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Beschreibung

The world is populated with many different objects, to which we often attribute properties: we say, for example, that grass is green, that the earth is spherical, that humans are animals, and that murder is wrong. We also take it that these properties are things in their own right: there is something in which being green, or spherical, or an animal, or wrong, consists, and that certain scientific or normative projects are engaged in uncovering the essences of such properties. In light of this, an important question arises: what kind of things should we take properties themselves to be?

In Properties, Douglas Edwards gives an engaging, accessible, and up-to-date introduction to the many theories of properties available. Edwards charts the central positions in the debate over properties, including the views that properties are universals, that properties are constructed from tropes, and that properties are classes of objects, and assesses the benefits and disadvantages of each. Attempts to deny the existence of properties are also considered, along with ‘pluralist’ proposals, which aim to accommodate the different kinds of properties that are found in various philosophical debates.

Properties is the ideal introduction to this topic and will be an invaluable resource for scholars and students wishing to learn more about the important roles that properties have played, and continue to play, in contemporary philosophy.

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Veröffentlichungsjahr: 2014

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Table of Contents

Series page

Title page

Copyright page

Dedication

Preface

1: Introducing Properties

1.1 Why Think that There Are Properties?

1.2 What Is a Theory of Properties?

1.3 A Methodological Strategy

1.4 The Jobs Properties Do

1.5 Definitions and Terminological Notes

1.6 Further Reading

2: Universals

2.1 Introduction

2.2 Transcendental Universals

2.3 Immanent Universals

2.4 Further Reading

3: Tropes

3.1 Introduction

3.2 The Basic Idea

3.3 Tropes and Causation

3.4 Properties as Sets of Tropes

3.5 The Relation between Objects and Tropes

3.6 Accounting for Resemblance between Tropes

3.7 Tropes and Universals

3.8 Further Reading

4: Properties Eliminated?

4.1 Introduction

4.2 Russell and Quine on Ontological Commitment

4.3 Ostrich Nominalism

4.4 Primitive Predication

4.5 Paraphrase

4.6 Objects and Properties

4.7 A Revised One Over Many Problem

4.8 Implications for Ostrich Nominalism

4.9 Implications for Universals and Tropes

4.10 Further Reading

5: Varieties of Nominalism

5.1 Introduction

5.2 Predicate and Concept Nominalism

5.3 Class Nominalism

5.4 Mereological Nominalism

5.5 Resemblance Nominalism

5.6 Chapter Summary

5.7 Further Reading

6: Pluralist Views of Properties

6.1 Introduction

6.2 The Distinction between Abundant and Natural Properties

6.3 Grounding the Distinction: Universals, Tropes and Primitive Naturalness

6.4 Degrees of Naturalness: Supervenience, Definability and Grounding

6.5 Universals, Tropes and Degrees of Naturalness

6.6 Graded versus Egalitarian Conceptions of Naturalness

6.7 Chapter Summary

6.8 Further Reading

7: Kinds of Properties

7.1 Introduction

7.2 Methodology: Descriptive and Prescriptive Metaphysics

7.3 Mathematical Properties

7.4 Mental Properties

7.5 Moral Properties

7.6 Chapter Summary

7.7 Further Reading

Conclusion

References

Index

Key Concepts in Philosophy Series

Joseph Campbell, Free Will
Roy T. Cook, Paradoxes
Ian Evans and Nicholas D. Smith, Knowledge

Copyright © Douglas Edwards 2014

The right of Douglas Edwards to be identified as Author of this Work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988.

First published in 2014 by Polity Press

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To Mum and Dad

Preface

The world is populated with many different objects: tables, chairs, roses, fire engines, blades of grass and human beings, to name just a few, each occupying its own special region of space–time. When we distinguish between them, though, we often don't just make use of the idea that they exist in different locations; we also talk about the different features, attributes, or properties that they have. For instance, you and I have the property of being human, whereas tables and chairs do not. Roses and fire engines have the property of being red (or at least some do), whereas blades of grass do not. Conversely, the properties that objects have also help us to make sense of the ways in which distinct objects are similar: roses and fire engines are similar in an important way, as you and I are, because of the properties they – and we – share. However, positing the existence of properties immediately raises some interesting metaphysical questions. For example, how do we make sense of the idea that the redness of a fire engine is the same as the redness of a rose, when the fire engine and the rose exist in different places? Does this mean that one thing – the property redness – exists in different places at once, and, if so, how?

