The Metaphysics of Privileged Properties · 2018-12-28 · perform certain jobs, such as featuring in laws of nature, or grounding similarity between objects. Metaphysical posits

The Metaphysics of Privileged Properties

A thesis submitted to the University of Manchester for the degree

of Doctor of Philosophy in the Faculty of Humanities

2016

Aaron Wilson

School of Social Sciences

2

Table of Contents

Abstract ..................................................................... 5

Declaration and Copyright Information ...................... 6

Acknowledgements ................................................... 7

Part One: Theories of Privileged Properties ................ 9

Chapter One: Introducing Privileged Properties ....... 10

1.1 Against privileged properties .............................................................................. 10

1.2 Properties ............................................................................................................ 12

1.3 Theories of privilege............................................................................................ 18

1.4 Justifying privilege ............................................................................................... 25

1.5 A strategy for rejecting privilege ......................................................................... 32

Chapter Two: Questions of Privilege ........................ 37

2.1 Issues in privilege literature ................................................................................ 37

2.2 Degrees of privilege ............................................................................................ 40

2.3 Joint-carving ........................................................................................................ 48

2.4 Problems of comparative privilege ..................................................................... 51

2.5 Gunk .................................................................................................................... 53

2.6 Microphysical universals in Armstrong ............................................................... 56

2.7 Microphysical perfectly natural properties in Lewis ........................................... 61

Chapter Three: Roles of Privileged Properties .......... 70

3.1 Dorr and Hawthorne on naturalness .................................................................. 70

3.2 Dorr and Hawthorne’s methodology .................................................................. 73

3.3 The nature of a ‘role’ .......................................................................................... 75

3.4 Supervenience ..................................................................................................... 80

3.5 Independence, Empiricism and Laws .................................................................. 87

3.6 Similarity-making roles........................................................................................ 93

3.7 Magnetism, intrinsic epistemic value and accounting for physical privilege ... 101

3.8 The structure of part two .................................................................................. 105

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Part Two: Criticisms of Privilege ............................. 107

Chapter Four: Genuine Similarity ........................... 108

4.1 Introducing genuine similarity .......................................................................... 108

4.2 Facts of genuine similarity ................................................................................ 112

4.3 Goodman’s seventh stricture on similarity ....................................................... 118

4.4 Moorean similarities ......................................................................................... 122

4.5 Moorean and non-Moorean facts of genuine similarity ................................... 128

4.6 Against non-Moorean genuine similarity ......................................................... 131

4.7 Prevailing properties ......................................................................................... 134

4.8 Similarity and Supervenience ............................................................................ 137

Chapter Five: Counterfactuals and Similarity .......... 139

5.1 Possible worlds semantics for counterfactuals ................................................. 139

5.2 Variants of the Lewisian possible worlds semantics for counterfactuals ......... 142

5.3 Similarity and the analysis of counterfactual conditionals ............................... 144

5.4 The role of context ............................................................................................ 147

5.5 Privilege constraints on the weightings of similarity judgements .................... 150

5.6 Privileged properties and the counterpart relation .......................................... 157

5.7 Privileged properties and the ordering of worlds ............................................. 161

5.8 Conclusion ......................................................................................................... 169

Chapter Six: Reference Magnetism ........................ 172

6.1 Privilege and indeterminacy of semantic content ............................................ 172

6.2 Lewisian interpretationism and convention ..................................................... 174

6.3 Global Descriptivism ......................................................................................... 180

6.4 Permutation arguments and the appeal to privilege........................................ 181

6.5 Henkin constructions as a new indeterminacy argument ................................ 184

6.6 Direct and indirect appeals ............................................................................... 193

6.7 Parochial eligibility as a better alternative to eligibility as naturalness ........... 197

6.8 Magnetism as work for privileged properties ................................................... 201

Chapter Seven: Implications for Theories of Privilege

.............................................................................. 203

7.1 Summary of findings ......................................................................................... 203

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7.2 Implications for support for privileged properties ........................................... 205

7.3 Prospects for egalitarianism ............................................................................. 207

Bibliography .......................................................... 212

Main text (including footnotes and endnotes) word count: 79814

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Abstract

Objects are characterised by their properties. If an object is a red postbox, then it has

the property of being red, and the property of being a postbox. This thesis is an attack

on a particular view of the metaphysics of properties, according to which some

properties are privileged over others. The most well-known theories of privileged

properties are Armstrong’s theory of sparse immanent universals (1979b) and Lewis’

natural properties (1983). According to their supporters, only privileged properties

perform certain jobs, such as featuring in laws of nature, or grounding similarity

between objects.

Metaphysical posits are theoretically virtuous if they can account for a range of

different phenomena in a relatively parsimonious manner. The ability of privileged

properties to perform a range of worthwhile ‘work’, therefore, is what justifies a belief

in them. The conclusion I reach is that a single group of properties is not capable of

satisfying the key roles commonly attributed to the privileged properties. Without

satisfying these roles in concert, a belief in mainstream versions of privileged properties

is not justified.

The first part of this thesis is devoted to an explication of privilege and the roles which

privileged properties are taken to perform. I conclude that three roles in particular,

Supervenience, Similarity and Magnetism are key roles for mainstream theories of

privilege. In part two, I show that the properties which satisfy the Supervenience role

are not the same as those which satisfy the Similarity and Magnetism roles. In the final

chapter of this thesis I discuss the implications of my findings for support for theories

of privilege.

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Declaration and Copyright Information

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.

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7

Acknowledgements

The following persons deserving of thanks are listed in chronological order of

contribution rather than importance. This list is incomplete and excludes the others too

many to name whose feedback in seminars and at conferences led to the present work,

so to conserve space I will thank them as a mereological sum before singling out

particularly important figures for individual acknowledgement.

First of all, Robert Wilson, who could have written this thirty years ago if his father had

been Robert Wilson. My mother, Shirley Wadsworth, who at one point was doing more

for my education than I was. Lesley Brown and Lois McNay, at that point both fellows

of Somerville College, Oxford, where I was an undergraduate. The former taught me

how to do philosophy phlegmatically, the latter taught me the very opposite. Though

others have affected it subsequently, there is very little in the present makeup of my

thought processes that wasn’t put there first by one of these two. I’m particularly

reminded of Lois every time I teach. My wife, Georgina Berritta, for everything in my

life that isn’t work. Sophie Gibb, currently reader in philosophy at the University of

Durham, was the one who persuaded me that all the questions in the philosophy of

mind that I was interested in were really questions in metaphysics. Nick Shea and the

late E.J. Lowe, not only for their expertise, but also for writing the recommendations

without which I would not have received the scholarship that made this thesis possible.

My supervisors, David Liggins and Chris Daly. Many people can tell you when something

has gone wrong, but David has the rare talent of being able tell you what that is and

why it keeps happening. Both the hardest and most important thing I’ve had to learn

to do over the past two years since David took over as my primary supervisor is not to

rely on him quite so much as I used to. My conversations with Chris have taught me a

great deal about argumentation, a little about how to make them and a lot about how

to break them. My former supervisors, Ann Whittle and Cynthia MacDonald, who

helped me through all the false starts and dead ends. Nathan Duckett, because whilst

friends are useful, interlocutors like Nathan are invaluable. It was my good fortune to

acquire one who is native to those reaches where I am a tourist.

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Finally, three philosophers in particular whose views are the foundation of the present

work. David Armstrong, David Lewis and Ted Sider. Although these three are not

exhaustive of ‘theorists of privilege’, they are by far the most forthright and the most

explicit regarding their commitments. In the closest possible world (whether that world

be an interconnected region of spacetime, a recombination of parts of the actual world,

or merely a very long sentence) lacking the contribution of even one of these thinkers

this thesis would have been much the poorer. Philosophy is the only academic

discipline where persistent opposition to someone’s life’s work is a higher form of

praise than agreement. If this is so, this thesis will show my esteem for these thinkers

far more effectively than can be expressed here.

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Part One: Theories of Privileged Properties

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Chapter One: Introducing Privileged Properties

1.1 Against privileged properties

This project aims to contribute to our understanding of properties. Everything that

exists does so in a certain way, and these ways of being are what we call the ‘properties’

of the object. For example, all gold has the property of being ductile, donkeys generally

have long ears and the Earth has the shape property of being an oblate spheroid.

Discerning properties is essential to our engagement with the world. They are the

means by which we categorise our surroundings and make predictions about their

future behaviour. We individuate material objects from their surroundings by

observing changes in properties from one region of space to the next. Reality is

characterised by the properties of the things which constitute it (Lewis, 1994a p474).

I aim to show that a certain view of properties originating in the last few decades is

mistaken. There are a number of different formulations of this view, but all hold that a

distinction can be made between ‘privileged’ or special ways of being and the rest. In

brief, theories of privilege state that a group of elite properties delineate categories in

an objective, fundamental reality that exists independently of any language or

behaviour of human beings. Privileged properties comprise a minority of the

categorisations that we employ in our everyday lives, but it is thought to be these

special properties which underlie the world as it appears to us. The goal of all scientific

inquiry is to discern some part of the structure of this fundamental level of reality, in

part through the identification of privileged properties.

Non-privileged properties, if they exist, are assumed to be derived from the privileged

properties. Where some object possesses some non-privileged property, it does so in

virtue of some part of the pattern of instantiation of privileged properties throughout

reality. An additional claim of theorists of privilege is that there are certain specialised

roles performed only by the elite minority of privileged properties, and never by those

which are not elite. The exact nature and extent of this specialisation differs in various

accounts, and is sensitive to differing opinions of the ways in which properties affect

the world in the first place, but common roles attributed to privileged properties

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include figuring in laws of nature, and of grounding relations of similarity between

objects.

Although the school of thought that I am concerned with is a modern phenomenon,

precursors to it have existed in philosophy since antiquity. It is present in the grand

cosmologies of the pre-Socratics, and Plato articulated a version of it through the

mouthpiece of Socrates:

The second principle is that of division into species according to the natural

formation, where the joint is, not breaking any part as a bad carver might.

(Plato 1952 265b-265e)

Despite the long heritage of this idea, the first modern attempt to really explain the

ontological underpinnings of the distinction and to draw conclusions from them can be

traced to the late 1970s, in particular D.M. Armstrong’s defence of Aristotelian

universals (1978b).1 According to Armstrong, properties are ‘sparse’ universals. A

universal is an entity that can be simultaneously located in indefinitely many regions of

space, contrasted with a particular, which occupies a single region of space and time

(Loux 2006 p19). At first glance, properties appear to have this ability of multiple

location, since many disparate objects may all possess one and the same property.

Objects like tables and chairs on the other hand seem to be particular in nature, since

they can only exist in a single space at a single time. Sparseness in this context means

that not every expression suggesting a way that an object is corresponds to a property-

universal. It is the recent philosophical tradition that has followed Armstrong (although

not always in taking properties to be universals) that I will be concerned with in this

project. This idea was notably adopted by Lewis, who over the next few years began

incorporating privileged, or ‘natural’ properties as he called them, into his wider

1 The distinction between ‘natural’ and ‘artificial’ kinds in connection with the topic of similarity was employed by Quine some years earlier (1969 pp114-138). Nonetheless Armstrong’s study of Aristotelian universals is the starting-point of a very specific tradition for engaging with properties, according to which privilege is a theoretical posit which needs to be justified on the basis of its philosophical utility. Quine did not seek to justify his talk of natural kinds, but simply took them for granted in formulating a response to Goodman’s ‘New Riddle of Induction’ (Quine 1969 p116, see also Goodman, 1983 pp72-81). An additional precursor to privileged properties comes from Quinton, who argued for the existence of properties, but denied that properties were as numerous as every class of particulars (Quinton, 1957 pp33-34).

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philosophical system as a solution to various theoretical problems in metaphysics

(1979a, 1983, 1984 and Langton and Lewis, 1998). The work of these two writers still

forms much of the backbone of the present debate over privilege, although in the years

since numerous philosophers have contributed their own commentary and alternative

formulations.

In the remainder of this chapter I will set out the scope of my investigation, and to

clarify the object of study. In particular, I will set out my use of the word ‘property’ in

this project in §1.2, and establish what I take a commitment to privilege to be in §1.3.

I will argue that supporters of privilege are inclined towards this view due to their

commitment to a scientific realist worldview, coupled with a wish to account for the

incredible success of scientific explanation in their ontology. An inclination towards a

certain viewpoint is not a justification for holding it. In order for privilege to be

acceptable as a theoretical posit, its supporters must show that we have reason to

endorse it. In §1.4 I will detail two kinds of justification offered for privilege, one based

on the apparent intuitive appeal of the theory, the other rooted in a notion of

‘theoretical virtue’. On the former account, privilege is attractive because it accords

quite well with our pre-existing notions of how the world works. On the latter account,

the virtue of a theoretical commitment lies in offering an explanation of various

philosophically interesting phenomena in a unified and economical manner. As it can

be very difficult to engage in worthwhile debate over whether a proposed notion has

intuitive appeal or not, it is the second of these justifications that is of the greatest

interest for the purposes of this investigation. I propose that the theoretical posit of

privilege is not capable of bringing together many of the roles that are considered most

important to it, and in §1.5 I will outline my strategy for showing this to be the case

over the course of this project.

1.2 Properties

As previously stated, the topic of this investigation is properties. However, recent

Western philosophical tradition offers no consensus on how to define a ‘property’.

There is disagreement over what exactly one is committed to when describing oneself

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as a realist about properties, or whether one may allow that statements which appear

to make reference to properties can be non-vacuously true or false if one does not class

oneself as a realist about properties. This section will be concerned with untangling

these competing conceptions and providing a careful account of what I will take a

property to be for the purposes of this investigation.

For Russell, to claim that there are properties is to claim that there is a category of

entities which are universal rather than particulars (1912 p28). Disparate objects can

all possess one and the same property, so to endorse properties is to endorse the

existence of entities which defy intuitive principles by being present in multiple

unconnected places and times. As objects which possess properties, such as tables and

chairs, are not capable of this kind of multiple realisation, it follows that properties are

distinct from the objects which possess them (1912 pp54-57). According to Russell

therefore, if there are properties, then they must be universals. More recently however

it has been proposed that properties may in fact be particular (see for example Williams

1953, Lewis 1983, Campbell 1990, Heil 2003, Ehring 2011). The range of terms

employed in the literature for properties and relations conceived of as particulars was

described by Armstrong as ‘truly horrifying’ (1997 p21), although the most popular

term nowadays is certainly Williams’ ‘tropes’ (1953).

Additionally we tend to see disagreement over whether or not there must be any

properties at all. We certainly are inclined to talk about properties as though they exist,

as we do when we say that the property of redness is found in both roses and cherries.

Examples like these lead Armstrong to conclude that if such sentences are true then

there must be properties (1978a pp58-63, see also Quinton 1957 pp37-38), however

an earlier proposal by Quine sought to eliminate them altogether. Quine argued that

the world was composed of particular objects, and nothing more (1948 p83). This

position, categorised by Armstrong as a kind of ‘cloak and dagger’ or ‘ostrich’

nominalism concerning properties, the latter name originating with ostriches’ fabled

tendency to stick their heads in the sand, has been taken up and defended more

recently by Devitt (1980), whilst some more cautious discussion of the ostrich’s themes

can be found in Van Cleve (1994) and Peacock (2009).

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There is further disagreement on the relation between properties and linguistic

expressions connoting ways of being. Some are happy to say that the meanings of all

predicates are supplied by properties, so that every predicate in fact makes reference

to a property. This is sometimes known as an ‘abundant’ conception of properties

(Lewis 1983 p191). Others prefer to reserve the word ‘property’ to pick out something

more specialised than this. This difference of opinion does not mirror a belief in

privilege. Although some proponents of privileged properties prefer the word

‘property’ to pick out something much rarer than the meanings of predicates (see in

particular Armstrong 1978b p11, Mellor 1991 p255, and Heil 2003 p26), others are far

more permissive in their use of the term (e.g. Lewis 1983 p194).

However we choose to define the word ‘property’, we will upset someone. Fortunately

however, most disagreement over the word is simply a matter of preference for one

kind of terminology over another. As long as it is clear what one takes the word

‘property’ to mean, it is possible to translate between differing uses of terms with

relatively little difficulty. Although there are indeed many substantive disagreements

concerning the way that objects and their attributes function, the meaning of the word

‘property’ is not one of them.

In this investigation I will adopt an abundant conception which takes a ‘property’ to

just be any way that a thing is, on the basis that this is the sense of the word which

most closely matches the way we speak of objects and properties in the vernacular.

Taking our everyday speech at face value, we attribute a great many different ways of

being to objects. We say that the White House and Bald Eagle are both symbols of the

USA, and that bottles of cologne and shower nozzles are both things found in a

bathroom, whilst none of these disparate objects are things likely to be found in outer

space. Our willingness to assert such things is part of the explanandum of a theory of

properties. Even if, as the supporter of privilege claims, there is a distinction between

the ways of being attributed to objects in examples like these and those ways of being

pertaining to some deeper level of reality, this does not seem like sufficient reason to

deny the word ‘property’ its most familiar reading, simply as a way that something is. I

will also take relations to be a kind of property that holds between multiple entities

rather than just one, as properties do. This is in keeping with the views of the majority

15

of theorists of privilege (in particular see Armstrong 1978b p75, Lewis 1983 p190,

Rodriguez-Pereyra 2002 p56). Throughout this project, whatever I take to be true of

properties can also be taken to apply to relations, unless otherwise noted.

Abundant conceptions of properties are very liberal, allowing even random collections

of objects to be united by a property possessed by just those objects and no other.

There are as many properties as there are ways of being, loosely construed, but we

have so far said nothing about whether there are ways which objects could be, and yet

no actual object is, or whether there are ways of being which nothing could ever

possess, such as the property of being a round-square cupola atop Berkeley college

(example from Quine 1948 p77). Similarly a question arises over whether there are

distinct properties which necessarily are possessed by the same set of objects, such as

triangularity and trilaterality. On all of these matters I will remain officially agnostic, as

nothing of great importance to the project at hand turns on my answers to them.

Where appropriate, I will accede to the position adopted by whichever theorist of

privilege is at that moment under discussion.

The most common argument against abundant conceptions of properties is the

supposition that properties must make a difference to the causal powers of the things

that have them. This position actually presupposes privilege. Not all ways that objects

can be make a causal difference to their objects, so the claim that all properties are

causal difference makers requires an understanding of the word ‘property’ as picking

out an elite category of entities distinct from other ways that an object can be.

Armstrong holds this view, maintaining that there can be no causally inert properties,

for if that were the case they would make no difference to the world and as such we

would have no epistemic access to them (1978b p11). Their uselessness would mean

that we would have no good reason to postulate them (Armstrong 1989 p7).

Armstrong’s insistence on all properties being causally efficacious is a constituent of his

own particular goals in developing a theory of properties in the first place (this view of

properties as necessarily causally efficacious is also shared by Shoemaker 1980 p233).

Properties are postulated to perform explanatory work, and the kind of explanatory

work Armstrong has in mind is not the kind that can be done by causally inert entities

(Armstrong 1989 p8). I do not reserve the word ‘property’ for theoretical postulates

16

which perform explanatory work, however. In using the word ‘property’ I aim to

describe the explananda of a theory of properties, the phenomenon which we hope to

account for. This is the phenomenon of objects differing with respect to their ways of

being, and these ways of being are what I call properties. Earlier we noted that the

tendency to speak as though objects have ways of being such as being a symbol of the

USA is widespread. It is the ability of objects to have ‘properties’ in this sense which we

hope to account for by a theoretical treatment of the metaphysics of properties.

Armstrong’s rejection of abundant, causally inert properties assumes by contrast that

the word ‘property’ is properly used to pick out the explanans of a theory of properties

instead, the means by which we account for the observed phenomena of objects and

their attributes.

The explananda of a theory of properties need not be a category of entities such

universals or tropes, and in fact may be as the ostrich nominalist claims them to be, in

which case the word ‘property’ would not refer to any entity at all. For convenience I

will nonetheless talk about properties as though they are entities. I will also allow

myself to speak of properties as ‘existing’ or being ‘instantiated’ by objects, although

this too is for convenience’s sake, and should not be taken as a commitment to any one

particular ontological status for properties.

For all the observed differences of opinion regarding properties and their ontological

nature, there are also a number of shared commitments amongst theorists of privilege.

Most importantly, they all share a commitment to an independent, objective reality,

the character of which is a matter of the distribution of properties within it.2 Properties

are therefore ‘worldly’, as opposed to being mental or semantic entities of any sort.

They are not categories which are brought into being by any actions of human beings.

2 This is true according to the definition of properties I offer. According to other competing terminologies, there may be more to the overall character of a world than just the distribution of properties within it. Laws of nature and modal facts need not themselves be properties, and so arguably play a role in characterising the world, over and above the distribution of properties. According to the loose definition I employ however, there will be such properties as being a world in which light travels at approximately 3.00×108 m/s in a vacuum or being a world in which certain modal facts are true, so any difference in laws of nature or facts of modality will make a difference to the properties of that world. My aim is for ‘property’ to simply mean any way that a thing can be, which can include facts about what laws are in operation there or what modal claims are true at that world.

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Properties do form at least some of the content of our language and mental states, but

they are not just this content (Mellor 1991 p257). There may be properties which no

sentient being will ever think or speak of, and the world had properties long before our

own existence. We do not create properties as tools to interact with the world, instead

we discover them in the world through empirical means, and subsequently come to

represent them in our minds and language.

This belief in an objective reality characterised by properties is compatible with my

loose account of properties as ‘ways of being’, although that may not seems

immediately apparent. My liberal conception of properties includes examples such as

being a President of the United States of America, or being within the borders of France.

These properties we do seem to create by dividing the world into countries and

assigning individuals public office within them. Granted humans do create countries

and titles, but the instantiation of the associated properties to various things can

nonetheless be thought of as being ‘out of our hands’. The borders of France are

created by human beings, but once this has been done the range of entities which have

the property of being within the borders of France is subsequently a completely

objective matter. No matter how many people insist that the Eiffel Tower is in Belgium

and not France, this will not make it true. This is because being within the borders of

France is but one way of describing an objective state of the world, albeit according to

metrics devised by humans. The only way the Eiffel Tower could be made to be in

Belgium would be to either shift the French border or to move the tower itself.

Another kind of potential counterexample is the instantiation of properties like being

frightening, or being appropriate. Whether or not an object is frightening is hardly an

objective matter, as it depends in large part on individual opinion. Likewise, what is

appropriate for one person may be extremely inappropriate as far as another is

concerned. I propose that rather than taking such cases to concern single properties

which are highly subjective in their application, we instead take them to concern

multiple distinct objective properties. For instance, when two people in possession of

all the facts disagree over whether or not a certain behaviour is frightening, this is

because one of them is ascribing a property to an event, perhaps frightening to

18

someone with a certain set of dispositions, which is not the same as the property that

the other is ascribing.

Just as there is agreement over the objectivity of properties, there are a number of

roles for properties about which there is a reasonably good consensus. Theories of

privilege are generally distinctive not in terms of the roles they believe properties as a

whole fulfil, but rather in the division of labour amongst properties. When two objects

are similar, for instance, this is because they have some property in common.

Properties and causation are likewise closely linked. All instances of causation depend

on how properties change or stay the same over time, and all forms of causal

explanation depend on some feature of the distribution of properties over time. When

a glass is dropped and shatters it loses the property of being intact and gains the

property of being broken, and we can explain this change in its properties in virtue of

the fragility of the intact glass and the hardness of the floor (see Oliver 1996 pp14-20

for a summary of the most common roles attributed to properties).

1.3 Theories of privilege

Theories of privilege vary considerably amongst themselves. The goal of this section is

to establish what exactly a theory of privilege is, what central commitments all versions

of privilege share, and the areas in which there is scope for disagreement between

them.

Theories of privilege vary with respect to their ideas of the roles which privileged

properties can be supposed to employ, the ontological status of properties themselves

(for instance whether properties are universals, tropes or sets of their instances) and

in terms of what differentiates the privileged properties from the non-privileged ones.

