Cover Page


Note on Contibutors



CHAPTER 1.1: Abstract Entities

1 What are Abstract Entities?

2 Why Believe there are Abstract Objects?

3 Examples of Work Abstracta Might Do

4 Pluses and Minuses

5 Conclusion


CHAPTER 1.2: There Are No Abstract Objects

1 The Thesis

2 Paraphrase

3 Abstract Objects in Scientific Explanations

4 Abstract Objects in Philosophical Explanations



CHAPTER 2.1: Nailed to Hume’s Cross?

1 Lawhood, Causation, and Bearing Hume’s Cross

2 Support for Anti-Reductionism and a Glance at Some Alternatives

3 The Metaphysical Concern

4 The Skeptical Challenge

5 Avoiding the Cross


CHAPTER 2.2: Causation and Laws of Nature: Reductionism

1 Clarifying the Thesis

2 Generalizing the Thesis

3 Defending the Thesis, Stage One: Causation

4 Defending the Thesis, Stage Two: Laws



CHAPTER 3.1: Concrete Possible Worlds

1 Introduction

2 No Primitive Modality

3 Concrete Worlds Exist

4 Actuality is Indexical

5 Modality De Re and Counterparts

6 Conclusion


CHAPTER 3.2: Ersatz Possible Worlds

1 Introduction

2 The Ersatzer’s Zoo

3 Actualism and Possibilism

4 Ersatz Ontology, Ersatz Ideology

5 Conclusion



CHAPTER 4.1: People and their Bodies











CHAPTER 4.2: Persons, Bodies, and Human Beings

1 Thomson’s View

2 Cases and Intuitions

3 Thomson’s Arguments

4 The Extrinsicness Objection

5 Thomson’s Ontological Argument

6 Are We Our Bodies?

7 Persons and Human Beings

8 The Identity of Animals

9 Empty Questions

10 Does Our Essence Matter?



CHAPTER 5.1: The Privileged Present: Defending an “A-Theory” of Time

1 Introduction

2 A-Theories and B-Theories

3 Competing Versions of the A-Theory

4 Yes, But Is It True?

5 An Objection to Presentism Based on the Need for “Truthmakers”

6 Objections to the A-Theory Based on Relativity

7 Why Think the A-Theory Is True?


CHAPTER 5.2: The Tenseless Theory of Time

1 Attractions of the Tenseless Theory of Time

2 Two Ways of Treating of Tenses as Indexicals

3 B-Theorist Critique of the A-Theory

4 “Thank Goodness That’s Over”

5 The Supposed Passage of Time

6 Presentism and Fatalism



CHAPTER 6.1: Temporal Parts

1 What Are Temporal Parts?

2 Change and Temporary Intrinsics

3 The Paradoxes of Material Constitution

4 The Argument from Vagueness and Anthropocentrism


CHAPTER 6.2: Three-Dimensionalism vs. Four-Dimensionalism

1 Space-time

2 The “Three-Dimensional Picture”

3 Conclusion



CHAPTER 7.1: Incompatibilism

1 Determinism and the Garden of Forking Paths

2 The Consequence Argument

3 Ultimate Responsibility

4 Can We Have Free Will?

5 Indeterminism and Responsibility

6 Responsibility, Luck and Chance


Suggested further reading

CHAPTER 7.2: Compatibilism, Incompatibilism, and Impossibilism

1 Defining the Problem

2 Rules of Debate

3 Fatalism

4 The Clarence Darrow Argument

5 The Forking Paths Argument

6 The Consequence Argument

7 Conclusion



CHAPTER 8.1: The Moon and Sixpence: A Defense of Mereological Universalism

1 Classical Mereology

2 Against Real Coincidence

3 Against Arbitrariness and Indeterminacy

4 Souls and Brutes

5 Question or Pseudo-Question?


CHAPTER 8.2: Restricted Composition

1 Introduction

2 The Special Composition Question

3 Unrestricted Composition

4 Nihilism

5 Contact

6 Fastenation

7 Van Inwagen’s Proposed Answer

8 Brutal Composition

9 The Serial Response

10 The Multi-Factor Approach

11 The Mystery Response

12 Conclusion



CHAPTER 9.1: Ontological Arguments: Interpretive Charity and Quantifier Variance

1 Charity in the Philosophy Room

2 Quantifier Variance


CHAPTER 9.2: The Picture of Reality as an Amorphous Lump

1 Introduction

2 Ontological Pluralism

3 A More Fundamental Worry

4 The Deflationary Conception of Ontology

5 Conclusion



Contemporary Debates in Metaphysics

Contemporary Debates in Philosophy

In teaching and research, philosophy makes progress through argumentation and debate. Contemporary Debates in Philosophy provides a forum for students and their teachers to follow and participate in the debates that animate philosophy today in the western world. Each volume presents pairs of opposing viewpoints on contested themes and topics in the central subfields of philosophy. Each volume is edited and introduced by an expert in the field, and also includes an index, bibliography, and suggestions for further reading. The opposing essays, commissioned especially for the volumes in the series, are thorough but accessible presentations of opposing points of view.