Understanding properties has been one of the main tasks of metaphysicians since the ancients, and a number of innovative proposals have been put forward. The aim of this book is to provide an accessible introduction to the main theories of properties: the view that properties are universals; the view that properties are constructed from tropes; and the view that properties are classes or sets of objects. We will chart these central positions in the debate and more, and we will note their strengths and weaknesses. We will address the main challenge to views that take properties seriously – that posed by Quine – which argues, contrary to what we said above, that we do not need properties to do any interesting explanatory work. We will address the question of what a theory of properties is intended to do, and we will take seriously the question of whether any single theory of properties is able to account for all the features that properties have been taken to have. We will also explore the connections between debates about properties and debates elsewhere in philosophy.

The first chapter introduces the topic under discussion and explores the main reasons for positing the existence of properties, including the ‘one over many’ argument. It then raises the question of what the constraints on a theory of properties are by considering the various jobs properties have been taken to do, before making some terminological distinctions. The second chapter discusses perhaps the most well-known view of properties, namely the view that properties are universals, and assesses both the transcendental view, attributed to Plato and developed by Bertrand Russell, and the immanent view, attributed to Aristotle and developed recently by David Armstrong. The third chapter introduces and assesses the view that properties are to be accounted for in terms of tropes. The fourth chapter assesses Quine's scepticism about properties and addresses his challenge to the theories under discussion in this book, which states that there are no properties at all. The fifth chapter explores various forms of nominalism about properties, particularly predicate nominalism, concept nominalism, class nominalism, mereological nominalism and resemblance nominalism. These views are all varieties of ‘nominalism’, as they deny – or at least claim to deny – the existence of universals or tropes. The sixth chapter explores pluralist approaches to properties, in particular David Lewis's influential distinction between ‘abundant’ and ‘natural’ properties. Finally, the seventh chapter examines some of the roles properties have in other debates in philosophy and discusses how the different accounts of properties explored in previous chapters might be affected.

As will become clear as we go through the book, we will rarely come across knock-down arguments against a view. Instead, the pattern that will become familiar is that each view has its own benefits and its own costs. Accordingly, the evaluation of competing views often takes the form of a cost/benefit analysis, and the choice of the view to adopt may not be particularly clear-cut. This is especially so in the case of the views under discussion in Chapters 2, 3 and 5, where we will see that different views privilege different reasons for positing the existence of properties. The views offered in Chapter 6 are designed to rectify this matter somewhat by attempting to show that incorporating different aspects of the previously discussed views into a new conception of properties can yield some progress. Whether they ultimately succeed, however, is a matter for debate.

I have approached this book as one does a series of phil­osophy lectures, in that the aim is to give a good understanding of the topic and to leave the audience primed and ready to investigate the subject, and the texts discussed, in greater depth. To this end I have included further reading lists at the end of each chapter, in addition to references throughout the main text. Many of the key texts in twentieth-century work on properties that are discussed are collected in D. H. Mellor and Alex Oliver's edited volume Properties (Oxford University Press, 1997). To make it easier for those who are using that book to find references in the text, for all the quotations from works reprinted in it I have included – apart from the page number of the original text – a reference to the corresponding page number in Mellor and Oliver. In some cases where the location of the original articles is hard to come by, I only have used the references to page numbers in the reprinted versions in the Mellor and Oliver volume, but included the full references in the bibliography.