Armstrong for instance takes privileged properties to be universals, and at least at one

point was eliminativist with respect to non-privileged properties (1978b p10). In later

work he proposes that there are some properties and relations that are not universals.

These he calls second and third-class properties which are constituents of second and

third-class states of affairs (1997 p44), although the difference between the second and

third classes is not directly relevant for our current project. Armstrong’s view of these

19

properties which are not universals is complicated. He argues that at least in some

cases they are real features of the world and cannot be eliminated through paraphrase,

for instance when we attribute the non-universal (and hence non-privileged) property

of being square to an object. On the other hand, he claims that they represent no

addition in being to universals and particulars, in virtue of their supervenience on the

universals themselves (Armstrong 1997 p45). My focus in this thesis need only be on

those properties which Armstrong takes to be privileged however, and these are

universals.

Lewis, by comparison, takes both natural (privileged) properties and non-natural

properties to be entities of the same kind: sets of their actual and possible instances

across all possible worlds (1983 p190). He is officially agnostic with respect to how

some sets come to be privileged properties, noting that they may be those sets whose

members are unified by being instances of certain families of related universals, or that

the distinction may simply be a primitive one (1983 pp193-194).3 These differences

with respect to the ontological underpinnings of privilege, whilst interesting in their

own right, will not concern us in this project save to the extent that they make a

practical difference to the membership or functioning of the elite minority of privileged

properties in one or the other system.

Differences aside, theories of privileged properties are distinguished by the view that

amongst properties there is a certain objective minority which are responsible for

performing a range of functions which are not performed by the non-privileged

properties. A complete summary of all the roles variously thought to be performed by

the privileged properties and the relative importance that should be accorded them

will be the topic of chapter three, but I have already mentioned the most frequently

cited roles. It is commonly held that privileged properties alone make for similarity

amongst their instances, that they alone feature in causal laws, and that the

3 See also Rodriguez-Pereyra, whose Resemblance Nominalism inhabits a very similar ontology to Lewis’ (Rodriguez-Pereyra 2002). Rodriguez-Pereyra takes properties to be sets of actualia and possibilia according to the same modal realist framework endorsed in Lewis (1986). Ehring too takes properties to be sets of actual and possible particulars, but in his case the particulars which comprise the membership of sets which are properties are all tropes, and he seeks to replace Lewis’ extravagant ontology of possible worlds with an actualist theory of modality (Ehring 2011 chapter 7).

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distribution of natural properties throughout the universe comprises a minimal

supervenience basis for the instances of all non-privileged properties. What is

distinctive about theorists of privilege is not that they claim that there is some division

of labour amongst properties, for it is quite plausible to assume that some properties

play a greater role with respect to certain functions than others. Consider two dogs,

Fido and Rex. A property like being a dog seems to count significantly toward the

overall similarity of Fido and Rex, whilst the property of having one particular hair at

the tip of the left pinna which is bent at a thirty six degree angle seems to have a far

smaller effect. What is common to the theorists of privilege, however, is the claim that

all of these specialised roles are concentrated in the same group of properties. Theories

of privilege hold that those properties which make for similarity are the same ones as

those which feature in causal laws and which constrain meaning. It is this aggregation

of functions within the same minority which this investigation seeks to reject.

In terms of the definition of properties I offered in the previous section, the supporter

of privilege believes that it is possible to make out a distinction between two different

kinds of properties. One kind, the privileged properties, has sole responsibility for a

variety of specialised functions. The other kind does not. In defining theories of

privilege in this way I am inevitably going to group together theorists in some

unexpected ways. Eddon and Meacham, for instance, attempt to provide an alternative

to Lewis’ theory of natural properties that retains many of the advantages Lewis claims,

such as defining duplication, and in theories of causation and reference (Eddon and

Meacham 2015). Their proposal is to replace natural properties with ‘surrogate’

properties, which they describe as a set of properties that can effectively play the role

of natural properties in Lewisian accounts, but in a ‘reductionist-friendly way’ which

does not require the introduction of a primitive predicate of naturalness (Eddon and

Meacham 2015 p127). The surrogate properties are those which feature in laws of

nature, according to a Best Systems account of lawhood (I discuss this approach to laws

of nature in more detail in §3.5). On my account, Eddon and Meacham are paradigm

theorists of privilege, because they propose that a single group of properties, the

surrogate properties, perform a certain range of specialised functions. At the same

time, another proposed alternative to the Lewisian view of naturalness as a primitive

predicate, Taylor’s ‘theory-cosy’ properties, are not privileged properties, because on

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Taylor’s view the properties that perform these specialised functions only do so relative

to a scientific theory. Taylor’s account makes no place for an objective minority of elite

properties (Taylor 1993 p89, see also §1.5).

A denier of privilege need not deny the existence of properties which feature in causal

laws, or make for similarity. To deny privilege is not to claim that all properties fall into

the ‘non-privileged’ categories, but rather to deny that there are objective categories

of ‘privileged’ and ‘non-privileged’ properties in the first place.

The motivation for this view can be seen as an outgrowth of a particular picture of

mind-independent reality, one that wishes to respect the tremendous power of

scientific inquiry to better explain and predict events in the world. There is broad

agreement amongst theorists of privilege on scientific realism, to be contrasted with

scientific instrumentalism (Lewis, 1994 pp474-475, Armstrong 1978a pxiii, Sider 2011

p19). Chakravartty notes that ‘it is perhaps only a slight exaggeration to say that

scientific realism is characterized differently by every author who discusses it’

(Chakravartty 2010 §1.1). I will not therefore speak of scientific realism as a set of well-

established doctrines, but rather as a general set of attitudes about the nature and

purpose of scientific theories. Loosely, scientific realism holds that scientific theories

aim to describe the world as it actually is, rather than merely functioning as useful

heuristic devices for the purposes of making good predictions. In the context of

philosophy, scientific realism sees philosophical enterprise as continuous with the

natural sciences, aiming to enable clear and comprehensive thought about the nature

of the universe, rather than, for instance, simply distinguishing between meaningful

and nonsensical statements (Smart, 1963 pp1-8). Modern science is taken to be

successful precisely because the theories it proposes manage to capture some

elements of a genuine underlying structure to reality. The best explanation for the

accurate predictions which result from the nuclear model of the atom, for example, is

that this theory approaches the truth, and that the most basic chemical elements are

indeed composed of protons, neutrons and electrons in varying proportions. This is not

to say that scientific realism requires a belief in the literal truth of every scientific

theory. Scientific theories contradict one another, and many are ultimately proved

false. Supporters of scientific realism hold that there is such a thing as a factually

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correct theory, which does not just do a good job of predicting future events but

actually describes such events as they actually are. This correct theory may or may not

be similar to the current state of the art in the sciences. Given the assumption that

successful scientific theories succeed in capturing the true character of the universe it

is a relatively short, intuitive leap to suppose that there are indeed properties and

categories of entity corresponding to those described by physics on which the entire

character of reality supervenes.

It should be noted at this point that this supervenience base need not necessarily

correspond to the science of physics alone, although Armstrong and Lewis certainly

approach the topic of privilege with such a view (Armstrong, 1978a pp126-127, Lewis

1994a p474). It is not necessary that all privileged properties be physical. Lewis points

out that if there are possible worlds where physicalism is false, then in those worlds

the physical properties would not suffice to be a supervenience basis for reality. Such

worlds would see instances of privileged properties that are not encountered in our

own, relating to irreducibly non-physical substances like minds or spirits (1983 p209).

Also, an alternative approach to privilege based on the Lewisian theory is suggested by

Schaffer, which disputes the claim that all privileged properties must be physical in our

world, even if there are no irreducibly non-physical substances. Instead Schaffer claims

that since there appear to be causal laws operating at the level of biology and

chemistry, just as there are at the level of physics, chemical and biological properties

should be regarded as equally privileged. This he calls the scientific conception of

natural (privileged) properties, rather than the fundamental or microphysical view

associated with Armstrong and Lewis (Schaffer 2004 p92).4 Amongst modern theorists

of privilege, however, Schaffer is the only notable exception to the microphysical

approach. Unless otherwise noted, I will henceforth assume a microphysical approach

to privileged properties, in keeping with the dominant line of thought on this issue.

4 Lewis did allow that the properties of higher-level sciences could play some roles associated with ‘natural’ properties, but in a lesser, more reduced sense. These ‘somewhat’ natural properties were to be contrasted with the ‘perfectly’ natural properties, which in the actual world are entirely microphysical (1983 p192). Schaffer’s argument aims to show that the properties of higher-level sciences may actually be regarded as perfectly natural, alongside the microphysical. I will reserve a full discussion of privilege as something which comes in degrees and the issues which arise from this notion for §2.2.

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We have so far said nothing about what roles the theorists of privileged properties take

non-privileged properties to perform. Amongst theorists of privilege, Lewis is the only

one to explicitly defend a specific role for non-privileged properties. Lewis claims that

non-privileged properties can benefit us by providing an adequate supply of referents

for linguistic expressions. Often we will be faced with sentences which appear to refer

to non-privileged properties, as in:

‘Red resembles orange more than it resembles blue.’

‘Red is a colour.’

In such cases, it isn’t clear what individual names like ‘red’ can be taken to denote, if

not properties (1983 p194). It is this concern which prompts Lewis to take properties

to be sets of their actual and possible instances rather than universals, although as

previously noted, the members of privileged property sets may indeed be unified by

instantiations of a universal (1983 p192). In no small part it is the identification of

properties with sets which secures this role for non-privileged properties. Sets are as

abundant as ways of grouping together objects, so even if one’s primary interest is in

the sets which correspond to privileged properties alone, one gets all the non-

privileged properties for free as part of the commitment to properties as sets. That

said, Ehring (2011 p9) and Rodriguez-Pereyra (2002 p56) are both theorists of privilege

who identify properties with sets, but only in the case of privileged properties. They

hold that sets which do not correspond to privileged properties are not properties at

all. Those who identify properties with sparse universals or tropes (rather than sets of

tropes) on the other hand tend towards being eliminativist about non-privileged

properties altogether, denying that there are any such properties as being a table,

being a chair or being a person (Armstrong 1978b p11, Heil 2003 p49).

A theory of privileged properties is one which reserves much of the metaphysically

interesting work for a select group of properties, and insists that there will be some

properties which do not fall into this select group. If this is all the definition we have,

however, then we are in danger of casting our net too wide. Previously we suggested

that denying privilege is simply to deny the existence of the select group of properties

which is solely responsible for the required range of roles. Does this then mean that a

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denier of privilege is committed to the claim that every property out of the abundant

multitude performs all of these roles to the exact same extent? This cannot be what a

denial of privilege requires, as it is simply implausible.

Consider a paradigm case of a non-privileged property, which we shall call Florb. There

are only three things which are Florb. One is the Eiffel Tower, one is a particular pear

that was picked and subsequently eaten in the Summer of 1732, and the other is the

left thumbnail of the Statue of Liberty. If the property of being Florb manifests any

causal role at all, then this is with respect to the way in which individuals informed

about which objects are Florb will be disposed to speak of them as being so. In any

event we could hardly claim that there is a law of nature which involves all and only

those things which are Florb.

Denying that Florb plays any kind of causal role would not suffice to make one a believer

in privileged properties. One can deny that there are privileged properties and still hold

that not every property performs every job. What distinguishes a theory of privilege is

that it takes a wide range of functions to be performed by one and the same group of

properties, generally considered to be a minority of the total number of properties that

actually exist. A denier of privilege need only claim that there is no such minority which

is solely responsible for all of these functions and that no property outside of this

minority ever performs these functions. It might be that there are some properties, like

Florb, which we are reluctant to describe as relevant to causation. Such properties will

nonetheless make for similarity amongst their instances, if only when we have a

particular interest in grouping objects by their Florbness. This claim is admittedly

controversial. In §3.6 I offer a detailed account of similarity that supports my claim that

being Florb can make for overall similarity between objects in appropriate contexts. In

chapters four and five I go on to defend the claim that the role of making for overall

similarity is indeed one for which non-privileged properties are required.

To summarise the findings of this section, a theory of privilege is one which holds that

it is possible to map a clear distinction between those properties which perform such

roles and the rest. A denial of privilege is the claim that no such distinction can be made.

According to the privilege sceptic, different properties will do different jobs to varying

extents, but it is not the case that there is a group of properties which are solely

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responsible for a variety of different jobs. Now we will move on to looking at how the

supporter of privilege justifies their position.

1.4 Justifying privilege

In the preceding section we noted that the supporters of privilege are led to this

supposition by a desire to build a metaphysical system around scientific realism. This

may be the initial motivation for preferring such a view, but this alone does not amount

to a defence of privilege as a theoretical position. We can be inclined to prefer one kind

of theory over another by psychological factors irrespective of whether such theories

are ultimately defensible. The real work of metaphysics in justifying a subscription to

the theories towards which we are inclined. Coming to an understanding of what is

wrong with the idea of privilege therefore requires an understanding of how its

supporters justify a belief in it. There are two main approaches to this that I will explore

in this section.

On the one hand, it is sometimes proposed that the agreement between privilege and

our intuitive idea of how reality works is so strong that it may safely be assumed from

the outset. For most theorists of privilege this is the view that they already take towards

scientific realism, so it is not unfair to assume that they might also be sympathetic to a

justification of privileged properties on the same basis. Even so, there is only one recent

defender of privilege who explicitly says that part of the justification for such a

theoretical posit is its intuitive plausibility. Sider proposes a version of privilege which

he calls ‘structure’, and argues that the existence of such a thing follows from the most

natural way of thinking about the world. This is the position he calls ‘knee-jerk realism’

(Sider 2011 p18). Like all other theorists of privilege, Sider maintains that there is an

objective reality, whose character we discover rather than create. He notes that this is

an unargued-for assumption of his, and that as deep as his conviction of it goes, he

would have no idea how to convince someone who did not share this intuition. In the

belief in an objective reality Sider does not depart too far from the versions of realism

that underlie Lewis and Armstrong’s theories of privilege. However, there is an

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additional feature to knee-jerk realism that is not an explicit commitment of either of

these two. Sider claims that knee-jerk realism actually commits one to privilege.

Suppose we have two sets of sentences A and B, the members of both of which are all

true. The sentences of A jointly offer a complete description of a single object x, in

terms of the fundamental physical particles which comprise it and the fundamental

physical properties it has. B also gives a complete description of x, but whereas the

former used only terms in the language of fundamental physics, the sentences of this

set employ bizarre, unnatural terms. Whereas the first set of sentences plausibly

includes a sentence like ‘At such-and-such a position within x, there is a particle which

has the property is an electron’, the second set contains an analogous sentence like ‘At

such-and-such a position within x, there is a particle which has the property is either an

electron or the Statue of Liberty’. According to Sider, knee-jerk realism includes a

requirement that we view the descriptions of x offered in the first set as better than

the descriptions in the second set. As he puts it, ‘knee-jerk realism is incompatible with

the belief that it’s just optional to think in physical terms, that it would be just as good

to pick wholly arbitrary carvings of the world… and think in those terms’ (Sider 2011,

p19). Furthermore, insists Sider, knee-jerk realism requires that the superiority of

certain ways of talking about the world must be objective and not grounded in the

simplicity or usefulness of the privileged terms. It is natural to instead conclude that

this superiority is a matter of the former set capturing a privileged structure to reality

(Sider, 2011 p19). In summary, Sider proposes that privilege is simply a corollary of the

kind of realism which Lewis and Armstrong assume in the first instance, and as such is

able to ‘inherit’ all of the plausibility of Lewis and Armstrong’s realism.

I do not hold that an inclination towards this kind of realism need also incline one

toward a belief in the superiority of certain ways of categorising reality. I see no

deficiency in a mind-independent reality with a wholly objective character that lacks

any distinction between privileged and non-privileged properties. Sider himself accepts

the point that attributions of gerrymandered categories like is either an electron or the

Statue of Liberty can be true, and we have already shown in §1.2 that the membership

of objects within those categories is just as objective as the supposedly privileged

properties. We should be perfectly content with an undifferentiated bundle of

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objective truths about the arrangement of properties in reality. Presented with such

knowledge, it is hard to see what else we could want. This however is the nature of

disagreements over intuition. As Sider himself has pointed out, when two people

disagree with respect to which of two positions is the more intuitive there is very little

that can be done by one to persuade the other (2011 p19). It seems as though we need

something more than just talk of agreement with our pre-theoretical understanding to

move beyond the impasse. For this reason my project will focus on the other key form

of justification for privilege, which takes theoretical posits to be acceptable just in case

they can be shown to be superior, according to a system for measuring the theoretical

virtue of a position, than some alternative.

The most well-known version of this justification comes from Lewis (1983).

Methodologically, Lewis held that metaphysical theories were to be constrained by

their ‘fruitfulness’ (Lewis 1991 p4). Lewis’ thought is that we would be justified in

positing a theory of privilege provided that in doing so we were able to account for a

range of differing phenomena with the greatest possible simplicity and unity (1983

p200). This defence mirrors the reasons he gives for realism about mathematics and

possible worlds (Lewis 1991 p4, see also Nolan 2005 pp205-206).

According to Lewis, it is the job of a systematic metaphysics to give an account of every

purported fact (1983 p198). By this we can take Lewis to mean that for every seemingly

true proposition, there is some work for a metaphysician to do in order to

accommodate that apparent truth into their worldview. If, as we suppose, the adult

composer of The Marriage of Figaro is identical with a baby born in Salzburg in 1756,

then we are owed an account of how objects with different physical characteristics can

nonetheless be numerically identical, in this case Mozart. If roses are red, then we are

owed an account of how material objects like roses can all come to possess this quality

of redness. The metaphysician has a number of options for giving accounts of these

facts. On the one hand, she may deny that it is really a fact at all, which would thereby

absolve her of the need to say anything further. If she accepts facts of this type

however, she must either accept them as primitive or else provide some analysis of

them which explains why they obtain. For Lewis, an analysis is just one type of account

that we can give of a fact (1983 p198, see also §3.3). In this context, ‘primitive’ simply

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means that a term has no further analysis. An analysis of the identity of the two Mozarts

might make reference to the unbroken bodily or psychological continuity between the

baby at one time and the adult composer at another. The redness of roses could be

explained in terms of their resemblance to all the other things which are red. The only

requirement is that there should be no accepted fact for which no account is offered.

In providing an analysis of purported facts, inevitably new purported facts are

generated. The resemblance of all red things itself must subsequently be accounted

for. Regardless of one’s skill as a philosopher, no one can keep on analysing each new

tier of facts indefinitely. Sooner or later, every chain of analysis must end with a

primitive. There may be nothing further that can be said about why all the red things

resemble each other, save that this is just what things that are red do. As inevitable as

it is that every theorist must take some facts as primitive however, there is something

unsatisfying about a theory which takes more than it needs to as primitive. According

to Lewis, a metaphysical theory should be as simple as possible, and that simplicity is

in part a matter of limiting the amount which one takes to be primitive (Lewis 1973a

p87; 1983 p200, however see also Rodriguez-Pereyra 2002 chapter 12 and Oliver 1996

pp2-7 for a more detailed account of this kind of parsimony consideration).

Although so far we have spoken of facts as being primitive just in case no analysis is

offered of how they come to obtain, this is not the only way we can talk about what it

means to take things as primitive. In common parlance amongst metaphysicians it is

common to talk about ontological categories such as universals and particulars as

primitive just in case these categories cannot be reduced to any others. Reduction in

this sense simply means to subsume certain categories into others (Oliver 1996 p7). For

example, Campbell endorses a single-category ontology of sparse tropes which takes

objects to be nothing more than bundles of these tropes standing in a specific relation

with one another, which he calls compresence (1981 p132). Recall that a trope is a

particularised instance of a property, so instead of a single property of redness which

is shared amongst all red things, Campbell is proposing that the redness of things is a

matter of having a single red trope, and that every red thing has a numerically distinct

red trope. Contrast this with trope theory as it is put forward by Williams, in which

objects are not reducible to bundles of tropes. For Williams, both objects and tropes

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are particular rather than universal, but particulars of two different types. A chair for

Williams is the combination of the object, which itself lacks all character, and its tropes

(1953 p113). We can easily integrate such talk with our previous talk of primitive facts.

We can say for instance that the category of particular objects like chairs and tables is

primitive just in case no analysis is offered for facts about the existence of such objects.

Campbell does offer such an analysis, for he analyses facts about chairs in terms of facts

about bundles of compresent tropes. Williams does not, for although he is content to

give an analysis of facts about the properties of chairs, the existence of any particular

chair is not given any such analysis. We can do something similar for talk of primitive

predicates or primitive logical expressions. A predicate is primitive just in case no

analysis is given for atomic facts which include it. I will persist in talking about primitive

predicates or notions, and primitive ontological categories so understood, on the

assumption that accounts of these can be given in terms of unanalysed facts.

A theoretical posit therefore is a good one just in case it leads to an explanatorily

powerful metaphysics which limits the total number of primitive notions it requires.

The supporters of privilege take it that this particular notion achieves this. Inevitably,

the introduction of privilege will itself require some new primitive notions enter into

our worldview. There are many ways of accounting for the privilege of properties, all

of which require some addition be made to the theory as a whole. One option would

be to take privilege itself to be primitive, and refuse to give an analysis of why certain

properties are privileged and some are not. Lewis considers this as one active possibility

(1983 p193), while Sider explicitly adopts this kind of primitivism (2011 pp9-10).

Alternatively, we could take the privileged properties to simply be universals, which of

course would require an additional ontological category besides particulars be

accepted. Another would be to equate them with those sets of objects whose members

all resemble each other to a certain minimum degree, but this would require an

account of how objects come to resemble in the first place, which might appeal to

universals again, or simply take facts of resemblance to be primitive (this latter option

is espoused by Rodriguez-Pereyra, 2002). Ultimately, however, its supporters believe

that the benefits of privilege to the simplicity of a total systematic metaphysics

outweigh whatever additional complexity it requires to make out.

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At this point it might be supposed that theories of privilege are inherently economical

because they seek to analyse facts about non-privileged properties in terms of facts

about privileged properties. According to Armstrong, facts about the properties of

objects are made true by facts about the instantiation of sparse universals, which are

themselves not further analysable (Armstrong 1978a pp109-111). It therefore seems

as though the fewer universals one accepts, the fewer of these primitive facts there are

going to be. This is a mistake, however, as what is of interest here is not the total

number of primitive facts there are, but rather the total number of types of primitive

fact there are (Lewis 1973a p87, see also Oliver 1996 p7). On closer inspection it is easy

to see why this should be the case. Suppose that the only universals instantiated in the

universe are to do with the strengths of a handful of fundamental fields, and that the

only things which instantiated such universals are space-time points. According to our

best scientific guess, however, the universe is currently expanding. There are now more

space-time points with field strength values and more primitive facts of instantiation

of universals now than when Armstrong proposed his theory in the late seventies. If we

take simplicity of a theory to be partly determined by the total number of primitive

facts it proposes, and that simplicity is a measure of how attractive a theory is, then we

would have to conclude that Armstrong’s ontology has become a worse candidate for

a metaphysical theory over the years since it was first proposed. This would be bizarre.

For this reason I will only concern myself with simplicity with respect to the types of

primitive facts that are permitted within a metaphysical model, and not with their

overall cardinality.

The virtue of privilege as a constituent of a metaphysical worldview therefore is

inextricably linked to its ability to account for a variety of different kinds of fact, such

as facts about similarity or the meanings of words, using the same theoretical

resources. The more issues of philosophical interest that privilege is applied to, the

greater its virtue. The price in terms of complexity need only be paid once, but will

remove the need to posit new entities and notions to fulfil all of the additional roles

which privileged properties are meant to fulfil. In addition to this, the more specialised

roles that the posit of privilege might fulfil, the less it can be accused of being an ad hoc

addition to a theory. The proposal here is that a primitive notion which is only

advantageous to adopt with respect to a single philosophical problem is less likely to

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reflect the nature of reality than one which is useful in a variety of different ways (see

Rodriguez-Pereyra 2002 pp210-211, Sider 2011 p10). Consider the following example.

