Two things become one thing, something having parts, and something becoming something else, are cases of many things being identical with one thing. This apparent contradiction introduces others concerning transitivity of identity, discernibility of identicals, existence, and vague existence. I resolve the contradictions with a theory that identity, number, and existence are relative to standards for counting. What are many on some standard are one and the same on another. The theory gives an account of the discernibility of identicals using (...) phrases like “insofar as”. And it holds that standards for counting remain or shift depending on our purposes. (shrink)

This chapter contains sections titled: 1 A Question about Composition 2 Some Answers 3 How Shall We Decide? 4 Common Sense and Unrestricted Composition 5 Common Sense and Compositional Nihilism 6 Compositional Nihilism and the Self 7 The Appeal to Science 8 Problem or Pseudoproblem? What To Do?

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)

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the (seemingly innocuous) thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly this composition relation is. Composition as Identity (CI) is the (...) view that the composition relation is the identity relation. While such a view has some advantages, there are many arguments against it. In this essay, I discuss several versions of the most common objection against CI, and show how the CI theorist can maintain that these arguments – contrary their initial intuitive appeal – are nonetheless unsound. (shrink)

Many of us think that ordinary objects – such as tables and chairs – exist. We also think that ordinary objects have parts: my chair has a seat and some legs as parts, for example. But once we are committed to the thesis that ordinary objects are composed of parts, we then open ourselves up to a whole host of philosophical problems, most of which center on what exactly the composition relation is. Composition as Identity is the view that the (...) composition relation is the identity relation. While such a view has some advantages, there are many arguments against it. In this essay, I will briefly canvass three different varieties of Composition as Identity, and suggest why one of them should be preferred over the others. Then I will outline several versions of the most common objection against CI. I will suggest how a CI theorist can respond to these charges by maintaining that some of the arguments are invalid. (shrink)

The topic of this book is material objects. Like most interesting concepts, the concept of a material object is one without precise boundaries.

While Michel Foucault’s writings have been taken up extensively to explore gender and sexuality, until recently there was little work drawing on Foucault’s writings to discuss race. In part, this was because Foucault seemed to have said almost nothing about race, aside from some comments on Nazism and eugenics in the final pages of Part V of The History of Sexuality, volume 1. With the 1997 and 1999 publication of two series of lectures that Foucault delivered at the Collège de (...) France between 1974 and 1976, Abnormal and “Society Must Be Defended” (both appearing in English translation in 2003), Foucault scholars have, however, become aware that he made more extensive and provocative observations about race than had previously been believed. Both of these lecture series gives a genealogical account of the ways in which modern, biological forms of racism emerged at a certain point in history, stressing the contingency of this emergence and its enmeshment in power struggles and modern forms of power. This paper provides an account of what Foucault argues about race and racism in the Collège de France lectures, and, more briefly, presents two of the most extended treatments of race coming from Foucauldian perspectives that have appeared in the wake of these texts. (shrink)

There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

In the late 1970s and early 1980s a number of philosophers, notably Churchland, Field, Stalnaker, Dennett, and Davidson, began to argue that propositional attitude predicates (such as believes that it’s sunny outside) are a species of measure predicate, analogous in important ways to numerical predicates by which we attribute physical magnitudes (such as mass, length, and temperature). Other philosophers, including myself, have subsequently developed the idea in greater detail. In this paper I sketch the general outlines of measurement‐theoretic accounts of (...) propositional attitudes, explaining in the briefest terms the basic idea of such accounts, why some have thought such accounts plausible, how these accounts might go, what their implications might be both for our conception of propositional attitudes and for their role in cognitive scientific theorizing, and where the potential problems with such accounts might lie. (shrink)

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be ‘coincidental’, ‘accidental’, or ‘fortuitous’. The notion of a ‘ mathematical coincidence’ has so far failed to receive sufficient attention from philosophers. I argue that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. I argue that although the components of a mathematical coincidence (...) may possess a common explainer, they have no common explanation ; that two mathematical facts have a unified explanation makes their truth non-coincidental. I suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. I also argue that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Contribution to a symposium on Keith DeRose's book, The Case for Contextualism: Knowledge, Skepticism, and Context.

This is a canvass to the critical reaction to Joseph Raz’s service conception of authority, as well as actual or possible replies by Raz. Familiarity is assumed with the theory itself, covered in a previous article. The article focuses primarily on direct criticisms of Raz’s theory, rather than replies developed in the context of a theorist’s wider project.

