In order to perfectly describe the world, it is not enough to speak truly. One must also use the right concepts - including the right logical concepts. One must use concepts that "carve at the joints", that give the world's "structure". There is an objectively correct way to "write the book of the world". Much of metaphysics, as traditionally conceived, is about the fundamental nature of reality; in the present terms, this is about the world's structure. Metametaphysics - inquiry into (...) the status of metaphysical questions - turns on structure. The question of whether ontological, causal, or modal questions are "substantive" is in large part a question of whether the world has ontological, causal, and modal structure - whether quantifiers, causal relations, and modal operators carve at the joints. (shrink)

Timothy Williamson gives an original and provocative treatment of deep metaphysical questions about existence, contingency, and change, using the latest resources of quantified modal logic. Contrary to the widespread assumption that logic and metaphysics are disjoint, he argues that modal logic provides a structural core for metaphysics.

On the now dominant Quinean view, metaphysics is about what there is. Metaphysics so conceived is concerned with such questions as whether properties exist, whether meanings exist, and whether numbers exist. I will argue for the revival of a more traditional Aristotelian view, on which metaphysics is about what grounds what. Metaphysics so revived does not bother asking whether properties, meanings, and numbers exist (of course they do!) The question is whether or not they are fundamental.

Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

_Naming and Necessity_ has had a great and increasing influence. It redirected philosophical attention to neglected questions of natural and metaphysical necessity and to the connections between these and theories of naming, and of identity. This seminal work, to which today's thriving essentialist metaphysics largely owes its impetus, is here reissued in a newly corrected form with a new preface by the author. If there is such a thing as essential reading in metaphysics, or in philosophy of language, this is (...) it. (shrink)

It is my aim in this paper to show that the contemporary assimilation of essence to modality is fundamentally misguided and that, as a consequence, the corresponding conception of metaphysics should be given up. It is not my view that the modal account fails to capture anything which might reasonably be called a concept of essence. My point, rather, is that the notion of essence which is of central importance to the metaphysics of identity is not to be understood in (...) modal terms or even to be regarded as extensionally equivalent to a modal notion. The one notion is, if I am right, a highly refined version of the other; it is like a sieve which performs a similar function but with a much finer mesh. (shrink)

Metaphysics is sensitive to the conceptual tools we choose to articulate metaphysical problems. Those tools are a lens through which we view metaphysical problems; the same problems look different when we change the lens. There has recently been a shift to "postmodal" conceptual tools: concepts of ground, essence, and fundamentality. This shift transforms the debate over structuralism in the metaphysics of science and philosophy of mathematics. Structuralist theses say that patterns are "prior" to the nodes in the patterns. In modal (...) terms this would mean that the nodes cannot vary independently of the pattern. But its postmodal meaning is unclear. Does it mean, e.g., that a fundamental account of reality somehow speaks only of patterns? What would that mean? Three structuralist positions are examined through a postmodal lens: nomic/causal/dispositional essentialism, structuralism about individuals (e.g., structural realism, e.g., ante rem mathematical structuralism), comparativism about quantities. The question of when theories are equivalent, and how that impacts the debate over structuralism, is also discussed. (shrink)

One of the central questions of material-object metaphysics is which highly visible objects there are right before our eyes. Daniel Z. Korman defends a conservative view, according to which our ordinary, natural judgments about which objects there are are more or less correct. He begins with an overview of the arguments that have led people away from the conservative view, into revisionary views according to which there are far more objects than we ordinarily take there to be or far fewer. (...) Korman criticizes a variety of compatibilist strategies, according to which these revisionary views are actually compatible with our ordinary beliefs. He goes on to respond to debunking arguments; objections that the conservative's verdicts about which objects that are and aren't are objectionably arbitrary; the argument from vagueness; the overdetermination argument; the argument from material constitution; and the problem of the many. (shrink)

Determinism is a perennial topic of philosophical discussion. Very little acquaintance with the philosophical literature is needed to reveal the Tower of ...

This paper distinguishes two kinds of realist issue -- the issue of whether the propositions of a given domain are factual and the issue of whether they are fundamental. It criticizes previous accounts of what these issues come to and suggests that they are to be understood in terms of a basic metaphysical concept of reality. This leaves open the question of how such issues are to be resolved; and it is argued that this may be done through consideration of (...) what grounds the facts of a given domain, when fundamentality is in question, and what grounds our engagement with the putative facts, when factuality is in question. (shrink)

Precis of my book by this title, for a symposium.