Privileged properties are sometimes supposed to solve a certain problem concerning

the indeterminacy of language. Assuming that the meanings of words are ultimately

rooted in the social conventions of the community that uses them, there seem to be

multiple equally good interpretations of most words, many of which are utterly bizarre

(this role for privileged properties will be detailed more fully in §3.7 and §6.2).

Privileged properties are proposed to constrain acceptable interpretations, so that

wherever possible our words will have the meaning closest to marking out some

privileged category that still fits acceptably well with how that word is used. If,

however, the only use for privileged properties was to provide a response to such a

problem, one might very well question why reality should include a specialised group

of properties whose sole function is to make workable a theory that otherwise is prone

to some serious objection. Their inclusion would be ad hoc, and therefore

unacceptable.

If privileged properties perform a variety of roles then it becomes more plausible that

they should perform any one of those roles. Consider again the example of privileged

properties constraining interpretations of a language. It is more plausible to suppose

that words in our own language pick out those properties that make for similarity

amongst objects and feature in laws of nature than a group of properties with no other

distinguishing features. These are the properties which it would make sense for us to

latch on to and communicate about with our language, as these are the ones which

would be of greatest utility to us in navigating our environment. In this way, the

combination of different kinds of work within the posit of privilege makes it a superior

solution to any one of the individual problems that it is proposed to solve.

In addition to any intuitive plausibility that may be attributed to the notion, privilege is

therefore justified by how useful it is to a systematic metaphysics. If certain theorists

find the idea of privilege intuitive, there is nothing I can say that will convince them

that it is not, but nor is there anything they can say to convince me that it is. For this

reason all supporters of privilege, even those like Sider who consider privilege to be a

consequence of a pre-theoretical realism about the world, also attempt to defend the

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posit of privilege on the basis of its theoretical virtue (Sider 2011 p15). It is this

justification that I will be concerned with in this investigation. I will now outline my

strategy for showing why we would do well to reject privilege.

1.5 A strategy for rejecting privilege

My goal in this project is a rejection of privilege, and the means by which I aim to

achieve this is to show that the most important theoretical gains cited as a reason to

endorse privileged properties cannot be performed by them. Consequently, an elite

minority of properties such as the one proposed by theorists of privilege is not capable

of the fruitfulness that is expected of it.

It must be noted that mine is not the only possible avenue of response to theories of

privilege. Taylor criticises privilege whilst accepting one of its supporters’ central

claims, that something like privilege is indeed necessary, and instead merely denies

that the relevant sorting of properties into specialised and non-specialised groups is a

mind-independent feature of reality. For Taylor, there is indeed something to be said

for accumulating specialised roles within a minority group of properties. His proposal

is simply that we endorse a ‘vegetarian’ alternative, replacing objective privilege with

‘cosiness with respect to a theory’ (Taylor 1993 pp88-89). The thought here is that we

may do away with the prescriptions of scientific realism with respect to the existence

of privileged properties, and instead take the best scientific theory itself to bring with

it its own set of fundamental terms. Any properties picked out by fundamental terms

in this theory are termed ‘cosy with respect to a theory’ or ‘T-cosy’. The ‘T-cosy’

properties operate in much the same way as the privileged properties, fulfilling all the

same functions in all the same way, but under Taylor’s view their suitability to fulfil the

roles they do is not rooted in capturing the objective structure of reality, but rooted in

their position with respect to our best scientific theory.

Taylor’s T-cosiness may well be successful in its goal of providing a vegetarian

alternative to privilege, but will not serve to convince one who is already a committed

scientific realist. The supporter of privilege may very well agree that certain properties

which feature in our best scientific theory are ‘T-cosy’, but since they believe in

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privileged properties anyway they might well suppose that Taylor’s apparatus is just

superfluous. We would have no motivation to prefer cosiness if we could be convinced

that there were objectively privileged properties out there in reality to do the job for

us. Taylor’s proposal only offers an alternative to privilege for those who are disinclined

to accept it in the first place. It does not show that there is anything wrong with the

theory of privilege itself. By instead scrutinising the roles proposed for privileged

properties and arguing that they cannot be performed by them, we might develop a

criticism that could serve to persuade someone sympathetic to the distinction.

The three proposed functions for privileged properties which I take them to be

incapable of performing are as follows. Firstly, the sharing of privileged properties

between numerically distinct objects is neither necessary nor sufficient to account for

our intuitions regarding relations of overall similarity. Secondly, the view that only

privileged properties make for similarity is in direct tension with Lewisian possible

world semantics for modality. Thirdly, privileged properties do not succeed in

constraining acceptable interpretations of contents of thought and language. In

robbing the theorist of privilege of an appeal to such properties as the basis for

sameness of type or as a constraining feature on metasemantics, there is no longer any

reason to regard privilege as a fruitful contribution to a systematic metaphysics. The

structure of this project is as follows.

Chapter two concerns an account of the nuances of the different theories of privilege

and the ways in which these are relevant to the kinds of work which the privileged

minority is assumed to perform. At the same time I will outline a number of related

terms and corollaries of theories of privilege, for instance the distinction between

privileged categories and those which are not themselves privileged, but ‘joint-carving’,

i.e. categories which are not themselves privileged, but mark out distinctions which are

also marked out by privileged properties. Certain specialised roles associated with the

posit of privilege are sometimes attributed to all joint-carving properties, rather than

just those which are themselves privileged. The property of being red, for instance, is

not a privileged property according to the standard microphysical account of privilege,

but it does appear to make the things which possess it similar. Facts about joint-carving

34

are analysed in terms of facts about privileged properties, and so we can claim that

roles for joint-carving properties are ultimately roles for privileged properties.

In chapter three, I will investigate the interrelation of roles for privilege and how they

reinforce one another as a means of justifying the distinction. The roles I identify for

privilege will be drawn from Dorr and Hawthorne’s recent survey of the debate over

natural properties (Dorr and Hawthorne 2013). Whilst Dorr and Hawthorne’s survey is

indeed very complete, they refrain from making any judgement concerning which roles

of privilege are the most important, preferring to map a terrain of possible viewpoints

rather than risk forcing all supporters of privilege into one mould. In taking this attitude

however, Dorr and Hawthorne ignore the evident hierarchy of roles that runs through

literature on privilege. I propose that the idea of privileged properties functioning as a

minimal supervenience basis in conjunction with the commitment to a scientific realist

worldview is essential to all approaches to privilege, as this is in all cases its starting

point. Scientific realism and the existence of a minimal supervenience basis is simply

assumed by all supporters of privilege. It is from this commitment that other key roles

for privilege originate, in particular the view that privileged properties alone make for

similarity, feature in causal laws, and make for eligible content of language. The

remaining roles that privileged properties are taken to fulfil all derive from these three

core roles. For instance, the ability to define duplication and intrinsicness and

extrinsicness of properties in terms of privilege is derived from the ability of privileged

properties alone to make for similarity. In addition, given some reasonable assumptions

about the nature of causal laws, it can be shown that the function of privileged

properties as a minimal supervenience basis is the motivation for holding that all causal

laws are explicable as relations between privileged properties. For this reason I direct

my attention to the core roles of privilege, a critique of which is the subject of chapters

four to six.

Chapter four will be concerned with the first part of my critique of the view that only

privileged properties make for similarity between objects. In this chapter I will be

focussing on an argument of Lewis’ for natural properties which draws on the seventh

of Goodman’s ‘seven strictures on similarity’ (1972 p443). Goodman points out that

overall similarity relations cannot simply be a function of all shared and unshared

35

properties between objects, because all objects share infinitely many properties and

fail to share just as many. Lewis argues that since there are relations of overall similarity

as a matter of common sense, there must be some minority of properties which alone

make for similarity (Lewis, 1983 p). This argument is flawed, and these common sense

facts of similarity do not actually demonstrate as much as Lewis claims they do.

Chapter five will consider a second way that similarity relations cannot simply be a

matter of the sharing of privileged properties, by applying this notion of similarity to

Lewis’ possible world semantics for modality, and arguing that the two are

incompatible. If we limit the similarity relations involved in the identification of

counterparts and the ordering of possible worlds with respect to closeness to the actual

world to those which take into account only privileged properties we must take some

plausibly true counterfactual statements to in fact be false.

Chapter six will investigate the usefulness of privileged properties with respect to

providing a solution to the problem of indeterminacy of language which arises for

interpretationist metasemantic theories. Here I conclude that something like the

‘eligibility’ constraint on meaning proposed by interpretationists as a solution to the

indeterminacy problem is essential, but deny that eligibility tracks joint-carving

categories. Several counterexamples can be generated to show that when the desired

or ‘intended’ interpretation of a language does track privileged categories, it does so in

virtue of some other feature of that category, for instance its ability to be discriminated

easily by human perception.

The final chapter of this project is a summary and conclusion of the findings of the

previous chapters, in which I will briefly draw together the various refutations of the

‘work’ for privileged properties and aim to answer the question of where that leaves

prospects for a realist worldview. I consider that the issues I have raised give us reason

to reject the idea of privileged properties, but this does not mean that we must

abandon the idea of a mind-independent world altogether. To my opponents,

convinced as they are of the sheer common sense of privileged properties, the kind of

picture of reality I aim to leave them with may sound thoroughly unappealing. I

maintain however that we can still hang on to everything that really matters. There will

still be such a thing as truth about the character of reality after we’re done, and that

36

truth will still be objective. Even without privileged properties, there will certainly be

enough work out there to occupy metaphysicians and scientists both for years to come.

Despite the seeming negative character of my project as a whole I persist in being

optimistic about its consequences. Absent privileged properties to tell us when we are

carving reality in the right way, we will have to make do with simply indicating what

carvings there are truthfully. Perhaps that’s all we ever needed.

37

Chapter Two: Questions of Privilege

2.1 Issues in privilege literature

In the previous chapter I attempted to clarify the notion of privilege in general and to

outline the motivations of its supporters in endorsing it. In this chapter we will look into

theories of privilege in more detail and seek to answer a variety of questions about the

way such theories actually work. Throughout this chapter I will focus predominantly on

the theories of privilege proposed by Armstrong and Lewis, for the philosophy of

properties in recent decades has been shaped by these two thinkers more than any

others (Oliver 1996 p2). In cases where some subsequent theorist of privilege has

departed from the frameworks laid down by these two authors with respect to any of

the questions under discussion in this chapter then care will be taken to note this.

Otherwise, it may safely be assumed that the consensus in the field is towards one or

other of the answers given by Lewis and Armstrong. The questions to be dealt with in

this chapter are as follows.

1. To what extent does privilege come in degrees?

2. How are degrees of privilege to be measured?

3. How do theories without (or with a limited) a conception of less-than-perfect

privilege cope with the roles associated with such properties?

4. Is the extent to which a property fulfils the roles of a privileged property

correlated with its degree of privilege?

5. Are there any non-privileged properties?

6. If there are no maximally privileged properties, how are degrees of privilege to

be measured?

7. Why does scientific realism imply that maximally privileged properties are

microphysical?

8. Are there any extrinsic privileged properties?

Questions 1-6 all concern the idea that the phenomenon of privilege is a matter of

degree, and providing answers to them will be the topic of §2.2-2.5. As discussed in

chapter one, almost all theorists of privilege begin with the view that the properties of

38

fundamental physics are privileged, but not all the roles attributed to privileged

properties are performed by microphysical properties alone. Properties such as being

golden or being a rabbit make for similarity amongst their objects and even make for a

certain causal unity amongst them, but are not microphysical. The proposal that

privilege is gradated suggests that whilst the microphysical properties alone function

as a minimal supervenience basis for reality, some higher-order properties can also be

privileged to a lesser extent. These properties, which we can call somewhat privileged

rather than maximally privileged, fulfil some of the associated specialised roles. In

practice, this proposal raises numerous questions which must be answered in order to

engage with the consequences of theories of privilege. §2.6 will address question six

on our list, outlining how the frameworks of Armstrong and Lewis can be adapted in

such a way as to accommodate the lack of a maximally privileged level of reality. So far

we have assumed that such a layer exists, acting as a foundation for the gradually less-

privileged and non-privileged properties on top. It is a possibility that there is no such

bottom layer, and that the structure of reality descends into realms of smaller and

smaller particles infinitely. This is sometimes known as the hypothesis that reality is

‘gunky’ (Lewis 1991 p20). In this section means of adapting theories of privilege in order

to accommodate gunk will be assessed. I conclude that the possibility of gunk is not an

insurmountable obstacle to theories of privilege.

Question 7 concerns the relationship between scientific realism and the microphysical

approach to maximally privileged properties. No theorist of privilege claims to offer a

complete inventory of privileged properties, as this task is would require empirical

study, and may not be worked out a priori (Armstrong 1978b pp7-8, Lewis 1983 p203).

All that a philosophical account of privilege can achieve is to give a rough idea of the

number of privileged properties. The precise number of privileged properties will

ultimately be determined by how complex it turns out reality is. This is what theorists

of privilege are attempting when they endorse a microphysical approach to the

maximally privileged properties. We may also compare theories of privilege with

respect to their permissiveness by looking at the strictness of the conditions they

propose for inclusion within the elite minority of maximally privileged properties.

Investigating why the generally given answer to this question is to identify the

39

maximally privileged properties with the microphysical ones will be the topic of §2.6-

2.7.

Question 8 asks whether there are any extrinsic privileged properties. In §2.8 I will

argue that the answer to this is ‘no’. I will show that the thesis that there are extrinsic

maximally privileged properties is incompatible with the claim that the maximally

privileged properties comprise a minimal supervenience basis for reality. It will also be

shown that thesis is incompatible with Armstrong and Lewis’ frameworks for theories

of privilege, and with most variations of these which do not share all of the same

commitments.

Throughout this chapter it will be necessary for us to have a convenient example of a

role for privileged properties to use for illustrative purposes. Where necessary, I will

use the similarity-making role of privileged properties in this capacity. To reiterate, it is

one of the central suppositions of theorists of privilege that when two things stand in

a relation of similarity, they do so in virtue of the sharing of privileged properties only.

Similarity comes in degree, so objects which share a greater proportion of their

privileged properties will be more similar to one another than objects which sharer a

smaller proportion. Two atoms of gold, for instance, are similar in virtue of their being

constituted by the same number of protons and electrons. An atom of gold and an atom

of lead are not as similar to each other as two atoms of gold, because these atoms differ

with respect to the number of protons and electrons within them. Let us suppose that

the atom of lead and the atom of gold are both located in Germany, and so this is one

property at least which the two atoms share. According to theorists of privilege,

however, the fact that both atoms are in Germany does not contribute to their being

similar. If in everyday speech we are inclined to talk in such a way as to suggest that

there is a sense in which all the things located in Germany are similar with respect to

their being located in Germany, then this sense of the word ‘similarity’ is either a

different kind of phenomenon to the one theorists of privilege mean by ‘similarity’ or

simply a loose way of talking. In either case, it is argued that there is a sense of the

word ‘similar’ that picks out a relation which holds only between those objects which

share privileged properties. This role for privilege is one that is more or less universally

40

endorsed by theorists of privilege and so will make a good benchmark when discussing

the connection between various types of property and roles.

We begin now by looking at the ways in which theorists of privilege conceive of distinct

degrees of privilege.

2.2 Degrees of privilege

Although the idea that privilege is something which properties can have to greater or

lesser degrees is most commonly associated with Lewis (1983 p192), numerous other

theorists of privilege make claims which approach this idea in practice, in particular

Armstrong and Sider. In this section I will briefly examine Lewis’ approach to degrees

of privilege and how the degree of naturalness of a property can be established in its

‘distance’ from the microphysical level of properties. I conclude that this distance

cannot simply be a matter of the length of a property’s definition in maximally

privileged terms, as is often supposed (Dorr and Hawthorne 2013 p15, Williams 2007

pp376-377), and as Lewis’ own comments sometimes suggest (1984 p228). Finally, I

will argue that Armstrong’s conjunctive universals are analogous in function to Lewisian

less-than-perfectly natural properties, and so Armstrong himself should properly be

understood to have a limited conception of degrees of privilege in his framework.

Lewis accepts that we have a need for privileged properties to perform certain

specialised roles, and as we shall see in §2.7, he believes that these privileged

properties will be microphysical. He does not however think that the properties of

fundamental physics are sufficient to do the jobs of grounding similarities between

objects, or featuring in causal laws. The property of being a rabbit is not a microphysical

property, and yet disparate objects which share this property certainly do seem to be

similar in some important respect. Similarly, chocolate is poisonous to dogs but not

humans, so it seems as though it makes sense to speak of chocolate of standing in

different causal relations to dogs and humans. Lewis concludes that in addition to the

initial category of microphysical privileged properties, which he now calls the ‘perfectly

natural’ properties, and those properties which are simply not privileged, we must also

speak of properties which are also natural although to a lesser extent than the perfectly

41

natural properties (1983 p192). Lewis does not give us much clear information

regarding the connection between the perfectly natural properties and the less-than-

perfectly natural properties. At one point, he suggests that the less-than-perfectly

natural property of being metallic might have something to do with instantiating one

of a family of close-knit universals, one of which is instanced by any metallic thing (1983

p192). Elsewhere he suggests that a property’s degree of naturalness is a matter of the

ease with which it may be defined in terms of the perfectly natural properties:

Indeed, physics discovers which things and classes are the most elite of all; but

others are elite also, though to a lesser degree. The less elite are so because

they are connected to the most elite by chains of definability. Long chains, by

the time we reach the moderately elite classes of cats and pencils and puddles;

but the chains required to reach the utterly ineligible would be far longer still.

(Lewis, 1984 p228)

Regardless, Lewis left few remarks on how exactly these definitions might be

constructed (Nolan 2005 p25). In fact, we have good reason to suppose that the

method of calculating degrees of naturalness by the lengths of their definitions in terms

of the perfectly natural properties cannot be the only arbiter of naturalness.

Consider the following example. Let us assume for the sake of argument that the

properties of being a member of a particular taxonomic class are all on a par with

respect to their naturalness. The property of being a reptile would therefore have

about the same length of definition in terms of arrangements of perfectly natural

properties as the property of being an amphibian and the property of being an avian.

If these three properties are all equally natural then the following disjunctive

compounds of these three properties, being a reptile or an amphibian, being a reptile

or an avian and being an amphibian or an avian, will all be as natural as each other. In

fact the science of biology does not consider these properties to be equally natural.

Reptiles and avians share much of their evolutionary heritage, so despite the apparent

physiological similarities between many reptiles and amphibians it is in fact a more

natural categorisation to put reptiles with avians rather than amphibians, although

both of these are certainly more natural groupings than that which places avians with

amphibians (Abdullah et al eds. 2015).

42

Additionally, if the only factor relevant to the naturalness of a property were the length

of its definition in terms of natural properties, it would follow that gerrymandered

conditions engineered from very natural properties would tend to be more natural

overall than some properties which seem to make for a greater unity amongst their

instances. The property Florb which we introduced in §1.3 does not seem to be a very

natural property at all. The three things which are Florb are not unified amongst

themselves. The problem is that the property of being Florb would have a much shorter

definition in terms of the natural properties than the property of being a star. Although

stars are relatively well-definable scientifically, their internal composition and energy

states can vary tremendously. The definition of what it is to be a star must be far shorter

than the definitions of biological properties such as that of being a reptile, but even so

it will contain far more connectives within it than the definition of being Florb, which

merely has to enumerate the perfectly natural properties of its three relatively small

members and no others. Even specifying the internal composition of a single star would

require vastly more space than this, and to expand that definition to include every kind

of star is almost beyond imagining.5

As such, I suggest that we take the length of a property’s definition in terms of perfectly

natural properties to be at best a fallible guide to its overall naturalness. All that we can

really say for certain about what Lewis had in mind is that the more natural properties

are those which are closer to the fundamental level, however this closeness is to be

measured. A systematic account of how exactly we should calculate the degree of

naturalness of properties must be far more complex than this, so complex in fact that I

would not even know how to begin such a task. I specify a ‘systematic’ account because

it is of course a possibility that the degree of naturalness of a property might itself be

primitive, just as Lewis suggests that the perfectly natural properties may be so

5 Additional criticisms of the straightforward measure of naturalness by length of definition in perfectly natural terms can be found in Sider (1995 pp362-363, 2011 p130). Of these the most interesting is that all properties with infinitely long definitions would be equally natural under this system. Note that this would only be so if we assume that all properties are natural to at least a certain extent. If there is a cut-off point beyond which properties are non-natural rather than just slightly natural, then we should expect that there are no natural properties that have infinitely long definitions. In §2.4 I will argue that it is not a commitment of Lewisian naturalness that every property should be natural to some extent, and that in fact there are serious problems with such views.

43

primitively (1983 p193). Doing so would come at the cost of a significant blow to the

economy of a theory, for it is undoubtedly simpler to show how the less-than-perfectly

natural properties may be grounded in the perfectly natural ones than to take the

application of each ‘level’ of naturalness to certain properties to be a new species of

primitive fact.

In Armstrong’s framework there are merely somewhat privileged properties as well,

although these are a much more limited category than Lewis’ less-than-perfectly

natural properties. For Armstrong, what makes a predicate pick out a privileged

property is for the set of objects to which this predicate applies to be identical to the

set of objects which instantiate a single universal (1978b p8), so any merely somewhat

privileged properties must stand in the same correspondence relation to some

universal as well. The only such universals Armstrong endorses are what he calls

‘conjunctive’ universals, those which correspond to the properties of expressing some

conjunction of other universals. ‘Negative’ or ‘disjunctive’ universals by comparison,

are rejected (1978b chapters 14-15). In the remainder of this section I will outline

Armstrong’s reasons for his position on compound universals, and conclude that the

status he claims for conjunctive universals is analogous to those of Lewis’ less-than-

perfectly natural properties.

Whether or not a universal is disjunctive or negative is nothing to do with how we

describe the world in any particular language. Although we have a word ‘charge’ in

English to pick out the property which is had by all particles which are not overall

electrically neutral, this property of having charge could just as easily be referred to by

an expression which included a negation, for example ‘not neutral’, or a disjunction, as

in ‘either positively charged or negatively charged’. The fact that we do not use a

negative or disjunctive expression to pick out ‘charge’ is merely an accident of language

(Armstrong 1978b p19). By a ‘negative’ universal, Armstrong means a universal

instantiated by just those objects which fail to instantiate some other universal. By a

disjunctive universal, he means a universal corresponding to a predicate which just

applies to those objects which instantiate at least one of a disjunction of universals.

Suppose that science furnishes us with knowledge of the existence of a variety of

universals. Armstrong denies that knowledge of these universals enables us to

44

extrapolate the existence of further universals corresponding to negations and

disjunctions of these.

It is important to note that there may nonetheless be universals which are not

themselves disjunctive or negative, but which can be expressed syntactically as

negations or disjunctions of other predicates which themselves correspond to

universals. Suppose, for instance, that there are only two fundamental types of particle

in reality, A and B. It could well be the case that there are distinctive causal profiles

associated with being either an A or a B, in which case there could be a universal

corresponding to being an A, and another corresponding to being a B, even though it

would be possible to express the condition of ‘being an A’ simply as ‘failing to be a B’.

Armstrong is not claiming that there is never a universal which is instantiated by all the

particulars which fail to instantiate some other universal, or which is instantiated by

some particulars which instantiate a disjunction of universals. All he wants to insist is

that we have no reason to simply assume that such universals exist. Identification of

universal predicates is intended as a scientific enterprise, and not something that can

be achieved by a syntactic test (Armstrong 1978b p19).