I would like to thank Emma Hutchinson and Pascal Porcheron at Polity for their help and guidance during the whole process of writing this book. I am extremely grateful to Stephan Torre and two anonymous reviewers for Polity for providing very detailed comments on the manuscript, along with Manuela-Maria Tecusan for copy-editing the text. I am also grateful to three anonymous reviewers for Polity for feedback on the initial proposal. I would like to thank Maria Baghramian, Michael Lynch and Crispin Wright for their advice and encouragement, and members of the Aporo Metaphysics group in Dublin and the NIP Pluralism seminar in Aberdeen for a number of useful conversations. Earlier versions of some of the material here were presented, with great benefit to the book, at the University of Manchester, University College Dublin, the University of Aberdeen and the University of Sassari. I would also like to acknowledge funding from the Irish Research Council for the Humanities and Social Sciences and a Marie Curie Intra European Fellowship within the 7th European Community Framework programme. Finally, I would like to thank Alexandra Plakias, who read and commented on many versions of the manuscript and was an invaluable interlocutor during many helpful discussions, and my parents, who provided moral support throughout, as always.

1

Introducing Properties

1.1 Why Think that There Are Properties?

In this book we will be primarily concerned with theories which try to give an account of the nature of properties. Before we get that far though, we need first of all to consider why we might have to give such an account of properties at all. In other words, we need to pose the question of why we should think that there are properties. There are perhaps three main reasons for thinking that properties exist: (1) the one over many argument; (2) the reference argument; and (3) the quantification argument. The one over many argument is what we might call a metaphysical argument: it argues for the existence of properties on the basis of considerations of what the world must be like. As we will see, this is different from what the reference argument aims to do, which is to provide an argument for the existence of properties stemming from the structure of language – in other words to provide a semantic argument for the existence of properties. It is a more complex matter to characterise the quantification argument, as, depending on how one sees the ideas expressed, that one is something of a mixture between the first two – the metaphysical and the semantic argument.

We will revisit these three reasons as we go through the book, particularly as not all those who write on the subject think that they have equal weight (if any weight at all); but let us have a look at them here first.

1.1.1 The One over Many Argument

The one over many argument holds that we need to posit the existence of properties in order to respond adequately to the one over many problem. In our everyday experience we become acquainted with many particular objects, each occupying its own region of space–time. For instance, you – a particular object – currently hold a particular book, are probably sitting in a particular chair, and there are particular photons of light making it possible for you to read. In view of this, it is tempting to say that only particular things exist. However, it does not take much to show that this idea runs into some problems. We can take it that many particular things exist, but it also seems that many different particular things share the same nature. For instance, you and I are distinct objects, but we both seem to share something significant: we are both human beings. Indeed you might think that this is something that is essential to both of us: we would not be the objects we are unless we were human. This suggests that we are, both, the same type of thing. Putting the point more technically, you might say that we are, both, tokens of the same type: we are, both, particular tokens of the type human being.

We can also notice that this is the case even when objects are of a certain kind despite not being part of that kind essentially. For instance fire engines, roses and London buses are all distinct objects, but they seem to share something in common, namely that they are all red. Notice, though, that they are not red essentially: fire engines, roses and London buses may have turned out not to be red, but the fact remains that they are all red, and thus they seem to be tokens of the type of red things.

We have said that individual objects such as you and I exist, so there should not be any harm in saying that the tokens in question exist. But should we also say that the type exists? If we say that it does, then we can make sense of the idea that we are both tokens of something, but at the cost that we no longer just admit the existence of particular objects: we must also admit the existence of types, which, it seems, do not exist in one particular region of space–time. If we deny the existence of types, however, then we maintain that only particular objects exist, but seemingly at the cost of being unable to say how it is that you and I are the same.

Returning to our talk of objects and properties, we can say that being of the same type entails the sharing of a property: objects that are tokens of a type have a property in common. Thus all the objects that are tokens of the type human share the property of being human; all the objects that are tokens of the type red share the property of being red. We can then translate the problem into talk of properties: do particular objects have properties? If so, then we can make sense of objects having characteristics in common, but at the cost of admitting non-object things into our ontology. If not, then we maintain the particularity of existence, but seemingly at the cost of being unable to hold that distinct objects have features in common.

The one over many problem1 thus takes it that different objects are of the same type (whether essentially or not), and holds that this is a problem if we stick to a perhaps intuitive ontological view which just posits the existence of particular objects. The one over many argument for properties takes positing the existence of properties as a solution to this problem. The one over many argument thus holds that, in order to make proper sense of the things that exist, we must accept that properties as well as objects exist. In other words, it takes into account that we need to accommodate the idea that different individual objects are, and can be, of the same type (whether essentially or not), and that the best way to explain this is to posit the existence of properties as well as the existence of objects. Evidently the work does not stop here, as positing the existence of entities that seem to exist in a number of different places at the same time seems to throw up more questions than it answers; but these are issues we will discuss in the coming chapters.

