BARNES, BRYANT, M.A. AUGUST 2019 PHILOSOPHY PROPERTY (66 pp.)

Thesis Advisor: Deborah C. Smith

This thesis will address the question of what individuates a property. In the current literature, the question is predominately answered in three ways. Quidditism takes properties to be categorical and individuated by their , that is, by the intrinsic of the property.

Structuralism takes properties to be individuated by the structural roles (e.g., causal or nomological) that they play. Causal structuralism, for example, maintains that a property is individuated by the causal relationships it enters. I will survey the strengths and weaknesses of these positions and conclude by arguing for John Heil’s mixed view, which takes properties to be both dispositional and categorical. However, because Heil’s mixed view is about the nature of properties and not individuation, I will have to construct individuation conditions appropriate for his theory regarding the nature of properties. My concluding chapter will consist of articulating and defending my individuation conditions for Heil’s mixed view.

PROPERTY INDIVIDUATION

A thesis submitted To Kent State University in partial Fulfillment of the requirements for the Degree of Master of Arts

by

Bryant Barnes

August 2019 © Copyright All rights reserved Except for previously published materials

Thesis written by Bryant Barnes B.A., King University, 2016 M.A. Kent State University, 2019

Approved by

______, Advisor

Deborah C. Smith

______, Chair, Department of Philosophy

Michael Byron

______, Dean, College of Arts and Sciences

James L. Blank

TABLE OF CONTENTS………………………………………………………………………...iv ACKNOWLEDGEMENTS……………………………………………………………………..vi INTRODUCTION………………………………………………………………………………...1 CHAPTERS 1. Introduction...……………………………...………………………………………………………………………..…..……1 1.1 The Scope of the Thesis and Terminology………………………………………………………….………1 1.2 A Brief Look at Quidditism………………………………………………………………………………….……..3 1.3 A Brief Look at Structuralism………………………………………………………………………………….….4 1.4 A Foray into the Nature of Properties………………………………………………………………….…….5 1.5 A Happy Middle…………………………………………………………………………………………….…………..6 2.Quidditism………………………………………………………………………………………………...……………...... 8 2.1 Structuralism and Quidditism……………………………………………………………………………..……..8 2.2 Why be a Quidditist?………………………………………………………………………………………….……10 2.3 What is a ?…………………………………………………………………………………………….……11 2.4 The Argument from Parsimony and Austere Quidditism…………………………………….……14 2.5 Extremely and Moderately Austere Quidditism……………………………………………………….16 2.6 Non-recombinatorial Quidditism……………………………………………………………………….…….17 2.7 Epistemological Arguments Against Quidditism…………………………………………….………...19 2.8 Non-recombinatorial Quidditism and Skepticism……………………………………………………..22 3. Role-Based Theories………………………………………………………………...... ……24 3.1 Structuralism…………………………………………………………………………………………………………...24 3.2 Ramsification and the Clarification of Roles………………………………………………………….….26 3.3 Nomological and Causal Structuralism………………………………………………………………….….28 3.4 Minimal and Relational Structuralism……………………………………………………………….……..30 3.5 The Symmetry Problem………………………………………………………………………………….………..35 4. Mixed Views……………………………………………………………………………………………………………….….42 4.1 Martin’s Dual Aspect Interpretation of Powerful Qualities……………………………………...42 4.2 Heil’s Identity Theory…………………………………………………………………………………………..…..45

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4.3 Identity Theory or DAI?...... 47 5. Conclusion………………………………………………………………………………...... 53 5.1 An Initial Articulation of the Individuation Conditions………………………………………….….53 5.2 A Problem with the Directionality of Dispositional Natures……………………………………..54 5.3 The Identity of Natures…………………………………………………………………………………………...58 5.4 A Kind of Quidditism……………………………………………………………………………………….……….60 REFERENCES………………………………………………………………………………………………………………………….…64

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ACKNOWLEDGEMENTS When I think back on writing this thesis, the words “That’s good for your project but not for your thesis” immediately come to mind. Of course, this came from my thesis advisor and mentor, Dr. Deborah C. Smith, who always kept me on track when I could not reign in all the tangents that would have otherwise been clumsily thrown into this thesis. I cannot thank her enough for keeping me on track throughout this process, providing immensely helpful comments on my initial chapter drafts (comments which, if combined, would probably exceed the length of this thesis), and always being available to bounce ideas off of.

I would also like to thank my readers, Dr. David Pereplyotchik, Dr. Frank Ryan, and Dr. Donald

White, who have been patiently waiting for this thesis to (finally) be completed. I value their time and greatly appreciate them devoting some of it to reading this thesis.

I would also like to thank those professors whose classes I have spent the most time in and impacted my growth as a student. Dr. Pereplyotchik whose Socratic style of questioning and energy in and out of the classroom is something that I try to emulate. Dr. Aldea, with whom I read roughly 10,000 pages of Husserl, ramping up my reading comprehension. Dr. Byron, whose careful attention to precision while answering questions in class has benefited me immensely as I have gone on to write and speak in philosophical settings.

I must also thank William Fenton, Cara Griffiths, and all my fellow graduate students for making my years at Kent State a wonderful experience and listening to me occasionally rant about the problems I ran into while writing this.

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Lastly, I would like to thank Dr. Craig Streetman from King University, who initially sparked my interest in philosophy and always indulged my various project ideas as an undergraduate.

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Chapter 1: Introduction

1.1 The Scope of the Thesis and Terminology

Arguably, the world is made up of objects and properties. Such objects include hearts, lungs, and individuals with both hearts and lungs. Properties include tallness, redness, negative charge, being happy to have one’s thesis finished, etc. A lot has been said about what individuates objects, especially individuals. There is a large literature on the putative haecceities (or individual ) of particular objects, but the question of what individuates properties is relatively new on the scene. It is this latter question that will be the focus of my thesis. I will call it the individuation question:

Individuation Question: What individuates a property across possible worlds, that is, what are the cross-world identity conditions for a property.

As Dustin Locke has articulated, the debate over what individuates a property is a “domestic dispute among property realists” (Locke 2012, 347). I take the existence of properties as an assumption that all those who discuss individuation share. So, I will not be engaging those who do not believe that properties exist. Furthermore, like most philosophers who engage the individuation question, I will assume that properties are universals rather than collections of tropes.1 However, it is beyond the scope of this thesis to defend this assumption.

1 A universal is a property that can be instantiated in different objects at the same time. If the property of redness were a universal, then everything that instantiates redness would be instantiating the same property. On the other hand, trope theory maintains that everything is particular. Every instance of redness would be unique. When a group of tropes are sufficiently similar, the trope theorist groups them under one concept (e.g., the concept of redness).

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A closely related question to property individuation regards the nature of laws (e.g.,

Coulombs’ laws or Newton’s laws of motion). How one answers the question of property individuation will entail answers for questions such as ‘what is a law of nature’ or ‘are the laws of nature necessary or contingent’. It is beyond the scope of this thesis to directly address these questions, but I will make it explicit when a theory of property individuation entails a particular answer to whether laws are necessary or contingent.2

Before I continue, I should get clear on the range of properties that I am considering here. I am not talking about all properties. Rather, I am writing about a specific class of properties: fundamental physical properties. Physical properties should be distinguished from abstract properties, such as the property of being a prime number. The former kind of property is instantiated in concrete physical objects, whereas the latter is not.

Fundamental properties can be explained in different ways. Following David Lewis, we can say that fundamental properties are those that act as a supervenience base for all other properties, they are intrinsic to objects, and they can “completely and without redundancy” characterize objects (1986, 60). Additionally, they “are not at all disjunctive, or determinable, or negative” (Lewis 2009, 204). Another explanation is that fundamental properties are those that would be featured in a completed science that describes the world at the most basic level

(Schaffer 2004; Bird 2009).3 So, properties such as spin, force, and charge are plausible candidates for fundamental properties. In the rest of this thesis, unless otherwise specified, I will use ‘properties’ and ‘property’ to talk about these fundamental properties.

2 Throughout this thesis, I will use ‘necessary’ and ‘contingent’ to refer to metaphysical necessity and contingency. 3 Many philosophers would consider to be the most fundamental science, hence a completed physics would name the fundamental properties (see Schaffer 2004).

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There will be various times in which I discuss a property’s nomological/causal role. By

‘role’, I mean the following: the role a property P plays involves all of its backwards looking causal relations (i.e., relations with properties whose instances would cause P to be instantiated) and all of its forward-looking causal relations (i.e., properties that instances of P would cause to be instantiated). The nomological role of a property will include the causal role of a property and the role a property plays in non-causal laws such as the law of conservation.

In chapter 3, I will discuss how to make the notion of a role more precise, but for now this should be thought of as a working account.

1.2 A Brief Look at Quidditism

A broad way to distinguish different theories on property individuation regards whether the theory takes properties to be individuated by their roles or maintains that properties are individuated independently of their roles. Quidditism falls in the latter category. I will briefly articulate the view as follows:

Quidditism: Properties are individuated by something akin to an intrinsic nature.

My articulation is purposely vague, for quidditism is a view with several variants. The variants largely differ with respect to what the ‘something’ is that individuates properties. But all proponents of quidditism agree on one simple point. Whatever individuates a property, it is not the role that the property plays.

In chapter 2, I will explore quidditism in more detail and raise various objections to the theory. The objections that I will raise against quidditism are largely epistemological. For, if properties are individuated by something other than their roles, then a few skeptical scenarios

3 will arise in which we cannot know what properties play what roles. These arguments begin with the premise that our knowledge of properties comes from their causal/nomological roles.

But if properties can freely recombine with their roles, then there can be distinct worlds in which one property plays two distinct roles, and individual worlds in which two distinct properties play the same role, etc. In the first case, we would mistakenly think that there were more than one properties when there are only one, and in the latter case we would mistakenly think that there is only one property when there are two. Such considerations have negative implications for everyday knowledge, and I will argue that the skeptical concerns present good reasons for rejecting quidditism.

1.3 A Brief Look at Structuralism

To alleviate the aforementioned skeptical concerns, some philosophers have maintained that properties are individuated by their roles. Thus, the identity conditions of a property are given by the role it plays. So, if property P plays role R in the actual world, then P will play R in any world in which P exists. This is the view that I am calling structuralism.4 It is obvious that the skeptical worlds generated by quidditism cannot be generated here. It follows from the structural identity thesis that two distinct properties cannot share the same role, and that a property cannot play a different role in another possible world.

Like quidditism, however, structuralism is not a single cohesive theory. In chapter 3, I will delineate different forms of structuralism that have so far gone unnoticed by philosophers who discuss structuralism or dispositionalism in the context of property individuation. In

4 The term ‘dispositionalism’ is sometimes used to refer to the range of views that I am calling ‘structuralism’.

4 addition, I will argue that some forms of structuralism are better than others. Yet, all forms of structuralism fall prey to the symmetry argument. Structuralism entails that two distinct properties cannot share the same role. Yet, the symmetry argument motivates the claim that there are symmetric worlds in which two distinct properties do share the same role. If such a possibility is accepted, then structuralism is false. I will also argue in the concluding chapter 5 that structuralist individuation conditions lead to a vicious regress.

1.4 A Foray into the Nature of Properties

In chapter 4, I will discuss a set of views that make claims about a property’s nature, that is, the kind of thing that a property is. On the one hand, C.B. Martin maintains that properties have two aspects – a dispositional aspect and qualitative aspect. In short, the dispositional aspect of a property is that in virtue of which a property’s instances bestow certain powers on the objects that instantiate it, and the qualitative aspect of a property is that in virtue of which a property contributes to the qualities of objects that instantiate it.