Negative universals are rejected by Armstrong on the basis that they would make

privileged properties, and hence the ways in which objects may be similar, far too

numerous. The property of failing to be a proton is one which is shared by objects of

any kind that aren’t protons. If the property of failing to be a proton made for similarity,

then electrons, neutrons, coffee mugs, numbers, football teams and Presidents of the

United States would all be similar in this respect. Armstrong claims that it is simply not

plausible that disparate objects can be made similar in virtue of something they don’t

possess. Similarly, it is false that in all cases where objects are united by a negative

property they share some causal powers. Electrons and lemon trees behave completely

differently, but all electrons and all lemon trees share the property of failing to be a

proton. Making a causal difference to the world is something Armstrong requires of

privileged properties (1978b pp23-25), so the fact that negative properties cannot

always be said to make such a causal difference is reason for him to reject them. An

additional consequence of the rejection of negative universals is that it permits

limitations on the types of particular which can be instances of universals. Let us

45

suppose that there are universals corresponding to the property of being each one of

the fundamental particles. Any particular can fail to be one of those fundamental

particles, not just those which are themselves fundamental particles of one sort or

another. If the only universals permitted are positive, then it allows for the possibility

that all of the objects which instantiate universals belong to a relatively restricted

domain of particulars, for instance the fundamental physical particles, just in case there

are no positive universals which apply to any other kind of particular.

The strongest reason Armstrong gives for denying the existence of disjunctive

universals is that they supposedly violate the rule Armstrong imposes that all universals

must confer causal powers on their instances (1978b p20). Predicates which apply to

objects instantiating one or other of a disjunction of universals will not in every instance

make for shared causal powers amongst all the objects to which they apply. In practice,

this means that universals will tend to correspond to the terms of fundamental physical

science rather than those of higher-order sciences such as chemistry. The term ‘crystal’

refers to a wide range of substances which possess a certain molecular structure, but

there are no causal powers shared by all crystals. Both snowflakes and diamonds are

crystals, but objects of these types are extremely different causally. The causal powers

of both diamonds and snowflakes must be attributable to some universals that they

each instantiate by the first of Armstrong’s conditions, but the property of being

crystalline itself cannot be such a universal on his view.

Given Armstrong’s views on negative and disjunctive universals, it at first seems odd

that he is prepared to allow that predicates which apply to objects which instantiate

conjunctions of universals themselves pick out universals. The only limitation he places

on the existence of such universals is that there must be at least one thing which

actually instantiates them, as is the case with all universals (1978b p30). There will not

therefore be a universal corresponding to the property of being an electron and having

an atomic number of one, even if there are universals corresponding to each of these

conjuncts, because no electron actually has an atomic number of one. Armstrong offers

two arguments for the acceptance of conjunctive universals. The first of these is that

conjunctive properties are required to deal with the possibility that reality is ‘gunky’, a

proposal that will be explored in detail in §2.5. The second argument he gives is that

46

conjunctive properties make for causal unity of their instances in a way that disjunctive

and negative properties do not (1978b p35). The property of being an atom of gold is

conjunctive, because it requires that exactly seventy-nine distinct parts of itself

instantiate the property of being a proton. Gold atoms feature in laws of chemistry,

and so the property of being an atom of gold makes for causal unity amongst its

members.

If conjunctive properties are allowed on this basis, it is unclear why the same cannot

be said of at least some disjunctive properties, in particular determinable properties.

Determinables are explicitly discounted by Armstrong as privileged properties because

they take the form of disjunctions of their determinates (1978b p117), but some

determinables do make for causal unity of their instances. Water is a solid when it has

the property of having a temperature below zero degrees Celsius, but such a property

is actually a disjunction of a range of determinate temperatures including having a

temperature below minus one degree Celsius, having a temperature below minus two

degrees Celsius, and so on. Armstrong suggests that with respect to determinable

properties, all the work of making for similarity and causal unity is being done by the

determinates rather than the determinable itself, and so there is no need to posit

determinable properties over and above their determinates (1978b pp118-119). If this

strategy relieves us of the need for disjunctive properties, however, it seems that it

should relieve us of the need for conjunctive properties also, as the work of conjunctive

properties too is being performed by its conjuncts rather than the conjunction itself.

This is evidenced by Armstrong’s remarks on the status of conjunctive universals as

nothing over and above their conjuncts.

Armstrong uses the analogy of a knife to illustrate the status he attributes to

conjunctive universals. A knife consists of two parts, a blade and a handle. Although we

might say that the blade, the handle and the knife are all objects, the knife is nothing

more than the combination of blade and handle. We do not wish to say that there are

three wholly distinct objects here (Armstrong 1978b p30). Armstrong’s acceptance of

some conjunctive universals means that he does endorse some form of privilege

attached to properties besides those relating to the most fundamental physical

processes. The precise mechanism by which conjunctive universals are instantiated

47

differs from that of a non-conjunctive universal. Instantiations of conjunctive universals

are nothing more than coinstantiations of their conjunct universals. What we see here

is a distinction between two kinds of universal. One kind is fundamental, the other is

not.

This presents a problem for arriving at a proper understanding of Armstrong. Privileged

properties are properties which are proposed to fulfil a range of certain specialised

roles and for Armstrong, the most important signifier of a property’s being privileged

is that it confers some unity of causal power upon the objects which instantiate it.

Armstrong proposes that conjunctive universals meet the standards for privilege, but

that disjunctive and negative universals do not. The inclusion of conjunctive universals

by Armstrong has been controversial even amongst supporters of his general theory,

in particular with Mellor (1991, 1992, see also Oliver 1992, Lewis 1983 p190).

I propose that the proper way to think of Armstrong’s conjunctive universals is in a

manner analogous to the less-than-perfectly natural properties put forward by Lewis.

This is because Armstrong’s conjunctive universals and Lewis’ less-than-perfectly

natural properties share a common feature. Whilst they do indeed perform many of

the roles associated with privileged properties, they do not form part of the minimal

supervenience basis for reality (1983 p192). For Armstrong, the instantiation of

conjunctive universals is ultimately no addition to reality over and above their

conjuncts, so conjunctive universals need not feature in the minimal supervenience

basis for reality, although they do make for similarity amongst their instances and grant

them a complement of distinctive causal powers. I will leave open the question of

whether or not Armstrong is right to endorse conjunctive universals as performing roles

associated with privileged properties whilst simultaneously rejecting disjunctive or

negative universals. We have already noted that this is not a majority point of view for

theorists of privilege, however, even amongst those who otherwise endorse something

like Armstrong’s framework. It is those theorists who reject the notion of degrees of

privilege who will concern us in the next section.

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2.3 Joint-carving

In talk of privilege, a common expression is that of a ‘joint-carving’ category, which is

used in an approximately similar way to the idea of a somewhat privileged property.

What is unusual is that this term is often employed by theorists who do deny that

privilege is a matter of degree, most notably Sider (2011 p128). In this section I will

show that theorists who deny degrees of privilege still acknowledge some roles for the

merely somewhat privileged properties found in Lewis and Armstrong’s account, and

that they reconcile these two positions by introducing the notion of ‘joint-carving’. A

property is joint-carving just in case its pattern of instantiation tracks a distinction

which exists at the level of privileged properties.

A property’s being joint-carving is grounded in the extent to which it tracks distinctions

in the privileged properties instanced by all the instances of that property. For some of

the roles ascribed to privilege, Sider seems to suggest at times that there are a variety

of specialised functions performed by categories which are not ‘structural’ (recall that

this is Sider’s preferred terminology for privilege), but rather are ‘joint-carving’ (2011

pp28-29). Much like Lewis and Armstrong, Sider takes the privileged properties to be

microphysical (2011 p20, p292), but not all of the categories he describes as joint-

carving are microphysical. Similarly, he talks on at least one occasion of a relation (the

reference relation) as neither being ‘perfectly joint-carving’ nor ‘wildly non-joint-

carving’ which suggests that he has something like Lewis’ account of less-than-perfect

naturalness in mind (2011 p28). It would be wise to avoid attaching too much

significance to Sider’s own use of this terminology, as elsewhere in the same book he

claims that to be joint-carving is just to be structural (2011 pvii). Nonetheless, it appears

as though there is an idea here that is worth drawing attention to, and ‘joint-carving’

captures the sense of it better than any other available term. Although he uses the term

‘joint-carving’ in a similar way to how Lewis uses ‘less-than-perfectly natural’, Sider

does not believe that structure is itself a thing that comes in degrees (2011 p128).

Although he does not use the term explicitly, something like Sider’s notion of joint-

carving can be found in Mellor (although Mellor does speak loosely of privileged

properties as the things which give nature its joints, Mellor 2012 p389). Mellor adopts

a framework much like Armstrong’s, but denies the existence of conjunctive universals

49

(Mellor 1991 p265), and so lacks any kind of less-than-maximal privilege in his account.

One of his reasons for denying the necessity of such universals will be discussed in §2.5,

in relation to the hypothesis of ‘gunk’. Mellor, like Armstrong, claims that there are as

many privileged properties as feature in all the laws of nature (Mellor 2012 p397).

Many laws of nature involve disjunctions of privileged properties. The example Mellor

offers are laws of chlorine chemistry, as chlorine occurs in two forms naturally which

behave in the same way chemically: 35Cl and 37Cl. The property of being either an atom

of 35Cl or 37Cl is not a universal for Mellor, but he does speak of such a property as being

a ‘complex joint’ of nature (2012 p404).

I propose that joint-carving properties are properties which perform certain specialised

functions in virtue of some privileged distinction between particulars which instance

that property and all other particulars. Note that joint-carving properties need not be

privileged themselves. All privileged properties will be joint-carving, but in many cases

joint-carving properties will not be privileged. The property of being red is not a

universal according to Armstrong’s framework, but the category of red things does

mark out a genuine joint in nature. The red things are heterogenous at the level of

privileged properties, for some of them reflect scarlet light, whilst others reflect

crimson light. It is this heterogeneity which bars them from being privileged in the

absence of an approach to privilege as a matter of degree. It is however possible to

show some distinction in terms of privileged properties between all the members of

the category of red things and all the members of the category of non-red things.

Although there is no single privileged feature of the red objects which gives them unity

as a category, we can identify all those privileged features or combinations of features

which are only had by entities which do not belong to the category of red things.

Objects which reflect no light, or light of a different colour, will not have a composition

like that of any of the red objects, and this, I suggest, is what we should understand as

a ‘joint of nature’, not necessarily a property which is itself privileged, but a property

whose boundaries can be understood in terms of some privileged difference between

its instances and the things are not its instances.

We can extend our example to biological properties of belonging to one or another

species. A rabbit might share relatively few privileged properties with all other rabbits.

50

Any one rabbit might have smaller ears, or longer legs, or its organs may be slightly

different shapes to all the other rabbits in its category. The property of being a rabbit

is a joint-carving one because whether or not a given object is a rabbit is explicable in

terms of a difference between rabbits and non-rabbits at the level of privileged

properties. No rabbit has a tail like a squirrel or scales like an eel, and this can be the

means by which we identify them, although they are an internally heterogeneous

category.

An example of a non-joint-carving category would be Florb. The only things which are

Florb are the Eiffel Tower, a particular pear that was picked and subsequently eaten in

the Summer of 1732 and the left thumbnail of the Statue of Liberty. It is not possible to

account for these objects being Florb in terms of some privileged difference between

them and all the things that are not Florb. The right thumbnail of the Statue of Liberty

could be a complete microphysical duplicate of the left down to the smallest detail, and

yet it would not be Florb, because only these three objects are Florb.

The Lewisian system of more or less-privileged properties can be thought of as a

particular approach to joint-carving, where a joint-carving property is simply a property

which is at least somewhat privileged. Throughout this project (and particularly in

chapter three, during which I detail the specialised roles proposed for privilege) I will

sometimes speak of privileged properties performing a certain role, and sometimes I

will speak of joint-carving properties performing a certain role. The similarity-making

role, for instance, is a role performed by joint-carving properties rather than privileged

properties alone. As joint-carving is based in privilege, specialised functions of joint-

carving properties still count towards the theoretical value of the posit of privilege, in

much the same way that the success of the atomic theory of chemistry lends support

to the theories of the subatomic particles from which they are composed.

According to Sider’s microphysical theory of privileged properties there is no structural

property of being red, even though red things certainly bear some similarity to one

another. With respect to Lewis’ theory, the joint-carving properties are just the

privileged properties, but in this respect Lewis is the exception. Most theorists who

speak of joint-carving intend to capture something broader than that of a privileged

property, although still rooted in them. In the manner described above we can arrive

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at a definition of joint-carving that appears to capture an idea at work in a number of

different theories of privilege.

2.4 Problems of comparative privilege

There are two questions generated by the idea of the specialised functions distinctive

of theories of privilege being performed by properties at varying distances from the

maximally-privileged level, either in the form of gradated naturalness or joint-carving

categories. Firstly, is it the case that the closer a property is to the fundamental layer,

the greater the extent to which it fulfils the specialised roles of privilege? Secondly, if

the degree of naturalness or joint-carving of a property decreases with distance from

the bottom layer, are there any properties whose degree of joint-carving is zero?

The answers to these questions are ‘no’ and ‘yes’ respectively. We will examine each

of these questions and their answers in turn.

It is often assumed that the extent to which properties perform the roles associated

with privilege decreases as their degree of joint-carving decreases. In fact, Dorr and

Hawthorne point this out as a source of tension between the similarity-making role and

the microphysical account of privilege. They claim that whereas determinate mass

properties such as having a mass of exactly three grams are plausibly much more

natural than having some mass or other, but two objects failing to share the latter

appear to be far less similar to one another than objects which fail to share the former.

They make analogous points about the relationships between degree of naturalness

and the ability to feature in causal laws and eligibility to be referred to (Dorr and

Hawthorne 2013 pp39-40). In fact there seems to be no good reason to think that the

degree to which a property is joint-carving is correlated with its ability to fulfil

specialised roles at all. This is certainly not something that Lewis ever explicitly commits

himself to, and the apparent tensions that Dorr and Hawthorne point out confirm that

no theorist of privilege should commit themselves to this principle. The fact that two

objects are both reptiles seems more important to overall similarity between them

than their overall charge, and yet the former is by far the less joint-carving category.

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The fact that fulfilling roles is not correlated to degrees of privilege tells us what the

right answer should be to our second question. If the degree to which properties

functioned as similarity-makers could be relied upon to fade away as they got gradually

further and further away from the fundamental level, then it might seem intuitively

sensible to say that all properties were joint-carving to an extent, but that beyond a

certain point the degree to which they made for similarity was so small as to be virtually

zero. However, we have already seen that there is no correlation between degree of

joint-carving and similarity-making ‘power’. If all properties are joint-carving to an

extent then positing privilege loses all purpose, as there is now no restriction which

privilege imposes on the properties that fulfil specialised roles. Recall that Lewis’

argument for natural properties from similarity relied on the idea that the number of

properties instantiated by a particular that count towards overall similarity must be

finite (1983 p192). If there is no cut-off point between natural and non-natural

properties, then this argument does not work.

In fact Lewis himself did speak as though there was indeed a cut-off point between

natural and non-natural properties, although he did not give much information on

where exactly the line between them was to be drawn. Lewis did however explicitly

deny that extrinsic properties were natural at all (Lewis 1983 p203). It is plausible to

suppose that Lewis’ treatment of the distinction between natural and non-natural

properties is intended to be quite similar to the way he describes vague terms in

Counterfactuals (1973a p93). Here he draws an analogy between the way that similarity

relations are fuzzy (see §5.4 for more detail on Lewis’ treatment of vagueness) and the

fuzziness of the boundary between green and blue.

The border delineating blue from green is only roughly fixed, but it is at least

roughly fixed. Not anything goes. We can find a color that is blue according to

some quite permissible delineations and green according to others, and

therefore indeterminate between blue and green. But it is not indeterminate

whether the sky is blue or green. (Lewis, 1973a p93)

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2.5 Gunk

Much philosophical writing takes it for granted that reality is not infinitely complex. It

has been a tacit assumption of this thesis until now. Although the past century has seen

the discovery of many new ‘levels’ of properties and objects each more fundamental

than the last, it is supposed that there is a level of reality whose behaviour is not

explainable in terms of something more fundamental. Some particles, perhaps yet to

be discovered, will prove to be the elementary constituents of reality. Whatever these

fundamental physical entities are, the properties associated with being entities of this

kind will correspond to the maximally privileged properties according to any

microphysical account of privilege. The degree of privilege attached to all other

properties will depend on their distance from these properties, however that is to be

calculated. In this section we will examine the consequences of this assumption proving

false, and show how Lewis and Armstrong’s frameworks can be adapted to support

such a conclusion.

The possibility that the structure of reality continues to descend towards smaller and

smaller particles infinitely is known as the hypothesis of gunk (Lewis 1991 p20). A world

is gunky just in case every object within it has proper parts. These parts are objects

themselves, which means that they too will have parts. A gunky world is not to be

confused with a junky world, which is a world in which every object is itself a part of

something. Junky worlds lack a top level rather than a bottom level, as gunky worlds

do (Schaffer 2010 p64). The possibility of gunk creates a problem for the theories of

privilege we have already looked at as it seems to imply that there will be no maximally

privileged properties, at most just an infinitely descending chain of more and more

privileged properties. As I will show in §2.6 and §2.7, maximally privileged properties

are generally assumed to be microphysical, in that they correspond to the properties

of the most fundamental objects. If the gunk hypothesis is true, however, there are no

fundamental objects and so no maximally privileged properties.

Various roles proposed for privileged properties, in particular the definition of

duplication (Lewis 1983 p202) appear to rely on the existence of maximally privileged

properties specifically. In addition, the degree of privilege of the merely somewhat

natural properties is based on distance from the maximally privileged properties.

54

Without a bottom layer of reality for the maximally privileged properties to constitute,

the entire theory of privilege as it has been presented so far is unstable. The gunk

hypothesis is introduced by Lewis in connection with his mereological approach to sets

(1991), and he does not offer any remarks on its implications for his wider metaphysics.

What we can say is that gunk would conflict with one of Lewis’ background assumptions

about the nature of reality as ultimately composed of fundamental space-time points,

which he calls Humean Supervenience (Lewis 1986b px, see also §2.7). Humean

Supervenience is regarded by Lewis as a contingent feature of reality. Even if it is true

in this world, it need not be true in every possible world. According to Lewis, the

evidence suggests that we inhabit one of the worlds where Humean Supervenience

holds, although ultimately scientific inquiry may prove him wrong on that score (1986b

pxi).6 Possibly this is why he does not qualify his theory in such a way that it can

accommodate gunky worlds. Regardless it seems as though we could imagine how such

a thing could be achieved. In gunky worlds there would be no perfectly natural

properties, because there would be no fundamental particulars to instantiate them. It

would still be possible to speak of a property’s being more or less natural than another,

and the degree of distance between these properties could be calculated in the same

way as distance from the perfectly natural properties was to be calculated. As we

descend down further into smaller and smaller parts, properties would become

increasingly natural, but at no point would we reach any ‘perfectly natural properties’.

The relation of duplication, which Lewis defines as the sharing of all perfectly natural

properties could be redefined as the sharing of all properties over and above a certain

degree of naturalness.

Although the gunk hypothesis is associated with Lewis, it is considered briefly by

Armstrong as well. It is in responding to gunk that we see some value in Armstrong’s

contentious conjunctive universals. For Armstrong, a gunky world is simply one in

which all universals are conjunctive (Armstrong 1978b p32). There is no work in

Armstrong’s system being done by the precise degree of privilege of a property. All that

matters to whether or not it forms part of the elite minority of properties which

6 Lately it has been argued that Humean Supervenience does not in fact accord with how modern physics views the universe. See Karakostas (2009) and Humphreys (2013 pp56-57).

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perform certain specialised functions is whether or not there is some universal that

corresponds to it. For this reason, gunk presents no special difficulties for Armstrong.

Alternatively, Mellor proposes that the possibility of gunk does not require the

acceptance of conjunctive universals in any case (Mellor 2012 p398).

According to Mellor, in a gunky world the laws of nature will be infinitely complex, but

this does not mean that they must involve complex universals. He makes the analogy

with a disjunctive law of chlorine chemistry. The two atoms 35Cl and 37Cl are

distinguished by the number of neutrons they contain, but behave in the same way

chemically. The laws governing the behaviour of chlorine therefore contain

disjunctions, since they hold between particulars which are either instances of 35Cl and

37Cl. A gunky world for Mellor is simply one in which every category that features in a

causal law is infinitely disjunctive or conjunctive, just as the property of being chlorine

is disjunctive. The property of being a quark in a gunky world will correspond to the

instancing of an infinitely long conjunction of more properties, and those properties

will themselves correspond to infinitely long conjunctions of properties, but Mellor

simply denies that we have any reason to call these conjunctions universals. One of the

founding principles of scientific realism concerning properties is, after all, that the

world of universals cannot simply be read off our linguistic practices and how we use

connectives (Mellor 2012 p398). As a solution to the problem of gunk this may be

successful, but we should deny that this results in something which is still a theory of

privilege. On Mellor’s view, every possible candidate for a privileged property is

disqualified for being conjunctive, so it follows that a gunky world will in fact contain

no universals whatsoever. The conjunctions that make up the properties of physics and

chemistry will quantify over no privileged properties, only infinitely long conjunctions

of conjunctions of conjunctions. To the extent that privileged properties are, as Mellor

supposes, the non-conjunctive constituents of laws of nature (Mellor, 1991), this is not

a theory which makes a place for them.

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2.6 Microphysical universals in Armstrong

In this and the next section I will show that with the exception of Schaffer’s atypical

approach to privilege, the domain of properties which are maximally privileged

correspond to those of a completed science of physics, excluding those of higher-order

sciences such as chemistry or biology. This is what we call the microphysical approach

to the maximally privileged properties. For Armstrong, the commitment to

microphysical maximally privileged properties follows from the combination of his

characterisation of universals as things which confer causal powers on their instances

and his stance on Boolean compounds of universals, in particular his denial of

disjunctive universals. Lewis’ position is less concerned with the need for all privileged

properties to be causal, but is instead informed by his posit of Humean Supervenience,

which is a background hypothesis concerning the nature of reality (see §2.7).

As noted in §1.3, scientific realism is the view that reality is, more or less, as it is

described by the sciences. The focus on physics as the science which identifies

privileged properties comes from the internal hierarchy acknowledged by the sciences

themselves. It is generally assumed that biological processes may be given a lower-level

explanation in terms of the chemical reactions taking place in the bodies of organisms,

whilst chemical reactions can be explained in terms of the motions of the fundamental

particles, the domain of physics. It must be reiterated at this point that the physics the

supporters of privilege have in mind here is not necessarily the current state-of-the-art

in that particular field, but rather an eventual completed physics that succeeds in the

goal of providing a truly general explanation of all worldly phenomena (Lewis 1994a

p474).

It does not immediately follow that just because physics aims at a completely general

account of reality, the privileged properties should be microphysical to the exclusion of

all others. It is often supposed that the privileged properties will jointly comprise a

minimal supervenience basis for reality (Dorr and Hawthorne 2013 p7), and the

properties constituting a completed physics would surely be a good candidate for that

criterion, but a theory of privilege is distinct from a mere claim about the supervenience

of one scientific discipline on another in that it proposes that a select group of

properties combine a variety of philosophically interesting roles. Just because there can

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be no difference in the chemical properties of the world without some difference in the

physical properties of the world it does not follow that all similarity relations track the

numbers of physical properties they share. Physically, hydrogen and helium are

extremely similar. They are relatively close together in weight, and differ only with

respect to the fact that helium has two protons in its nucleus while hydrogen has one.

Certainly they are more similar physically than helium and xenon, which has fifty-four

protons in its nucleus. This is not the case when these elements are viewed from the

perspective of chemistry. Hydrogen is far more reactive than helium, which is in this

respect closer to xenon. Some evidence must be given in support of the view that the

physical properties can serve as the basis for all the roles of privileged properties, such

as similarity-making, and featuring in causal laws. In the work of Armstrong and Lewis

the nature of this connection between physics as a minimal supervenience basis and

the other functions differs somewhat. In this section we will focus on Armstrong’s

account.