We can also note that the one over many argument is a metaphysical argument, as it is drawn from a puzzle about what exists. This is the main problem we will focus on; but it is perhaps worth noting that there is a distinct semantic version of the argument that occasionally surfaces in the literature. The semantic version of the argument begins by asking a slightly different question: why is it that we apply the same predicate to many different objects? For instance, take the predicate ‘is red’. This is one predicate, but it applies to a multitude of different things: fire engines, roses, Rudolph's nose, and so on. We might take this – the fact that we apply the same predicate to many different objects – to be in need of explanation.

Notice, though, that this is not the same problem as the one we have just discussed. That problem was a problem about what exists, and a solution to it will have to offer some account of what does and what does not exist. But this other problem is a problem about why we use items of language in a particular way, and a solution to it need not say anything about what exists. We might, of course, answer the question in such a way as to make claims about what exists – as we would if we were to say that the reason why we apply the predicate in each case is that each of the objects instantiates the same property; but we need not do so. We might, for example, offer a psychological explanation of why we use the same word for different objects, and this need not make any significant claims about what exists. For these reasons we will work with the metaphysical version of the one over many argument.

1.1.2 The Reference Argument

The reference argument, as noted above, is what we might call a semantic argument for the existence of properties, in that it uses considerations of language to argue that properties exist. The central idea is that we must posit the existence of properties to make sense of the meanings of certain kinds of linguistic entity; and there are two strands to this argument, stemming from two different kinds of linguistic entity. The first, and perhaps most prominent, idea is that we need properties to understand the meanings of predicates. The second is that we need properties to understand the meanings of a certain class of singular terms.

Singular terms (as the name suggests) are terms that have a unique referent. Classic examples are proper names (such as ‘Jane Austen’) and definite descriptions (such as ‘the writer of Pride and Prejudice’). Each of these terms picks out a single and unique entity. We will call the referents of singular terms ‘objects’ to signify that they are distinct entities. Standard declarative sentences that philosophers tend to take interest in are formed of a singular term and a predicate, which we can express generally as ‘a is F’. Here ‘a’ is the subject term of the sentence, typically a singular term, and ‘is F’ is the predicate term of the sentence. Some examples of sentences of this pattern are ‘snow is white’, ‘the substance is alkaline’, ‘Jane Austen is human’. In cases of this sort, the subject term of the sentence picks out an object and the predicate term provides some description of that object. The sentence is true just in case the object picked out fits the description given by the predicate term. As we shall see, the referents of predicate terms are more contentious than the referents of subject terms, but, for now, we shall say that subject terms refer to objects and predicate terms refer to properties. That is, in the sentence ‘Jane Austen is human’, the subject term refers to Jane Austen and the predicate term refers to the property of being human. The sentence as a whole says that the object Jane Austen has the property of being human.

We have looked, then, at two basic components of language: predicates and singular terms. The reference argument takes as a basic premise that each linguistic entity of these two sorts refers to something. In most cases, for singular terms, this will be some existing object – which serves as the referent of that term. For predicates, it seems as though we cannot simply use objects; for, as we have seen, objects are singular entities, whereas predicates ascribe the same thing to many different objects. Properties, however, would seem to be good candidates to serve as referents of predicates: the predicate ‘is red’ is something that is predicated of many things, and we can equally well say that the property of being red is possessed by many different things. As a consequence, we get the natural semantic picture mentioned above, in which singular terms refer to objects, predicates refer to properties, and those properties are ascribed to objects.

