Contemporary Debates in Metaphysics

Theodore Sider, John Hawthorne, Dean W. Zimmerman, Theodore Sider, John Hawthorne, Dean W. Zimmerman

• Publisher: Wiley-Blackwell
• Year: 2013
• ISBN:
  9781118712320
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophical Metaphysics

In a series of thought-provoking and original essays, eighteen leading philosophers engage in head-to-head debates of nine of the most cutting edge topics in contemporary metaphysics.

• Explores the fundamental questions in contemporary metaphysics in a series of eighteen original essays - 16 of which are newly commissioned for this volume
• Features an introductory essay by the editors on the nature of metaphysics to prepare the reader for ongoing discussions
• Offers readers the unique opportunity to observe leading philosophers engage in head-to-head debate on cutting-edge metaphysical topics
• Provides valuable insights into the flourishing field of contemporary metaphysics

CHAPTER ONE

ABSTRACT ENTITIES

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.

CHAPTER 1.1

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.

Propositions

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.

Although explicit discussion of abstract entities has a fairly recent history, they are central to debates over venerable philosophical issues, including the nature of mathematical truth, the meanings of words and sentences, the features of causation, and the nature of cognitive states like belief and desire. These debates also lie at the center of many perennial disputes over realism and anti-realism, particularly standard flavors of nominalism. Discussions about the existence of abstract objects may also illuminate the nature of human beings and our place in the world. If there are no abstract objects, nothing that transcends the spatiotemporal causal order, then there may well be no transcendent values or standards (e.g., no eternal moral properties) to ground our practices and evaluations. And if there is also no God, it looks like truth and value must instead be somehow rooted here in the natural order. We are more on our own.

2 Why Believe there are Abstract Objects?

The central questions about abstract objects are: Are there any? If at least some kinds of abstract objects exist, can we discover what they are like? How can we decide such issues? (This question is a problem because it seems to be difficult to make contact with abstract objects in order to learn about their nature.) In this section I will offer an answer to the first question that also suggests an answer to the second.

A good way to get a handle on the issues involving abstract entities is to begin by focusing on the point of introducing them in the first place. Philosophers who champion one or another type of abstract object almost always do so because they think those objects are needed to solve certain philosophical problems, and their views about the nature of these abstracta are strongly influenced by the problems they think they are needed to solve and the ways in which they (are hoped to) solve them. Hence, our discussion here will be organized around the tasks abstracta have been introduced to perform. These tasks are typically explanatory, to explain various features of philosophically interesting phenomena, so to understand such accounts we need to ask about the legitimacy, role, and nature of explanation in metaphysics.

2.1 Philosophical explanations and existence

Ontology is the branch of metaphysics that deals with the most general issues about existence. Of course we know a great deal about what sorts of things exist just from daily life: things like trees, cats, cars, other people, the moon. And science tells us more about what sorts of things there are: electrons, molecules of table salt, genes. But ontology attempts to get at the most general categories or sorts of things there are, e.g., physical objects, persons, numbers, pr...