For Armstrong, the predicates which correspond to privileged properties are just those

which pick out the instances of some universal, and all universals make a difference to

the causal profiles of the objects which possess them. In his preferred terminology,

universals confer some causal powers on the objects which instantiate them (1978b

pp43-44). He admits that he cannot see how we would ever have good reason to posit

the existence of such ‘causally idle’ universals, as any universals which did not endow

their possessors with any causal powers whatsoever must be completely undetectable

by us (1978b p10). In making this claim Armstrong is not insisting that there are causal

powers possessed by all the particular objects to which a predicate applies. Although

there will be causal powers common to all those objects to which certain predicates

apply (those predicates which apply only to instances of a single universal), there will

be many more that signify nothing about the causal powers of objects.7 The examples

7 An additional reason Armstrong has for rejecting the notion that every predicate corresponds to some universal is the existence of predicates which do not apply to anything at all. Armstrong subscribes to an account of universals as ‘immanent’ rather than ‘transcendent’. To hold that universals are transcendent is to hold that universals have an existence independent of their instances. Immanent universals by contrast exist ‘in’ their instances (1978a p76). This commits him to the view that all properties and relations are properties and relations of some particular or particulars (1978a, pp75-76). If there are no particulars to which a predicate applies, ever has

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he gives of such predicates are ‘being identical with itself’ and ‘exists’. Armstrong claims

that it is difficult to see how there could be any causal powers conferred upon a thing

by properties corresponding to such predicates, as they apply to every object (1978b

p11). It may well be pointed out here that the application of the predicates of self-

identity and existence to an object are in fact implied by any objects’ having any kind

of causal efficacy whatsoever. Whilst there may be no specific causal powers shared by

all things which exist, existence does appear to be a prerequisite for an object's having

any causal powers at all. Clearly Armstrong has something stronger than this in mind.

Armstrong summarises his view of which predicates correspond to universals by the

following four conditions, inspired in part by the ‘mark of being’ offered by the Eleatic

stranger in Plato’s Sophist (Armstrong 1978b pp45-46).

1. The causal powers of particulars are all conferred upon them by the universals

they instantiate.

2. Every universal bestows some active or passive power upon the particulars

which instantiate it.

3. A universal bestows the very same power upon any particular which

instantiates it.

4. Each universal bestows some different powers upon the particulars which

instantiate it. (Armstrong 1978b pp43-44)

To this we may add an additional requirement of Armstrong’s, that all universals be

instanced by some actual object, past, present or future. Armstrong’s universals do not

exist independently of their instances (1978a pp75-76). Lewis holds a similar but more

permissive principle in his own theory. Properties are sets of particulars for Lewis (1983

p189), so the only property which lacks any instances is the empty set. Lewis accepts

the existence of possible particulars as well as merely actual ones, and possible

particulars can be members of properties. Although this would rule out impossible

properties (or at least make them all identical with the empty set) this still guarantees

applied or ever will apply, there can be no property to which that predicate corresponds (1978b, p10).

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that there will be many properties, among them many natural properties, which are

not possessed by any actual particular (1983 p189-190).

The first of these four conditions of Armstrong’s is simply a restatement of his initial

assumption concerning the link between the idea of properties and causation, while

the second rules out causally idle properties. The final two conditions do more to

illuminate how many privileged properties Armstrong takes there to be. Predicates

such as ‘exists’ and ‘is self-identical’ cannot correspond to privileged properties

according to the third condition, as there are no causal powers shared by all objects to

which they apply. The fourth condition states that if two universals confer identical

causal powers on their objects, then we have no reason to postulate that they are

distinct. In conditions two, three and four we may note that Armstrong is appealing to

Occam’s Razor. This agrees with the discussion we made of the theorist of privileges

background assumptions in §1.4, where we noted that all parties to the debate over

privilege are concerned not to multiply entities beyond necessity.

The four conditions Armstrong gives us would allow universals for properties that lie

outside scientific discourse, but we noted in §1.3 that this is something Armstrong is

keen not to do. While it is true that properties such as Florb are excluded from being

universals because there are no causal powers common to all Florb objects, there are

many other non-scientific properties which meet the four conditions. For instance, all

the objects which possess the property of being an intact coffee mug have certain

shared causal powers. Under the proper conditions and when correctly oriented in the

Earth’s gravitational field, all coffee mugs have the ability to contain certain liquids and

prevent them running away. Additionally, the precise suite of causal powers conferred

upon an object by being a coffee mug can be distinguished from those of other

properties. Assuming there are some fairly well-understood standards for an object’s

being a coffee mug, it seems as though any objects which possess the property of being

a coffee mug are going to produce certain kinds of experience in the minds of observers

unlike those produced by observation of teacups, and unlike paper cups, coffee mugs

are rigid rather than easily deformed. It seems as though being a coffee mug meets

Armstrong’s standards for being a universal.

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This permissiveness is a consequence of Armstrong’s approach to universals as

discoverable only through empirical methods and not a priori reasoning (1978b pp7-8).

The four conditions are not by themselves intended to account for a microphysical

approach to maximally privileged properties, but rather illustrate those circumstances

in which we might plausibly take universals to be distinct from one another. Science

and not philosophy will tell us whether being an intact coffee mug is a universal. It is

nonetheless the case that Armstrong takes universals to be the microphysical

properties only. This is guaranteed by the stance Armstrong takes on conjunctive,

disjunctive and negative universals. If the property of being an intact coffee mug is a

universal it must be conjunctive. We can know this because coffee mugs are complex

objects with proper parts. If an object is a coffee mug it must be at least partly so in

virtue of the makeup of its parts, so the property of being an intact coffee mug must

correspond to some conjunction of properties concerning the arrangement of those

parts.8 Armstrong’s conditions permit the existence of conjunctive universals, and

universals are privileged properties, but conjunctive universals cannot be maximally

privileged. In §2.2 it was shown that the most plausible interpretation of Armstrong’s

conjunctive universals is in a manner analogous to Lewis’ conception of less-than-

perfect naturalness. Maximally privileged properties must be those which cannot be

expressed as conjunctions of other universals. This rules out any properties which

things have in virtue of the way their parts are from the highest level of privilege. We

should therefore expect the maximally privileged properties to be those which divide

objects with differing arrangements of their microphysical parts.

8For the purposes of this example it is helpful to distinguish between the properties instantiated by the parts of the coffee mug, and the properties which the coffee mug instantiates by having the parts it does. A silicon atom within the mug will instantiate the property of having a nucleus containing fourteen protons, but the mug itself will not, because only atoms can instantiate such a property. The coffee mug will instantiate the property of having a part which has fourteen protons, however. It is properties of this latter kind which will be conjuncts of the universal being an intact coffee mug. It isn’t clear whether Armstrong would take a property like this to be itself a candidate for a non-conjunctive universal, or if he would hold that only the properties of the smallest parts of objects instantiate non-conjunctive universals. If not, there would have to be an additional sense in which universals can be said to be conjunctive or disjunctive just in case the parts of the objects which instantiate them always instantiate certain universals or disjunctions of universals. This is an interesting question in its own right, but sadly is beyond the scope of this project to explore.

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2.7 Microphysical perfectly natural properties in Lewis

Lewis, by contrast, is far more explicit about which properties he takes to be privileged

and the roles that such properties perform. He is also far more explicit concerning

degrees of privilege, which merely lie implicit in Armstrong’s talk of conjunctive

universals. In Lewis’ thought properties may be ‘perfectly natural’, ‘less-than-perfectly

natural’, or ‘not at all natural’ (1983 p192). All natural properties fulfil some of the

specialised roles of privileged properties. Although we noted in §2.2 that Lewis is not

entirely explicit about how the degree of naturalness of a less-than-perfectly natural

properties is to be established, one potential (although fallible) method of measuring

closeness to the perfectly natural properties is based on the length of the definition of

those properties in terms of the perfectly natural properties (Nolan 2005 p24). The

perfectly natural properties are therefore the basis for the edifice of merely somewhat

natural properties built on top of them. The most important questions raised by the

topic of less-than-perfect naturalness were covered in §2.4, and so now I will focus just

on those properties which are foundational to Lewis’ theory of privilege, the ‘perfectly

natural’ properties. As with Armstrong’s universals, these can be identified with the

properties of a completed microphysics.

Throughout Lewis’ work in metaphysics it is possible to identify two foundational

threads. One of these we have already examined: his commitment to scientific realism

(see §1.3). The other is the posit of ‘Humean Supervenience’. Both inform Lewis’ views

on the number of perfectly natural properties. In Lewis’ own words, Humean

Supervenience is a contingent hypothesis about the nature of ‘worlds like ours’ (Lewis

1994a pp473-475). He does not claim that our own world is undoubtedly a Humean

Supervenience world, only that there are good reasons to suppose that it might be

(Lewis, 1986b xi). Humean Supervenience is the claim that the world is an arrangement

of perfectly natural, intrinsic and maximally local qualities, and nothing more (Lewis,

1986b px).

Lewis’ supervenience thesis is ‘Humean’ in the sense that he denies the existence of

necessary connections between objects, just as Hume famously denied that events

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were necessitated by one another (Hume 1739 chapter VII). For Lewis, the character of

reality as a whole is a function of the intrinsic natures of the individual space-time

points, which are the only fundamental objects (1994a p474). Although there are

regularities amongst the pattern of distribution of properties at this level, Lewis posits

no fundamental relations between space-time points. This is a supervenience thesis in

the sense that Lewis takes all non-fundamental states of affairs, instances of non-

perfectly natural properties or relations between space-time regions, to ultimately

depend on the intrinsic natures of points in space-time. Lewis notes that this approach

to ontology might be seen as eliminativist, although he himself rejects this accusation

(1983 p205). In fact, he is perfectly content to allow the existence of macroscopic

objects like tables and chairs along with the corresponding properties of being a table

and being a chair. Just as in Armstrong’s account, Humean Supervenience implies that

the privileged properties will be any and all those which feature in a completed

subatomic physics. Such properties are the only ones that could possibly satisfy the

requirement that perfectly natural properties be ‘maximally local’.

Although Lewis is aligned with Armstrong to the extent that he considers it to be a mark

of a perfectly natural property that it features in causal laws, Lewis’ view of causation

is very different to Armstrong’s. Whereas Armstrong takes causal laws to be relations

of genuine necessitation between universals (Armstrong 1997 pp223-226), Lewis

endorses a counterfactual theory of causation (Lewis, 1973). Note that this is still a

Humean approach to causation, since the semantics for counterfactuals he endorses

reduces talk of one event’s causing another to talk of what is the case in other possible

worlds. When we say that a moving billiard ball striking another at rest counterfactually

implies that the second ball begins to move, Lewis does not take this to be a matter of

one event existing in a relation of necessitation with another. Instead, this is simply

taken to mean that there is no possible world that is importantly similar to our own in

which an event of the first kind occurs without an event of the second kind occurring

immediately afterwards (Lewis 1973a pp4-13, see also Lewis 1968 pp164-167, Loux

2006 pp198-200). No necessary connections between events are posited. The sense of

causation Lewis therefore aims to pick out is quite a loose one, since he takes there to

be a cause anywhere one sees a counterfactual conditional holding between events:

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We sometimes single out one among all the causes of some event and call it

‘the’ cause, as if there were no others. Or we could single out a few as the

‘causes’, calling the rest mere ‘causal factors’ or ‘causal conditions’. Or we

speak of the ‘decisive’ or ‘real’ or ‘principal’ cause. We may select the abnormal

or extraordinary causes, or those under human control, or those we deem good

or bad, or just those we want to talk about. I have nothing to say about the

principles of invidious discrimination. (Lewis 1973b p162)

Even so, Lewis does believe there are laws of nature. For Lewis, a law of nature is just

a causal dependence between types of events which features in the simplest

articulation of what we have already characterised as completed physics (1983 p215).

The perfectly natural properties, being the same ones which a completed physics

attempts to categorise, are also those which feature in laws of nature by default. There

is no explicit requirement in Lewis that all less-than-perfectly natural properties confer

a unity of causal powers on their objects, as Armstrong requires that non-fundamental

universals must.

Both Armstrong and Lewis therefore take the maximally privileged properties to be

microphysical. This approach is also explicitly endorsed by Sider, who leans towards a

broadly Lewisian framework for privilege (2011 p292). It is fair to say that this

represents the mainstream point of view regarding privileged properties. There is but

one theorist of note who can be classed as a supporter of privileged properties and a

denier of the microphysical approach to properties. This lone voice of dissent amongst

supporters of privilege comes from Schaffer, who rejects not only the idea of privileged

properties as exclusively microphysical (2004 p92), but as comprising a minimal

supervenience basis for reality as well. Schaffer endorses a metaphysical worldview he

calls ‘priority monism’, according to which the most fundamental substance is the

cosmos itself. As he defines his position:

The monist holds that the whole is prior to its parts, and thus views the cosmos

as fundamental, with metaphysical explanation dangling downward from the

One. (Schaffer 2010 p31)

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As much as Schaffer’s views on fundamental substance differ from those of Armstrong

and Lewis, his views on privileged properties align quite closely with the scientific

realism derived approach they endorse. Schaffer accepts that there are privileged

properties corresponding to the theoretical terms involved in the natural sciences, and

acknowledges many of the same roles for them, including similarity-making and

featuring in causal laws (2004 pp93-94). The properties posited by the sciences are

properties of parts of the cosmos, however, often very small parts. As such, the view

that privileged properties comprise a minimal supervenience basis for reality and

correspond to the scientific realist worldview is in direct conflict with priority monism.

Since Schaffer rejects the view of privileged properties as a minimal supervenience

basis in the first place, he is under no compulsion to locate all privileged properties

within physics. In fact, he takes the privileged properties to be drawn ‘from all levels of

nature’, and include all those which form part of the scientific understanding of the

world (Schaffer 2004 p92). He makes no distinction between perfect or maximally

privileged properties and less-privileged properties. Given that all entities and

properties which form part of the scientific understanding of the world are proposed

to be less fundamental than a single all-encompassing substance, there can be no such

properties which claim to be fundamental in a metaphysical sense, although it is easy

to see how physics may be more fundamental amongst the sciences from the point of

view of the generality of the explanations it offers. Schaffer’s reason for preferring this

account of privileged properties to the microphysical version is that causal laws and

similarity relations appear to hold between entities at the levels of the higher-order

sciences as well as at the level of microphysics (2004 pp94-95), which becomes a

decisive consideration against the microphysical approach when the requirement of

minimality is also rejected.

I mention Schaffer’s view in order to concede that the microphysical approach is not

completely universal. Although it may be the dominant position amongst theorists of

privilege it would be a mistake to view privilege as necessarily committed to the

microphysical approach. Even so we may conclude that, with one notable exception,

the most privileged properties are widely held to be no more numerous than those

which feature in a fundamental, completed physics. Physics is an empirical discipline,

so it is impossible to say a priori how many privileged properties there are exactly. In

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the following section I will show that it is at least possible to show one additional

restriction on the range of privileged properties on an a priori basis: all privileged

properties are intrinsic.

2.8 The Intrinsicness of privilege

An extrinsic property is a property which a thing has partly in virtue of the properties

possessed by something other than itself. Correspondingly, an intrinsic property is a

property which a thing has independently of the properties of any other thing. An

object’s having a mass of 2kg is entirely determined by the composition of that object

itself, and so is an intrinsic property. The property of being Winston Churchill’s cigar

cutter on the other hand is not intrinsic, as possessing such a property relies on certain

features of the world external to the object itself. It relies on there being an object,

Winston Churchill, who smoked cigars and habitually used that particular device to cut

them. An extrinsic property is distinct from a relation, although an object’s possessing

an extrinsic property usually does imply the existence of some relation that the object

stands in, just as being Winston Churchill’s cigar cutter implies a relation which holds

between itself and Winston Churchill.9 As discussed in §1.3, a relation can be thought

of as a multiple-place property. Extrinsic properties on the other hand, are often single-

place.10 The property of being Winston Churchill’s cigar cutter does not hold between a

cigar cutter and Winston Churchill. It is a property of the cigar cutter alone, although

one it has in virtue of some features of Winston Churchill. Extrinsic properties therefore

are found where an object’s having a property is partly or wholly determined by the

9 Not all extrinsic properties imply relations. The property of not being within a mile of a dragon can be had by objects even though there are no actual dragons to be related to (Weatherson and Marshall 2012). Such properties still imply something about the instantiation of other single-place properties in the world however: they imply that everything within a mile of a certain object has the property of not being a dragon. 10 There can be multiple-place extrinsic properties, because relations are a type of property. We can suppose that a relation is extrinsic just in case it depends on more than its relata for its application. The relation of being heavier than is a relation of this kind. Unlike mass, the weight of an object depends on the strength of the gravitational field it is subject to, which is not intrinsic to its relata.

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nature of something other than that object. In this section it will be shown that all

accounts of privilege must deny that extrinsic properties are part of the elite minority.

In the systems of Armstrong and Lewis there is an obvious reason why there cannot be

any extrinsic properties at the level of greatest privilege, what Armstrong thinks of as

the non-conjunctive universals and Lewis calls the perfectly natural properties. This

fundamental level is intended to function as a minimal supervenience basis for reality

(see also §3.4), and the inclusion of extrinsic properties as well as intrinsic properties

would violate that minimality. Consider a simple interaction between particles, such as

the repulsion of two positively charged ions in a particular region of space over a

particular stretch of time. The intrinsic properties of the interacting objects at this point

will include properties such as having a mass of 2kg or having a positive charge of 1.

There may also be relations holding between the interacting objects which we should

take into account. Like properties, relations will be part of the minimal supervenience

basis just in case their instantiation does not supervene on the instantiation of any of

the properties already in the supervenience basis (see §3.4, where I also discuss an

exception to this rule). For example, the relation x is the same kind of particle as y

supervenes on the properties of x and y, and is therefore not part of the minimal

supervenience basis. On the other hand, the relation x is five millimetres away from y

arguably does not supervene on any of the (intrinsic) properties of x or y. This example

assumes that spatiotemporal location is not an intrinsic feature of particulars. As we

shall see, this is something Lewis denies.

By the definition I gave at the start of this section all extrinsic properties supervene on

the pattern of instantiation of other properties or relations and so appear to be

redundant. There is however an additional complication in that this supervenience of

extrinsic properties on intrinsic properties and relations is often mutual. Suppose that

a particular interaction between particles was mediated by a relation R, and that a

particle x stands in relation R to y. Suppose additionally that this relation does not

supervene on any intrinsic properties of x and y. Note that there may not be any such

relations in this, the actual world. There can be no difference in the pattern of

instantiation of the extrinsic property of being a particle standing in relation R to

particle y without some difference in the instantiation of the relation R, but likewise

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there can be no difference in the instantiation of relation R without some difference in

the pattern of instantiation of the extrinsic property of being a particle interacting with

another. It would appear that for any relation there will be some extrinsic property or

properties on which that relation supervenes, so there is at least an option of

populating the minimal supervenience basis with extrinsic properties rather than

intrinsic properties or relations.

A minimal supervenience basis that included extrinsic properties rather than relations

would be far larger than one which did not however. To replace the single relation R in

the minimal supervenience basis with extrinsic properties would require an extrinsic

property for every particular that stood in that relation. The single state of affairs of x’s

standing in relation R to y would require that x had the property of being a particle

standing in relation R to particle y and y had the property of being a particle standing

in relation R to particle x. We would require more such properties in the minimal

supervenience basis for every pair of particulars that stand in relation R with each

other. We may therefore conclude that a minimal supervenience basis which included

some extrinsic properties rather than intrinsic properties or relations would be far less

simple than one which does not, and is therefore eliminable by Occam’s razor.

Even granted that minimality requires that all privileged properties are intrinsic at the

lowest level, in §2.2 we noted that the minimality constraint does not apply to less-

privileged properties. Nothing about the requirement that the most privileged

properties comprise a minimal supervenience basis has the consequence that less-

privileged properties must be intrinsic. Nonetheless, we have very good reason to

assume that they are.

To the extent that Armstrong accepts the existence of less-privileged properties, he

characterises them as conjunctions of distinct but coinstatiated universals. If all non-

conjunctive universals are intrinsic, however, then there is no possible conjunction of

them that would be extrinsic. The property of possessing any particular conjunction of

intrinsic properties cannot itself be extrinsic. Armstrong’s framework would still have

the consequence that all privileged properties were intrinsic even if we altered his

theory to permit disjunctive and negative universals in addition to conjunctive ones.

For Lewis, the intrinsicality of all properties with some degree of naturalness is

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guaranteed by Humean Supervenience. According to Humean Supervenience, the

character of a region of space-time supervenes on the intrinsic character of the space-

time points from which it is constituted, in the same way that a mosaic picture is built

up out of the colours of the tiles that constitute it (Nolan 2005 ch2). The problem is

that the instantiation of extrinsic properties does not supervene just on the constituent

parts of the object which possesses them. Suppose that a given object has the property

of being Winston Churchill’s cigar cutter. The instantiation of this property by an object

must supervene on Winston Churchill too, for if Winston Churchill had never existed,

then nothing could have been his cigar cutter. If there are extrinsic natural properties,

then they must violate Lewis’ supervenience thesis.

Although Lewis himself is committed to intrinsic less-than-perfectly natural properties,

it remains to be shown that a version of Lewis’ theory that did away with Humean

Supervenience still must deny that there are any extrinsic natural properties. Note that

a denial of Humean Supervenience alone is not sufficient to raise the possibility of

extrinsic natural properties. If we take the generally accepted view that less-than-

perfectly natural properties are defined from the perfectly natural ones by conjunction,

disjunction and negation, then all natural properties must be intrinsic for the same

reason that Armstrong must take all conjunctive universals to be intrinsic. One cannot

generate extrinsic properties out of Boolean compounds of intrinsic properties.

Recall that Lewis does not officially commit himself to any view of how less-than-

perfectly natural properties are related to perfectly natural ones (see §2.2). It is

possible to conceive of a Lewis-inspired theory of privilege which denied Humean

Supervenience and employed a measure of less-than-perfect naturalness other than

the length of a property’s definition in terms of the perfectly natural properties. Such

a theory could accommodate natural extrinsic properties, although there are reasons

why a supporter of privilege should nonetheless be reluctant to do so. Remember,

amongst the useful features of privileged properties is the fact that no object would

ever have infinitely many of them (Lewis 1983 p192). This would not be the case if

extrinsic properties could be natural, as I will show.

Let’s assume a reasonable limitation on those extrinsic properties which might be

considered natural and say that extrinsic properties are natural just in case the objects

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which instantiate them do so partly in virtue of the arrangement of intrinsic natural

properties in the world beyond themselves. The property of being more than ten feet

from a Florb object would then fail to be a natural property, but the property of being

orbited by an electron would be. This is intuitively appealing as it allows the acceptance

of natural extrinsic properties to be continuous with the standards set for the inclusion

of intrinsic natural properties. The problem is that there are infinitely many properties

of even the smallest particles that would pass this test. Every quark in the actual world

would have the property of being part of the same world as at least two electrons, an

extrinsic natural property which differs extensionally (when extension is allowed to

include merely possible particulars) from the property of being part of the same world

as at least three electrons, and so on. It isn’t clear how there could be a criterion for

naturalness of extrinsic properties that could accept some natural extrinsic properties

whilst denying these. At any rate I have shown that the burden is on the supporter of

extrinsic natural properties to show what such a criterion might look like. In the

absence of such we can conclude that allowing extrinsic natural properties would result

in particulars in fairly crowded worlds like ours possessing infinitely many such

properties, which would make them unsuitable to play the roles of similarity-makers.

For this reason, I propose that we make the assumption from this point on that all

theories of privilege which adhere to a fairly mainstream view of the roles of privileged

properties are committed to the notion that all privileged properties are intrinsic.

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Chapter Three: Roles of Privileged Properties

3.1 Dorr and Hawthorne on naturalness

My project concerns the roles of privileged properties and the theoretical benefits that

supposedly come from attributing these functions to a single group of properties.

Chapters one and two were dedicated to a detailed account of theories of privilege,

their motivations and specific commitments. In this chapter we will be primarily

concerned with an understanding of the roles themselves and how they interact. In

particular, I will establish that the three most important roles for privileged properties

are in providing a minimal supervenience basis for all reality, making for overall

similarity between particulars when shared, and acting as ‘reference magnets’ in

certain theories of metasemantics. The second part of this thesis will examine the

plausibility of combining these roles into a single unified notion of privileged properties.