1.    Contemporary Debates in Philosophy of Religion edited by Michael L. Peterson and Raymond J. Vanarragon

2.    Contemporary Debates in Philosophy of Science edited by Christopher Hitchcock

3.    Contemporary Debates in Epistemology edited by Matthias Steup and Ernest Sosa

4.    Contemporary Debates in Applied Ethics edited by Andrew I. Cohen and Christopher Heath Wellman

5.    Contemporary Debates in Aesthetics and the Philosophy of Art edited by Matthew Kieran

6.    Contemporary Debates in Moral Theory edited by James Dreier

7.    Contemporary Debates in Cognitive Science edited by Robert Stainton

8.    Contemporary Debates in Philosophy of Mind edited by Brian McLaughlin and Jonathan Cohen

9.    Contemporary Debates in Social Philosophy edited by Laurence Thomas

10.   Contemporary Debates in Metaphysics edited by Theodore Sider, John Hawthorne, and Dean W. Zimmerman

Forthcoming Contemporary Debates are in:

Political Philosophy edited by Thomas Christiano and John Christman

Philosophy of Biology edited by Francisco J. Ayala and Robert Arp

Philosophy of Language edited by Ernie Lepore



Notes on Contributors

Phillip Bricker is Professor and Head of Philosophy at the University of Massachusetts, Amherst. His interests range broadly over metaphysics, philosophical logic, philosophy of science, and philosophy of mathematics.

John W. Carroll is Professor of Philosophy at NC State University in Raleigh, North Carolina. He works in the areas of metaphysics and the philosophy of science. His interests center on the topics of laws of nature, causation, explanation, and time travel. He is the author of Laws of Nature (Cambridge University Press, 1994) and such articles as “Ontology and the Laws of Nature” (Australasian Journal of Philosophy, 1987), “The Humean Tradition” (Philosophical Review, 1990), “Property-Level Causation?” (Philosophical Studies, 1991), and “The Two Dams and that Damned Paresis” (British Journal for the Philosophy of Science, 1999). He is the editor of Readings on Laws of Nature (Pittsburgh University Press, 2004).

Cian Dorr received his BA from University College Cork, and his PhD from the University of Princeton, where he was a student of the late David Lewis. He is currently Assistant Professor of Philosophy at the University of Pittsburgh.

Matti Eklund is an Associate Professor of Philosophy at Cornell University. He has published articles in metaphysics, philosophy of language, and philosophy of logic.

John Hawthorne is Waynflete Professor of Metaphysical Philosophy at the University of Oxford. He is author of Metaphysical Essays (Clarendon Press, 2006), and has published widely in metaphysics, epistemology, philosophy of language, and Leibniz studies.

Eli Hirsch is Professor of Philosophy at Brandeis University. He is the author of a number of works in metaphysics, including Dividing Reality (Oxford University Press, 1993).

Robert Kane is University Distinguished Teaching Professor of Philosophy at the University of Texas at Austin. He is author of The Significance of Free Will (Oxford University Press, 1996), Through the Moral Maze (Paragon House, 1994), A Contemporary Introduction to Free Will (Oxford University Press, 2005) and editor of The Oxford Handbook of Free Will (2002), among other works in the philosophy of mind and ethics.

Ned Markosian is a philosophy professor at Western Washington University. He grew up in Montclair, New Jersey, graduated from Oberlin College, and received a PhD from the University of Massachusetts. He has worked mainly on issues in the philosophy of time and the mereology of physical objects.

Joseph Melia is a Reader in Metaphysics at the University of Leeds. His main interests are in modality, ontology, and the philosophy of physics. He is currently working on a book on ontology.

Derek Parfit was born in China in 1942 and received an undergraduate degree in Modern History at Oxford in 1964. Since 1967 he has been a Fellow of All Souls College, Oxford. He has often taught in the United States, and is now a regular Visiting Professor to the Departments of Philosophy of Rutgers, New York University, and Harvard. His first book, Reasons and Persons, was published by Oxford University Press in 1984. A second book, Climbing the Mountain, is nearly completed, and will also be published by Oxford University Press. This book will be about reasons and rationality, Kant’s ethics, contractualism, and consequentialism.

Jonathan Schaffer is Professor of Philosophy at the Australian National University. He works mainly in metaphysics and epistemology. Further information about his work may be found on his website: <>.