There is widespread disagreement as to what the facts are concerning just when a collection of objects composes some further object; but there is widespread agreement that, whatever those facts are, they are necessary. I am unhappy to simply assume this, and in this paper I ask whether there is reason to think that the facts concerning composition hold necessarily. I consider various reasons to think so, but find fault with each of them. I examine the theory of composition as (...) identity, but argue that the version of this doctrine that entails universalism is implausible. I consider the claim that the a priority of such facts leads to their necessity, but give a defence of substantial contingent a priori truths. I ask whether the contingency of such facts would lead to unwelcome possibilities, but argue that the worrying looking possibilities can be blocked if it is desired. Next, I argue against the thought that the Lewis-Sider argument against restricted composition might give us reason to accept the necessity of universalism. Lastly, I respond to two objections from the 2006 BSPC. I conclude in favour of the contingency of the facts concerning when some things compose some thing. (shrink)

David Lewis in the short monograph Parts of Classes (PC) undertakes a fundamental re‐examination of the relationship between mereology, the general theory of parts, and set theory, the general theory of collections. Given Lewis's theses, to be an element of a set or member of class is just to have a singleton that is a part thereof. Lewis in PC adds a claim of kind of ontological innocence, comparable to that of first‐order logic, for mereology. The only substantive assumption of (...) plethynticology is that for any condition there are some things such that they are precisely the things for which the conditions hold. All the alternatives, making do with a single domain of individuals, have in common that they involve the axiom of choice. Restated in Hazen's terminology rather than Frege's, the fallback assumption is that there are no more small species than individuals. (shrink)

A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.

According to the Truthmaker Principle: every truth has a truthmaker. Attempts to come to grips with the Truthmaker Principle played a prominent role in Lewis’s metaphysical writings over the last fifteen years of his career. Although Lewis agreed that the truth of propositions must somehow be ontologically grounded, the Truthmaker Principle was too strong: it conflicted with two of Lewis’s most fundamental metaphysical assumptions, the uniqueness of composition and the Humean denial of necessary connections. Lewis endorsed instead a weaker principle: (...) Truth Supervenes on Being. But towards the end of his career, he changed course, noting that his critique of the Truthmaker Principle rested on essentialist assumptions that he, as a counterpart theorist, does not accept. Once freed from those assumptions, a counterpart theorist can accept the Truthmaker Principle after all without buying into unmereological composition and mysterious necessary connections. (shrink)

I argue via examples that there are cases in which things that are not two distinct things qualitatively differ without contradiction. In other words, there are cases in which something differs from itself. Standard responses to such cases are to divide the thing into distinct parts, or to conceive of the thing under different descriptions, or to appeal to different times, or to deny that the property had is the property lacked. I show these responses to be unsatisfactory. I then (...) gather and systematize available ways of talking about such cases with phrases like ‘insofar as’, ‘qua’, ‘to the extent that’, ‘in some respect’, etc., while paying special attention to the scope of ‘not’ when used with these phrases. This allows me to show how we can speak of self-differing without contradiction. (shrink)

This essay interprets Butler’s distinction between identity in the loose and popular sense and in the strict and philosophical sense. Suppose there are different standards for counting the same things. Then what are two distinct things counting strictly may be one and the same thing counting loosely. Within a given standard identity is one-one. But across standards it is many-one. An alternative interpretation using the parts-whole relation fails, because that relation should be understood as many-one identity. Another alternative making identity (...) relative to sort fails, because whole and parts can be of the same sort. (shrink)

Die Grundlagen gehören zu den klassischen Texten der Sprachphilosophie, Logik und Mathematik. Frege stützt sein Programm einer Begründung von Arithmetik und Analysis auf reine Logik, indem er die natürlichen Zahlen als bestimmte Begriffsumfänge definiert. Die philosophische Fundierung des Fregeschen Ansatzes bilden erkenntnistheoretische und sprachphilosophische Analysen und Begriffserklärungen. Studienausgabe aufgrund der textkritisch herausgegebenen Jubiläumsausgabe (Centenarausgabe). Mit Einleitung, Anmerkungen, Literaturverzeichnis und Namenregister.