The most detailed analysis of privilege as a combination of roles in recent years comes

from Dorr and Hawthorne’s survey of the debate, in which they focus quite heavily on

a specifically Lewisian version of privilege (Dorr and Hawthorne 2013). Aspects of the

methodology they propose will be extremely advantageous to the project at hand, in

particular their focus on the co-satisfiability of individual purported roles. Introducing

Dorr and Hawthorne’s methodology will be the topic of §3.2. Dorr and Hawthorne base

their analysis of theoretical roles on a particular treatment of theoretical terms known

as the Lewis-Ramsey-Carnap method (Dorr and Hawthorne 2013 p4, see also Lewis

1970, Ramsey 1929). There are, however, certain roles for privilege relevant to the

project at hand which cannot be adequately captured in this way. In particular, claims

about the ‘betterness’ of describing the world in joint-carving terms cannot be

captured by the expanded postulate of privilege (Sider 2011 p61). I will instead

advocate a looser definition of a ‘role’ than Dorr and Hawthorne’s, and take a role for

privileged properties to be simply a distinguishing feature of privileged properties that

is not possessed by any non-privileged property. This will be the subject of §3.3.

A second respect in which I depart from Dorr and Hawthorne is in their refusal to claim

that any role for privilege is more important than any other. I agree with them to the

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extent that I do not take any role of privilege to have definitional status (2013 p10), by

which I mean that I do not claim that there is any role which a theory of privilege must

attribute to the privileged properties. I do however believe that there is a hierarchy

amongst the roles proposed for privileged properties, something which Dorr and

Hawthorne do not consider. I have already claimed that theories of privilege are to be

justified on the basis of their theoretical virtue (see §1.4), and viewed through this lens

there are certain roles for privilege that only contribute to the overall value of the posit

when combined with certain other roles. This demonstrates my conclusion, that the

three roles already mentioned are indeed the most theoretically important for

privilege. In §3.4 and §3.5 I show how several of the roles which Dorr and Hawthorne

identify for privileged properties, specifically Laws, Independence, Simplicity and

Empiricism can be seen to derive from the privileged properties as a minimal

supervenience basis.

In §3.6 I will turn to the similarity-making role, and show how this role underlies Dorr

and Hawthorne’s Duplication role, and all of the ancillary notions which Lewis originally

used the notion of duplication to account for, including supervenience, divergence and

convergence of worlds, and the idea of an intrinsic property. I will reserve a detailed

discussion of the role of privilege in metasemantics for chapter six, however in §3.7 I

will show how it and Sider’s proposal of inherent epistemic value can be shown to have

similar motivations (2011 p61). We may therefore identify Supervenience, Similarity

and Magnetism as three keystone roles for privileged properties. In the final section of

this chapter I will lay out my strategy for the second half of this project.

It should first of all be noted that there are two of Dorr and Hawthorne’s roles I will not

be discussing in this chapter. The first of these is what Dorr and Hawthorne call

Simplicity, which they formulate as follows:

One property is more natural than another iff the former has a definition in

terms of the perfectly natural properties that is simpler than any definition of

the latter in terms of perfectly natural properties. (Dorr and Hawthorne 2013

p19)

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In §2.2 I argued that the length of a property’s definition in terms of the perfectly

natural properties can tell us something about its degree of naturalness, but only

fallibly. There is more to having a high degree of naturalness than just having a short

definition. In part two I intend to focus on the most compelling version of the posit of

privilege for criticism, and therefore Simplicity is something we should be reluctant to

attribute to supporters of privilege.

The second of these roles is Necessity, which is the claim that any property has its

degree of privilege necessarily, and so there can be no variation in a property’s degree

of privilege from one possible world to the next (Dorr and Hawthorne 2013 pp31-32). I

will leave this claim unscrutinised because its acceptance depends not on what one

takes the natures of privileged properties to be, but on what one takes the nature of

properties themselves to be. In the frameworks of Armstrong and Lewis, facts about

properties being privileged to any degree are non-contingent because properties are

not world-bound entities. For Lewis, properties are sets of particulars drawn from all

possible worlds (Lewis 1983 p190). It is not the case that the property of being red can

be privileged in one world and not privileged in another, simply because each world

has the exact same class as their property of being red. The only difference is that the

members of the class that are actual from the point of view of one world, are possible

from the point of view of another, and vice versa.11 According to Armstrong’s

combinatorialist theory of modality, possible worlds are arrangements of entities from

the actual world (Armstrong 1986 p575, see also Armstrong 1989). No possible world

11I am claiming that privilege is not indexical, and so properties cannot vary in privilege from world to world, in the same way that The Eiffel Tower is both here and there, depending on where one is standing. We can reject indexical privilege for the following reason. Suppose that the property of being a quark was variably privileged, being fundamental in one world and not fundamental in others. It would follow that the instantiation of this property in some worlds would supervene on the instantiation of other, more fundamental properties found only in those worlds. The cross-world membership of properties does not vary from world to world. The red things in world w1 are members of the property of redness in w2 as well, even though w1’s red things are not part of w2. The set which is the property of red things is the same everywhere. The supervening instances of being a quark would be part of the class in every world, so there would be no world where no members of the property of being a quark did not supervene on the instantiations of any other properties, as required by the Supervenience role (see §3.4). Either a property is privileged to a degree everywhere, or nowhere.

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will contain instantiations of first-class universals (see §1.3) that are not found in the

actual world, although it may lack some universals found here.

This leaves nine roles proposed by Dorr and Hawthorne, plus Sider’s claim of inherent

epistemic value still to be accounted for. We begin with an outline of Dorr and

Hawthorne’s methodology for investigating privilege.

3.2 Dorr and Hawthorne’s methodology

Although Dorr and Hawthorne focus primarily on Lewis’ theory of naturalness, it is clear

that they intend their work to apply to Armstrong’s sparse universals framework as

well, along with various hybridisations and permutations of each. This is a consequence

of their particular approach to the posit of privilege as a combination of theoretical

roles. Rather than identifying a single theory of ‘naturalness’, Dorr and Hawthorne

instead set out to catalogue the various roles that have at one time or another been

ascribed to privileged properties by their various supporters. A theory of privilege is

simply one which holds that at least some of the naturalness role is satisfied by some

group of properties (Dorr and Hawthorne 2013 p5). They make no presumption about

how many or which roles must be satisfied for a theory to be considered a theory of

naturalness.

Dorr and Hawthorne propose their methodology in opposition to a particular kind of

discourse, which they think is characteristic of the privilege debate. Too often, they

claim, a difference of opinion regarding the posit of privilege comes down to a

difference in the attitudes of the parties to the debate. Those who are sceptical of

privilege are described as ‘rejecting’ the posit, while supporters ‘accept’ or

‘countenance’ it (2013 p3). Such talk is a close cousin to the all-too-familiar

metaphysical argument of last resort, the argument from the intuitive plausibility of

one option relative to the intuitive craziness of another. The problem with arguments

of this sort is that intuitions are rarely universal, and when the only motivation for the

disagreeing parties is a difference in what strikes them as intuitively plausible then

there is very little scope to advance philosophical debate. Dorr and Hawthorne are

therefore quite right to insist that the disagreement between sceptics and enthusiasts

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of privilege needs to be given a characterisation that does not just boil down to a

difference in attitudes.

It is perhaps unfair of them to suggest that this has historically been the norm in the

literature on privilege, however. In fact, when one looks at the kinds of arguments

offered in support of theories of privilege in Lewis and Armstrong’s work, one finds a

similar approach to the debate to the one Dorr and Hawthorne ultimately endorse, one

that takes a piecemeal approach to the various roles that privileged properties fulfil.

Armstrong argued for privilege on the basis that only certain properties featured in

laws of nature (1978b p11), and that only these properties made for facts of

resemblance between particulars when shared (1978b pp96-98). Lewis adopted much

the same approach in putting forward his own version of privilege, offering a detailed

list of all the various theoretical gains to be had in accepting natural properties (1983

pp191-192). Dorr and Hawthorne’s proposed methodology for investigating privilege

has much the same form as this existing debate. They advocate identifying roles for

privilege and determining through debate whether those roles are satisfiable by one

and the same group of properties, just as Lewis and Armstrong do.

A more charitable interpretation of Dorr and Hawthorne’s criticism of attitude-centred

debate is possible. We noted in §1.3 that all mainstream supporters of privilege take

scientific realism to be a presupposition of their theory, and that this presupposition is

the primary motivation for a belief in privilege. This could well be the kind of attitude

that Dorr and Hawthorne single out for reproach, but again as we noted in §1.4, there

is a difference between the motivation for adopting a position and how that position is

justified. It is not the case that the theorists of privilege we have drawn attention to so

far have attempted to justify their belief in privilege in terms of their attitudes to an

unargued for assumption. The value of Dorr and Hawthorne’s work is not in giving a

new structure to the debate over privilege that was previously lacking, but rather in

articulating that structure in a clear and illuminating manner.

If there can be no fruitful debate over whether one or other undefended

presupposition is justified, progress can be made on the question of whether or not a

variety of theoretical roles are satisfied. In Dorr and Hawthorne’s terminology, a

thoroughgoing sceptic concerning privilege would claim that none of the theoretical

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roles attributed to privileged properties are satisfied, whereas a thoroughgoing

‘enthusiast’ (as Dorr and Hawthorne refer to proponents of privilege) would claim that

all or a very large part of the total theoretical role of privilege is satisfied by some group

of properties (Dorr and Hawthorne 2013 p6). Aside from labelling someone a sceptic

or enthusiast of a greater or lesser degree, Dorr and Hawthorne’s approach allows for

a great deal of variety in the potential positions that can be adopted (Dorr and

Hawthorne 2013 p6). Two moderate enthusiasts about privilege can nonetheless

disagree considerably about which roles of privilege are satisfied. As such, Dorr and

Hawthorne relocate the debate about whether there are privileged properties to a

series of more manageable questions about the performance of individual roles. This

will be reflected in the second half of this project. Although my goal is broadly sceptical

concerning privilege I will not set out to say ‘There are no such things as privileged

properties’. Instead I will focus on the ability (or rather, the inability) of a few key

theoretical roles to be jointly satisfied. It is entirely possible that a supporter of privilege

could agree with all of the observations I make regarding the co-satisfiability of these

roles and still persist in their belief in an elite minority of privileged properties in some

form or another. Any version of privilege which would remain untouched by my

criticisms would be a very different one from the one described in the frameworks of

Armstrong and Lewis, however.

3.3 The nature of a ‘role’

The purpose of this section will be to clarify the sense of ‘role’ that we will be using.

Dorr and Hawthorne offer a very specific account of a ‘role’ based on the Lewis-

Ramsey-Carnap method of defining theoretical terms, which I will briefly outline in

contrast to Lewis’ notion of ‘work’.12 It will not be desirable for the purposes of this

project to adopt their approach to roles wholeheartedly, however. Some roles of

12 In addition, this method for defining terms features quite heavily in Lewis’ interpretationist metasemantics. Dorr and Hawthorne’s Magnetism role for privileged properties is primarily concerned with solving certain problems with interpretationist metasemantics. As such, I will reserve a fully detailed analysis of this particular method of defining terms for chapter six, which deals exclusively with Magnetism and interpretationist metasemantics.

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privileged properties cannot be articulated in accordance with this framework, for

instance Sider’s claim that descriptions cast in joint-carving terms have an inherent

epistemic value (Sider 2011 p61, see also §3.7). Instead I intend to adopt a looser

account of a role than Dorr and Hawthorne: I will take a role to be simply a feature of

privileged properties that is not a feature of non-privileged or non-joint-carving

properties. In addition to accommodating some roles which Dorr and Hawthorne

ignore, this account accords well with the variety of different ways privilege is spoken

of in contemporary literature.

There are a number of terms which we have so far used or noted the use of to refer to

the characteristics of privileged properties. Lewis talks about ‘work’ for privilege (1983

p188), whereas Dorr and Hawthorne speak of theoretical ‘roles’ (2013 p5) and Sider

talks about ‘connections’ between privilege and topics of interest in metaphysics (Sider

2011 p21). In all of these different cases the idea to be captured is the same: some

distinguishing feature of the privileged properties by which they can be separated out

from the non-privileged properties, although the differences in terminology reflect a

difference in focus amongst theorists in the privilege debate. On my account therefore,

featuring in laws of nature counts as a ‘role’ for privileged properties, because this is

proposed as a feature of privileged properties which is not shared by non-privileged

properties. This account of a role is loose enough to accommodate both Dorr and

Hawthorne’s use of the term as well as the sense it is given by theorists such as Lewis.

Lewis is primarily concerned with justifying his posit of naturalness, and so when he

speaks of ‘work’ for natural properties he is talking about philosophical problems that

natural properties can solve. These problems have a very specific form. According to

Lewis:

An effort at systematic philosophy must indeed give an account of any

purported fact. There are three ways to give an account. (1) ‘I deny it’ – this

earns a failing mark if the fact really is Moorean. (2) – ‘I analyse it thus’ – this is

Armstrong’s response to the facts of apparent sameness of type. Or (3) ‘I

accept it as primitive’. Not every account is an analysis! (Lewis 1983 p198)

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On this understanding of Lewis the objects of philosophical inquiry are accounts of all

purported facts. Natural properties are a good addition to an ontology if they are able

to account for a variety of different kinds of fact using no additional resources. ‘Work’,

for Lewis, is just the ability to account for certain kinds of fact. It is for instance a

purported fact that Cambridge’s Bridge of Sighs is similar to Oxford’s Bridge of Sighs.

Such a fact can be given an analysis in terms of natural properties by claiming that any

two particular objects are similar just in case they share a high proportion of their

natural properties.

Dorr and Hawthorne’s project is not to justify privilege as a theoretical posit. They make

no claims about the value to a theory of various roles being satisfied (2013 p10). Their

goal, as we noted in §3.2, is simply to structure the debate in such a way that it can be

sensibly questioned whether or not such roles are jointly satisfiable by some group of

properties, and for this purpose the Ramsey-Lewis-Carnap method is well suited. This

method relies on the notion of an expanded postulate, which they define as follows.

Any theory expressed using a newly introduced predicate ‘F’ is equivalent to its

expanded postulate – the claim that there is a unique property that does all the

things that F-ness does according to the original theory. (A theory’s expanded

postulate is a close relative of its Ramsey sentence, which omits the uniqueness

claim.) (Dorr and Hawthorne 2013 p4)

Ramsey proposed that theoretical terms could in principle be eliminated in favour of

existentially quantified bound variables (Ramsey, 1929). We may demonstrate how

such a construction would operate by means of the following example. Suppose that a

particular theory of electromagnetism employs certain theoretical terms introduced by

this theory, such as ‘charge’. This term features in certain statements of theoretical

axioms, such as ‘objects which carry the same charge repel one another’. Suppose first

of all that we use conjunction to combine all of the axioms of the theory of

electromagnetism into a single sentence (T) which captures the entire theory, as in the

below example. Occurrences of novel theoretical terms within the sentence T are

indicated by Tn.

T[𝑇1 … 𝑇𝑛]

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Ramsey suggests that we can replace every instance of the word ‘charge’ in this theory

with higher-order variables, which we then bind by an existential quantifier. The

resulting higher-order sentence (known as a Ramsey sentence) tells us that there is a

range of entities, x1…xn which satisfy the theory T:

∃𝑥1 … 𝑥𝑛T[𝑥1 … 𝑥𝑛]

The expanded postulate differs from the Ramsey sentence in two key ways. First of all,

on Lewis’ account the expanded postulate of a theoretical term does not require

existential quantification of the variables within, and as such does not assume that

there is anything in the world which that term picks out, whereas the Ramsey sentence

does (Lewis, 1970 p430). In Lewis’ terminology there may be nothing that realises a

certain theoretical term. Note that as the earlier quotation indicates, Dorr and

Hawthorne use a notion of ‘expanded postulate’ which differs slightly from the

Lewisian one. Their use of the term suggests that they take an expanded postulate to

include the claim that something realises it. This is only a minor difference, and has no

impact on my overall project. Secondly in order for there to be a realisation of a term’s

expanded postulate, there must be one and only one n-tuple of entities that satisfies it

(Lewis, 1970 p432). The expanded postulate can be viewed as a set of conditions which

tell us what needs to be the case in order for a theory to be true. From the point of

view of our project this means that if there is any group of entities which uniquely

satisfy the expanded postulate of ‘privilege’ then the theory of privilege comes out

true.

I will not be adopting this approach to theoretical terms for the purposes of

investigating privilege because doing so would exclude from scrutiny certain roles

which supporters of privilege have proposed in favour of the posit. In particular, Sider

proposes two such features of privilege, that of the inherent epistemic value of joint-

carving descriptions, and the usefulness of privilege in accounting for the priority of the

science of physics. These roles may be understood as follows.

Sider takes it to be better to describe the world using joint-carving properties than non-

joint-carving properties. He asks that we consider a hypothetical world divided

vertically down the middle into two regions, one red and the other blue. We can call

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this vertical dividing plane A. Now imagine a diagonal plane B which separates most of

the red half and some of the blue half off from the rest of the world. In this example

there is supposed to be nothing privileged about the categories of being to the right or

left of plane B. On either side the space is neither completely red or completely blue.

Sider’s point is that whilst the inhabitants of this world may have words which

correspond to the properties of being on the left or right of B, in employing such words

they are making a mistake, even if they use those words competently and without

speaking falsely. They do worse in dividing the world than observers who divide the

world along the boundary between the red and blue regions (Sider 2011 p61).

For Sider, this value is a feature of privileged properties, just as it is a feature of

privileged properties that they make for similarity amongst their instances and feature

in laws of nature. The reason why the scientists who devise physical theories should

prefer that laws be understood in terms of the most privileged properties is because it

is simply better to think of the world in such a way. This value is not merely instrumental

to our successful navigation of the world, but rather is a ‘constitutive aim of the practice

of forming beliefs, as constitutive of the more commonly recognised aim of truth’ (Sider

2011 p61). Inherent epistemic value seems to pass all the tests we could require for

being counted as a role for privileged properties. It is a feature of privileged properties

that is not possessed by non-privileged properties, and if Sider is to be believed, it

provides unity of explanation to the other roles proposed for privilege. If there is such

a thing as inherent epistemic value then it follows that there will be facts about it, which

means it must be accounted for. Privilege would be one means of doing this. It cannot

be understood in terms of Dorr and Hawthorne’s strategy because of the peculiar way

this role is connected with the idea of privilege itself.

Inherent epistemic value is a new idea introduced by a theory of privilege itself. It is,

according to Sider, a form of value which attaches to descriptions of the world cast in

joint-carving terms. This does not fit in with Dorr and Hawthorne’s preferred account

of a role because the question is not one of whether or not there is a group of

properties which feature in inherently epistemically valuable descriptions. Rather, it is

because descriptions are cast in joint-carving terms that they are inherently

epistemically valuable in the first place. In introducing inherent epistemic value Sider

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does not propose that there is a group of properties which have this feature,

coincidentally the same group of properties that play a variety of other theoretical

roles. Sider claims that given the existence of a privileged domain it is intuitively better

to employ certain categories when dividing reality rather than others (Sider 2011 p61).

This betterness cannot be expressed as a theoretical role, because the existence of such

a role presupposes the existence of such a thing as privilege. Regardless of one’s stance

on privilege there will be a group of properties which satisfies the role of constituting

a minimal supervenience basis for reality. The group which contains every property will

be a supervenience basis, and if no smaller supervenience basis is possible then it will

also be a minimal supervenience basis (see §3.4). The question of whether such a group

of properties exists can be answered independently of one’s views on privilege itself.

This cannot be done with Sider’s inherent epistemic value. If there are no privileged

properties then there are no inherently epistemically valuable descriptions. No sense

can be made of this role independently of Sider’s theory of privilege taken in its

entirety. Nonetheless it is a contributing factor to the theoretical virtue of such a

theory. For this reason I propose that we adopt the looser definition of ‘role’ for

privileged properties in all subsequent discussion.

3.4 Supervenience

The first role that we have reason to view as foundational to theories of privilege is one

that we have touched on frequently in the previous two chapters. This is the role of

privileged properties in constituting a minimal supervenience basis for all reality. In this

section I will lay out the meaning of this claim in detail, and in the following section I

will demonstrate how certain other roles identified by Dorr and Hawthorne

(Independence, Laws and Empiricism) are inextricably linked to the commitment to

Supervenience. For now however, I will show that Dorr and Hawthorne’s account of the

Supervenience role leaves out two important features of this role as it is employed by

supporters of privilege. Firstly, the supervenience basis for reality that theorists of

privilege are interested in is the smallest possible supervenience basis, and secondly

the only privileged properties which feature in this smallest possible supervenience

basis are the maximally privileged properties (which we mentioned briefly in §2.2).

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First of all, it will be necessary to understand what exactly we take ‘supervenience’ itself

to be. In a nutshell, supervenience is a claim about a lack of independent variation

between types of events. The sense of the word ‘event’ I have in mind here is a loose

one, including both momentary happenings and persisting states of the world. We can

understand this lack of independent variation by means of an example. The species to

which an organism belongs supervenes on its genetic makeup, because having a certain

genetic makeup guarantees the species of the organism, at least according to one

common means of defining species membership. On this account an organism could

not belong to a different species without having a different genetic makeup. The

relation between the two kinds of events is not a causal one, but in this case the

possession of a certain genetic makeup actually constitutes what it means to belong to

a certain species (Braddon-Mitchell and Jackson 2007 p22). Supervenience of species

on genetics does not imply the supervenience of genetics on species. Two organisms

can be of the same species but differ genetically.

Although supervenience indicates a regularity between types of events, it is important

to note that this regularity can be coincidental, or indirect. In biological taxonomy,

animals are organised into clades based on species. When deciding which clade a

particular specimen belongs to, it is the species which biologists pay attention to and

nothing else. Two animals alike in species cannot differ with respect to clade, and so

the clade to which an animal belongs supervenes on their species. Additionally, an

organism’s species supervenes on its genetics, and so clade too supervenes on genetics,

because two animals alike in genetics will be alike in species, and two animals alike in

species will be alike in clade. Supervenience is transitive.

Supervenience can also hold between event types that are related only coincidentally.

The magnitude of the gravitational constant in the actual world supervenes on the total

number of cakes which exist in it at any one time. The gravitational constant can never

change, and so cannot vary independently of the number of cakes in the world also.

This is enough for supervenience of the gravitational constant on the number of cakes

to hold. The kind of supervenience claim we are interested in with respect to the

privilege debate does not talk about event types, however, but about groups of

properties.

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Dorr and Hawthorne talk about a group of properties as the basis for a supervenience

claim (Dorr and Hawthorne 2013 pp10-11). When we call a group of properties a

supervenience basis we mean that the type of event which is supervened on comprises

all those events which exclusively concern the instantiation or arrangement of

instantiations of those properties which make up the supervenience basis.13 If the

whole of reality is said to supervene on the maximally privileged properties as a

supervenience basis, this means that there can be no variation in any feature of the

world whatsoever independently of some variation in the arrangement of maximally

privileged properties. When we say ‘any feature of the world’ we mean the

instantiation or arrangement of instantiations of any property anywhere in the world.

The Supervenience role identified by Dorr and Hawthorne is a claim of this kind,

although they favour a variety of articulations according to which the relevant

supervenience relation is between the truth values of propositions about

arrangements of properties in a world rather than events (Dorr and Hawthorne 2013

p12). Whether we view supervenience as a relation between event types or truth

values of propositions does not matter for the project at hand, however.

As we noted at the beginning of this section, Dorr and Hawthorne’s proposal for how

to think of privileged properties as a supervenience basis omits two important features

of the role as it is employed by supporters of privilege. The first of these is the

requirement of minimality, that the properties which comprise the supervenience basis

should be as few as possible. This extra requirement makes a big difference to the

claim. Suppose that the only stricture on privileged properties was that they had to

comprise any supervenience basis for all reality, minimal or otherwise. This

requirement can be trivially satisfied by the group which contains all properties.