One strand of the reference argument, then, is that we need to posit the existence of properties to serve as the referents for predicate terms in our language. However, we can note that we also find a certain kind of singular terms, which seem to refer to properties instead of objects. Consider the following series of sentences, given by David Lewis:

(1) Red resembles orange more than it resembles blue.
(2) Red is a colour.
(3) Humility is a virtue.
(4) Redness is a sign of ripeness. (Lewis 1983: 348/1997: 194)

Here we see terms like ‘red’ and ‘humility’ appearing in the singular term position of a sentence – and in a seemingly innocuous fashion, as all of these sentences seem to be unproblematically true. But, if we are taking objects to be entities that have a single spatiotemporal location, then it seems difficult to say that the singular terms in (1)–(4) refer to objects, as redness and humility seem to be things that are found in a number of different places at once. However, on the semantic picture we are operating with, they must refer to something, otherwise the sentences would not come out as true. As a result, we might wish to say that, for a certain class of singular terms – sometimes referred to as abstract singular terms – the proper referent is not an object, but a property. Thus the singular terms in (1)–(4) can be taken to refer to properties. This also shows – as should be clear – that properties can also have features predicated of them, and thus they can themselves have properties. This is, then, the second strand of the reference argument, which holds that we need to posit the existence of properties to serve as the referents of abstract singular terms.

1.1.3 The Quantification Argument

The reference argument argues for the existence of properties from a particular theory of meaning, which assigns entities to serve as the meanings of linguistic items. The quantification argument proceeds along similar lines, but without the need for a particular theory of meaning. Thus it can serve either as a complement to the reference argument or as a separate argument altogether.

The argument proceeds from some considerations of ontological commitment, which ask when we are committed to the existence of a particular entity, or kind of entities. A popular answer, and one we will explore in more detail in Chapter 4, is that one is committed to the existence of the entities that one quantifies over when making true statements. This is different from the reference argument, as there need not be any explicit reference to the entities in the given sentences. For example, consider the following sentences, also from David Lewis:

(5) He has the same virtues as his father.
(6) The dresses were of the same colour.
(7) There are undiscovered fundamental physical pro­perties.
(8) Acquired characteristics are never inherited.
(9) Some zoological species are cross-fertile. (Lewis 1983: 350/1997: 196)

These sentences, if true, all have existential commitments. For example (5) entails that there exist some virtues that are shared between the individual and his father, and (6) entails that there exists some colour that both the dresses have. So the thought is, if (5)–(9) are to be considered true, then there must exist entities of the type mentioned. However, as we saw with the reference argument, it is, at least on the face of it, hard to see how objects could serve as the things that must exist here. Virtues, for example, don't seem to be the kind of things that would be considered objects; rather they seem like features that various objects can exhibit. The same goes, as we have seen, for colours, and also – plausibly – for acquired characteristics and zoological species. So, again, it looks as though properties would be better suited to be things that are required to exist if these sentences are to come out true. If this is so, then we have another argument for the existence of properties.

1.2 What Is a Theory of Properties?

We have looked, then, at some of the arguments which suggest that we need to take the existence of properties seriously. In the rest of the book we will explore the various theories that have been proposed to account for them (or indeed to explain them away). Before we do so, though, it is worth pausing to consider what a theory of properties is and what it might hope to achieve.

The theories of properties that we will be looking at are all trying to give some account of the nature of properties; they try to tell us what properties are. Sometimes this will be done in the form of attempting to show how properties are reducible to other kinds of entities (such as classes), other times it will be done differently. Broadly speaking, though, this project – of trying to explain the nature of properties – is the focus of the present book. This is not to say that the task of accounting for what properties do will be ignored: on the contrary, it is an important part of the project of accounting for what properties are that we consider what properties do.

1.3 A Methodological Strategy

If we want to give a theory of something, we need first to have some idea of what the thing is that we are trying to give a theory of – just as, if we want to find something, we need to have some idea of what it is we're looking for. For example, if a sheriff wants to find Mahoney, a dangerous criminal, she constructs a ‘Wanted’ poster that depicts the key features of Mahoney, which mark him out as Mahoney – such as, say, a scar across his cheek or a tattoo reading ‘Mum’ on his left biceps. These features serve as a guide to finding Mahoney: if we come across an individual that exhibits these features, we can be pretty sure that we've found him.