In this chapter, I survey what I call Lewisian approaches to modality: approaches that analyze modality in terms of concrete possible worlds and their parts. I take the following four theses to be characteristic of Lewisian approaches to modality. (1) There is no primitive modality. (2) There exists a plurality of concrete possible worlds. (3) Actuality is an indexical concept. (4) Modality de re is to be analyzed in terms of counterparts, not transworld identity. After an introductory section in which (...) I motivate analyzing modality in terms of possible worlds, I devote one section to each of these four theses. For each thesis, I take Lewis’s interpretation and defense as my starting point. I then consider and endorse alternative ways of accepting the thesis, some of which disagree substantially with Lewis’s interpretation or defense. There is more than one way to be a Lewisian about modality. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

The Forrest-Armstrong argument, as reconfigured by David Lewis, is a reductio against an unrestricted principle of recombination. There is a gap in the argument which Lewis thought could be bridged by an appeal to recombination. After presenting the argument, I show that no plausible principle of recombination can bridge the gap. But other plausible principles of plenitude can bridge the gap, both principles of plenitude for world contents and principles of plenitude for world structures. I conclude that the Forrest-Armstrong argument, (...) when fortified in one of these ways, demands that unrestricted recombination be rejected. The appropriate restriction comes from a consideration of what world structures are possible. I argue that, although there are too many worlds to form a set, for any world, the individuals at that world do form a set. To defend it I invoke a principle of Limitation of Size together with an iterative conception of structure. (shrink)

"Composition as identity" is the radical claim that the whole is identical to the parts - radical because it implies that a single object can be identical to many objects. Composition as identity, together with auxiliary assumptions, implies the principle of "collapse": an object is one of some things if and only it is part of the fusion of those things. Collapse has important implications: the comprehension principle of plural logic must be restricted, plural definite descriptions such as "the Cheerios (...) in the bowl" are empty, Composition as identity does not preclude emergent properties (contrary to what McDaniel has argued), and drastic simplifications of mereological and logical ideology are extensionally available. (shrink)

David Lewis‘s Parts of Classes is a great book, in all respects. But one of its most interesting thesis, in my mind, is not its core thesis that standard set theory — ZFC — reduces to classical mereology + plural quantification + a primitive singleton-relation, but rather its sub-thesis of how to understand classical mereology, what Lewis calls the thesis of Composition as Identity: (CAI): a whole is the same portion of reality as its many parts taken together; it is (...) them collectively, they collectively are it. CAI is needed as an assumption for the core thesis of Parts of Classes — the reduction of ZFC — on pain of it being unmotivated.1 But CAI is the most interesting in its own right. It is also as such it is presented by Lewis, and received in the literature. In what follows, I critically assess CAI as Lewis presents it in Parts of Classes. I first argue that Lewis‘s presentation of CAI has been misunderstood in the literature (section 1). I then argue that the best (if not the only) way to understand it entails a slightly revisionary semantics for a certain form of predication (section 2). I finally end by showing that this might create more trouble than it solves for Lewis (section 3). (shrink)

In this paper I argue that composition as identity entails unrestricted composition. I also briefly consider a new take on the special composition question.

I am a realist of a metaphysical stripe. I believe in an immense realm of "modal" and "abstract" entities, of entities that are neither part of, nor stand in any causal relation to, the actual, concrete world. For starters: I believe in possible worlds and individuals; in propositions, properties, and relations (both abundantly and sparsely conceived); in mathematical objects and structures; and in sets (or classes) of whatever I believe in. Call these sorts of entity, and the reality they comprise, (...) metaphysical. In contrast, call the actual, concrete entities, and the reality they comprise, physical. Physical and metaphysical reality together comprise all that there is. In this paper, it is not my aim to defend realism about any particular metaphysical sort of entity. Rather, I ask quite generally whether and how any brand of realism about metaphysical sorts of entity could be justified? (shrink)

Region R Question: How many objects — entities, things — are contained in R? Ignore the empty space. Our question might better be put, 'How many material objects does R contain?' Let's stipulate that A, B and C are metaphysical atoms: absolutely simple entities with no parts whatsoever besides themselves. So you don't have to worry about counting a particle's top half and bottom half as different objects. Perhaps they are 'point-particles', with no length, width or breadth. Perhaps they are (...) extended in space without possessing spatial parts (if that is possible). Never mind. We stipulate that A, B and C are perfectly simple. We also stipulate that they are connected as follows. A and B are stuck together in such a way that when a force is applied to one of them, they move together 'as a unit'. Moreover, the two of them together exhibit behavior that neither would exhibit on its own — Perhaps they emit a certain sound, or glow in the dark — whereas C is.. (shrink)

Quine said that the ontological question can be asked in three words, ‘What is there?’, and answered in one, ‘everything’. He was wrong. We need an extra word to ask the ontological question: it is ‘What is there, really?’; and it cannot be answered truthfully with ‘everything’ because there are some things that exist but which don’t really exist (and maybe even some things that really exist but which don’t exist).