However, John Heil and Martin (in Martin’s later work) later take a property to be identical to its dispositional and qualitative aspects. Note that the articulation of these aspects is the same, and the primary between this view and the former is the three-way identity between a property and these aspects. So, both Martin’s earlier position and

Heil/Martin’s later position share commonalities with both structuralism and quidditism.

However, neither view has explicit individuation conditions. Near the conclusion of chapter 4, I will construct individuation conditions for Martin’s earlier view. My contention will be that the

5 individuation condition for Martin’s earlier view either collapse into a different theory of the nature of properties, or lead to skeptical concerns similar to those raised by quidditism.

1.5 A Happy Middle

In the concluding chapter, I will argue that Heil’s view will have quiddistic individuation conditions. So far in the literature, the individuation conditions attributed to Heil by his commentators are structuralist in spirit. However, this seems like a misguided approach. I will argue that there is a clear direction of dependence between a property and the role that it plays on Heil’s theory that does not allow the theory to be given structuralist-like individuation conditions. Further, the only way to properly account for the three-way identity invoked in

Heil’s theory of properties requires a quiddistic individuation condition.

It will be my contention that, once the individuation condition is properly articulated, it will be able to circumvent the skeptical problems that some forms of quidditism give rise to.

For, Heil’s theory of properties still poses a necessary relation between a property and the role it plays, and any individuation condition crafted for Heil’s theory will need to account for this.

Further, by not placing the burden of individuation on a property’s role, the individuation condition that I provide for Heil will be able to circumvent the structuralist’s concern with symmetric worlds and infinite regresses. I will conclude that the conjunction of Heil’s view on the nature of properties and quiddistic individuation conditions is preferable to quidditism alone and the structuralism.

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Chapter 2: Quidditism

For a long time, and perhaps even now, Humeanism about the nature of laws was the predominant view.5 On this view, laws are contingent, such that, there could be possible worlds with the same properties as the actual world with different laws. It is no surprise, then, that quidditism has been endorsed by prominent Humeans (Lewis 2009; Schaffer 2005). Since many versions of quidditism allow for the recombination of properties and nomological/causal roles, it fit in well with the Humean account of laws. In this chapter, I will articulate different versions of quidditism, and present the skeptical concerns against quidditism and conclude that these skeptical worries give us prima facie reason to reject quidditism.

2.1 Structuralism and Quidditism

As noted in the previous chapter, structuralism is the theory according to which properties are individuated by their causal/nomological roles (see page 4). In the following chapter, I will talk about structuralism in more detail. For now, we only need a cursory understanding of structuralism, because quidditism is often defined as being opposed to structuralism. For example, Tyler Hildebrand says that “…quidditism holds that some properties are individuated not by their roles in causal/nomological structures, but instead by something else” (2016, 517). Likewise, Stephen Barker holds that “A property possesses a quiddity just in

5 On a Humean view about laws, nothing constrains the way properties may be instantiated in space and time and laws simply supervene on the spatiotemporal spread of property instantiations in any given world.

8 case its identity is fixed by something independent of the causal-nomological roles it may enter into” (2009, 242). Both Hildebrand and Barker have negative definitions of quidditism, whereby

‘quidditism’ is defined as a rejection of structuralism. This is the notion of quidditism captured by Deborah C. Smith’s “I-quidditism” (2016, 239). Regarding I-quidditism, she says that

“quidditism is contrasted with [structuralism], a view according to which properties are individuated by their causal powers or nomological roles” (Smith 2016, 239).

With the preceding discussion in mind, I will define ‘quidditism’ as follows:

Quidditism: Properties are individuated by something other than their causal/nomological roles.

This definition is purposefully broad, and it is meant to range over the definitions of quidditism that Smith has categorized as I-quidditism.6 While the definitions I appealed to are negations of structuralism, there are more positive articulations which hold that the numerical identity of properties across possible worlds is primitive (see Black 2000, Whittle 2006).7 But, if numerical identity is primitive, then properties are not individuated in virtue of the roles they satisfy.

Along this vein, Jennifer Wang says that:

According to quidditism, properties do not play their causal roles essentially. This is often combined with the claim that properties have primitive identities, trivial essences, or ‘float free’ of their causal roles (2016, 3).

Endorsing a primitive identity between properties entails the definition of quidditism given above.

6 See Smith (2016, 239) for a more comprehensive list of the various definitions of ‘quidditism’. 7 By ‘primitive’, I mean that the cross world identity of properties is simple and unanalyzable.

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2.2 Why be a Quidditist?

Why would one think fundamental properties are individuated by something other than their causal/nomological roles? One of the best arguments for quidditism comes from the combinatorial theory of possibility (see Lewis 1986, Armstrong 1989). Regarding the combinatorial theory of possibility, David Lewis says that:

We can take apart the distinct elements of a possibility and rearrange them. We can remove some of them altogether. We can reduplicate some or all of them. We can replace an element of one possibility with an element of another. When we do, since there is no necessary connection between distinct existences, the result will itself be a possibility…. Combinatorialism tells us that the laws of nature are contingent (2009, 209-210).

The principle of recombination at work here is simple: if x and y are distinct existences, then there are possible worlds with only x, only y, or both x and y (Schaffer 2005, 9). Possible worlds, according to Lewis, are recombinations of distinct existences in different possible worlds.

Lewis (2009) argues that the recombination principle requires quidditism. Assume that structuralism is true, and that an instantiation of A causes B to instantiate, and an instantiation of B causes C to instantiate. Properties A, B, and C are distinct existences. But if structuralism is true, then there can be no worlds that include an instantiation of A without also including an instantiation of B and C. So, if structuralism is true, the recombination principle is false. Why should the fact that it entails the falsehood of the recombination principle be a problem for structuralism? Because, as Lewis (1986) and Schaffer (2005) hold, our best theory of metaphysical modality requires the truth of the recombination principle.

The argument for quidditism from recombination briefly stated above is a variation of one of Schaffer’s (2005) arguments for quidditism. He thinks that many of our best theories concerning modality, counterfactuals, propositions, conceivability, and recombination all

10 require quidditism. I will not survey all of his arguments here, but I will look at one other theory he thinks requires quidditism: our best theory of conceivability. According to Schaffer, out best theory of conceivability holds that “If it is conceivable that p, then there is a possible world at which p is true” (2005, 9). He then contends that it is conceivable that like charges attract and poses the following argument:

(1) If the relation between properties and their powers is necessary, then it is inconceivable that like charges attract; (2) It is conceivable that like charges attract; (3) Therefore: the relation between properties and their powers is not necessary (Schaffer 2005, 10).

The idea is that, if we can conceive of a world in which like charges attract, then there is a possible world in which like charges attract. If structuralism were true, then there could be no such possibility. But there is, so structuralism is false and hence quidditism is true.

2.3 What is a Quiddity?

So far, I have tried to present and motivate a cohesive quidditist view, but it becomes less cohesive when we ask what is it that individuates properties. Saying that it is something other than a property’s causal/nomological role is not very informative. One’s immediate reaction may be that properties are individuated by their quiddities. Along this line, Dustin

Locke characterizes quidditism as “the view that properties are individuated by their quiddities”

(2012, 348). But what exactly is a quiddity? Johnathon Schaffer characterizes a quiddity as follows:

A quiddity is the ‘suchness’ of a property. It is its intrinsic nature. If a property such as charge confers different powers at different worlds, then what unifies these instances as many instances of one property is their quiddity, their

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common nature…. A quiddity is in some ways analogous to a haecceity (2005, n. 2).

So, a quiddity is like a haecceity for properties. This interpretation of quiddity is also endorsed by Denis Robinson, who says that quiddities “comprise a kind of ‘real ’ or ‘property haecceity’” (1993, 19).

Since this analogy between quiddities and haecceities is one drawn in the literature, we might be able to understand what a quiddity is by understanding what a haecceity is. Robert

Adams defines a haecceity (a “thisness”), as the property that one has of being identical to oneself (not the property of being self-identical) (1979, 6).8 My haecceity is the property of being identical to Brant Barnes, and your haecceity is the property of being identical to yourself.

We should not confuse a haecceity with the property we all share of being self-identical.

Presumably, everything has the property of being self-identical, but only I have the property of being identical to Brant Barnes. There is also a possibility that haecceities are non-qualitative

(Adams 1979, 6). By this, Adams means that the haecceity of an individual cannot be analyzed in terms of a set of qualities possessed by and only by the individual. We can draw three things from Adams’ account of haecceities:

(1) A haecceity is the property of being identical to oneself (not of being self- identical); (2) A haecceity can be non-qualitative; (3) Haecceities are distinct from the individuals that have them.

If we take the analogy between quiddities and haecceities seriously, we can say that quiddities have three analogous characteristics:

8 Adams is careful to note that his use of ‘property’ is supposed to be metaphysically unloaded. He wants to use a notion of property that carries the least amount of metaphysical baggage. Unfortunately, he does not give a positive account of what he does mean by property.

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(1) A quiddity is the property that a property possesses of being identical to itself (not of being self-identical); (2) Quiddities can be non-qualitative; (3) Quiddities are something distinct from the properties that instantiate them.

The first characteristic gives us an account of what a quiddity is, while (3) is entailed by (1). It can be argued that (1) explains how properties can have a primitive identity across possible worlds. As Adams notes, the primitive identity of individuals across possible worlds consists in the sharing of a haecceity (1979, 5). So, if the analogy between haecceities and quiddities is to hold, then properties would stand in primitive identity relations to properties in other possible worlds in virtue of having the same quiddity.

It is not clear to me how far this analogy between quiddities and haecceities is supposed to go. If a quiddity is something like a haecceity, then mass’ quiddity is the property of being identical to mass, which no other property except mass possesses. But, if this is the case, then it is hard to see how possessing the mass quiddity is any different than simply being identical to mass. To say that mass has the property of being identical to mass is to individuate it as being that property and e.g., not the property of being identical to charge (which only charge has).

However, this is just to say that mass does not have the property of being identical to anything else except itself. So, what distinguished mass from charge is that mass is not identical to charge. But there is a divide in the literature over whether quiddities are qualitative or non- qualitative. So, it isn’t clear that we should include the analogue of Adam’s (2) (e.g., quiddities can be non-qualitative) in our account of quiddities.

There is another facet here. Quiddities are often described as something akin to an intrinsic nature. Whatever a quiddity is, it is generally taken to be (i) something distinct from the property it is individuating, (ii) something intrinsic to a property, (iii) sufficient for

13 individuating a property, and (iv) something more robust than bare numeric identity. (iv) holds because there is something in virtue of which (a quiddity) properties are either numerically identical or distinct.

2.4 The Argument from Parsimony and Austere Quidditism

The postulation that quiddities are something distinct from the properties that have them gives rise to an important objection. Hawthorne (2001, 368) notes that science only needs causal explanations to make sense of the world. There is no talk of a property’s quiddity in our best scientific theories. These are conceptual constructions that the scientist does not need. So, he asks, “Why posit from the armchair distinctions that are never needed by science?”

(Hawthorne 2001, 369).

Locke has recently articulated the implicit premise in the preceding argument as follows:

When given a choice between two metaphysical theories, one of which posits only ontological resources posited by empirical science, and the other of which posits the same resources of the first plus something that is not posited by empirical science, we have, all other things being equal, reason to reject the second theory in favor of the first (2012, 349).

Note that this is not a claim about choosing between metaphysical theories based on the sizes of their respective ontologies, nor is it a claim about choosing a metaphysical theory whose posits do not go beyond empirical science (Locke 2012, 349). Rather, if there is a choice between two theories, and one theory goes beyond what science posits without some theoretical benefit, then we ought to choose the theory that posits only what science already needs (Locke 2012, 349). Since scientists do not need quiddities (where these are distinct from

14 the properties that have them) for successful scientific explanations, we should choose the theory that does not posit quiddities.