Theodore Sider is Professor of Philosophy at New York University. He has published articles in metaphysics and philosophy of language, is the author of Four-Dimensionalism (Oxford University Press, 2001), and is co-author (with Earl Conee) of Riddles of Existence: A Guided Tour of Metaphysics (Oxford University Press, 2005).

J. J. C. Smart is Emeritus Professor, Australian National University, and is now living in Melbourne. He is an honorary in the School of Philosophy and Bioethics at Monash University. His most recent publication is a paper “Metaphysical Illusions” which is pertinent to the chapter in the present volume.

Chris Swoyer is Professor of Philosophy and Affiliated Professor of Cognitive Psychology at the University of Oklahoma. He has published, and continues to work on, the philosophy of logic, metaphysics, philosophy of science, and history of modern philosophy (especially Leibniz).

Judith Jarvis Thomson is Professor of Philosophy at MIT. Her published work is on topics in moral theory, metaethics, and metaphysics.

James Van Cleve taught for many years at Brown University and is now Professor of Philosophy at the University of Southern California. He works in metaphysics, epistemology, and the history of modern philosophy.

Kadri Vihvelin is Associate Professor of Philosophy at the University of Southern California. Her publications include “The Dif” (Journal of Philosophy, 2005); “Freedom, Foreknowledge, and the Principle of Alternate Possibilities” (Canadian Journal of Philosophy, 2000); “What Time Travelers Cannot Do” (Philosophical Studies, 1996); “Causes, Effects, and Counterfactual Dependence” (Australasian Journal of Philosophy, 1995); and “Stop Me Before I Kill Again” (Philosophical Studies, 1994).

Dean W. Zimmerman is an Associate Professor in the Philosophy Department at Rutgers University. He is editor of Oxford Studies in Metaphysics and author of numerous articles in metaphysics and philosophy of religion.


Theodore Sider

There is something strange about metaphysics. Two strange things, really, although they are related. Metaphysics asks what the world is like.1 But the world is a big and varied place. How can one meaningfully ask what apples, planets, galaxies, tables, chairs, air conditioners, computers, works of art, cities, electrons, molecules, people, societies... are like? The question is hopelessly general and abstract! One would normally ask first what apples are like, and then ask what planets and the rest are like separately. What meaningful questions are there about such a broad and heterogeneous subject matter? Furthermore, you’d think that you’d need to ask a biologist what apples are like, an astronomer what planets are like, and so on. What can a philosopher contribute?

Let’s have a look.

Consider a certain apple. What is it like? Well, it’s red, and it’s round. But this information doesn’t come to us from philosophy. We need to observe the apple to learn its color and shape.

Consider another thing, Mars. It has iron oxide on its surface, and it is 6.4185 × 1023 kg in mass. This information about Mars, again, isn’t something that philosophy can tell us about; we learn it from astronomers.

So far, we have found no philosophical subject matter. But if we abstract from certain details, we find things in common between our two examples; we find a recurring pattern despite the diverse subject matters. Here are the facts we cited:

The apple is redMars has iron oxide on its surface
The apple is roundMars is 6.4185 × 1023 kg in mass

Notice that in each case, an object is said to have a feature. For example, in the first case, the object is the apple, and the feature is being red. Philosophers call objects that have features particulars, and they call the features “had” by particulars properties. Thus, we have:


In fact, this pattern is quite general. Think of other facts:

This table is brokenthe tablebeing broken
Electron e is negatively chargedelectron enegative charge
The stock market crashedthe stock marketcrashing

The particular-property pattern keeps recurring. It appears that every fact about the world boils down to particulars having properties.2 So it would seem that the world contains two different sorts of entities: particulars and properties. We have already uncovered a general fact about the world. Just as a scientist establishes generalizations about what the world is like in some limited sphere (for instance that charged particles repel one another or that the planets move in elliptical orbits), we have established a generalization – albeit a much broader and more abstract one – about the world. And we did it without detailed input from the sciences.

Of course, since this is philosophy we are talking about, there is controversy at every turn. The statement that there are two different sorts of objects in the world, particulars and properties, can be challenged. Nominalists, for example, believe in particulars, but not in properties. According to a nominalist, there simply is no such thing as the property of being red.

Put that baldly, the statement is misleading. It suggests that nominalists think that there is no such thing as a red object. But nominalists are not crazy. They agree that red objects exist; they just deny that redness exists.

The nominalist’s position can be made clearer by thinking about the sentence ‘The apple is red’. The nominalist agrees that the sentence is true. But now, consider the two parts of the sentence: its subject, ‘The apple’, and its predicate, ‘is red’. What the nominalist thinks is that, whereas the subject does stand for an object (namely, the particular in question, the apple), the predicate does not stand for an object. The predicate ‘is red’ is of course meaningful; it’s just that it doesn’t stand for an object. Just as a comma is meaningful without standing for an object, predicates can be meaningful without standing for objects. The apple is red, even though there is no such thing as its redness.