A popular approach to philosophical analysis suggests that we do the same with subjects philosophers are interested in. One test case for this can be found in the study of pain. Suppose that we want to know what pain is. We might start by listing all of the things that are distinctive of pain (pain is caused by tissue damage, pain causes people to say ‘ouch!’, pain is generally unpleasant, and so forth). Once we have a complete list of features such as these, we have a ‘Wanted’ poster for pain: we know what it is we are looking for. What we then need to do is look, for example, at the physical states of human beings and find which state is activated when a person exhibits the characteristic features of pain; and then we will have found pain. This kind of approach constitutes what is called a ‘functionalist’ approach to philosophical analysis (and it will be explored further in Chapter 7). The basic idea is that the features we are gathering – in this case, the features of pain – are distinctive of the particular role, or function, of the entity we are interested in – in this case the role that pain has in a human organism. In other words, to understand what pain is, we must first look at the job pain does.

We can now consider applying this method to properties. If we can construct a list of the features taken to be characteristic to properties, then this will be a big help when it comes to assessing the various theories of properties that have been proposed. In particular, we will be looking for the roles philosophers have taken to be distinctive of properties. By doing this we will glean insights into the function of properties, which will help us in the project of discerning what properties are: to find the essence of properties, we need to look for those entities that discharge the jobs of properties.

Of course, as we will see, things might not be so simple in this case though, as a cursory look at the study of properties suggests that properties have a number of different – and perhaps incompatible – features. This might tell us that some of these features are not really features of properties at all, or perhaps it may tell us that we need different kinds of properties to do all the different jobs that properties are taken to do.

1.4 The Jobs Properties Do

We can take four initial alleged features of properties from the arguments for properties that we have looked at so far. These are:

Properties are things that different objects can have in common We noted that it looks as though we need properties to explain what it is that different objects have in common. For instance, the property of being red is something that fire engines and roses have in common. This is one job that properties have been taken to do, then: be the kinds of things that different objects have in common.
Properties mark genuine similarities In addition to properties being the kinds of things that objects have in common, we also noted that they are able to show how different objects can be similar in a very genuine way. For example, we noted that you and I both have the property of being human. This is a property that we (and many others) share, and it marks something significant about how we are similar. This is another job that properties can do: they can mark genuine similarities as well as similarities.2
Properties serve as the semantic values of predicates We also saw that properties can do the job of being the semantic values of predicates. For example, ‘the rose is red’ is a standard subject–predicate sentence of the form ‘a is F’, where ‘the rose’ (the subject term) refers to an object: the rose. What about the predicate ‘is red’? What does this refer to? Not to a single object, as many objects are red; instead it refers to the property of being red.3
Properties serve as semantic values of abstract singular terms We noted that most singular terms refer to a single object, but that there are some which do not seem to fit this model, such as ‘redness’ and ‘humility’. Another job that properties can do is to serve as referents of these abstract singular terms; so the property of redness can serve as the referent of ‘redness’, for example.

These are all jobs that we can take properties to do, and they stem from the core arguments for the existence of properties: they are jobs that, it is claimed, it would be very difficult for any other kind of entity to fulfil. There are also other jobs that some philosophers have proposed for properties, which do not originate directly from the core arguments. We will look at some of these jobs as we progress through the book, so it is worth discussing them briefly here.

Properties ground duplication This is a job that, we might think, follows from the jobs mentioned earlier, which take properties to ground similarities between objects. If two objects that are similar have some properties in common, we might think that two objects that share exactly the same properties are perfect duplicates.
Properties ground the causal powers of objects Many phil­osophers think that a key job that properties can do is ground the causal powers of objects. In other words, the properties that an object has determine the causal powers that that object has. We might think that it is because of certain properties an object has that it has the causal powers it does: it is because the table has the property of being solid that I cannot put my fist through it.

As you can see, there are many different features that properties have been taken to have. In particular, we can note that there seems to be both metaphysical jobs that properties do (ground similarities, causal powers, and duplication), and semantic jobs that properties do (serve as referents for predicates and abstract singular terms). As we will see as we go along, it may be difficult to give a theory of properties that is able to do justice to all of these features. Whether this means that some of the features have to go or whether the theories are no good is a matter that we will discuss as we progress.