Is this parsimony argument successful against quidditism? Not necessarily. Above, I defined ‘quidditism’ as the view that properties are individuated by something other than their causal/nomological roles. Whether the parsimony argument succeeds or fails depends on how one cashes out ‘something other than’. If the quidditist must accept that properties are individuated by their quiddities, and that quiddities are something distinct from the property, then the parsimony argument is successful. But this is not the only way to understand quidditism. Locke differentiates between two forms of quidditism:

Extravagant Quidditism: Properties are individuated by their quiddities, and Austere Quidditism: Properties are individuated by numerical identity (2012, 351).

These are two answers to the question of what individuates properties. The parsimony argument is only effective against extravagant quidditism, while austere quidditism is untouched by it. Austere quidditism only posits properties, and it does not additionally posit quiddities. This is the same ontology accepted by the structuralist, so the parsimony argument does not pull in favor of structuralism.

To make Locke’s argument clearer, let us take a closer look at his austere quidditism. His full articulation of austere quidditism is as follows:

Austere quidditism…is simply the denial of counterpart theory for properties: according to austere quidditism, de re representation is precisely a matter of numerical identity (2012, 357).

Locke thinks that a counterpart theory is one that makes representation across possible worlds a matter of something other than numerical identity and may treat properties as world bound

15 entities, and that any theory that posits a counterpart relation between properties without a good reason has a methodological disadvantage relative to theories that do not (2012, 357-

359). On extravagant quidditism, a non-actual world w represents actual property P as being such-and-such a way by containing property P* that possesses P’s quiddity. But, properties P and P* may both be world bound entities. So, Locke’s austere quidditism is comprised of three theses:

(1) A rejection of a counterpart theory for properties, and an acceptance of genuine transworld identity of properties; (2) A rejection that properties in one possible world represent properties in another possible world in virtue of sharing a quiddity; (3) Representation across distinct possible worlds is a matter of numerical identity.

The first thesis expresses the position that properties are not world bound entities. The same property can exist in different possible worlds. The second encapsulates Locke’s rejection of extravagant quidditism, because he sees it as the best way to circumvent the parsimony argument. The third is an explicit statement of the theory of de re representation of properties on austere quidditism.

2.5 Extremely and Moderately Austere Quidditism

Once we give up extravagant quidditism, we cannot say that property P in w and P* in w* are identical in virtue of sharing a quiddity. In light of this, the austere quidditist will likely have to say that the cross-world identity of properties is brute and unanalyzable. However,

Locke goes beyond this, saying that, when two properties are distinct, they are barely numerically distinct (2012, 345). There is nothing qualitative (a quiddity) in virtue of which properties are identical or distinct. One property is distinct from another in virtue of being

16 numerically distinct from that property. Smith characterizes this application of bare numerical distinctness to quidditism as extremely austere quidditism:

Extremely austere quidditism: fundamental properties are barely, numerically distinct and have nothing genuinely qualitative that would distinguish them (2016, 244).

She distinguishes this view from what she calls moderately austere quidditism:

Moderately austere quidditism: fundamental properties are qualitatively distinct though their identity and distinctness is simple and unanalyzable (Smith 2016, 244).

Locke’s view seems to fit under extremely austere quidditism, but holding that property individuation is brute and unanalyzable in general does not lead to extremely austere quidditism.

There are three questions regarding moderately austere quidditism that one may be pressed to ask. Does invoking the notion of qualitative distinctness allow moderately austere quidditism to be a form of austere quidditism, and what does it mean to say that properties are qualitatively distinct? What makes moderately austere quidditism a form of austere quidditism is that the qualitative nature of the property is not something distinct from the property itself.

Rather, properties are qualities (Smith 2016, 244). This is what allows the moderately austere quidditism to say that properties are individuated by qualitative differences.

2.6 Non-recombinatorial Quidditism

According to moderately austere quidditism, properties are individuated by being brute unanalyzable qualitative natures. That is, fundamental properties are qualities. What does this view entail regarding the recombination of properties and their roles? The answer seems to be

17 nothing. Properties may or may not be free to recombine with different roles than they actually possess. Any limit (or lack thereof) to recombination will depend on whether the qualities themselves restrict recombination.

The view that Smith calls ‘non-recombinatorial quidditism’ takes the relationship between properties and their roles (or a subset of the role a property plays) to be metaphysically necessary. Smith says that “On [non-recombinatorial quidditism], the relationship between a fundamental property and (at least part of) its nomological profile will be metaphysically necessary rather than contingent” (2016, 250). Whether a property has part of its role necessarily will depend on the qualitative nature that the property is. Regarding non- recombinatorial quidditism, Smith says that:

…it is in virtue of [a property’s] qualitative nature that instances of the property have the causal powers that they do. As such the qualitative nature of a fundamental property is distinct from and in no way exhausted by its nomological profile (2016, 250-251).

The order of explanation in non-recombinatorial quidditism is inverted relative to structuralism.

Instead of a property’s role determining the identity of a property, a property’s role is determined by the qualitative nature that the property is, and it is the qualitative nature that the property is which individuates it.

Unlike the structuralist, who maintains that a property’s complete role is metaphysically necessary, the non-recombinatorial quidditist can say that a property’s qualitative nature metaphysically determines only a proper part of the complete role a property plays. In this regard, Smith says that:

The non-recombinatorial quidditist can (although need not) maintain that it is metaphysically possible that the fundamental role [the role a property possesses in virtue of its qualitative nature] determined by a fundamental property would

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underdetermine its complete nomological profile. Other, non-fundamental aspects of its nomological profile might vary from world to world in a way consistent with (relatively) unrestricted recombination (2016, 251).

We can understand Smith’s notion of “fundamental role” as follows: for any property P and any role R that a property plays in the actual world, R need not be metaphysically necessary.

Rather, only a subset of the complete role needs to be metaphysically necessary. Let ‘R*’ denote the subset of R that a property plays in virtue of its qualitative nature, and hence the subset of the property’s role that it plays necessarily. R* is the property’s “fundamental role”

(2016, 251).

2.7 Epistemological Arguments Against Quidditism

One of the earliest attacks on quidditism comes from Sydney Shoemaker (1980). His principle concerns with quidditism are epistemological in nature. He believes that, for us to know of a property, instances of that property must have some interaction with our sensory apparatus. For example, we can have indirect knowledge of negative charge by the causal relations its instances stand in to scientific instruments whose readings we are able to perceive.

In this case, our knowledge about negative charge is dependent upon the causal interactions between its instances and our senses. To this effect, Shoemaker states that:

Observing something is being causally influenced by it in certain ways. If the causal potentialities involved in the possession of a property are such that there is a fairly direct causal connection between the possession of it by an object and the sensory states of an observer related to the object in certain ways…we say the property itself is observable (1980, 116).

So, according to Shoemaker, a property being causally efficacious is a necessary condition for one to have knowledge of that property. Take this to be our starting point:

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(1) For anyone to have knowledge of a property, it must be causally efficacious.

Lewis additionally notes that:

(2) Any two worlds that are causally identical are observationally identical (2009, 207).

Now consider mass (M), charge (C), and their respective roles R1 and R2. If we take the general characterization of quidditism above (e.g., the view according to which properties are individuated independently of their causal/nomological roles), we should expect the following:

(3) There is a possible world w1 that differs from actuality (w0) except that at w1, M plays R2 and C plays R1. (4) There is a possible world w2 that differs from w0 except that C is replaced by an alien property ‘schmarge’ (S) that plays R2. (5) There is a possible world w3 structurally identical to w0 wherein two distinct properties play R2 (see Yates 2013, 96). (6) In w0, it is epistemically possible that there are properties that do not enter into causal relationships (Shoemaker 1980, 116).

By hypothesis, w1, w2, and w3 have the same causal structure. The distinction between these worlds and the actual world resides in the properties playing R1 and R2. Lewis focuses on scenarios (3) and (4), arguing that, since two causally identical worlds are observationally identical, we cannot know whether the actual world is w0, w1, or w2 (2009, 211-214). So:

(7) In the actual world, we cannot know what properties occupy which roles.

Alexander Bird (2007, 76-79) and Shoemaker focus on scenario (5). Shoemaker says that:

…if two properties can have exactly the same potential for contributing to causal powers, then it’s impossible for us even to know (or have any reason for believing) that two things resemble one another by sharing a single property (1980, 258).

For, if two distinct properties play the same role in w3, then it follows that these two distinct properties will interact with our sensory apparatus in the same way. So, in w3 we would not

20 know that the two properties are distinct. Additionally, if w3 and w0 are causally indistinguishable, it follows from (1) and (2) that we cannot know whether we are in w0 or w3.

So:

(8) In the actual world, we cannot know whether two objects resemble each other by sharing a property.

The skeptical scenario in (8) can also be generated by scenario (6). Two distinct objects could share an indefinite number of causally inefficacious properties, and we would have no way of knowing. So, we would not know whether two objects resemble each other by sharing properties. Shoemaker thinks that we should reject both (7) and (8), but his argument focuses on rejecting (8). Imagine that Jones sees two copies of the same books sitting on a bookshelf, and he takes them both down to compare the wear and tear of each. After examining the books, Jones concludes that they resemble each other quite closely. Yet, if (8) is correct, then

Jones is not warranted in this conclusion. Since giving up such everyday knowledge is too high a price to pay, we should reject quidditism.

Regarding (7), we are inclined to think that we do know which properties fill each role. If not, then widely accepted scientific theories would become open to question. The scientist would not be warranted in saying that “this property is mass, because it has such-and-such an effect,” because it could be the case that charge actually plays the mass role and vice versa. So, all the scientist could claim to know is the particular causal structure of a world and not the properties that satisfy those roles. The worry is that, if quidditism is true, then for all we know, there is only one property that plays every role in a given world.

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2.8 Non-recombinatorial Quidditism and Skepticism

Smith has argued that non-recombinatorial quidditism can alleviate some of these skeptical concerns (2016, 255). Recall that non-recombinatorial quidditism posits a necessary connection between a property and its fundamental role – a subset of the complete role a property plays. In an attempt to avoid skeptical conclusions, the non-recombinatorial quidditist may make this claim stronger by saying that a property’s fundamental role is its complete role.

So, a property possesses its role in all possible worlds in which the property exists. It should be clear that this position would eliminate (3). There could be no worlds w1 and w2 such that property P plays R1 and property P* plays R2 in w1, but P plays R2 and property P* plays R1 in w2.

But let us recall the other ways of generating skeptical concerns:

(4) There is a possible world w2 that differs from the actual world except that C is replaced by an alien property ‘schmarge’ (S) that plays R2. (5) There is a possible world w3 wherein two distinct properties play R2 (see Yates 2013, 96). (6) In w0, there are properties that do not enter into causal relationships (Shoemaker 1980, 116).

There is nothing about a property C possessing a role R2 necessarily that would delimit what other properties could also fill R2. Unless C uniquely grounds R2, which we have no reason to suspect that it does on non-recombinatorial quidditism, then an alien C1 property could fill R2. Indeed, C1 would have to play R2 in all possible worlds in which it exists. The skeptical concern arises: in the actual world, is C or C1 playing R2?