We talk as if there are lots of things, when really, those things don’t exist. We talk, for instance, as if there are such things as holes. We’ll say: “Look at the size of that hole in the wall!” “Bring me the piece of cheese with three holes in it.” “I can’t wear that shirt because there is a hole in it.” But surely there aren’t really such things as holes, are there? What kind of object would a hole be? Surely what really exist are the physical objects that the holes are “in”: walls, pieces of cheese, shirts, and so on. When one of these physical objects has an appropriate shape - namely, a perforated shape - we’ll sometimes say that “there is a hole in it.” But we don’t really mean by this that there literally exists an extra entity, a hole, which is somehow made up of nothingness. The nominalist thinks that all subject-predicate sentences are a bit like sentences about holes. It might seem at first that the predicates refer to entities, but they really don’t.

Are nominalists right? Do properties exist or don’t they? This is no easy question, and Chris Swoyer and Cian Dorr (chapter 1) come to opposite conclusions on this and related matters. But in this brief look at nominalism, we have at least glimpsed what metaphysicians are after: patterns in apparently diverse phenomena, and generalizations that accurately describe these patterns. This book contains chapters in a number of areas of metaphysics; in each area, the goal is to find generalizations about abstract patterns:


Scientists tell us of the laws of nature. Physicists tell us of the laws of physics, for example that like-charged particles must repel one another. Chemists tell us of the laws of chemistry, for example that if methane reacts with oxygen, it must produce carbon dioxide and water. Economists tell us of the laws of economics, for example that when demand increases then prices must increase as well. In each case, we have scientists telling us what must happen in certain conditions. What exactly are these laws of nature; what is the status of these “musts”? Laws of society exist because governing bodies have legislated them. But there is no governing body that has legislated the laws of nature. Physicists try to discover the laws of physics; they do not create them (chapter 2). And if everything happens as these laws of nature specify, human actions must conform to their dictates. How then can we have free will (chapter 7)? Further, there are other cases of “mustness”. Every bachelor must be male; every prime number other than two must be odd. In what does the mustness of these facts consist (chapter 3)?


Objects of all sorts, the objects of physics, chemistry, biology, and other sciences, last over time. This raises many philosophical questions. What does it mean for the same object to exist over time? A person at age 50, for instance, is the same person as she was as a child, even though nearly all of the matter that made up her body as a child no longer is with her at age 50. What makes a person the same over time? And indeed, what is it for time to pass at all (chapters 4–6)?


Different sciences describe different objects. Physics describes subatomic particles, biology describes organisms, and so on. But must we believe that the objects from each science really exist? Consider organisms, for example. Could we not stick with the physicist’s objects, and say that the only objects that really exist are subatomic particles? We could still agree that there are distinctively biological phenomena, even though there do not exist distinctively biological objects. For even if human organisms (for example) do not exist, there are nevertheless certain systems of particles that exhibit biological behavior. These are the systems involving particles that one ordinarily thinks of as being parts of a single biological organism. Thus, we have very general ontological questions (existence questions) about objects with parts (chapter 8). Other ontological questions include the question discussed above of whether properties exist, the question of whether numbers exist, and even the “metaontological” question of what it means to investigate whether objects of a certain sort “really” exist (chapter 9).

Within these and other areas of metaphysics, certain themes recur. For example, metaphysicians tend to fall into two camps: those who go around trying to reduce phenomena, and those who prefer instead to “leave the world as they found it.” Consider the law of nature saying that like-charged particles repel one another. Of one thing we can be sure: the existence of such a law guarantees a regularity: everywhere and at any time, every pair of like-charged particles will indeed repel each other. Jonathan Schaffer (chapter 2.2) is a member of the reductionist camp. He wants to say that, roughly, there is nothing more to this law beyond the regularity. The law reduces to the regularity. What the physicists discover is simply that it is universally true that every two charged particles in fact repel each other. John W. Carroll disagrees (chapter 2.1); he is from the anti-reductionist camp. According to him, reductionists like Schaffer leave out something crucial. They leave out the mustness, the necessity, of laws. It doesn’t just happen to be the case that charged particles repel one another. When you give two particles the same charge, they must repel each other. So there’s something more to a law than just the fact that objects everywhere act in accordance with the law; you need to add necessity to a regularity to get a law.