The general overarching theme of the book, though, will be that it might be a mistake to think that there is just one kind of entity that can do all of these jobs. In other words, we might find that the best way to think about properties is to take a ‘pluralist’ approach and keep being open-minded about the idea that there might be different kinds of properties suited to perform different kinds of jobs.

1.5 Definitions and Terminological Notes

The final task of this chapter is to give some definitions and make some terminological notes. As you may well know, debates in philosophy are often made more confusing by the fact that different people sometimes use the same term in different ways, often meaning different things. This is particularly so in debates about properties, where the terms ‘universal’ and ‘nominalism’ are perhaps the main offenders. In this final section I will briefly document some of the different uses of some of the terms you might come across, and I will state clearly how I will be using these terms in the present book.

Universal A term reserved for a particular kind of entities, which some philosophers identify with properties. Sometimes the noun ‘universals’ is used to designate what I here mean by ‘properties’, but, given the influence of Armstrong's theory of universals, it is more accurate to say that universals constitute a particular account of what properties are, ‘properties’ being the more general and neutral term. Thus, for example, views that deny the existence of universals do not necessarily deny the existence of properties.
Realism A term sometimes used to describe the view that properties are universals. I will avoid using it in this way in this book, primarily because the term ‘realism’ is notoriously vague, and also in order to avoid confusion with its applications elsewhere in philosophy, as discussed in Chapter 7.
Nominalism Sometimes ‘nominalism’ is a term used to describe any theory that denies a particular view of properties, namely that properties are universals.4 Included in this bracket, though, are a wide variety of views: trope theory, ‘class’, ‘predicate’, ‘concept’ and ‘mereological’ nominalism, and ‘ostrich’ nominalism, to name a few. In this book I will use the term to denote any view that denies that properties constitute a distinct, sui generis ontological class, which I take to be the most natural distinction between theories of properties. So, for the purposes of this book, nominalism equates the denial that properties are universals or tropes.
Relations Properties are usually taken to be picked out by ‘one-place’ predicates of the form ‘is F’ – such as ‘is red’, ‘is metallic’. Relations are picked out by predicates that have more than one place, such as two-place predicates like ‘is the father of’ or ‘is to the left of’. Most of what I say about properties also applies to relations, but I will flag moments where this may not necessarily be the case.
Object/Particular The primary kind of thing that is the bearer of properties. I use the terms ‘object’ and ‘particular’ interchangeably throughout the book.
Predicate A linguistic construction of the form ‘is F’ – such as ‘is red’ and ‘is human’. These are often the linguistic entities that are taken to ascribe properties to objects in simple sentences of the form ‘x is F’ – such as ‘the rose is red’. Some views take it that properties are the semantic values of predicates.
Singular term A term that refers to a single object; the category includes names such as ‘Jane Austen’ or ‘Hillary Clinton’ and definite descriptions such as ‘the president of the USA’ or ‘the tallest mountain in the world’. Singular terms take up the position of ‘x’ in simple sentences of the form ‘x is F’, and they are the things predicates ascribe properties to.
Abstract singular term A term that takes up the ‘x’ position in a simple ‘x is F’ sentence but seems to refer to an entity that exists in more than one place. Some examples are ‘redness’, ‘humanity’, and ‘electronhood’. Properties are taken by some to serve as the referents of abstract singular terms.
Identity conditions for properties Some philosophers5 complain that properties are suspect entities because there are no clear identity conditions for them: that is, there are no clear conditions set out for what makes one property identical to another. Given the variety of views we will examine in this book, such a complaint is not entirely unwarranted, as the controversy over the nature of properties inevitably yields unclarity about the identity conditions for properties. What we can do, though, is show that identity conditions for properties drop out of the various views we will consider, and thus what one takes the identity conditions for properties to be will depend on the view of properties one adopts. We need not get bogged down in details at this point, but here are some brief examples of statements of identity conditions for properties from some of the views we will consider. These will make a handy guide for us to refer back to: transcendental universals (Chapter 2): property A = property B if and only if [= iff] the Form of A = the Form of B;immanent universals (Chapter 2): property A = property B iff the causal powers of A = the causal powers of B;trope theory (Chapter 3): property A = property B iff the class of A tropes = the class of B tropes;predicate nominalism (Chapter 5