Additionally, a property distinct from C (call it M) may necessarily ground both

R1 and R2. So, any world in which M exists but C does not will still be a world in which

22 the causal/nomological laws associated with R2 will exist. This possible situation makes

(5) more interesting, because, for all we know, we are in a world in which there is one property playing what we think are two different roles. For example, for all we know, we are in a world in which only the property of negative charge exists and, unknown to us, negative charge is also playing the nomological role that we associate with mass. Or we might be (in an epistemic sense of ‘might’) in a world in which two distinct properties play the same role. If the non-recombinatorial quidditist does not accept a complete overlap between a property’s fundamental role and its complete role, then this problem will arise in a different regard. M could necessarily fill R1 while accidentally filling R2 in some possible world. In all of these cases, we can generate the skeptical concerns associated with (5).

Additionally, on non-recombinatorial quidditism, there is nothing that would prevent a property from being causally/nomologically inert. A property plays its role necessarily, but if a property does not play any role, then it also does so necessarily. For, if a property played a role in any possible world, then it would play it in all possible worlds. So, there is the possibility that there are properties that necessarily play no role.

Again, we generate the worries associated with (6).

So, all versions of quidditism have problems with generating skeptical possibilities. While non-recombinatorial quidditism fairs better than other versions of quidditism, it is still susceptible to skeptical concerns. In the following chapter, I will introduce various versions of structuralism that circumvent these concerns by individuating properties in terms of their causal/nomological role.

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Chapter 3: Role Based Theories

In this chapter, I will explore what I call role-based theories of property individuation.

Unlike quidditism which, broadly, puts emphasis on the nature of properties regarding property individuation, role-based theories put the emphasis on the role a property satisfies. The claims of each theory surveyed here differ in their degree of metaphysical robustness. That is, they differ in the claims they make about the ontological nature of properties. Structuralism, on the other hand, distinguishes between a property and the role is plays. In both cases, though, emphasis is placed on the role of a property.

3.1 Structuralism

Sydney Shoemaker articulates the view that I am calling structuralism as follows:

The formulation of the causal theory of properties I now favor…says that the causal features of a property, both forward-looking and backward-looking, are essential to it. And it says that properties having the same causal features are identical (1998, 64).

Shoemaker endorses the view that I will later call causal structuralism.9 He thinks that properties are individuated by the causal role they play. However, structuralism is broader than causal structuralism. Other structuralists emphasize a property’s nomological role instead of its

9 The term ‘causal structuralism’ was, to my knowledge, coined by Johnathan Hawthorne (2001).

24 causal role. I will explain this difference in more detail below, but for now we can isolate two main structuralist theses:

Essentialist Thesis: a property essentially possesses the causal/nomological role it satisfies; Identity Thesis: a property is individuated by the causal/nomological role it satisfies.10

So, if the property of negative charge causes anything which instantiates it to repel other negatively charged objects, then negative charge exhibits this effect in any world in which it exists. Additionally, there cannot be two distinct properties that share the same role. Properties can share causal/nomological features, but any properties that share the same role are the same property.

These two theses have been formalized by David Yates (2013) as follows:

ET: ∀퐹∀Φ(Φ is essential to 퐹 ↔ □∀푃(P=F → ∀푥(푃(푥) □ → Φ(푥)))11 12 13 IT: ∀퐹∀Φ(Φ individuates 퐹 ↔ □∀푃(P=F ↔ ∀푥(푃(푥) □ → Φ(푥))) (103). ’

ET can be read as saying that Φ is essential to F iff in every possible world and for every property P, if P=F, then if anything were to instantiate P, it would also instantiate the role Φ. IT can be read as saying that Φ individuates F iff for every possible world and for every P, P=F iff if anything were to instantiate P, it would instantiate Φ. In short, the essentialist thesis can be understood as saying that, if a property F satisfies a role Φ, then F will satisfy Φ in any possible world in which there is something that is F. Likewise, the identity thesis says that, if F is

10 Bird also endorses these two theses. He argues that the only things a theorist writing on property individuation should accept is that (i) a power is an ontic property that has a dispositional essence and (ii) a power is an ontic property whose identity is given by its causal/dispositional/nomic role (Bird 2016, 345). 11 I am using ‘□ →’ as a Lewis conditional. It can be read as ‘If Φ were the case, then Ψ would be the case’. The conditional is true iff in the closest possible world in which Φ is true, Ψ is also true. 12 Yates uses ‘individual essence’ in the place of ‘individuates’, but Yates thinks that the individual essence of a property will individuate it (see also Hawthorne 2001). 13 This formalization assumes that properties are transworld entities.

25 individuated by Φ, then any property in any possible world that satisfies Φ is numerically identical to F.

Shoemaker further writes that “What makes a property the property it is, what determines its identity, is its potential for contributing to the causal powers of the things that have it” (Shoemaker 1980, 212 my emphasis). He also writes that “properties are individuated by their causal features – by what contribution they make to the causal powers of the things that have them” (1998, 61 my emphasis). In both quotations we see Shoemaker’s use of

‘contribution’. In this paper, I will use ‘bestows’ to denote this idea that properties contribute causal powers to the objects that instantiate them. A property bestows causal powers on the objects that instantiate it just in case that property contributes to the objects’ causal powers.

Along a similar vein, Hawthorne entertains the idea that properties “drag causal powers along with [them]” (2001, 373). The structuralist thinks that properties and the roles they bestow are distinct. With this in mind, I introduce a third structuralist thesis:

Bestowal: Properties bestow powers onto the objects that instantiate them, and so are distinct from the powers they bestow.

The notion of the bestowal of powers makes it easier to explain what is meant by saying that properties possess certain causal/nomological roles. A property P possesses a certain role R just in case P would contribute the causal powers/nomological relationships entailed by R to the objects that instantiate it.

3.2 Ramsification and the Clarification of Roles

Before discussing structuralism in more detail, it will be helpful to understand how the structuralist clarifies the roles that individuate properties. In this regard, the structuralist uses

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Ramsification.14 The first step in Ramsification is to posit a complete and final scientific theory

T.15 We then differentiate between T-terms – theoretical terms defined by T, and O-Terms – pre-theoretical terms. These pre-theoretical terms are those we use in everyday discourse and that have their definitions fixed independently of T (Lewis 2009, 206). We then formulate the postulate of T, T(t1…tn), where the ti are theoretical terms and any other language that appears in the postulate belongs to the O-language. To create a Ramsey sentence out of the postulate, we replace each T-term with a unique variable (x1…xn) and prefix a unique existential quantifier to each variable. Our Ramsey sentence will then look like: ꓱ!x1…ꓱ!xnT(x1…xn). This reads: ‘there exists a unique ordered n-tuple of objects that satisfy the postulate of T.

This is all fairly abstract, so it may help to look at an example of Ramsification from

Dustin Locke (2012). Suppose that the world is Newtonian, and that we want to Ramsify those laws in which mass features. There would be two such laws:

First, there is the law of gravitation: between any two individuals with mass, there is an attractive force proportional to the product of their masses divided by the square of the distance between them. Second, there is Newton's Second Law of Motion: the net force on an object is equal to the product of its mass and its rate of acceleration (Locke 2012, fn.6).

To Ramsify these laws, we conjoin the two laws, replace any theoretical terms (T-terms) with variables, and equip unique existential quantifiers for each variable. Here I am treating the terms ‘mass’, ‘attractive force’, ‘net force’, and ‘acceleration’ as T-terms. Our Ramsey sentence

14 The use of Ramsification has become ubiquitous in contemporary literature on structuralism. See Hawthorne (2001), Johnathon Jacobs (2011), Locke (2012), Henry Taylor (2018). The use of Ramsification without additional qualification is what gives rise to the problems inherent in the view I will call minimal structuralism. 15 David Lewis (2009) discusses what to expect in the theory T. He says, “So if we had a true and complete ‘final theory’ [T], it ought to deliver a true and complete inventory of those fundamental properties that play an active role in the actual workings of nature” (Lewis 2009, 205). So, T would not only contain an inventory of fundamental properties. It would also articulate the relations between fundamental properties.

27 will look like this: ‘ꓱ!x1ꓱ!x2ꓱ!x3ꓱ!x4(between any two individuals with x1, there is an x2 proportional to the product of their x1 divided by the square of distance between them & the x4 on an object is equal to the product of x1 and its rate of x3).’ Everything that has not been turned into a variable is counted as the O-language. I will use ‘Ramsified lawbook’ to denote a theory that has been Ramsified in this way.

The structuralist uses Ramsification to make the roles they are concerned with more precise. A property is said to be individuated by its place in a Ramsified lawbook, because this place defines the property’s role. Consider the preceding example. The structuralist would say that mass is individuated by its place in the Ramsified Newtonian lawbook. That is, mass is individuated by the open sentence resulting from dropping its corresponding existential quantifier. So the open sentence: ‘ꓱ!x2ꓱ!x3ꓱ!x4(between any two individuals with x1, there is an x2 proportional to the product of their x1 divided by the square of distance between them & the x4 on an object is equal to the product of x1 and its rate of x3)’ defines mass. Since mass satisfies the open sentence, the role played by variable x1 is said to individuate mass.

3.3 Nomological and Causal Structuralism

The preceding example is in line with what has been dubbed nomological structuralism.16 The nomological role that a property plays is specified by the laws the property functions in. To individuate all the natural properties of a world, one would need to conjoin all the nomological laws true at that world. Then each of the properties mentioned in these laws would be replaced by a variable and prefixed by a unique existential quantifier. According to

16 Nomological structuralists include Chris Swoyer (1982).

28 the nomological structuralist, the open sentence that results from dropping an existential quantifier individuates the property that satisfies the open sentence.

The causal structuralist also makes use of Ramsification, but not in the way previously described.17 Instead of Ramsifying a nomological lawbook, the causal structuralist makes use of a causal lawbook. This sort of lawbook will consist in a subset of laws contained in a nomological lawbook. Let us suppose that there is a very simple world in which five properties are instantiated (A, B, C, D, E). Furthermore, let ‘R’ denote causal relations that hold between

18 property instances. ‘R(x1, x2)’ can be read as ‘instances of x1 cause instances of x2’. We can then posit a causal lawbook for this world that includes R(A,B), R(A,C), R(B,D), R(D,E)

(Hawthorne 2001, 369).19 This lawbook can be Ramsified by first conjoining all the causal laws:

R(A,B) & R(A,C) & R(B,D) & R(D,E). Then the property names are replaced by distinct variables

(P1…Pn) and prefixed by a unique existential quantifier. Our final Ramsified lawbook will then look like: ꓱ!P1ꓱ!P2ꓱ!P3ꓱ!P4ꓱ!P5[R(P1,P2) & R(P1,P3) & R(P2,P4) & R(P4,P5)]. Again, to find the individuation conditions for a property we only need to drop the corresponding existential quantifier. This will lead to an open sentence, and the property in question can be individuated as the property that satisfies the open formula. For example, consider the open formula with variable ‘P1’ free: ‘ꓱ!P2ꓱ!P3ꓱ!P4ꓱ!P5[R(P1,P2) & R(P1,P3) & R(P2,P4) & R(P4,P5)].’ In this open formula, R(P1,P2) and R(P1,P3) are the specific roles individuating property A.

17 Causal structuralists include Shoemaker (1998) and Hawthorne (2001). 18 I am borrowing the use of ‘R’ and ‘R(x1, x2)’ from Jacobs (2011). 19 The causal structure of a possible world would be more complicated than this lawbook indicates. I am using a simple lawbook for a smoother explanation.

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3.4 Minimal and Relational Structuralism

The structuralist picture I have painted above is metaphysically thin. Let us call it minimal structuralism, and articulate it as:

Minimal Structuralism: a property is individuated by its place in a Ramsified lawbook.20

Minimal structuralism does not say anything about the nature of the properties being individuated or the nature of laws that comprise the lawbook. All it says is that there is a lawbook which describe the various relations properties enter, and that once the lawbook is

Ramsified, a property is individuated by whatever relation it satisfies. There are several problems that arise with this articulation of structuralism that stem from the fact that minimal structuralism is silent about the nature of the laws comprising a lawbook.