Another example: time’s passage. We ordinarily think of time as something that “moves”. J. J. C. Smart (chapter 5.2) takes a reductionist approach to time’s passage. According to him, time is just another dimension like space. And like space, it is not really correct to describe time as moving. What we ordinarily think of as time’s passage just arises from the fact that at any given moment in time, we can only remember what has occurred in one direction through time (the direction we call the “past”). But objects in this direction are not “gone.” Just as objects that are spatially distant - for example, objects on Mars - are just as real as objects around here, so, objects that are temporally distant - for example, dinosaurs - are just as real as objects around now. Dean Zimmerman, on the other hand, resists this reduction (chapter 5.1). Our ordinary belief about the matter is correct: time has passed since the time of the dinosaurs, and the dinosaurs are now gone. And this does not just mean that they are far away in time, just as Mars is far away in space. The dinosaurs simply do not exist.

A second (and related) recurring theme in metaphysics is the relationship between a scientific outlook and our ordinary beliefs. What science tells us doesn’t always fit neatly with our ordinary beliefs about the world. In cases of conflict, should we revise science so that it doesn’t conflict with our ordinary beliefs? Should we revise the ordinary beliefs in light of science? Or is it a mistake to think that they conflicted in the first place?

Time’s passage again provides an example. The picture of time we get from physicists, especially from Einstein’s theories of relativity, is Smart’s picture of space-like time. But where, in this picture, is there room for our ordinary belief that time passes? According to Smart, our ordinary belief must be revised to fit it into the scientific picture, whereas according to Zimmerman, it is the scientific picture that must be revised, or at least augmented.

Or consider the problem of free will and determinism. Science tells us of a world governed by laws of nature. An electron has no choice about where to move; if another charged particle is in its vicinity, it cannot help but be repelled. The laws of nature must be obeyed. But on the face of it, this threatens our ordinary conception of ourselves as having free choices. We blame evildoers because we think that their choices were not inevitable; they freely chose to do wrong. Robert Kane (chapter 7.1) argues that these two pictures genuinely conflict. If the laws of nature fully determined what each and every object in the world was going to do, then there would be no room for any human freedom. (Fortunately, there is reason to think that the laws of nature that scientists have actually discovered are not quite so restrictive.) Kadri Vihvelin, on the other hand, tries to fit human freedom into the world of science, even a scientific world in which all human behavior is determined (chapter 7.2). But Vihvelin does not think that this calls for a revision of our ordinary beliefs about freedom. (In this way her position is unlike Smart’s.) According to Vihvelin, it was a mistake to think that the two world-pictures were in conflict in the first place.

What should we trust when doing metaphysics: science or ordinary beliefs? The question leads some to extremes. At one end, we find those who think that all metaphysics can do is report science. At the other end, we find those who think that metaphysics should ignore science and listen only to ordinary beliefs. Each extreme is questionable.

The first extreme ignores the fact that science does not settle all metaphysical questions, and also the fact that scientists are influenced by their metaphysical presuppositions. We need a metaphysics that goes beyond reporting science in order to address the unsettled questions and evaluate the presuppositions.

The second extreme subdivides. It includes those who think that science and ordinary beliefs can never conflict, because they address “different worlds” (the “world of ordinary life” and the “world of science”). And it includes those dogmatists who think that ordinary beliefs can never seriously be doubted. The problem with each subdivision is that neither ordinary beliefs nor science is intended to be about a novel subject matter. Each is about the world. Ordinary folks, naturally, have beliefs about the world; but they hope to learn more about it through science. In addition to believing that objects move in space over time, that actions take time, and that objects take up space, ordinary believers also expect science to tell us the underlying nature of space and time. Nor do scientists step into another world when they don their lab coats. The point of science is to understand how the world, the one world, the world in which ordinary folks live, works.

A moderate view of the relation between science and ordinary beliefs seems in order: metaphysics must listen to, but is not exhausted by, science. This, however, leaves the exact nature of the relation wide open. Perhaps ordinary beliefs are epis-temic starting points - claims with which we are entitled to begin our inquiries, but which may later be revised, perhaps because they conflict with science, perhaps because they conflict with one another. Perhaps not all ordinary beliefs should be taken equally seriously. We might, for example, grant more weight to beliefs that are fundamental to the structure of our thought about the world (recall the discussion of particulars and properties above), and grant little (if any) weight to ordinary beliefs about matters more properly addressed by the sciences. Perhaps the mere fact that a belief is an ordinary one counts for nothing at all; perhaps we should instead trust reason, a faculty capable of guiding both philosophically sophisticated scientists and scientifically informed philosophers.

Any metaphysician is bound, sooner or later, to face the following challenge. Science has been wildly successful. It has led to increasingly successful theories, technological advances, and consensus as to the truth. The history of metaphysics, on the other hand, has been as much one of wild goose chases as progress. Metaphysicians (like all philosophers!) continue to disagree about the same issues for millennia, and have not sent anyone to the moon.