This concise book introduces nonphysicists to the core philosophical issues surrounding the nature and structure of space and time, and is also an ideal resource for physicists interested in the conceptual foundations of space-time theory. Tim Maudlin's broad historical overview examines Aristotelian and Newtonian accounts of space and time, and traces how Galileo's conceptions of relativity and space-time led to Einstein's special and general theories of relativity. Maudlin explains special relativity using a geometrical approach, emphasizing intrinsic space-time structure rather than (...) coordinate systems or reference frames. He gives readers enough detail about special relativity to solve concrete physical problems while presenting general relativity in a more qualitative way, with an informative discussion of the geometrization of gravity, the bending of light, and black holes. Additional topics include the Twins Paradox, the physical aspects of the Lorentz-FitzGerald contraction, the constancy of the speed of light, time travel, the direction of time, and more.Introduces nonphysicists to the philosophical foundations of space-time theory Provides a broad historical overview, from Aristotle to Einstein Explains special relativity geometrically, emphasizing the intrinsic structure of space-time Covers the Twins Paradox, Galilean relativity, time travel, and more Requires only basic algebra and no formal knowledge of physics. (shrink)

Four- Dimensionalism defends the thesis that the material world is composed of temporal as well as spatial parts. This defense includes a novel account of persistence over time, new arguments in favour of the four-dimensional ontology, and responses to the challenges four- dimensionalism faces." "Theodore Sider pays particular attention to the philosophy of time, including a strong series of arguments against presentism, the thesis that only the present is real. Arguments offered in favour of four- dimensionalism include novel arguments based (...) on time travel, the debate between spacetime substantivalists and relationalists, and vagueness. Also included is a comprehensive discussion of the paradoxes of coinciding material objects, and a novel resolution of those paradoxes based on temporal counterpart theory. In conclusion Sider replies to prominent objections to four- dimensionalism, including discussion of the problem of the rotating homogenous disk. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

In a revolutionary new book, a theoretical physicist attacks the foundations of modern scientific theory, including the notion of time, as he shares evidence of ...

What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to it.

In this book, Lawrence Sklar demonstrates the interdependence of science and philosophy by examining a number of crucial problems on the nature of space and ...

Structural realism is considered by many realists and antirealists alike as the most defensible form of scientific realism. There are now many forms of structural realism and an extensive literature about them. There are interesting connections with debates in metaphysics, philosophy of physics and philosophy of mathematics. This entry is intended to be a comprehensive survey of the field.

We naturally think of the material world as being populated by a large number of individuals . These are things, such as my laptop and the particles that compose it, that we describe as being propertied and related in various ways when we describe the material world around us. In this paper I argue that, fundamentally speaking at least, there are no such things as material individuals. I then propose and defend an individual-less view of the material world I call (...) “generalism”. (shrink)

A lot of people believe that distinct objects can occupy precisely the same place for the entire time during which they exist. Such people have to provide an answer to the 'grounding problem' – they have to explain how such things, alike in so many ways, nonetheless manage to fall under different sortals, or have different modal properties. I argue in detail that they cannot say that there is anything in virtue of which spatio-temporally coincident things have those properties. However, (...) I also argue that this may not be as bad as it looks, and that there is a way to make sense of the claim that such properties are primitive. (shrink)

One often hears a complaint about “bare particulars”. This complaint has bugged me for years. I know it bugs others too, but no one seems to have vented in print, so that is what I propose to do. (I hope also to say a few constructive things along the way.) The complaint is aimed at the substratum theory, which says that particulars are, in a certain sense, separate from their universals. If universals and particulars are separate, connected to each other (...) only by a relation of instantiation, then, it is said, the nature of these particulars becomes mysterious. In themselves, they do not have any properties at all. They are nothing but a pincushion into which universals may be poked. They are Locke’s “I know not what” (1689, II, xxiii, §2); they are Plato’s receptacles (Timaeus 48c–53c); they are “bare particulars”.1 Against substratum theory there is the bundle theory, according to which particulars are just bundles of universals. The substratum and bundle theories agree on much. They agree that both universals and particulars exist. And they agree that a particular in some sense has universals. (I use phrases like ‘particular P has universal U ’ and ‘particular P ’s universals’ neutrally as between the substratum and bundle theories.) But the bundle theory says that a particular is exhaustively composed of (i.e., is a mereological fusion of) its universals. The substratum theory, on the other hand, denies this. Take a particular, and mereologically subtract away its universals. Is anything left? According to the bundle theory, no. But according to the substratum theory, something is indeed left. Call this remaining something a thin particular. The thin particular does not contain the universals as parts; it instantiates them. (shrink)

Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.