Everything is a supervenience basis for itself, so if we expand the list of properties which

comprise the supervenience basis until it includes every way that the world is or might

be, then we are assured that what we have is a supervenience basis for all reality. This

13 I do not wish to commit myself to any one account of an ‘event’ here. For this reason I am speaking of events as ‘concerning’ properties rather than being composed of properties, as with ‘Kimian’ events (Kim 1976), or simply by having descriptions which make reference to properties, as with ‘Davidsonian’ events (Davidson 1967a, 1970b). Lewis also offers a definition of an event as a ‘local matter of particular fact’ (Lewis 1986 p216, p243).

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is clearly not what the supporters of privilege intend by their claims of supervenience.

Supervenience claims are interesting only if the supervenience basis is smaller than the

domain of properties whose instantiation supervenes on it. As for why that basis should

not only be smaller than the domain of supervenient properties but should also be the

smallest possible, that too is a feature of theoretically interesting supervenience claims.

Consider our previous example, in which the identity of the President of the United

States supervenes on the votes cast in the Presidential election. If the holder of the

Presidency supervenes on this, then it must also supervene on the conjunction of the

votes cast in the election and the global population of aardvarks and the candidates’

abilities to whistle showtunes. Although it is certainly true to say that the identity of

the President supervenes on all these things just in case it supervenes on a single one

of them, there is more that is theoretically interesting about the supervenience claim

which identifies the smallest possible supervenience basis.

As with most features of mainstream theories of privilege, the motivation for the belief

in a minimal supervenience basis for reality derived from the privileged properties can

be traced to scientific realism, and in particular the identification of maximally

privileged properties with the categories marked out by a completed science of physics

(see §1.3 for previous discussion of this). Physics aims to explain all phenomena using

a single fundamental theory. In adopting the belief that the universe is more or less the

way that science supposes it to be, supporters of privilege also take on the belief that

this fundamental theory describes a supervenience basis for all reality as well.14 It is

because theories in physics aim for the greatest possible explanatory power with the

greatest possible simplicity that supporters of privilege take the supervenience basis to

be the smallest possible. It is not enough for the supporters of privilege that the

privileged properties comprise a supervenience basis for all reality: it is equally

14 The fact that I here describe a supervenience basis for all reality as being a theory of physics should not be taken to imply that theorists of privilege are committed to what is often called physicalism, although it is true that many theorists of privilege are also physicalists (Armstrong 1968, Lewis 1994 p474, Sider 2011 p292). Physicalism, as I will understand the term, is the view that all reality is ultimately physical, and that all seemingly non-physical phenomena such as mental processes or abstract entities such as numbers are either identical with some physical process or eliminable in favour of some physical process (Lowe 2000 p26). If physicalism is false, and the world does indeed contain irreducibly non-physical things, then a supervenience basis for all reality would have to include some non-physical properties as well as physical ones.

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important to their worldview that this supervenience basis should be as small as

possible.

Note that it is still compatible with the claim of minimal supervenience that every

property is a privileged property. It may well be that in some worlds the smallest

supervenience basis possible just is the one which includes all properties, although

even a cursory acquaintance with our own world would suggest that it is not one of

these worlds. It must be borne in mind however that the minimality requirement itself

does not guarantee that Supervenience will be theoretically illuminating. If we already

know that everything can supervene on itself then we know that there has to be at

least one supervenience basis for all reality, even if that supervenience basis is identical

with the very thing which supervenes on it.

Although minimality is not an explicit requirement of Dorr and Hawthorne’s

Supervenience role, they do not ignore it completely. They note that the conjunction of

Independence and Supervenience implies minimality of the supervenience basis, but

allow for the possibility that one can be a supporter of Supervenience without

Independence, and vice versa (Dorr and Hawthorne 2013 p13). I have already shown

how Supervenience without the minimality constraint is not of any theoretical interest

to supporters of privilege, and in §3.5 I will show that not only do Independence and

Supervenience imply the minimality constraint, but Supervenience and the minimality

constraint imply Independence. In short, I do not think Dorr and Hawthorne are correct

to separate these roles out. Both follow naturally from the scientific realist worldview

shared by privilege theorists.

The second feature of the supervenience role which Dorr and Hawthorne omit is

something we established already in §2.2. Only the maximally privileged properties are

part of the proposed minimal supervenience basis. The fact that only maximally

privileged properties feature in the supervenience basis for reality is a direct

consequence of the commitment to minimality. For a group of properties to be a

minimal supervenience basis they must meet two requirements. Firstly, every actual

event must either concern only properties in the supervenience basis, or itself

supervene on events concerning only properties in the supervenience basis. Secondly,

no part of that supervenience basis may itself supervene on any other part of the

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supervenience basis, barring the odd exceptional case, one example of which I discuss

below. This second condition ensures minimality, as any properties whose instantiation

was supervenient on some other part of the supervenience basis could be safely

eliminated from the supervenience basis without violating the first condition. Less-

than-maximally privileged properties are properties of precisely this kind, as their

instantiation does supervene on the instantiation of maximally privileged properties.

The characterisation of the minimality condition in terms of non-supervenience of any

part of the supervenience basis on any other part works reasonably well under normal

circumstances, but there are strange cases where it might be possible for instantiations

of a property in the supervenience basis to itself be supervenient. This is due to the

possibility of mutually supervenient properties. One way in which properties can

mututally supervene is as follows.

Consider a world containing but a single type of particle capable of being in differing

states corresponding to two properties, F-ness and G-ness. Assume that the entirety of

fundamental physics in this world can be expressed in terms of the spatiotemporal

location of all the particles and all instantiations of F-ness and G-ness. The speed and

direction of the movement of particles through the space of this world depends on

whether the particle has F-ness or G-ness at that moment, and particles switch from

one to the other at random, although no particle can have both F-ness and G-ness at

the same time. It seems that both F-ness and G-ness have good claims to being

maximally privileged properties in this world. They both feature in a minimal

supervenience basis for what goes on in this world (because everything that happens

in this world depends on which particles have F-ness or G-ness), and they both confer

some different causal powers on the thing that instantiates them. They are not,

however, non-supervenient on one another. There can be no variation of the number

of F-ness particles in this world without some corresponding change in the number of

G-ness particles, as the only way for an extra particle to become F-ness is for some

particle to stop being G-ness, and vice versa. F-ness is supervenient on G-ness, and G-

ness is supervenient on F-ness. If they were excluded from the supervenience basis

according to the assumption of minimality as non-supervenience, however, then

events concerning the instantiation of F-ness and G-ness in this world would not be

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accounted for by the remaining supervenience basis.15 It is not an option for just one

property, either F-ness or G-ness, to comprise the minimal supervenience for this

reality. This would imply the existence of particles with no fundamental properties

whatsoever. Such particles would have location and velocity through the vacuum but

be completely without character according to the fundamental physics of this world. It

is hard to see how a part of space could be non-empty and yet fail to instantiate any

fundamental properties at all.

Note that arguably either F-ness or G-ness (but not both) in this example would be an

example of a negative property. As we established in §2.2, negative properties are

properties which are instantiated by those particulars which fail to instantiate some

other property. Recall that negative properties are not explicitly disallowed from being

maximally privileged by either Armstrong or Lewis. Armstrong merely claims that there

will not automatically be a maximally privileged property (a universal) corresponding

to the failure to instantiate some other property (1978b p26). Such properties are

allowed to be maximally privileged in cases like the one I describe here because each

property has an independently good claim to privilege on the basis of the causal powers

it confers on its instances.

Excepting cases of mutual supervenience, the non-supervenience version of the

minimality requirement will function acceptably well. For this reason I propose that we

define minimality of a supervenience basis as non-supervenience of any part of the

supervenience basis on any other part, except in cases where supervenience is mutual

due to one part of the supervenience basis corresponding to the negation of another.

Note that these parts of the supervenience basis need not be single properties, but can

also be groups of properties. For instance, if we assume that all dice have a numerical

value from one to six determined by the number of dots on whatever happens to be

their uppermost face at the time, then the property of having a value of six will be

15 Note that this example is also a counterexample to Armstrong’s claim that properties which are mutually supervenient (or ‘symmetrically supervenient’, as he calls them) are identical (Armstrong 1997 p12). My thanks to Chris Daly for pointing out this other consequence of the argument I make here.

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supervenient on the group of properties corresponding to the other numerical values

it might have had.

In summary, the amended Supervenience role for privileged properties is satisfied just

in case there is a group of properties on which every event in reality supervenes, and

no part of which supervenes on any other part, except in cases of mutual

supervenience. Bear in mind that the group of properties which function as a

supervenience basis in this way are only the maximally privileged properties. If there

are less-than-maximally privileged properties (or alternatively, merely joint-carving

properties, as described in §2.3) these will not form part of this supervenience basis. If

Supervenience were the only theoretical role we were to ascribe to privileged

properties then it would be trivially true that there were such things as privileged

properties. The group containing all properties will always be a supervenience basis for

all reality, and if there is no smaller supervenience basis than this, then the group

containing all properties will be a minimal supervenience basis. The existence of a

group of properties which satisfies Supervenience (and the roles which derive from it,

as will be demonstrated in §3.5) alone is not enough to make privilege a theoretically

interesting posit. To be theoretically interesting, it must be combined with other roles

which are not explicitly derived from the commitment to Supervenience.

3.5 Independence, Empiricism and Laws

Now that we have removed Simplicity and Necessity from consideration (see §3.1),

there are nine roles remaining that Dorr and Hawthorne identify as proposed roles of

privileged properties. In this section I will show that three of these roles, Independence,

Empiricism and Laws draw their theoretical significance from the commitment to

maximally privileged properties as a minimal supervenience basis. Independence is in

fact implied by the amended Supervenience role proposed in §3.4, as does Laws given

certain reasonable assumptions about what laws of nature are. That privilege of

properties is empirically discoverable is then implied by Supervenience combined with

Independence and Laws.

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First we will show how Supervenience with the added minimality requirement involves

a commitment to Independence, excepting cases of mutual supervenience. In fact,

Independence as it is articulated by Dorr and Hawthorne will only be true of privileged

properties in worlds where there is no mutual supervenience of maximally privileged

properties. Rather than taking this as evidence that either mutual supervenience is

incompatible with privilege or that Independence should not be regarded as a role of

privilege at all, I propose a small modification to Independence along the lines of the

modification we made to Supervenience.

Dorr and Hawthorne articulate Independence as the claim that ‘the perfectly natural

properties are mutually independent’ of one another (Dorr and Hawthorne 2013 p13).

They present three different ways of understanding this claim of mutual independence

as it is found in Lewis, although it is the weakest form they present that is most relevant

for our purposes. This is non-supervenience, in the sense that a property is independent

of another just in case the pattern of instantiation of one in a world does not

supervenene on the pattern of instantiation of the other. Earlier we established that

exactly this kind of non-supervenience amongst members of a supervenience basis is

implied by the minimality requirement, but noted the difficulties with this formulation

in cases of mutual supervenience.

Dorr and Hawthorne themselves note that taken together, Independence and the

unmodified Supervenience imply the minimality requirement (Dorr and Hawthorne

2013 p13). Independence and the unmodified Supervenience do indeed imply that no

part of the supervenience basis will supervene on any other part, but as we saw, the

possibility of mutual supervenience means that this claim is false. I propose we rescue

Independence by rephrasing the claim as non-supervenience of any part of the

supervenience basis on any other part, except where mutual supervenience is a

consequence of one part of the supervenience basis corresponding to the negation of

the other. This is the same move we made in order to rescue Supervenience, and so

shouldn’t worry us unduly.

Independence modified to except mutual supervenience together with the unmodified

Supervenience do indeed jointly imply the minimality condition we arrived at by the

end of §3.4. Allowing for those modifications designed to accommodate mutual

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supervenience, so far Dorr and Hawthorne are exactly right. However, in the previous

section I argued that Supervenience should include a minimality requirement for its

own sake. Supervenience with its added minimality condition itself implies the truth of

Independence, because as we established, both the minimality condition and the

Independence role are claims of non-supervenience under all but a few exceptional

circumstances. It is therefore not open to the theorist of privilege who accepts the most

reasonable view of Supervenience to deny Independence, but nor can the supporter of

Independence deny Supervenience. List all the properties which do not themselves

supervene on anything else or else mutually supervene in an acceptable way, and this

will be a minimal supervenience basis for reality. All remaining properties must

supervene either on other properties which are themselves supervenient in an

unacceptable way, or on the non-supervenient properties. As such, the two roles are

not usefully separable from one another. They are rather aspects of the same

Supervenience role.

Next we turn to the connection between the Supervenience role and Dorr and

Hawthorne’s Laws role, which they define as follows.

The laws of nature all follow from some proposition that can be expressed simply

in terms of perfectly natural properties. (Dorr and Hawthorne 2013 p21)

In other words, laws of nature do not concern nomic relations between any properties

save the maximally privileged ones. This can be shown to follow from the

Supervenience role in the theories of both Lewis and Armstrong, although for different

reasons. For Lewis, the association between Supervenience and Laws we wish to show

stems from his commitment to minimality of laws themselves. With Armstrong’s

system, things are a little different. His commitment to laws as states of affairs means

that only maximally privileged properties could ever feature in laws in the first place.16

16 As we noted in §1.3, Armstrong’s views evolve over time, and in his later work introduces the

notion of ‘second and third’ class properties and states of affairs (1997 p45). Armstrong does

note that second-class properties in particular confer causal efficacy on the particulars which

instantiate them. Recall however that by virtue of the supervenience of second and third-class

states of affairs on the first-class, these additional states of affairs are no ‘addition in being’ to

the first-class states of affairs (see §1.3, Armstrong 1997 p45). Any causal efficacy attributed to

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As we noted in §2.7, Lewis’ approach to laws is a regularity theory. For Lewis a law of

nature is just a regularity between types of events that features in an ‘ideal system’ of

laws. An ideal system of laws is one which maximises the range of phenomena it can

account for in the simplest possible way (1983 p215). This is a feature we would be able

ascribe to a completed physical science, since physics aims at complete explanatory

power in the simplest possible terms (see §3.4). Minimality of laws is therefore an

explicit part of Lewis’ account of a law of nature, deriving from his views on the primacy

of physics as the fundamental science.

This minimality of laws implies that they will hold between maximally privileged

properties only for the following reason. If the maximally privileged properties are the

smallest possible supervenience basis for all events in reality, then the smallest set of

laws that would be needed to account for all relations of nomic dependence in reality

would simply be those that governed the behaviour of these properties.

Armstrong, by contrast, is not a regularity theorist. In fact, he defines laws in terms of

connections between sparse universals. A law of nature for Armstrong is just a relation

between universals such that the instantiation of certain universals necessitates the

subsequent instantiation of others. In Armstrong’s opinion, regularity theories fail to

do an adequate job of distinguishing merely accidental regularities from cases of

genuine nomic necessity. We need not be too concerned with his reasons for thinking

this here, however (Armstrong 1978b p149, 1997 p223). We are in fact more interested

in the consequences of this view. The only thing that separates Lewis’ laws out from

regularities of phenomena which are not laws is their featuring within the best system

of laws. There is no difference at the level of ontology between the two. For Armstrong

on the other hand the holding of a law is a state of affairs in its own right, whereas

regularities which are not laws aren’t (1997 p226). There are no first-class states of

affairs on Armstrong’s account relating to the instantiation of less-than-maximally

privileged properties so all first-class laws must hold between the maximally privileged

ones. The approach to the ontology of properties in general which Armstrong endorses

second-class states of affairs should not therefore be seen as evidence of laws which are an

addition to first-class laws.

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restricts those ways of being he can take to feature in laws. Whichever properties

Armstrong takes to be maximally privileged, Laws must also hold. The alignment

between properties of the minimal supervenience basis and those which feature in

laws is therefore guaranteed.

Laws and Supervenience therefore go together, but only in accordance with the

worldview we have ascribed to mainstream theorists of privilege. It is instructive to

note that Schaffer’s rejection of Supervenience (see §2.7) is motivated by his dispute

with Lewis over the nature of a law. Lewis is committed to a minimalist view of laws

which guarantees that all laws of nature will be laws of physics, whereas Schaffer claims

that dependences amongst chemical and biological events deserve to be called laws as

well (Schaffer 2006 p93). If one holds this view of Schaffer’s, then Laws is certainly false.

In the previous section I showed that Schaffer is not committed to Supervenience

either.

Finally in this section, we will examine Dorr and Hawthorne’s Empiricism role. This

states that the proper method for identifying which properties (according to the

abundant conception introduced in §1.2) are in fact maximally privileged is one of

empirical inquiry (2013 p18). Given Supervenience, facts about which properties are

maximally privileged depends on the web of supervenience relations between

properties. The fact that certain properties supervene on each other has observable

consequences in the world. On this basis, we can demonstrate that Supervenience

implies Empiricism.

We can divide facts into three categories with respect to the manner in which they are

knowable. Facts which are knowable a priori are knowable without any recourse to

experience of the world whatsoever. A fact is empirically discoverable just in case it is

not knowable a priori, and its holding implies certain observable phenomena. Facts

which are not knowable a priori but imply no observable phenomena are simply

unknowable.

If Supervenience holds, facts about which properties are maximally privileged imply

some observable phemonena and are not knowable a priori. As such they are

empirically discoverable. We can show this by means of the following example.

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Let us suppose that the spin of an electron is mediated by maximally privileged

properties, so that the property of being a particle with spin of one half is maximally

privileged. According to Supervenience, this property’s being maximally privileged

means that there are no more fundamental properties on whose arrangement the

property of being a particle with spin of one half supervenes.

For a fact to be knowable a priori, then it must be possible to come to know it through

reflection alone (Pritchard 2006 p102). For instance, we can know that all bachelors are

unmarried simply by reflecting on the meanings of words ‘bachelor’ and ‘unmarried’.

In contrast, we cannot come to know that the property of being a particle with spin of

one half is part of a minimal supervenience basis based on reflection alone. Suppose

for instance we one day find that the quality of spin is incapable of varying

independently of perturbations in some yet to be discovered field, and that

arrangements of spin properties were multiply realisable by different arrangements of

properties of the new field. Arrangements of spin would in this case be supervenient

on this new field. We need empirical data to be reasonably confident that such a field

as this does not in fact exist. Facts about the properties which comprise a minimal

supervenience basis for reality therefore cannot be knowable a priori, because our

knowledge of them relies on some empirical knowledge of the world.

Facts about what properties feature in a minimal supervenience basis also imply certain

observable phenomena, again due to Supervenience. We know that if the property of

being a particle with spin of one half is maximally privileged, it will conform to

Independence, Laws and it will feature in a minimal supervenience basis for reality. All

of these things are empirically discoverable. We can for instance observe particles with

this property to see if they all behave in identical ways in all the same circumstances

(or in the event that the universe is indeterministic, that they all have the same

probabilities to act in identical ways). This is what Laws tells us. If their behaviour is

only approximately similar in identical circumstances, then although this suggests a

nomic relation, it indicates that the behaviour of objects with this property supervenes

on something more fundamental than that property itself.

In order for facts about which properties are maximally privileged to be empirically

discoverable, there has to be some distinctive role of the maximally privileged

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properties by which they can be distinguished from non-privileged properties in an

empirical fashion. It is therefore impossible for Empiricism to be adopted completely

independently of any other role for privileged properties. If Empiricism holds for

maximally privileged properties, there must be some other role or combination of roles

which makes empirical discovery the proper method for establishing facts about

maximal privilege of properties. I propose that out of the three roles we have identified

as potentially of the greatest importance for the posit of privilege, Supervenience,

Similarity and Magnetism, Supervenience is the only one which guarantees Empiricism.

Similarity is unsuitable, for as we shall see in §3.6, the relation of similarity relevant to

the notion of privilege can only be defined in terms of privileged properties themselves.

The requisite similarity relations track the privileged properties, not the other way

around. As such, Similarity makes no observable difference to the world that can be

empirically discovered. The Magnetism role is not suitable for this purpose either.

Magnetism is proposed to settle cases where meaning is underdetermined by empirical

data. The restrictions on meaning it imposes go beyond that which can be observed

about how we use language. Properties which constrain language in this way cannot

therefore be empirically discoverable in virtue of the fact that they constrain language.

Supervenience therefore implies Empiricism, just as it implies Independence and Laws.

A theory of privilege which commits itself to Supervenience is therefore also going to

be committed to these three roles. This singles Supervenience out as one of the

keystone roles for privileged properties, and a central part of the mainstream posit.

3.6 Similarity-making roles

In this section I will clarify what supporters of privilege mean by the claim that joint-

carving properties alone are ‘similarity-making’. Dorr and Hawthorne’s account of this

particular role, which they term Similarity, is flawed, and in fact contradicts the

principle we established in §2.4 that the extent to which privileged properties fulfil the

roles proposed for them does not increase with their degree of privilege. I will propose

a more plausible version of Similarity, and show that three of Dorr and Hawthorne’s

remaining roles for privilege, Dissimilarity, Duplication and Non-Duplication depend on

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a commitment to Similarity in the same way that Independence, Laws and Empiricism

depend on a commitment to Supervenience. Dissimilarity-making is a component of

overall similarity relations just as similarity-making is, and so the two should properly

be considered parts of the same role rather than two separate roles, whilst Duplication

and Non-Duplication rely on a notion of shared nature introduced by means of the

position that only joint-carving properties are ever similarity-making. First though, we

must be explicit about what the similarity-making role actually is.

Theorists of privilege hold that the phenomenon of similarity is rooted in the sharing of

privileged properties (we first introduced this claim about similarity and privilege in

§1.1). This is in fact one of the most important and frequently talked about ideas

underlying the notion of privilege. Things which share privileged properties are said to

‘have the same nature’ (Armstrong 1978a p111). No human being lacks at least a rough

understanding of what it means for two things to be similar, for the ability to recognise

sameness and difference between distinct entities is one of the most fundamental tools

by which we interact with the world. Perhaps because of this, it is extremely difficult to

give ‘similarity’ a precise definition. One thing of which we can be fairly confident of is

its heterogeneity. The claim that groups of objects are similar can be understood in a

variety of different ways. In this section I will attempt to lay down the most plausible

understanding we can give to the theorists of privilege’s claim that similarity is rooted

in the sharing of privileged properties.

I will restrict myself to a discussion of similarity between particular objects only. I will

say nothing about the similarity properties may bear to one another. For example, the

property of having a mass of 1kg is more similar to the property of having a mass of

1.1kg than it is to the property of having a mass of 70kg. My reasons for this are

twofold. Firstly, the criticisms I take theories of privilege to be susceptible to in part

two of this thesis deal explicitly with similarity between particulars rather than

properties. Secondly, there is far less agreement amongst theorists of privilege on the

question of whether and how properties can themselves be similar to one another.

Armstrong, for instance, proposes that universals can be similar to one another in the

same way as particulars, by sharing ‘the same nature’. If a universal is complex (see

§2.2), then it will be similar to any other universal which has one of the same universals

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as conjuncts. Armstrong interprets this similarity as a case of partial identity between

complex universals which share some of the same parts (Armstrong 1978b p121). Lewis

gives us no detail on how he thinks properties might resemble each other, but suggests

that similarity amongst universals might give us a means of measuring degrees of

naturalness. Properties which unify the instances of similar universals could for

instance be more natural than properties that unify the instances of dissimilar

universals (Lewis 1983 p192). Sider makes no mention of similarity amongst properties

at all in his treatment of privilege (Sider 2011).

I do not suggest that we retain Dorr and Hawthorne’s account of the similarity-making

role of privileged properties. They characterise the role as the claim that the more

privileged a property is, the more similar are any two objects which share it (Dorr and

Hawthorne 2013 p21). In §2.4 we already established that this is not the case, and that

the degree to which a property is privileged does not correspond to the extent to which

it fulfils the similarity-making role. We decided this in part due to some of Dorr and

Hawthorne’s own comments concerning the incompatibility of their Dissimilarity role

with microphysical maximally privileged properties (2013 p45). As to the nature of

similarity itself, Dorr and Hawthorne offer no suggestions. I will now briefly outline

three possible ways we might think of similarity, and propose that it is the second of

these, overall similarity, which is relevant to the privilege debate. Making out a clear

distinction between these three kinds of similarity now will make the task of

scrutinising the Similarity role in chapters four and five simpler.