Since minimal structuralism is silent about the nature of laws, it will be consistent with the Humean account of laws described by Lewis (1994). On Lewis’ view, there are no connections between distinct existences. There are just local matters of fact of the sort ‘a is F and G’. Laws are contingent regularities (i.e., true generalizations) that supervene on the distribution of fundamental properties in space and time. They are generalizations over local matters of fact. Of course, not all regularities are laws. Laws are regularities that are theorems of the best explanatory system. In this regard, Lewis says that “The best system is the one that strikes as good a balance as truth will allow between simplicity and strength. A regularity is a law iff it is a theorem of the best system” (1994, 478).21

20 Minimal structuralism does not favor either causal or nomological structuralism. Instead, the types of structuralism discussed in this section will all have causal/nomological variants. As such, the types of structuralism discussed in this section should be thought of as broader than causal/nomological structuralism that are open to both causal and nomological variants. 21 By ‘strength’, Lewis means ‘informative’.

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This theory of laws gives us a thin picture of causal and nomological relationships. There is nothing about instantiating one property that brings about the instantiation of another. It just happens to be the case that certain properties are generally co-instantiated. So, the causal relationship used in the lawbook can be read as one of contingent co-instantiation. It is a contingent regularity that objects which instantiate P also instantiate Q. I should also note that there is nothing that requires that all instances of P are co-instantiated with an instance of Q. If laws are true generalizations, then it is consistent with the Humean account of laws that instances of P are not always co-instantiated with instances of Q. It only needs to be the case most of the time.

But there seems to be an explanatory gap with Lewis’ view of laws. Suppose that there is a law that all F’s are G, formalized as ∀푥(F(x) → 퐺(푥)). But why is it the case that some object o instantiates G? The Humean may appeal to that fact that o instantiates F and to the law relating Fs to Gs. Yet the law itself is just based on the spatiotemporal spread of instances of F and G. So, the explanation looks like this: o instantiates G because it instantiates F and nothing that is F fails to be G. Great, but why is it the case that nothing that instantiates F fails to be G? The answer that the Humean account provides us with is that it is the way things happen to be.

Since minimal structuralism is consistent with this Humean account of laws, it inherits a similar explanatory gap. Why do objects that instantiate properties with a certain position in a

Ramsified lawbook have the causal powers that they have? For example, why is it the case that an object which instantiates P also instantiates Q? On the Humean account of laws, it would be a brute fact that an object instantiates both P and Q. The causal law that anything which

31 instantiates P instantiates Q would be a generalization over all the instances of P and Q, so there would be no sense in which the fact that an object instantiates P brings it about that the object instantiates Q.

An initial approach to abating the aforementioned problem would be to provide a non-

Humean account of the nature of laws. However, fully explicating and defending such an account would be beyond the scope of this thesis. I can only gesture at what this account would look like. Consider Alexander Birds’ articulation of laws:

The laws of a domain are the fundamental, general explanatory relationships between kinds, quantities, and qualities of that domain, that supervene upon the essential natures of those things. (2007, 201).

The important thing to note here is that laws supervene, not upon regularities, but upon the essential natures of properties (e.g., kinds, quantities, and qualities). In this sense, laws serve a descriptive function. They describe the essential natures of properties.

If causal structuralism is true, then properties are essentially causal.22 If instantiating P causes an instantiation of Q, then instances of P cause instances of Q essentially. A law that says

∀푥(P(x) → 푄(푥)) would be a description of the essential causal relationship between instances of P and Q. On this theory of laws, we have an answer to why an object which instantiates P also instantiates Q. It is because the law describes their essential causal relationship. Thus, an object which instantiates a property with a certain position in a Ramsified lawbook will instantiate other properties (in accord with the lawbook), as a result of the essential relationship between property instances.

22 Although I am talking about causal structuralism here, the same point can be applied mutatis mutandis to nomological structuralism.

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One may think that structuralism just needs to be equipped with the right account of laws. If you start with minimal structuralism – and stipulate that the laws of the lawbook are descriptive in Bird’s sense – then you can circumvent the problems with minimal structuralism.

Call this minimal structuralism+:

Minimal Structuralism+: a property is individuated by its place in a Ramsified lawbook, and the laws that have been Ramsified are descriptions of the essential relationships that properties stand to each other.

While minimal structuralism+ may help abate some of the problems with minimal structuralism, one may worry that it ultimately places ontological priority in the wrong place.

According to minimal structuralism+, properties are individuated by their place in a Ramsified lawbook. So, the Ramsified lawbook should be ontologically more basic than the properties.

However, the Ramsified lawbook is less basic than the original lawbook, because there needs to be a lawbook to be Ramsified. Yet, lawbooks as Bird envisions them describe the necessary relationships that properties bear to one another. Properties are already individuated and lawbooks describe the relations between already individuated properties. So, there would seem to be an inconsistency in minimal structuralism+. The Ramsified lawbook should be ontologically prior to the properties it individuates. However, the existence of a Ramsified lawbook requires the existence of an original lawbook that is ontologically posterior to the properties.

So, the burden of individuation cannot be placed on the lawbook. This would be true without the addition of Bird’s theory of laws, but his theory makes the problem worse by making laws descriptive. I think that the solution to this problem is to shift the burden of individuation away from the lawbook and onto the essential relations that properties enter

33 into. The idea that what individuates a property is a second-order relation instantiated by a more fundamental property is an idea that has been picked up by contemporary authors.

According to Locke, for example, the role of the Ramsified lawbook is to define a second-order relational property that is instantiated by the first-order property which satisfies an open

Ramsey sentence (2012, 348).23 Let us consider one of the Ramsified causal lawbook given above: ꓱ!P1ꓱ!P2ꓱ!P3ꓱ!P4ꓱ!P5[R(P1,P2) & R(P1,P3) & R(P2,P4) & R(P4,P5)]. The open sentence that would result from dropping an existential quantification defines a second-order relational property that the property that satisfies the open sentence possesses.

According to minimal structuralism, the property A is just individuated by its place in a

Ramsified lawbook. However, according to what I will call relational structuralism, the relations satisfied by a property define a second-order relational property possessed by A. So, it is not the place in the lawbook that individuates A. Rather, it is the second-order property defined by the lawbook that individuates A.24 Thus, let us articulate relational structuralism as follows:

Relational Structuralism: fundamental properties are individuated by the second- order relational properties they necessarily instantiate.

Notice that this shifts the burden of individuation from the Ramsified lawbook to second-order properties. On this picture, Ramsification is used to describe the second-order properties that first-order fundamental properties necessarily possess. This theory is more metaphysically robust than minimal structuralism, because it holds that properties necessarily possess the second-order causal/nomological relations that they enter into. It is built into relational structuralism that properties have their relationships essentially. If laws do describe relations

23 This is also the articulation endorsed by Barker (2009). 24 At this point, we can think of a property’s role as the second-order property it instantiates.

34 between properties, then relational structuralism entails that the relationships these laws describe are necessary.

As far as explanations go, we have an answer to why objects that instantiate properties with a certain place in the Ramsified lawbook instantiate other properties as specified by the

Ramsified lawbook. It would not be the case that objects just happen to always instantiate both

P and Q. Rather, any object that instantiates P must instantiate Q. Why? Because instances of P are necessarily related to Q. It is in virtue of the relationship between instances of P and Q, as described by relational structuralism, that any object which instantiates the former instantiates the latter.25

What about ontological priority? Relational structuralism does not place ontological priority onto the lawbook. Rather, the priority is placed on second-order relational properties.

Again, the role of a lawbook is descriptive. So, the relational structuralist can say that properties are individuated without appealing directly to a Ramsified lawbook. This is still a form of structuralism, since the relationships a property enters are doing the individuation. But it does not require placing ontological priority on a lawbook.

3.5 The Symmetry Problem

In the literature on structuralism, there is an interesting symmetry problem. Indeed,

Jennifer Wang lists it as one of the primary reasons to give up structuralism (2016, 171).

Imagine that there is a world with four properties (P, T, Q, S), such that, when an object

25 I am not offering this as an explanation of why property instances stand in the causal relationships that they do. It could be a brute fact that instances of P necessarily cause instances of Q. What I am suggesting is that the causal relationship explains why objects which instantiate P also instantiate Q.

35 instantiates P it cause instances of Q, when an object instantiates T it causes Q to instantiate, and when an object instantiates both P and T it causes instances of S. Note that P and T are distinct properties, and this distinctness is secured by their mutual instantiation causing S. Call this the symmetric world.26

Now consider the Ramsified lawbook of the symmetric world: ꓱ!P1ꓱ!P2ꓱ!P3ꓱ!P4(R(P1,P3)

& R(P2,P3) & R(P1 & P2, P4). If we want to identify P, we drop the existential quantification and have: ꓱ!P2ꓱ!P3ꓱ!P4(R(P1,P3) & R(P2,P3) & R(P1 & P2, P4). Does this open sentence provide the individuation conditions for P? No. The same set of R relations that are satisfied by P are also satisfied by T. This means that, given structuralism, we have no way to distinguish between P and T even though they are distinct. Since P and T share the same role, then they are the same property.

The argument is that, if symmetrical worlds are possible, then structuralism is false. If true, structuralism would make symmetrical worlds impossible. Properties with the same role are the same property, and there is no room for two properties to have the same roles. But, symmetrical worlds are possible. So, structuralism is false. 27 One may object that the symmetry argument begs the question against structuralism by contending that symmetrical worlds are possible. But this response only holds if we have independent reasons for accepting the limits structuralism places on what worlds are genuinely possible. That is, the symmetry problem is

26 I have described the symmetry problem as one for causal structuralism, but everything I say in this section can be applied mutatis mutandis to nomological structuralism. 27 To be more specific, the symmetry argument is meant to show that structuralism as I have described it is false. For example, Hawthorne (2001), Denis Robinson (1993), and Locke (2012) think that this symmetry argument leads to the conclusion that structuralism cannot be a theory of property individuation within a single possible world. In response, Hawthorne proposes that structuralism should be a theory according to which two possible worlds cannot share the same causal structure while differing in the properties represented by those possible worlds (2001, 374-375).

36 only question begging if we assume that structuralism is true. Since the viability of structuralism is what is currently on the table, the symmetry argument in not question begging. Additionally, there are philosophers who think that if we can conceive of some x, there is a possible world in which x is the case (see Schaffer 2005). If this is true, then the conceivability of a symmetrical world is enough for it be a counterexample to structuralism.

While the symmetry argument has been used as an objection to structuralism broadly construed, it is not clear that it is equally telling against all the forms of structuralism that I have isolated. Hawthorne (2001) first articulates the symmetry problem as an argument against a minimal structuralism, and one may wonder whether it applies as well to relational structuralism. Indeed, Johnathan Shaffer (2005) thinks that individuating properties in terms of their place in a Ramsified lawbook is what leads to the symmetry problem. He says that:

For instance, the modal and nomic necessitarians do not allow that there is a world containing only four properties: F, G, H, and I, and two laws: F => G, and H => I…. For the nomic necessitarian, this is impossible because F and H have the same nomic role, as do G and I. The Ramsified lawbook reads: (ꓱ!P1)(ꓱ!P2)(ꓱ!P3)(ꓱ!P4)(P1 => P2 & P3 => P4). Any role-based distinction between F and H is erased.… But for the causal necessitarian, this is possible, since F and H differ in their effects: F causes G, while H causes I. Likewise G and I differ in their causes (Schaffer 2005, 3-4).