This paper looks at the relationship between spacetime functionalism and Harvey Brown’s dynamical relativity. One popular way of reading and extending Brown’s programme in the literature rests on viewing his position as a version of relationism. But a kind of spacetime functionalism extends the project in a different way, by focussing on the account Brown gives of the role of spacetime in relativistic theories. It is then possible to see this as giving a functional account of the concept of spacetime (...) which may be applied to theories that go beyond relativity. This paper explores the way in which both the relationist project and the functionalist project relate to Brown’s work, despite being incompatible. Ultimately, these should not be seen as two conflicting readings of Brown, but two different directions in which to take his project. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically significant” about (...) metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

The dogma that the propositional logic of metaphysical modality is S5 is rebutted. The author exposes fallacies in standard arguments supporting S5, arguing that propositional metaphysical modal logic is weaker even than both S4 and B, and is instead the minimal and weak metaphysical-modal logic T.

According to material plenitude, every material object coincides with an abundance of other material objects that differ in the properties they have essentially and accidentally. Although this kind of plenitude is becoming increasingly popular, it isn't clear how to make sense of the view beyond its slogan form. As I argue, it turns out to be extraordinarily difficult to do so: straightforward attempts are either inconsistent or fail to capture the target idea. Making progress requires us to engage in more (...) delicate metaphysics than we might have expected and, along the way, reveals substantive constraints on the material world. In this article, I argue that any attempt to develop a coherent version of plenitude is subject to two under-appreciated challenges, and I develop a version of plenitude (global plenitude) capable of overcoming both. (shrink)

This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. The form of relationism appropriate to the Special Theory of Relativity is also able to evade the problems raised by Field. I survey (...) the effect of the General Theory of Relativity and of plenism on these considerations. (shrink)

This essay revisits some classic problems in the philosophy of space and time concerning the counting of possibilities. I argue that we should think that two Newtonian worlds can differ only as to when or where things happen and that general relativistic worlds can differ in something like the same way—the first of these theses being quaintly heterodox, the second baldly heretical, according to the mores of contemporary philosophy of physics.

In his paper ``What is Structural Realism?'' James Ladyman drew a distinction between epistemological structural realism and metaphysical (or ontic) structural realism. He also drew a suggestive analogy between the perennial debate between substantivalist and relationalist interpretations of spacetime on the one hand, and the debate about whether quantum mechanics treats identical particles as individuals or as `non-individuals' on the other. In both cases, Ladyman's suggestion is that an ontic structural realist interpretation of the physics might be just what is (...) needed to overcome the stalemate. The main thesis of this paper is that, whatever the interpretative difficulties of generally covariant spacetime physics are, they do not support or suggest structural realism. In particular, I hope to show that there is in fact no analogy that supports a similar interpretation of the metaphysics of spacetime points and of quantum particles. (shrink)

Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this paper, (...) I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (shrink)

I argue that Norton & Earman's hole argument, despite its historical association with General Relativity, turns upon very general features of any linguistic system that can represent substances by names. After exploring various means by which mathematical objects can be interpreted as representing physical possibilities, I suggest that a form of essentialism can solve the hole dilemma without abandoning either determinism or substantivalism. Finally, I identify the basic tenets of such an essentialism in Newton's writings and consider how they can (...) be updated to apply to the case provided by General Relativity. (shrink)

We attempt to extend the nominalistic project initiated in Hartry Field's Science Without Numbers to modern physical theories based in differential geometry.

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including the General Theory of Relativity. The argument has given rise to an industry of searching for a metaphysics of spacetime that delivers the right modal implications to rescue determinism. In this paper, I first argue that certain prominent extant replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. As part of my argument, (...) I show that threats to determinism of the sort brought out by the hole argument are more general than has heretofore been recognized. I then use these results to propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I go on to argue that once we realize what an essentialist doctrine about spacetime must look like in order to address the hole argument, we should reject all such doctrines, because they can't fulfill their ambition of improving on standard modal replies to the argument. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some general morals for contemporary metaphysics, in particular about (i) whether essence can be used to articulate a precise structuralist doctrine, and (ii) the relationship between essence and modality. (shrink)

Particularists in material-object metaphysics hold that our intuitive judgments about which kinds of things there are and are not are largely correct. One common argument against particularism is the argument from arbitrariness, which turns on the claim that there is no ontologically significant difference between certain of the familiar kinds that we intuitively judge to exist (snowballs, islands, statues, solar systems) and certain of the strange kinds that we intuitively judge not to exist (snowdiscalls, incars, gollyswoggles, the fusion of the (...) my nose and the Eiffel Tower). Particularists frequently respond by conceding that there is no ontologically significant difference and embracing some sort of deflationary metaontology (relativism, constructivism, quantifier variance). I show -- by identifying ontologically significant differences -- that the argument can be resisted without retreating to any sort of deflationary metaontology. (shrink)