This leads some philosophers to doubt that metaphysics has any value at all. A certain empiricist tradition in epistemology says that the only route to truth is through the senses, and ultimately through science. If you can’t do an experiment to settle a question, the question isn’t worth asking. At best, it is an idle question whose answer we will never know; at worst, the question is meaningless.

The empiricist is moved by an admirable desire to rid philosophy of undisciplined speculation. But the only empiricism that flatly rules out all metaphysics is one based on a naive view of science. Real scientists do not just “summarize what they see.” Scientists must regularly choose between many theories that are consistent with the observed data. Their choices are governed by criteria like simplicity, comprehensiveness, and elegance. This is especially true in very theoretical parts of science, for instance theoretical physics, not to mention mathematics and logic.

A realistic picture of science leaves room for a metaphysics tempered by humility. Just like scientists, metaphysicians begin with observations, albeit quite mundane ones: there are objects, these objects have properties, they last over time, and so on. And just like scientists, metaphysicians go on to construct general theories based on these observations, even though the observations do not logically settle which theory is correct. In doing so, metaphysicians use standards for choosing theories that are like the standards used by scientists (simplicity, comprehensiveness, elegance, and so on).

Emphasizing continuity with science helps to dispel radical pessimism about metaphysics; the humility comes in when we remember the discontinuities. Observation bears on metaphysics in a very indirect way, and it is far less clear how to employ standards of theory choice (like simplicity) in metaphysics than it is in science. But metaphysicians can, and should, acknowledge this. Metaphysics is speculative, and rarely if ever results in certainty. Who would have thought otherwise?

Exactly what one should say about empiricism and metaphysics is a deep philosophical question in its own right, and it’s unlikely that anyone will decisively answer it anytime soon. But that shouldn’t, on its own, deter you from thinking about metaphysics. Philosophy is the one discipline in which questions about the value of that discipline are central questions within that very discipline. The philosopher must therefore live with uncertainty about whether her life’s work is ultimately meaningful - that is the cost of the breadth of reflection demanded by philosophy. Philosophy’s reflective nature is generally a good thing, but the down side is that it can lead to paralysis. Don’t let it. You don’t need to have answers to all meta-questions before you can ask first-order questions (just as you don’t need to sort out the philosophy of biology before doing good work in biology). The meta-questions are certainly important. But the history of philosophy is full of sweeping theories saying that this or that bit of philosophy is impossible. Take heart in the knowledge that these have all failed miserably.


1 As opposed to, for example, what the world ought to be like (ethics), what we know about the world (epistemology), how we think of and talk about the world (philosophy of mind and language), and so on.

2 Some facts consist of multiple particulars having a “multi-place” property, also known as a relation. Philadelphia is 100 miles from New York: the particulars Philadelphia and New York have the 100 miles from relation.



1.1 “Abstract Entities,” Chris Swoyer
1.2 “There Are No Abstract Objects,” Cian Dorr

“Concrete” entities are the entities with which we are most familiar: tables, chairs, planets, protons, people, animals, and so on. “Abstract” entities are less familiar: numbers (for example, the number seven), properties (for example, the property of being round), and propositions (for example, the proposition that snow is white). Do abstract entities really exist? No one has ever seen, touched, or heard an abstract entity; but Chris Swoyer argues that they exist nevertheless. Cian Dorr argues that they do not.


Abstract Entities

Chris Swoyer

One of the most puzzling topics for newcomers to metaphysics is the debate about abstract entities, things like numbers (seven), sets (the set of even numbers), properties (triangularity), and so on. The major questions about abstract entities are whether there are any, if so which ones there are, and if any do exist, what they are like.

My aim here is to provide a brief and accessible overview of the debates about abstract entities. I will try to explain what abstract entities are and to say why they are important, not only in contemporary metaphysics but also in other areas of philosophy. Like many significant philosophical debates, those involving abstract entities are especially interesting, and difficult, because there are strong motivations for the views on each side.

In the first section, I discuss what abstract entities are and how they differ from concrete entities and in the second section, I consider the most compelling kinds of arguments for believing that abstract entities exist. In the third section, I consider two examples, focusing on numbers (which will be more familiar to newcomers than other types of abstract objects) and properties (to illustrate a less familiar sort of abstract entity). In the final section, I examine the costs and benefits of philosophical accounts that employ abstract entities. 1

1 What are Abstract Entities?

Prominent examples of abstract entities (also known as abstract objects) include numbers, sets, properties and relations, propositions, facts and states-of-affairs, possible worlds, and merely-possible individuals (we’ll see what some of these are in a bit). Such entities are typically contrasted with concrete entities – things like trees, dogs, tables, the Earth, and Hoboken. I won’t discuss all of these examples, but will consider a few of the more accessible ones as case studies to help orient the reader.