Schaffer simply assumes that G is not the same property as I, which entails that F is not the same property as H. If this assumption is correct, then such a world is possible on the structuralist account. The question is whether this assumption is warranted, and whether there is a role-based distinction in the world Schaffer describes.

Let’s consider Schaffer’s world without the supposition that there are four distinct properties. Per structuralism, the individuation conditions of a property are the relations it enters into. So, let us say that there is a property (call it ‘F’) whose instances cause another

37 property (call it ‘G’) to instantiate. Likewise, there is a property (‘H’) whose instances cause a property (‘I’) to instantiate. Since no property can cause itself, the property whose name is ‘F’ is not the property whose name is ‘G’. For the same reason, the property named ‘H’ is not the property named ‘I’. The question is whether ‘F’ or ‘G’ name the same property as ‘H’ or ‘I’, respectively.

Two answers are available to the structuralist:

(1) There are four distinct properties corresponding to each name; (2) There are two distinct properties each with two names.

(1) is consistent with structuralism. Since F causes G and H causes I, we do not have to worry about symmetry. Both causes cause different properties to instantiate. (2) is also consistent with structuralism. The world has two properties F and G, which happen to have different names. Note that the structural description of Schaffer’s world does not rule out either. All the causal description tells us is that there are at least two properties: a cause and something caused.

I cannot glean anything from the causal description that would settle a dispute between

(1) and (2). This is interesting, because it is not the same symmetry problem described at the beginning of this section. Neither (1) nor (2) is inconsistent with structuralism. However, in worlds that are structured like Schaffer’s world, structuralism cannot give a definite account of how many properties exist at that world. I take this to be a primarily epistemological concern. If science is in the business of giving causal descriptions of the world, and if that description delivered a world structured like Schaffer’s, then the structuralist would not be able to discern the number of properties at that world. For, there are distinct epistemically possible worlds corresponding to (1) and (2).

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Note that I have proceeded using a structural description of Schaffer’s world, but the symmetry problem does not follow directly from symmetrical structural descriptions. However, if properties are individuated by causal descriptions, as in minimal structuralism and minimal structuralism+, then the symmetry problem does arise. Is the same true for relational structuralism? For the symmetry argument to show an ontological problem with relational structuralism, it would have to show that the symmetric world is inconsistent with relational structuralism. What this means is that a symmetric world must be one in which two properties have numerically identical second-order relations.

However, it is not at all clear that two properties which satisfy the same open sentences in a causal description instantiate the same second-order relation. What is true is that instances of P and T share causal relations with the same properties. But it seems that the second-order relations are not identical in virtue of this fact. By hypothesis, P and T are distinct. This means that the second-order relations they instantiate are distinct in virtue of having different relata.

Imagine that my friend Joe and I participated in a pumpkin smashing competition, and by a stroke of luck we both smash our pumpkins. It’s true that Joe and I stand in the same relation to our smashed pumpkins – perhaps a smashed relation – but the relational properties Joe and I instantiate are different. Joe and I are different people, and our pumpkins were different. I – not Joe – stand in the smashed relation to my – not Joe’s – pumpkin. Likewise, in some cases it is an instance of P – not T – that stands in a relation to an instance Q and vice versa.

So, P and T are not the same property according the relational structuralism. Their relational properties are not numerically identical because they have different relata. That they have different relata is secured by the supposition that there are n number of distinct

39 properties at worlds with symmetric causal descriptions. Nevertheless, I think this points to an additional problem with relational structuralism. If the relational structuralist is going to accept this response to symmetry, then the relational structuralist will have to insist that P and T are individuated by something other than their relational properties.

The response I have offered accepts the supposition that P and T are distinct, and their distinctness as relata is what provides an answer to the symmetry problem. But it was supposed to be the second-order relational properties that determined whether the properties named are identical or distinct. If the second-order relational properties that first-order properties enter into are differentiated by their relata, then it would seem that the relations are ontologically dependent on their relata. However, if this is true, then relational structuralism is false.28 For relational structuralism would place the burden of individuation on second-order relational properties whose individuation conditions rely on the distinctness of first-order properties. Hence, whether the second-order relational properties meant to individuate properties are numerically identical or distinct already depends on the prior individuation of their relata.

It seems, then, that the structuralist is stuck. Minimal structuralism and minimal+ structuralism are immediately disqualified by the symmetry objection. Prima facie, relational structuralism has an available response to the symmetry problem. Unfortunately, the response would seem to be inconsistent with relational structuralism. Of course, there might be more

28 This is where I think Schaffer goes wrong with what he calls ‘causal necessitarianism’. He assumes that the properties which stand in relations to each other are distinct without appealing to the structure of the world he has described. But he can only make this assumption if the properties are individuated by something other than the structure of the world.

40 options available that I have not considered here. For now, though, I will conclude with this unfavorable dichotomy.29

29 The epistemological problem raised in my discussion of Schaffer still stands in regard to relational structuralism. If all we have is a structural description of the world, how is the relational structuralist supposed to say when properties with symmetrical descriptions are the same or different properties? There may be an ontological difference prompted by different relata, but the structural description cannot deliver a verdict on when two relata are indeed different.

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Chapter 4: Mixed Views

In this chapter, I will articulate what has become known as the powerful qualities view.

According to the powerful qualities view, properties are both qualitative and dispositional.

There are two prominent ways that this claim has been understood in the literature. The first is that properties have dispositional and qualitative aspects, and the second is that a property is identical to its dispositional and qualitative natures. Presumably, both of these articulations have individuation conditions according to which a property is individuated by its dispositional and qualitative natures. However, I will save a full exploration of the individuation conditions for the latter view and its advantages to the final chapter.

4.1 Martin’s Dual Aspect Interpretation of Powerful Qualities

Perhaps the earliest version of the powerful qualities view is what I will call the dual aspect interpretation. To my knowledge, this view originated with Martin, and we can articulate it as follows:

Dual Aspect Interpretation (DAI): A property has two aspects, one of which is qualitative and the other of which is dispositional.

What does it mean for a property to have two aspects? The idea is not sufficiently expounded on by Martin, but he uses telling language. In many places, he says that the aspects of a property belong to that property (see Martin 1993, 1996). So, one is led to think that these aspects are something distinct from the property itself. The position that DAI takes is the

42 following: there is some property P which possesses a qualitative aspect Pq and a dispositional aspect Pd, and P≠Pq, P≠Pd, and Pq≠Pd. Further, these aspects are intrinsic to the properties which possess them.

I want to further clarify what an aspect of a property would be. Objects have qualitative features, the paradigm examples being roundness, squareness, sphericity, etc. As Martin says, these qualities are “really ‘there’ in the object” (1996, 74). There is other telling language in the following quote from John Heil:

…qualities are categorical; qualities are here and now, actual not merely potential, features of the objects of which they are qualities (Heil 2012, 59).

The qualitative aspect of a property is that in virtue of which objects that instantiate it have certain qualitative features.

The dispositional aspect of a property is that in virtue of which an object instantiating the property possesses a given power (Martin 1993, 183).30 It is solely in virtue of instantiating a property with a dispositional aspect that an object will manifest particular property instances when the object co-instantiates two properties with dispositional aspects. Of course, all properties have dispositional aspects on this view, and it is not the case that the co- instantiation of any two properties will lead to an object manifesting a new property. The co- instantiation of two properties will only lead to the manifestation of a new property when those two properties are reciprocal disposition partners.

We can understand reciprocal disposition partners as follows: P1 is the reciprocal disposition partner of P2 iff, were an object O to co-instantiate P1 and P2 at time t, then O would

30 I want to mark the difference between ‘powers’ and ‘dispositional aspect’. A dispositional aspect belongs to a property, whereas objects have powers.

43 manifest P3 (or a set of properties) at t (or some suitable time interval) determined by the dispositional aspects of P1 and P2 (Martin 1993, 184). Consider the following example:

A salt crystal manifests its disposition to dissolve in water by dissolving in water. But this manifestation is a manifestation of both the salt crystal's disposition to dissolve in water and the water's reciprocal disposition to dissolve salt (Heil 2005, 350).

A salt crystal dissolves in water in virtue of possessing a property instance with a dispositional aspect to dissolve in water and the property instance whose dispositional aspect gives water the power to dissolve salt. If one of these property instances were absent at the moment a salt cube is placed in water, then the salt cube would not dissolve. Even if a salt crystal were never placed in water, the property of dissolving salt would still be the reciprocal dispositional partner of salt’s property of dissolving in water because these two properties would lead to a new property manifesting if they were co-instantiated.31

The dispositional aspect of a property will limit its possible reciprocal disposition partners, such that, not every co-instantiation of it and another property will result in a manifestation (Martin 1993, 184). Additionally, the property that an object comes to instantiate when two or more reciprocal disposition partners are co-instantiated will be determined by the dispositional aspects of the properties that are reciprocal disposition partners. But we should not understand dispositional aspects relationally, as if a dispositional aspect is a relation between the dispositional aspects of reciprocal disposition partners and a possible manifestation (Martin 1993, 185).

31 Both, the property of salt in virtue of which it dissolves water and the property of water in virtue of which it will dissolve in salt are not fundamental properties.

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4.2 Heil’s Identity Theory

More recently, however, Heil and Martin have expressed displeasure with the DAI interpretation of the powerful qualities view. They say that:

The notion that real empirical properties might be purely non-dispositional or qualitative, the notion that they might be wholly ‘categorical’, is as much an abstractive myth as is the idea of pure dispositionality. Although we are not entirely happy with the terminology, what is qualitative and what is dispositional for any property is less like a two-sided coin or a Janus-faced figure than it is like an ambiguous drawing (Heil & Martin 1998, 289).

What does it mean to say that a property is like an ambiguous drawing? The idea seems to be that the dispositional and qualitative aspects of a property are one and the same aspect considered differently. Indeed, Heil says that “A property’s dispositionality and its qualitativity are, as Locke might have put it, the selfsame property differently considered” (2003, 112). The difference between a property’s dispositional and qualitative aspects is a conceptual abstraction and not an ontological difference.

The rejection of DAI in the preceding remarks only implies that the qualitative and dispositional aspects of a property are numerically identical (Pq=Pd). That is consistent with the aspects being something which belong to, but are distinct from, a property. However, this is not the line that Heil’s identity theory takes. Heil expresses general dissatisfaction with the idea that a property could have an aspect, asking what it would even mean for a property to have an aspect (2003, 119).

Rather than posit distinct intrinsic aspects of a property, the identity theory holds a three-way identity between a property, its dispositional nature, and its qualitative nature:32

32 Note the change of language here. ‘Aspect’ changes to ‘nature’ (or simply ‘dispositionality’ and ‘qualitativity’) from the DAI to the identity theory. My impression is that this change of language is meant to emphasize the fact

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If P is an intrinsic property of a concrete object, P is simultaneously dispositional and qualitative; P’s dispositionality and qualitativity are not aspects or properties of P; P’s dispositionality, Pd, is P’s qualitativity, Pq, and each of these is P: Pd=Pq=P (2003, 111). The qualiativity of a property just is its dispositionality. Therefore, a property is individuated by both its qualitative nature (as in in some forms of quidditism) and its dispositional profile (as in structuralism).33 The difference between the identity theory and these other views is that the qualitative nature and dispositional profile of a property are numerically identical. Indeed, they are numericaly identical to the property itself.

