparky, which is neither determinately part of Kilimanjaro nor determinately not part of it. Let Kilimanjaro(+) be the body of land constituted, in the way mountains are constituted by their constituent atoms, by the atoms that make up Kilimanjaro together with Sparky, and Kilimanjaro(–) the one constituted by those other than Sparky. On the one hand, there seems to be just one mountain in the vicinity of Kilimanjaro. On the other (...) hand, both Kilimanjaro(+) and Kilimanjaro(–)—and indeed many other similar things—seem to have an equal claim to be a mountain: all of them exhibit the grounds for something being a mountain—like being an elevation of the earth’s surface rising abruptly and to a large height from the surrounding level,1 or whathaveyou—; and there seems to be nothing in the vicinity with a better claim. Hence, the problem of the many. (shrink)

According to standard, pre-philosophical intuitions, there are many composite objects in the physical universe. There is, for example, my bicycle, which is composed of various parts - wheels, handlebars, molecules, atoms, etc. Recently, a growing body of philosophical literature has concerned itself with questions about the nature of composition.1 The main question that has been raised about composition is, roughly, this: Under what circumstances do some things compose, or add up to, or form, a single object? It turns out that (...) it is surprisingly difficult to give a satisfactory answer to this question that accords with standard, pre-philosophical intuitions about the universe's composite objects. In fact, the three rival views in response to this question that have received the most support in the literature are (i) that there are no objects composed of two or more parts (which means that there are no stars, chairs, humans, or bicycles);2 (ii) that the only objects composed of two or more parts are living organisms (which still means no stars. (shrink)

One winter’s Saturday Clarence wakes up. He realises he has left his umbrella at work. The office is locked, and he can’t get in. Being one of those people who punish themselves for their mistakes, he can’t bring himself to buy a replacement. He has an engagement six kilometres down the road and starts wondering whether it will rain. Normally, this would not be a problem, but his motor vehicle has broken down because he forgot to have it serviced. And (...) of course, he blames himself for this mistake, so it is only natural that he can’t bring himself to hire a cab or take a bus. He really should hope that it rains and that he gets drenched on the way to his engagement, but he is only human after all, and a small part of himhopes that it is a sunny day. (shrink)

Supervaluational treatments of vagueness are currently quite popular among those who regard vagueness as a thoroughly semantic phenomenon. Peter Unger's 'problem of the many' may be regarded as arising from the vagueness of our ordinary physical-object terms, so it is not surprising that supervaluational solutions to Unger's problem have been offered. I argue that supervaluations do not afford an adequate solution to the problem of the many. Moreover, the considerations I raise against the supervaluational solution tell also against the solution (...) to the problem of the many which is suggested by adherents of the epistemic theory of vagueness. (shrink)

A plausible desideratum for an account of the nature of objects, at, and across time, is that it accommodate the phenomenon of vagueness without locating vagueness in the world. A series of arguments have attempted to show that while universalist perdurantism – which combines a perdurantist account of persistence with an unrestricted mereological account of composition – meets this desideratum, endurantist accounts do not. If endurantists reject unrestricted composition then they must hold that vagueness is ontological. But if they embrace (...) unrestricted composition they are faced with the problem of the many, and cannot plausibly accommodate vagueness. This paper disambiguates two related sub-problems of the problem of the many, and argues that universalist perdurantism is not superior to universalist endurantism with respect to either of these. (shrink)

It is argued that, given certain reasonable premises, an infinite number of qualitatively identical but numerically distinct minds exist per functioning brain. The three main premises are (1) mental properties supervene on brain properties; (2) the universe is composed of particles with nonzero extension; and (3) each particle is composed of continuum many point-sized bits of particle-stuff, and these points of particlestuff persist through time.

Naive mereology studies ordinary, common-sense beliefs about part and whole. Some of the speculations in this article on naive mereology do not bear directly on Peter van Inwagen's "Material Beings". The other topics, (1) and (2), both do. (1) Here is an example of Peter Unger's "Problem of the Many". How can a table be a collection of atoms when many collections of atoms have equally strong claims to be that table? Van Inwagen invokes fuzzy sets to solve this problem. (...) I claim that an alternative treatment of vagueness, supervaluations over many-value valuations, provides a better solution. (2) The Special Composition Question asks how parts compose a whole. One who rejects van Inwagen's answer in terms of constituting a life need not provide some alternative answer. Even if all answers to the Special Question fail, there are a multitude of less general composition questions that are not so difficult. (shrink)

As anyone who has flown out of a cloud knows, the boundaries of a cloud are a lot less sharp up close than they can appear on the ground. Even when it seems clearly true that there is one, sharply bounded, cloud up there, really there are thousands of water droplets that are neither determinately part of the cloud, nor determinately outside it. Consider any object that consists of the core of the cloud, plus an arbitrary selection of these droplets. (...) It will look like a cloud, and circumstances permitting rain like a cloud, and generally has as good a claim to be a cloud as any other object in that part of the sky. But we cannot say every such object is a cloud, else there would be millions of clouds where it seemed like there was one. And what holds for clouds holds for anything whose boundaries look less clear the closer you look at it. And that includes just about every kind of object we normally think about, including humans. Although this seems to be a merely technical puzzle, even a triviality, a surprising range of proposed solutions has emerged, many of them mutually inconsistent. It is not even settled whether a solution should come from metaphysics, or from philosophy of language, or from logic. Here we survey the options, and provide several links to the many topics related to the Problem. (shrink)

Assume also that it is vague, in some sense, which hairs are hairs of that cat. Then one might think that it is indeterminate in some sense which thing is the cat on the mat.

Recently four different papers have suggested that the supervaluational solution to the Problem of the Many is flawed. Stephen Schiffer (1998, 2000a, 2000b) has argued that the theory cannot account for reports of speech involving vague singular terms. Vann McGee and Brian McLaughlin (2000) say that theory cannot, yet, account for vague singular beliefs. Neil McKinnon (2002) has argued that we cannot provide a plausible theory of when precisifications are acceptable, which the supervaluational theory needs. And Roy Sorensen (2000) argues (...) that supervaluationism is inconsistent with a directly referential theory of names. McGee and McLaughlin see the problem they raise as a cause for further research, but the other authors all take the problems they raise to provide sufficient reasons to jettison supervaluationism. I will argue that none of these problems provide such a reason, though the arguments are valuable critiques. In many cases, we must make some adjustments to the supervaluational theory to meet the posed challenges. The goal of this paper is to make those adjustments, and meet the challenges. (shrink)

If one believes that vagueness is an exclusively representational phenomenon, one faces the problem of the many. In the vicinity of Kilimanjaro, there are many many ‘mountain candidates’ all, apparently, with more-or-less equal claim to be mountains. David Lewis has defended a radical claim: that all the billions of mountain candidates are mountains. This paper argues that the supervaluationist about vagueness should adopt Lewis’ proposal, on pain of losing their best explanation of the seductiveness of the sorites.

If one believes that vagueness is an exclusively representational phenomenon, one faces the problem of the many. In the vicinity of Kilimanjaro, there are many many ‘mountain candidates’ all, apparently, with more-or-less equal claim to be mountains. David Lewis has defended a radical claim: that all the billions of mountain candidates are mountains. This paper argues that the supervaluationist about vagueness should adopt Lewis’ proposal, on pain of losing their best explanation of the seductiveness of the sorites.