Numbers and sets

Thought and talk about numbers are extremely familiar. We learn about the natural numbers (like three, four, and four billion), about fractions (rational numbers, like ⅔ and ⅞), and about irrational numbers (like the square root of 2 and e). And we learned a bit about sets in school – for example, the empty set, the set containing just 3 and 4, and the set of even numbers; we even learned to write names of sets using notation like ‘{3,4}’.

But what are numbers and sets? We cannot see them or point to them; they do not seem to have any location, nor do they interact with us or any of our instruments for detection or measurement in any discernible way. This may lead us to wonder whether there really are any such things as numbers, and whether, when we say things like “there is exactly one prime number between four and six,” we are literally and truly asserting that such a number exists (after all, what could it be?). But, as we will see in section 3.1, there are also strong philosophical arguments that numbers do exist. Hence a philosophical problem: do they or don’t they?

Properties and relations

The world is full of resemblances, recurrences, repetitions, similarities. Tom and Ann are the same height. Tom is the same height now as John was a year ago. All electrons have a charge of 1.6022 × 10-19 coulomb. The examples are endless. There are also recurrences in relations and patterns and structures. Bob and Carol are married, and so are Ted and Alice; the identity relation is symmetrical, and so is that of similarity. Resemblance and similarity are also central features of our experience and thought; indeed not just classifications, but all the higher cognitive processes involve general concepts. Philosophers call these attributes of qualities or features of things (like their color and shape and electrical charge) properties. Properties are the ways things can be; similarly, relations are the ways things can be related.

Assuming for the moment that there are properties and relations, it appears that many things have them. Physical objects: The table weighs six pounds, is brown, is a poor conductor of electricity, and is heavier than the chair. Events: World War I was bloody and was fought mainly in Europe. People: Wilbur is six feet tall, an accountant, irascible, and married to Jane. Numbers: three is odd, prime, and greater than two. All of these ways things can be and ways they can be related are repeat-able; two tables can have the same weight, two wars can both be bloody. The two adjacent diamonds in figure 1 are the same size, orientation, and uniform shade of gray.

Champions of properties hold that things like grayness (or being gray) and triangularity (or being triangular) are properties, and that things like being adjacent and being a quarter of an inch apart are relations. Since the goal here is just to give one prominent example of a (putative) sort of abstract object, I will think of properties as universals (as many, but not all, philosophers do). On this construal, there is a single, universal entity, the property of being gray, that is possessed or exemplified by each of the two diamonds in our figure. It is wholly present in both a and b, and will remain so as long as each remains gray.

Figure 1 Resemblances and Ways Things Can Be


Philosophers who concur that properties exist may disagree about which properties there are and what they are like, but at least many properties (according to numerous philosophers, all) are abstract entities. Perhaps a property like redness is located in those things that are red, but where is justice, or the property of being a prime number, or the relation of life a century before? Such properties and relations exist outside space and time and the causal order, so they are rather mysterious. But, as we will see, there are also good reasons for thinking that properties and relations can do serious philosophical work, helping explain otherwise puzzling philosophical phenomena. This is a reason to think that they do exist. Another problem.


Two people can use different words to say the same thing; indeed, they can even use different languages. When Tom says “Snow is white” and Hans says “Schnee ist weiss,” there is an obvious sense in which they say the same thing. So whatever this thing is, it seems to be independent of any particular language. Philosophers call these entities propositions. They are abstract objects that exist independently of language and even thought (though of course many of them are expressed in language). Propositions have been said to be the basic things that are true or false, the basic truth-bearers, with the sentences or statements that express them being derivatively true or false.

In addition to saying that snow is white, Tom also believes that snow is white; and Hans, who speaks no English, also believes that snow is white (although he expresses the belief by saying “Schnee ist weiss”). Again, there is an obvious sense in which they believe the same thing. Some philosophers urge that the best way to explain this is to conclude that there is some one thing that Tom and Hans both believe. On this view, propositions are said to be the contents or meanings of beliefs, desires, hopes, and the like. They are also said to be the objects of beliefs. Thus the object of Tom’s belief that red is a bright color is the proposition that red is a bright color.

On this view propositions are abstract objects that express the meanings of sentences, serve as the bearers of truth values (truth and falsehood), and are the objects of belief. But like numbers, propositions are somewhat mysterious. We can’t see them, hear them, point to them. They don’t seem to do anything at all. This gives us reason to doubt their existence. But, there are also reasons to think that they exist. Problems, problems, problems.

1.1 What abstract entities are (nearly enough)

Debates about abstract objects play a central role in contemporary metaphysics. There is wide agreement about the paradigm examples of abstract entities, though there is also disagreement about the exact way to characterize what counts as abstractness. Perhaps this shouldn’t come as a surprise; if any two things are so dissimilar that their difference is brute and primitive and hard to pin down, abstract entities and concrete entities (abstracta and concreta) are certainly plausible candidates.