Despite this three-way identity claim, there are several points in which the identity theory agrees with the earlier DAI interpretation. Heil and Martin make use of the same notions of ‘dispositional’ and ‘qualitative’ that were explicated in the DAI interpretation. Indeed, Heil says that:

I shall use ‘dispositional’ to designate properties that bestow powers on their possessors in the following sense: it is solely by virtue of possessing a given dispositional property that an object possesses a given power. Dispositional properties, if there are any, have their powers ‘built in’ (2003, 79).34

So, the identity theory endorses the same notion of the dispositionality that the DAI interpretation holds. Objects have certain powers in virtue of instantiating a property with a certain dispositional nature. The important caveat here is that an object which instantiates a property does not have powers in virtue of an aspect of the property.

that the dispositional nature of a property is not something distinct from the property itself, as we would have in the DAI. 33 This is an imprecise and tentative articulation of the individuation conditions on the identity theory. In the following chapter, I will make the individuation conditions for this view of properties more precise. 34 Heil provides this definition of ‘dispositional’ before he articulates his identity theory. According to his identity theory all properties (including non-fundamental properties) are dispositional.

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Rather, that in virtue of which a property bestows powers on objects that instantiate it is not something distinct from the property itself.

Let’s take stock. The identity theory maintains that P=Pd=Pq. Properties are both dispositional and qualitative, and the dispositionality/qualitativity of a property is not to be understood as something distinct from the property. In light of the explications the dispositional and qualitative natures of a property given above, we can reasonably translate this three-way identity as saying: A property is that in virtue of which objects that instantiate it have some of the powers and qualities that they do.

4.3 Identity Theory or DAI?

Is there any reason to prefer either the identity theory or the DAI? For the sake of argument, assume that the identity theory and DAI do not have any advantage over each other as answers to the question of property individuation. If this is true, then we have prima facie reason to accept the identity theory. To follow a general principle of parsimony, all other things being equal, it is better to accept the theory which postulates fewer entities. And it seems as though the identity theory postulates fewer entities.

Aspects are most plausibly second-order properties (Heil 2003, 119). So, DAI is committed to the existence of first-order fundamental properties and two different types of second-order properties: dispositional and qualitative aspects. For every property, there will also be a qualitative aspect (a second-order property) and a dispositional aspect (another second-order property). The three-way identity in the identity theory view eliminates this

47 commitment, because the powerful qualities view is only committed to first-order fundamental properties.

Recall Hawthorne’s parsimony argument against quidditism (see page 13). To reiterate,

Hawthorne asks “Why posit from the armchair distinctions that are never needed by science?”

(2001, 369). That is, if there is a choice between two rival theories, one ought to choose the theory (if there is one) that does not posit anything empirical science does not. DAI can be charged with positing aspects that are not posited by science. Science seems to posit only properties and their causal roles. So, when forced to choose between DAI and the identity theory, Hawthorne’s parsimony argument tells in favor of the identity theory. The identity theory only posits properties. By making the dispositional and qualitative natures of a property identical to the property itself, it would seem that DAI’s posits do not go beyond science.

But there may be another problem for DAI involving individuation. DAI and the identity theory are not explicitly about property individuation. Indeed, little is said by either Martin or

Heil concerning the individuation conditions for properties. However, the following seems to be a plausible account of the individuation condition on the DAI:

IDAI: Properties are individuated by their dispositional and qualitative aspects.

IDAI gives us an account of individuation which holds that two properties P and Q are numerically identical iff Pq=Qq and Pd=Qd. What are the alternative accounts of individuation for

DAI? It cannot be the case that properties are barely numerically distinct, for properties have intrinsic aspects akin to quiddities. So, on DAI, distinct properties cannot be barely distinct in the sense required by Locke’s extremely austere quidditism (see page 16). Further, properties cannot be individuated as they are in moderately austere quidditism (see page 16). On

48 moderately austere quidditism, properties are individuated by being distinct qualitative natures

(so P=Pq). According to DAI, properties aren’t basic qualities as they are on moderately austere quidditism. Rather, properties have qualitative natures, so P≠Pq. So, these two ways of understanding property individuation are out. Furthermore, any theory of individuation one adopts would need to do justice to both aspects, since Martin claims that neither aspect has any ontological priority. Thus, we must appeal to the aspects of a property for individuation.

The problem is that the offered account of property individuation on DAI (P=Q iff Pq=Qq and Pd=Qd) leads to skeptical concerns akin to those facing quidditism. It follows from this individuation condition that: P≠S if Pq≠Sq and Pd=Sd. This will lead to the skeptical concern noted by Shoemaker which arise out of the possibility of two distinct properties sharing the same role

(see pages 19-20). One may try to abate this worry by holding that a property necessarily possesses its aspects, but this would not get one very far. P and S could both necessarily share the same dispositional aspect while necessarily not sharing their qualitative aspects. There is nothing about one property necessarily possessing a dispositional aspect that prevents another property from sharing the same dispositional aspect.35

There are two broad ways of circumventing this skeptical concern. One way is to add a postulate that would block the interference from P=Q iff Pq=Qq and Pd=Qd to P≠S if Pq≠Sq and

Pd=Sd. An initially plausible approach would be to add that the distinct aspects of a property are necessarily related. In any world in which a property has the qualitative aspect q1 it would have the dispositional aspect d1, so it could not be the case that S could have the same dispositional

35 This response is analogous to my arguments that non-recombinatorial quidditism gives rise to skeptical concerns (see pages 21-22).

49 aspect as P without also having the same qualitative aspect. This would successfully block the inference, since P would be numerically identical to S. However, some explanation of the necessary connection would be required.

One such explanation would consist in endorsing an intermediary step between DAI and the identity theory according to which the dispositional and qualitative aspects of a property are identical. This is not DAI proper, because a property no longer has two distinct aspects. So, it would consist in rejecting DAI in favor of a different view.36 Of course, we could also explain the necessary connection by equating the two aspects of a property with the property itself, but here we would have the identity theory and not DAI. In general, there is nothing internal to

DAI that would explain a necessary relation between the aspects. So, to block skeptical concerns, the proponent of DAI could accept a necessary connection between a property’s two aspects. However, any explanation of this necessary connection seems to involve giving up DAI.

The proponent of DAI could also argue against the individuation condition I have provided. There are two moves here: (i) properties are individuated solely by their dispositional aspects or (ii) properties are individuated solely by their qualitative aspects. It should be clear that (ii) is a non-starter if one hopes to avoid skeptical worries. If properties are individuated by their qualitative aspects alone, then nothing would prevent the recombination of dispositional aspects. However, (i) would stop the skeptical concerns. It would be the case that P=Q iff Pd=Qd, so it would not follow that P≠S if Pd=Sd. But what makes dispositional aspects so special?

Dispositional aspects and qualitative aspects are, according to Martin, ontologically on par.

36 The same result follows if one endorses either P=Pq or P=Pd. Since there would not be two aspects in either case, it would constitute giving up DAI.

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Neither is more basic, and they are both intrinsic to the properties which possess them. The only difference is what each aspect contributes to the objects which instantiate properties with those aspects. I cannot see anything special about the contribution of certain powers to objects that would make the dispositional aspect responsible for individuation.

A more pressing concern with (i) would be that it seemingly deprives the proponent of

DAI of motivation for postulating the qualitative aspect of a property. It has been maintained that a property’s dispositional role is sufficient to account for what theorists initially took to be purely qualitative features of objects. Take shape properties as an example of what was once considered a paradigmatically qualitative (non-dispositional) property. Stephen Mumford has said that:

The shape of a thing clearly does dispose it to behave in a certain way…. It might be claimed that the essence of a shape is not to be found in powers but in some geometrical definition.… But this assumes that geometrical properties are also not powerful. Can any object that possesses those geometrical properties [of sphericity] not behave as a sphere does…. But are there other possible worlds in which rectangles behave like circles? It is dubious that there are (2009, 97-98).

The point of this passage is to say that paradigmatically qualitative features of objects can be reduced to the powers that the objects possess in virtue of instantiating a dispositional property. And if the DAI theorist commits to the claim that properties are individuated by their dispositional aspects, and we have reasons to believe that the role a property plays can account for the qualities that the property bestows on objects, then there seems to be no reason to posit a qualitative aspect. Such a view, while perhaps having its own merits, deprives the proponent of DAI of motivation for positing qualitative aspects.

DAI faces both concerns about parsimony and skeptical concerns that result from the recombination of dispositional aspects. One way to circumvent this problem was to pose a

51 necessary connection between the two aspects of a property. However, offering an explanation of this necessary connection would plausibly require giving up DAI. Additionally, the proponent of DAI could place the burden of individuation onto a property’s dispositional aspect, but such a view is unmotivated and deprives the proponent of DAI of the need to postulate a qualitative aspect.

The identity theory does not face these same problems. It avoids problems with parsimony because of the identity between a property and its dispositional and qualitative natures. Additionally, the identity prohibits the recombination of dispositional natures by explaining the necessary connection between these natures (and the property) in terms of the three-way identity. So, the identity theory is preferable to DAI as a theory of property individuation. In the next chapter, I will explore various ways of providing individuation conditions for properties on the identity theory. I will ultimately argue that the identity theory should be viewed as a version of moderately austere quidditism.

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Chapter 5: Conclusion

My goal in this chapter is simple, though the road to get there is not. I will attempt to sketch a single theory of property individuation for the identity theory (hereafter ‘IT’) that does justice to the nature of properties qua dispositional and qua qualitative. Since P=Pq=Pd, any individuation condition given for IT must do justice to each way of thinking about a property.

While this may seem simple, I will argue here that recent attempts to give an individuation condition for IT placed the burden of individuation on Pd while failing to take Pq seriously. My final position will be that IT is best understood as a form of quidditism that I will call ‘powerfully qualitative quidditism’. I do not claim, however, that either Martin or Heil would be sympathetic to this position. Rather, I claim that the view is consistent with what they say about properties, and that it is a tidy individuation condition for IT. I will argue that the view that emerges is preferable to the sort of quidditism discussed in chapter 2 and to structuralism.

5.1 Potential Individuation Conditions for the Identity Theory

Prima facie, there are three ways that a property may be individuated on IT:

(i1) Properties are individuated simply by being the property that they are and not some other property. In other words, whether two properties are identical or distinct is a brute unanalyzable fact. (i2) Properties are individuated by their dispositional natures. (i3) Properties are individuated by their qualitative natures.

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Given the three-way identity in IT, (i1)-(i3) are (or at least may be) different ways of making the same claim. If what individuates a property is its dispositional nature, and Pd=Pq=P, then a property is also individuated by its qualitative nature. If these natures are brute and unanalyzable then (i1) holds as well. I will say more on this entire picture below, but for now I want to focus on (i2).

5.2 A Problem with the Directionality of Dispositional Natures

What does it mean for a property to be individuated by its dispositional nature? Henry

Taylor argues that, on IT, properties are individuated by the powers that they bestow on the objects which instantiate them (2018, 1436). To understand individuation this way is to say that a property is individuated by the set of stimulus and manifestation conditions of the powers that it bestows on the objects which instantiate it. This leads Taylor to endorse a particular dependence direction of properties and the powers they bestow:

(D1) The powers a property with a dispositional nature bestows on the objects that instantiate it determine the identity of the property.

Here, properties depend on the powers they bestow to be the properties that they are.

Yet it is not clear that this is the proper direction for IT. Consider the following:

(D2) An object possesses certain powers in virtue of instantiating a property with a certain dispositional nature.

The direction of dependence in D2 has been reversed from that given in D1. If D2 holds, then a property’s dispositional nature is ontologically prior to the set of powers that a property’s instances bestows on objects. Yet if this is the case, a property, which is numerically identical to

Pd, cannot be individuated by the powers that the property’s instances bestow. For a property

54 to be individuated by the powers it bestows, it would be dependent on those powers.

According to D2, the powers are dependent on the property. Since dependency relations are anti-symmetrical, D1 and D2 are mutually exclusive. However, as I have explicated IT in the preceding chapter, D2 is the direction of dependence endorsed by IT.

So, should the proponent of IT choose D1 or D2? Since (i2) and (i3) are different ways of expressing the same individuation condition, then any individuation condition that applies to one will apply to the others. So, if one chooses D1 and applies it to (i2), then it will apply to (i3) as well. The IT theorist would be forced to say that a property’s qualitative nature is individuated by the powers that a property’s instances bestows on objects. But this seems wrong.

Consider a world with nothing but objects instantiating two distinct properties that I will call ‘blueness’ and ‘yellowness’. Objects which instantiate blueness attract objects which instantiate yellowness and repel other objects which instantiate blueness; objects which instantiate yellowness attract objects which instantiate blueness and repel objects which instantiate yellowness (Heil 2012, 74).37 Now, if D1 is accepted, then blueness is individuated by the power it bestows on objects which instantiate it – the power to attract yellow objects and to repel blue objects. Likewise, yellow is individuated by being a property whose instantiation has the power to attract blue objects and repel yellow objects.

An application of D1 would completely individuate blueness in terms of the power to attract yellow objects and repel other blue objects that blueness bestows on its instances. But this would lead us back to the symmetry problem, because blueness and yellowness bestow

37 I have altered Heil’s example for the sake of explication.

55 symmetrical powers on the objects which instantiate them (see pages 34-40). Additionally, Heil thinks that individuating a property by the powers that it bestows on objects leaves out the qualitative nature of the property. It isn’t that blueness is individuated solely by the powers to attract yellow objects and repel other blue objects that it bestows on its instances and yellowness is individuated solely by the powers to attract blue objects and repel other yellow objects it bestows on its instances. If that were the case, we wouldn’t have anything clearly sufficient to individuate the distinct qualitative natures of these properties. What we want to say instead is that it is in virtue of the fact that a blue object instantiates a property with a certain qualitative nature it has the power to attract yellow objects. Similarly, we want to say that it is in virtue of the fact that a yellow object instantiates a property with a certain qualitative nature that it is attracted by blue objects. Along this vein, Heil says that:

You might be skeptical that powers have the reciprocal character I have attributed to them. Maybe all it takes is that blue spheres have an attractive power; yellow spheres passively cooperate. What, then, distinguished the power possessed by blue spheres from other powers? It is a powers to attract yellow things…in virtue of their yellowness….we have a qualitative mode of individuation for a power (Heil 2012, 74).

It is in virtue of the qualitative nature of yellowness that objects which instantiate it are attracted by blue objects. The qualitative properties play an important role in explaining why objects which instantiate them behave the way that they do.

I maintain that accepting D1, and hence Taylor’s position, fails to do justice to the role that the qualitative nature of a property plays in the powers of objects which instantiate it. If a property can be wholly individuated by the powers that a property bestows on objects which instantiate it, then there is no place for a qualitative nature in IT. For, the qualitative nature of a property is left out of the explanation of what individuates a property. It makes no sense, then,

56 to say that a property is individuated by its qualitative nature. We would only need (i2) to individuate a property.

Perhaps this would be acceptable to some. If Pq=Pd, then it is fine if all individuation is reduced to the powers that a property bestows on objects which instantiate it. However, E.J.

Lowe (2006, 138) has argued that such a position is susceptible to a regress objection. Let us imagine that there are three properties: x, y, z. If we want to individuate x by the powers that it bestows on objects, then these powers will be cashed out in terms of the stimulus and manifestation conditions under which some object would instantiate a new property. Let us say that an object O1 which instantiates x would be stimulated by the instantiation of y and manifest the new property z. Yet z would be individuated by the stimulus and manifestation conditions of the powers that it bestows on objects, which would be further properties that would need to be individuated by the stimulus and manifestation conditions of the powers that those properties bestow on their instances, etc. In the imagined world with only three properties, this clearly leads to a vicious circularity in which every property is individuated by appeal to a further property until the circle is closed. If we imagined a world with an infinite number of properties, then we could generate an infinite regress of properties being individuated by appeal to further properties.38

Bird (2007, 524) formalizes Lowe’s argument as follows:

(1) Every real property must have a determinate identity (see Bird 2007, 524); (2) The identity of a property is determined by the powers it bestows on objects that instantiate it (D1); (3) But this last premise leads to a regress, because every manifestation will be a property instance which has its identity fixed by further manifestations; (4) So, either there is an infinity of properties or there is circularity;

38 Note that this objection would also apply to structuralist accounts of property individuation.

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(5) Neither side of the disjunct can account for the identity of a property in a determinate way. (6) So, no real property can have a determinate identity.

The proponent of IT can avoid this argument by accepting D2 and thus rejecting (2). Of course, rejecting D1 leaves the proponent of IT at an explanatory disadvantage. D1 entails a theory of individuation, whereas D2 does not entail any individuation claim. So, it now falls on me to explicate the individuation conditions that can account for the direction of dependence in D2.

5.3 The Identity of Natures

I think that a more careful analysis of a property’s dispositional nature will shed light on an individuation condition that can account for the direction of dependence in D2. We already have Heil’s articulation of the dispositionality of properties as “it is solely by virtue of possessing a given dispositional property that an object possesses a given power” (2003, 79). With this in mind, I offer the following criterion that any x would have to satisfy to be identical to a property’s dispositional nature:

Dispositionality Condition: Any x is identical to a property’s dispositional nature iff x is intrinsic to the property and x is that in virtue of which objects that instantiate x have the powers that they do.

And I propose the following articulation for what it means for an object to possess certain powers: An object O possesses a certain power p1 iff

(i) O instantiates a property P; (ii) P has a non-empty set of reciprocal disposition partners R, such that, if O were to instantiate every member of R, then O would manifest a complete set of properties S appropriate to the co-instantiation of P and R.

What sort of thing could x be in the dispositionality condition (DC)? As I have argued above, certain objects have the powers that they do in virtue of instantiating properties with a certain

58 qualitative nature. In the “blue and yellow” world, it is in virtue of the blueness of one object that it attracts yellow objects. The explanation of the “blue” object having this power relies on our ability to invoke the qualitative nature of blueness, and it would seem that Heil wants to say that it is in virtue of the qualitative nature of the property we are calling ‘blueness’ that an object has the powers that it does.

Therefore, I propose that Pq should stand in for x in (DC). We would then hold that Pq is identical to Pd insofar as Pq is intrinsic to the property and Pq is that in virtue of which an object has various powers. We can re-articulate what it means for an object to possess a given power in the following way: An object O possesses a certain power p1 iff

(i) O instantiates a property with a certain qualitative nature Pq, (ii) Pq determines a non-empty set of reciprocal disposition partners R, such that, if O were to instantiate Pq and every member of R, then O would manifest a complete set of properties S determined by the co-instantiation of Pq and R.

This maintains that a property’s qualitative nature determines both the reciprocal disposition partners and the properties that will be manifested in any object that instantiates all of the reciprocal disposition partners.

The identity between Pd and Pq also plays an important metaphysical role. If there is any world w1 in which an object O1 has a set of powers p1 in virtue of instantiating a property with

Pq, then in any other world in which O2 instantiates a property with Pq, O2 will also possess p1.

Thus, the identity of Pq and Pd secures that the powers a property bestows are metaphysically necessary. A property with a certain qualitative nature will bestow the same powers on objects that instantiate it in every possible world in which the property is instantiated.

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5.4 A Kind of Quidditism

So far, I have argued for two claims regarding IT:

(1) A property cannot be individuated by the role it plays, and (2) An object has certain powers in virtue of instantiating a property with a certain qualitative nature.

Now, it follows from (2) and Heil’s articulation of dispositionality that a property’s qualitative nature is identical to its dispositional nature. If we suppose that a property is a qualitative nature, then it follows that a property is identical to its dispositional nature. So, we have a way to understand the three-way identity that makes IT unique. A property is a qualitative nature

P=Pq, it is in virtue of IT that an object possesses certain powers so Pq=Pd, and by transitivity of identity P= Pq=Pd. I take the identity between P and Pq to be brute and unanalyzable. With the appropriate articulation of dispositionality, we can then infer the three-way identity.

With this in mind, I suggest that IT is a form of moderately austere quidditism:

Moderately austere quidditism: fundamental properties are qualitatively distinct though their identity and distinctness is simple and unanalyzable (Smith 2016, 244).

Moderately austere quidditism appropriately captures the brute identity between P and Pq.

Since moderately austere quidditism alone does not capture Heil’s inference from P=Pq to

Pq=Pd, I suggest the following form of quidditism to account for this entailment:

Powerfully Qualitative Quidditism: properties are qualitatively and dispositionally distinct though their identity and distinctness is simple and unanalyzable.39

39 We could also articulate the individuation conditions for IT as moderately austere quidditism plus the condition that a property’s qualitative nature necessarily grounds the powers that it bestows onto the objects which instantiate it. For the sake of conciseness, though, I have built this condition into powerfully qualitative quidditism with the addition of ‘dispositionally distinct’.

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I take this position to be perfectly consistent with IT as I have articulated it here. A property is identical to its dispositional and qualitative natures and can be said to be those natures. When an object instantiates a fundamental property, it instantiates a simple and unanalyzable nature

(we could say ‘two natures’, but the identity renders this superfluous).

But this only entitles me to say that, on IT, a property can be individuated by Pq, not that this is the individuation condition the proponent of IT should accept. If the proponent of IT adopts Taylor’s suggested individuation condition (D1), three problems arise. By accepting D1, one cannot also accept D2, but D2 is the direction of dependence endorsed by Heil. Accepting

D1 also deprives the proponent of IT with the ability to do justice to the qualitative nature of the property. Lastly, the individuation condition in D1 would lead to both the symmetry and regress problems. It is only by adopting powerfully qualitative quidditism that the proponent of

IT preserves the important role for the qualitative nature of the property and is able to explain why that qualitative nature is the dispositional nature of the property.

Taken in context, this reason has more force than one may initially notice. The reason that one may be hesitant to say that IT is a form of quidditism is because IT places an emphasis on the dispositional nature of a property. And, it has been customary to hold that views which pose a sort of necessary relationship between a property and its dispositionality are in stark contrast to quidditism. Smith has already shown why this is a bad custom by carving out space for a version of quidditism that poses a necessary relation between a property and the role it plays. Here, I have tried to take that further and subvert the usual order. Since it is usually the focus on dispositionality that would distance a view from quidditism, it should strike one as

61 interesting that the reason to accept that IT is a form of quidditism relies on the roll that the qualitative nature of a property plays in its dispositionality.

I should also note that articulating IT as a form of quidditism does justice to all the ways of conceiving how properties are individuated on IT. I think that powerfully qualitative quidditism accomplishes this goal, whereas focusing on one of the individuation conditions (as

Taylor seemingly does) leads to a failure to do justice to a property’s qualitative nature.

Powerfully qualitative quidditism does not place the burden of individuation on any single nature of the property. Rather, by taking P=Pq as a brute and unanalyzable identity, and providing the correct conception of a property’s dispositionality, powerfully qualitative quidditism does justice to every way of conceiving of a property on IT.

I will conclude with this articulation of IT. I believe that it is supported by Heil’s work on

IT, as well as independently motivated by the problems which arise in articulating IT in different ways. Additionally, I have argued throughout this chapter that my articulation of IT can alleviate the skeptical concerns which arise from quidditism (section 5.4), the symmetry objection against structuralism (section 5.2), and Lowe’s regress objection (section 5.2). While the case that I have made for powerfully qualitative quidditism is defeasible, I believe that I have presented prima facie reasons to prefer it to the other theories of property individuation examined in this thesis. So, I will conclude will the modest claim that powerfully qualitative quidditism circumvents the problems with theories of property individuation that I have covered in this thesis.

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