Even so, the philosophically important features of the paradigm examples of abstracta (like those listed above) are pretty clear. They are atemporal, non-spatial, and acausal – i.e., they do not exist in time or space (or space-time), they cannot make anything happen, nothing can affect them, and they are incapable of change. Neither they, their properties, nor events involving them can make anything happen here in the natural world. We don’t see them, feel them, taste them, or see their traces in the world around us. Still, according to a familiar metaphor of some philosophers, they exist “out there,” independent of human language and thought.

Being atemporal, non-spatial, and acausal are not all necessary for being abstract in the sense many philosophers have in mind. Thus, many things that seem to be abstract also seem to have a beginning (and ending) in time, among them natural languages like Urdu and dance styles like the Charleston. It may seem tempting to say that such things exist in time but not in space, but where exactly? Moreover, this claim can’t be literally true in a relativistic world (like ours certainly seems to be), where space and time are (framework-dependent) aspects of a single, more basic thing, namely space-time.

And not all are sufficient. For example, an elementary particle (e.g., an electron) that is not in an eigenstate for a definite spatial location is typically thought to lack any definite position in space. The technicalities don’t matter here; the point is just that although such particles may seem odd, they do have causal powers, and so virtually no one would classify them as abstract. Again, according to many religious traditions, God exists outside of space and time, but he brought everything else into existence, and so many would be reluctant to classify him as an abstract object.

All this suggests that the division into concrete and abstract may be too restrictive, or that abstractness may come in degrees. I won’t consider such possibilities here, however, because the puzzles about abstract entities that most worry philosophers concern those entities that are, if they exist, atemporal, non-spatial, and acausal. And we don’t need a sharp bright line between abstracta and concreta to examine these.

A philosopher who believes in the existence of a given sort of abstract entity is called a realist about that sort of entity, and a philosopher who disbelieves is called an anti-realist about it. Abstract entities are not a package deal; it is quite consistent, and not uncommon, for a philosopher to be a realist about some kinds of abstract entities (e.g., properties) and an anti-realist about others (e.g., numbers).

Not-quite existence

Finally, some champions of abstract entities claim that there are such things, but grant them a lower grade of being than the normal, straightforward sort of existence enjoyed by George Bush and the Eiffel Tower. They often devise esoteric labels for this state; for example, numbers, properties, and the like have been said to have being, to subsist, to exist but not be actual, or partake of one or another of the bewildering varieties of not-quite-full existence contrived by philosophers. Such claims are rarely very clear, but frequently they at least mean that a given sort of entity is real in some sense, but doesn’t exist in the spatiotemporal causal order. Which is pretty much just to say it is abstract.

We will not pursue such matters here, however, since many of the same problems arise whether the issue about the status of abstracta is framed in terms of the existence or merely the subsistence or being of such things. Whatever mode of being the number two possesses, we still cannot perceive it, or pick it out in any way, and it seems to make no difference to anything here in the natural world. Because many of the most debated issues arise for all the proposed modes of being of abstract objects, I will focus on existence.

Why questions about abstracta matter

Explicit discussion of abstract entities is a relatively recent philosophical phenomenon. Plato’s Forms (his version of universal properties) have many of the features of abstract objects. They exist outside of space and time, but they seem to have some causal efficacy. We can learn about them, perhaps even do something like perceive them, though perhaps only in an earlier life (this is Plato’s doctrine of recollection).

Soon after Plato, properties and other candidate abstracta – e.g., merely possible individuals (individual things, e.g., persons, that could have existed but don’t) – were reconstrued as ideas in the mind of God. This occurred through the influence of Augustine and others, partly under the influence of Plotinus and partly under that of Christianity. Human beings were thought to have access to these ideas because of divine illumination, wherein God somehow transferred his ideas into our minds. In later accounts like Descartes’ we had access to such ideas because God placed them in our minds at birth (they are innate). Such views persisted though medieval philosophy and well into the modern period. In this period, philosophers like Locke began to view what we thought of above as properties (e.g., redness, justice) as ideas or concepts in individual human minds.

It was really only in the nineteenth century, with work on logic and linguistic meaning by figures like Bernard Bolzano and Gottlob Frege, that abstract entities began to come into their own. They emerged with a vengeance around the turn of the twentieth century, with work in logic, the theory of meaning, and the philosophy of mathematics, and, more generally, because of a strongly realist reorientation of much of philosophy at this time in the English- and German-speaking worlds. After a few decades, interest in abstract entities subsided, but by the end of the twentieth century, there was perhaps more discussion of a wider array of abstract objects than ever before.