Firstly, there is aspectual similarity. When two objects share a property, they can be

said to stand in a relationship of similarity with respect to that property, which is

aspectual similarity. Objects can be aspectually similar in some respects, but different

in others. For example, postboxes are similar to roses with respect to the fact that they

each red, but they fail to be similar with respect to both being plants. This form of

similarity relation does not come in degrees. Two objects are either alike in a respect

or not alike in that respect, with no middle ground possible.17 Secondly, there is overall

17 This view assumes that having a property is never a vague matter. Holding such a view requires that any apparent vagueness in the instantiation of properties be explained as ‘semantic indecision’ on the part of a speaker between two or more candidate meanings for a

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similarity. Overall similarity involves aggregating individual aspectual similarities to

arrive at a measure of the similarity between particulars considered as a whole. Unlike

aspectual similarity, overall similarity does come in degrees. We can for instance note

that lions and tigers have a higher degree of similarity to each other overall than either

does to a shark. Finally, there is similarity in appearance. This is when two objects are

similar in virtue of how they impact the senses. For example, a vase which is duck egg

blue and a vase which is eau-de-nil look similar. This kind of similarity requires that the

experiences had by an observer of the two objects are themselves similar in one of the

other two senses of similarity, but even so, similarity of appearance should be

considered a separate kind of similarity. Two objects can be similar in appearance

whilst sharing very few properties, and yet it is natural to locate this similarity in the

objects themselves rather than the experiences we have of them. Consider the

following example.

A photograph of Fido the dog looks very similar to Fido himself. The problem is that

photographs and dogs are constituted from completely different materials, and so

share comparatively few properties. Fido is constructed from complicated protein

molecules and organic compounds, whereas the photograph is made from certain

chemicals which adhere to a sheet of paper according to a particular pattern. They are

completely different. The two objects do indeed provoke similar experiences in the

mind of the observer, but the question remains as to why this should be the case. We

might say that the photograph is a representation of Fido and this is why observers are

liable to have similar experiences when viewing the two objects, but this merely

relocates the question rather than answering it. Why should this photo be a

representation of Fido and not some other dog? It seems we have to acknowledge

some kind of similarity between Fido and the photograph which is not grounded in their

being of similar composition. Similarity in appearance is the kind of similarity which

Goodman has in mind in his ‘Seven Strictures on Similarity’. This approach informs

many of his observations, in particular his seventh stricture (1972 p443), which forms

the basis for one of Lewis’ arguments for the claim that natural properties only are

vague term, following a proposal of Lewis’ (1986a p212). I will reserve a detailed account of this method for resolving apparent vagueness for §5.4.

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similarity-makers (see chapter four, and in particular §4.3 for a more detailed

discussion of Goodman’s seventh stricture).

The claims about similarity which supporters of privilege make are not based in

similarity of appearance, however. Similarity of appearance is not based on possession

of the same nature, otherwise dogs and photographs of dogs could never be similar in

this way. Nor are they concerned with aspectual similarity. For two objects to be similar

with respect to a property is just for them to have that property in common, and no

supporter of privilege would insist that only privileged properties could ever be shared.

There are for instance three things which have our paradigm non-privileged property

Florb (introduced in §1.3), and these are the Eiffel Tower, a particular pear that was

picked and subsequently eaten in the Summer of 1732, and the left thumbnail of the

Statue of Liberty. All of these things are aspectually similar with respect to their being

Florb. Aspectual similarity cannot be connected with privilege. Overall similarity is the

only kind of similarity which can make sense of the supporters of privilege’s claim that

only privileged properties are similarity-making. The degree of overall similarity

between particulars is a function of all the aspectual similarities they share, and

theorists of privilege claim that the only aspectual similarities which make a difference

to the degree of overall similarity between particulars are those had in virtue of the

sharing of joint-carving properties.

One additional feature of overall similarity is that the judgements we make about how

overall similar objects are to each other varies based on context. This point was most

famously made by Lewis in connection with his possible worlds semantics for

counterfactual statements (Lewis 1986b, p52). Suppose we were to ask two historians

about which historical personages they thought were most similar to Ronald Reagan. A

historian of American cinema might suggest Phil Silvers, who was born in the same year

as Reagan and began working in film in roughly the same era after having a number of

small jobs elsewhere in the entertainment industry. A historian who was more

interested in American politics on the other hand would probably suggest someone like

Margaret Thatcher, a fellow conservative premier in the 1980s. The possibility that Phil

Silvers would be similar to Ronald Reagan would probably not cross their mind. Neither

historian is wrong about who is most similar to Reagan. The disagreement simply

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comes from assigning different weight to certain respects of similarity. Each of them is

working with a different idea of which features are most important to making two

personages similar. An acceptable account of overall similarity should make a place for

this.

Given that overall similarity is contextual, the claim that only joint-carving properties

count towards overall similarity can be given a weak or a strong reading. According to

the weaker reading, non-joint-carving properties do not count towards overall

similarity between particulars because non-joint-carving properties are never of

pragmatic interest to us when making similarity judgements. On this view there is

nothing about non-joint-carving properties that means that they cannot in principle

count towards overall similarity, but similarity with respect to non-joint-carving

properties is so bizarre and artificial that any similarity relation that took them into

account must also seem bizarre and artificial. On the stronger reading, non-joint-

carving properties do not count towards overall similarity because sharing non-

privileged properties does not make things more similar. It is not simply that similarity

relations which take into account non-joint-carving properties are bizarre, but that

there are simply no such relations of similarity in the first place. Any relation based on

the sharing of such properties would not deserve to be called ‘similarity’. The criticisms

I offer of the Similarity role in chapters four and five are applicable to both readings.

Now we turn to the three roles, Dissimilarity, Duplication and Non-duplication. In the

remainder of this section I will show that the acceptance of each of these as part of a

theory of privilege can be traced back to a commitment to Similarity.

Dorr and Hawthorne’s Dissimilarity role is, as the name implies, the flipside of their

Similarity role. Whereas sharing of privileged properties makes particulars more

similar, Dissimilarity says that being divided by privileged properties makes particulars

less similar (Dorr and Hawthorne 2013 p21). Pairs of particulars are divided by a

property just in case one of them instantiates it and the other does not. For instance, a

bear and a cat are made more similar by the fact of their both being mammals, and less

similar by the fact of one being a cat and the other failing to be a cat.

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As they did with the Similarity role, Dorr and Hawthorne link dissimilarity-making

power to a property’s degree of privilege. Once again, we should reject this view, as

there is simply no reason to suppose that more privileged properties perform their

specialised roles to a greater extent. Dorr and Hawthorne distinguish Similarity from

Dissimilarity on the basis that it is the way in which objects are divided rather than

unified that best lends itself to the oft-repeated metaphor of ‘carving nature at its

joints’ (Dorr and Hawthorne 2013 p22). When we speak of joint-carving it appears that

we are interested in the boundaries drawn by differences in particulars as much as the

mutual similarity of the members of a single category. Even if we accept that Similarity

and Dissimilarity should in fact be considered separate roles, we can still show that a

theorist of privilege who endorsed one must be committed to the other. The following

example shows how a commitment to Similarity but not Dissimilarity yields

counterintuitive results.

Suppose that there are three objects, a, b and c. Object a has only three privileged

properties F-ness, G-ness and H-ness. Object b has five privileged properties, F-ness, G-

ness, H-ness, I-ness and J-ness. Object c has three privileged properties, F-ness, G-ness

and H-ness. If sharing of privileged properties made particulars more similar, but being

divided by privileged properties did not decrease similarity, then it would follow that

a, b and c are all equally similar to one another, because they all share the same number

of properties with one another. This seems counterintuitive, as a and c are an exact

match with each other whereas b is not an exact match with either of them. We want

to say that the fact that b possesses properties that a and c lack makes b less similar to

them than if b had only the properties F-ness, G-ness and H-ness. Without Dissimilarity,

no account of overall similarity can be given that satisfies our intuitions.

The final two roles which can be traced back to Similarity are Duplication and Non-

duplication. Duplication is a relation which holds between objects which share all their

privileged properties, in the same arrangement (whilst non-duplication is simply failing

to be duplicates). The term was introduced in the context of the privilege debate by

Lewis, who suggested that it was the relation which held between an object and copies

of it produced by a hypothetical perfect copying machine (1983 p202). Duplicates do

not share all their abundant properties, because no two objects can be exactly alike

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with respect to all properties. On an abundant conception of properties, there will be

singleton properties which pick out only the original object and nothing else

whatsoever, or only the copy. If two coffee mugs are duplicates, then one will still have

the property of being this coffee mug rather than that one, whilst the other will have

the property of being that coffee mug rather than this one. It is impossible that these

properties could be shared by any two objects, no matter how perfectly copied.

Duplication is of interest in defining various notions of philosophical interest according

to Lewis, such as divergence and convergence of worlds, and supervenience. A pair of

possible worlds can be said to ‘diverge’ just in case they are duplicates of each other

up until a certain point in time, and fail to be duplicates thereafter. Convergence is the

opposite, where two worlds are duplicates after a certain point, but not before. Lewis

defines a group of properties or facts as supervenient just in case they cannot differ

between duplicates (Lewis 1983 pp204-208).18

The connection between the duplication relation and overall similarity relations should

already be apparent. Duplication is the sharing of all privileged properties, whereas the

degree of overall similarity is a function of shared privileged properties. Given this

understanding, duplication can simply be defined as the maximum possible degree of

similarity between particulars, with one caveat. Overall similarity relations are context-

sensitive, whereas the duplication relation isn’t. We can intentionally ignore some

features for the purposes of calculating overall similarity. For instance, we can say that

the manifestos of two political parties are qualitatively identical just in case they

propose the same policies, ignoring differences in wording, font and layout, despite the

fact that these are arguably more joint-carving properties than the properties such as

being a manifesto endorsing nuclear disarmament.

18 With respect to supervenience, this is hard to accept. Duplication is exact similarity with respect to privileged properties, which on the mainstream view are all microphysical (see §1.3). If supervenience relations were all claims about which properties could not differ between duplicates, it would be impossible for any supervenience thesis to take anything other than the microphysical properties as a supervenience basis. This means that we could not, for instance, propose that economic behaviour supervened on psychological behaviour, or that the species that an organism belonged to supervened on its genome. Lewis suggests that his definition of supervenience in terms of duplication works for all ‘interesting’ supervenience theses (1983 p205), but the above examples certainly seem like interesting supervenience theses that do not involve duplication. It is unclear how we should read Lewis in this instance.

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In the sense Lewis intends it, duplication is all or nothing. Either two objects are perfect

copies, sharing all their privileged properties, or they are not. We can think of

duplication as the highest possible degree of overall similarity between particulars from

a context which takes into account all privileged properties. The connection goes

further than a simple analysis of duplication in terms of similarity, however. The two

notions in fact derive from the same idea, that of distinct objects having the same

nature. Sharing privileged properties is supposed to indicate that the objects in

question have some sameness of nature (Armstrong 1978b p95) which objects which

share non-privileged properties only do not have. This is the only possible motivation

for holding that similarity with respect to privileged properties is more special or more

deserving of note than similarity with respect to non-privileged properties, and the

same goes for duplication. There would simply be no reason to hold that the

duplication relation was any more deserving of particular focus as a form of similarity

unless we took it to be the case that there was something about those particular

similarities that was especially interesting (although see chapter four for my criticisms

of this approach to similarity). For this reason, Duplication and Non-Duplication too can

be seen to derive from the role of Similarity.

3.7 Magnetism, intrinsic epistemic value and accounting for physical privilege

The final role I wish to introduce as particularly important to the posit of privilege is

Magnetism. Again, this is a role for privileged properties introduced by David Lewis

based on a suggestion by Merrill (see Merrill 1980, Lewis 1983 pp218-227, 1984). I will

reserve a complete account of the doctrine of Magnetism for chapter six, where I will

offer criticisms of this view. Instead I offer only a brief summary in this section. I will

also show why a commitment to this role requires a commitment to the view that

capturing joint-carving categories in language is valuable for its own sake. In doing so,

I will establish that the role of Magnetism requires a commitment to Sider’s proposed

role for privileged properties, that of an inherent epistemic value.

Dorr and Hawthorne define Magnetism as the claim that more privileged properties

are ceteris paribus easier to refer to than less-privileged properties (Dorr and

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Hawthorne 2013 p27). This is something of an oversimplification. A more accurate way

to define Magnetism would be to say that when looking at a natural language as a

whole, more joint-carving properties will be selected as meanings of words than non-

joint-carving properties. This tendency to be referred to in practice is what Dorr and

Hawthorne mean by ‘ease’ of referring. We can introduce the problem that Magnetism

is intended to solve as follows. Note that although this issue applies to any intentional

content, both linguistic and mental, I will restrict myself to discussion of Magnetism as

it applies to language here for the sake of simplicity.

The kind of metasemantic theory we are interested in is one which Williams

characterises as interpretationism (see Williams 2007 p363). According to an

interpretationist theory, there are no fundamental semantic facts. By this we mean that

words in a language do not have their semantic contents primitively, but instead they

have them in virtue of some non-semantic features of the world. The non-semantic

features of the world which are generally held to give words their meanings are facts

about the way those words are used by a linguistic community. For example, the English

word ‘red’ is used by English speakers in a range of specific ways that suggest that the

word picks out the property of being red. Given what we know about the practice of

English speakers, excluding unusual cases where speakers make mistakes, speak

metaphorically or are being intentionally deceptive, we note that the word ‘red’ is only

used when talking about things which are in fact red, never about things which are

another colour. The meaning being red is a good fit with the way the word ‘red’ is

actually used.

The problem is that facts of usage leave the meanings of many words

underdetermined. To borrow an example of Sider’s, the English word ‘pig’ is used in

such a way that it is consistent with a range of meanings, not just pig, but also the

property of being either a pig or the Statue of Liberty’s right thumbnail, being a pig born

before 10000AD etc. Clearly, ‘pig’ means pig, but the problem lies in accounting for why

‘pig’ means pig and not one of the other candidate meanings. As Sider puts it, the

‘semantic glue’ which pairs up meanings with words does not appear to be sticky

enough, going off facts of use alone (Sider 2011 p23). Magnetism aims to provide that

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extra stickiness, by making joint-carving categories ‘attract’ words as though they were

magnetic.

Analogies aside, this ‘reference magnetism’ amounts to the claim that joint-carving

categories are better candidates for the meanings of words in natural languages than

non-joint-carving categories. We therefore have two criteria for a successful

interpretation of a language, where an interpretation pairs up words in that language

with semantic contents. On the one hand, we try to ensure that the meanings we assign

to words would fit with the way they are used by a linguistic community (see §6.2).

Secondly, a good interpretation will attempt to select the most joint-carving meanings

for words in a language. These criteria can, and frequently do, conflict. One way to

maximise the joint-carvingness of the word ‘pig’ would be to specify that that this word

referred to some very privileged property of subatomic particles, such as the spin of an

electron. This would not fit very well with the way the word ‘pig’ was used, of course.

The best interpretation is one that succeeds in getting the best trade-off between these

two competing criteria (Lewis, 1984 p228).

We can apply this notion to Sider’s ‘pig’ example. The meaning pig is the most joint-

carving of the potential meanings we could assign to the word ‘pig’, and so is a much

better candidate than the others. Note that although Lewis himself is credited with this

proposal, he did not use the term ‘reference magnetism’ to describe it. This term was

coined by later commenters on his work, originally as a pejorative. The word

‘magnetism’ conjures up images of an occult fundamental semantic force of attraction

operating between properties and words, which is somewhat implausible. As I will

demonstrate in §6.2, this criticism is undeserved, and the Lewisian theory requires no

such commitment to a fundamental semantic force. Despite its origins, ‘reference

magnetism’ has since become the generally accepted term for this metasemantic

theory (Sider 2011 p27, see Hodes 1984 p135 for the first use of this name in

connection with a related view).

Although a commitment to Magnetism requires no occult forces at work in the world,

it does require us to believe that the connection between our words and joint-carving

categories is because of something special about joint-carving categories themselves.

It would not for instance be compatible with Magnetism to say that natural language

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tends towards joint-carving meanings because joint-carving meanings tend to be of

more practical interest to the speaker to think and speak about, or because they tend

to be those which are more easily picked out by human senses. We could for instance

claim that because humans have an interest in prolonging their survival, we should

expect the English word ‘food’ to pick out a relatively joint-carving collection of

substances which all share certain chemical traits in common, and do not include

chemicals which might be harmful to the body. Alternatively we could suppose that the

reason we are more likely to think and speak of the redness of things rather than their

being Florb is simply because our senses can identify red objects in the world more

easily than the Florb ones.

The categories which Magnetism picks out as more eligible candidates for being

referred to do not align with those picked out by these other standards. For example,

the most joint-carving category in the region of the English word ‘fish’ is one which

includes mackerel and cod, but excludes whales and dolphins (Sundell 2012 p748). If

our language selected for meanings on the basis of what was most useful to fishermen,

then the meaning of the word ‘fish’ should probably include whales and dolphins as

well. Magnetism requires a belief that joint-carving categories are better candidates

purely for their own sake.

Here we can see why Magnetism requires Sider’s proposal concerning inherent

epistemic value to be true. Sider proposed that we take capturing the world in terms

of joint-carving categories to be one of the goals of belief, alongside truth.

The goal of inquiry is not merely to believe truly (or to know). Achieving the

goal of inquiry requires that one’s belief state reflect the world, which in

addition to lack of error requires one to think of the world in its terms, to carve

the world at its joint. Wielders of non-joint-carving concepts are worse

inquirers. (Sider 2011 p61)

This is quite a strong claim, but it seems that its key observation must be believed in

order for Magnetism to also be believed. This is the claim that joint-carving categories

must have some value which makes them better candidates for the contents of thought

and belief in virtue of the fact that they are joint-carving alone, or alternatively in virtue

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of some feature common to all joint-carving categories. Given that joint-carving

categories are not always pragmatically useful, or easily discerned, these will not suffice

for such a feature. Sider’s claim, that capturing joint-carving categories with our words

is epistemically valuable, is one way to do this. If capturing joint-carving properties was

one of the goals of belief then this would account for why it is better to assign joint-

carving meanings to mental and linguistic entities, wherever possible.

I conclude that Magnetism requires a belief in some kind of normative value attaching

to joint-carving categories. An acceptance of Magnetism will therefore commit a

theorist of privilege to a claim of joint-carving value like Sider’s, although not

necessarily Sider’s own account of that value as epistemic. All that is necessary for

Magnetism is the belief that joint-carving properties are inherently better suited to

being the meanings of words, by virtue of the peculiar metasemantic value of joint-

carving properties themselves.

3.8 The structure of part two

Dorr and Hawthorne refused to assign importance to individual roles, but in this

chapter I have shown that three roles in particular, Supervenience, Similarity and

Magnetism, are of particular note. All the other roles which Dorr and Hawthorne

identify (excluding Necessity and Simplicity, see §3.1), plus Sider’s claim of inherent

epistemic value, are contained within these three roles. In addition, it is particularly

interesting to note that these three keystone roles are themselves independent of each

other. Supervenience does not imply Similarity, nor do either of these imply

Magnetism. If Supervenience is true, then all facts about overall similarity will of course

supervene on microphysical reality, but this is perfectly compatible with non-privileged

properties like Florb contributing to overall similarity between particulars. Given

Supervenience, the instantiation of Florb supervenes on the privileged properties, so it

follows that any similarity had in virtue of the sharing of the Florb property will itself be

supervenient, by transitivity (see §3.4). Adopting Similarity likewise does nothing to

suggest that the maximally privileged properties will comprise a minimal

supervenience basis for reality. Meanwhile the Magnetism role, with its accompanying

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commitment to capturing joint-carving categories to be inherently valuable, cannot be

traced back to either of the other two keystone roles. Supervenience and Similarity are

endorsed by all mainstream theorists of privilege, and Magnetism is a commitment of

both Lewis and Sider, influential theorists of privilege both (Lewis 1983 p220, Sider

2011 p23). If one is inclined to criticise the posit of privilege, then these three roles

should be the objects of scrutiny. Part two of this thesis will engage with these three

roles in precisely the manner proposed by Dorr and Hawthorne, by examining their co-

satisfiability (see §3.2).

In part two I will be looking specifically at whether or not Similarity and Magnetism are

each compatible with Supervenience. Although Supervenience does not explicitly

guarantee that the maximally privileged properties are just those of the most

fundamental level of fundamental physics, in §3.4 we noted that this is strongly

suggested by taking into account the current state of scientific inquiry. For this reason,

I will be assuming that Supervenience commits us to a microphysical view of maximally

privileged properties in all subsequent chapters. Chapters four and five will be

concerned with the compatibility of this view of privileged properties with the

Similarity role, chapter six with the Magnetism role.

In chapter four I will investigate a particular argument for privileged properties

marshalled by Lewis based on the idea of privileged properties as makers of genuine

similarity. Genuine similarity is the overall similarity relation that holds between

objects on the basis of their shared privileged properties only. I will show that the

argument fails to demonstrate its conclusion, and conclude that our everyday

understanding of similarity points to non-joint-carving properties contributing to

overall similarity. In chapter five I will show that the conjunction of Supervenience and

Similarity is incompatible with the influential semantics for counterfactuals proposed

by David Lewis (1968, 1973). Finally, in chapter six I will show that reference magnetism

gives us unintuitive results regarding the meanings of words when joint-carving

categories are rooted in microphysical distinctions. This will be followed by a brief

concluding chapter in which I will summarise my findings and propose that we have

reason to reject theories of privilege on that basis.

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Part Two: Criticisms of Privilege

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Chapter Four: Genuine Similarity

4.1 Introducing genuine similarity

In this and the following chapter, I will be concerned with the Similarity role for

privileged properties. In this chapter I will be concerned with a particular argument

employed by theorists of privilege, which I call ‘the argument from genuine similarity’.

The purpose of this argument is to justify the Similarity role as ‘work’ for privileged

properties, by showing that there is a certain class of similarity facts for which an elite

minority of properties would be able to provide an account (see §3.6).

In this chapter I will not be attempting to argue that the properties which make for

genuine similarity are not the same as those which satisfy the Supervenience role

(although this will be the goal of chapter five). In fact, genuine similarity between

particulars is conceived of in such a way that the properties which contribute to it are

indeed those which satisfy Supervenience. In §4.2 I show that the sense of ‘going

together’ characteristic of genuine similarity cannot help but appeal to privileged

properties themselves. The function of what I am calling the argument of genuine

similarity is to provide an independent, non-circular justification for the belief in the

elite minority of privileged properties.

The argument in question is an inference to the best explanation. Its supporters begin

with the claim that particulars stand in relations of genuine overall similarity to each

other, the existence of which is justified by our everyday experience. With the addition

of some reasonable assumptions about the nature of overall similarity relations, the

conclusion reached is that such facts of similarity can best be explained by the sharing

of an elite minority of properties. I will not attempt to dispute that there are facts of

genuine similarity. Instead, my goal is to show that the account of such facts offered by

supporters of privilege is not in fact the best account of facts of genuine similarity

available to us. I present an alternative account which not only accounts for facts of

genuine similarity amongst particulars, but also accords with our experience of genuine

similarity better than the privileged properties account. If this is so, and the alternative

explanation on offer is no less economical than the privileged properties solution, then

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the Similarity role as it was established in §3.6 should not be accepted as work for the

posit of privileged properties. It can be struck from the list of roles, and its co-

satisfiability with Supervenience should count for nothing towards the justification of

privilege. In the remainder of this section I will outline the argument from genuine

similarity and the structure of this chapter.

This particular argument is most notably endorsed by Lewis (1983 pp191-192) and Sider

(2011 p3) in defence of their own versions of privilege. The argument proceeds by

identifying a special status for certain facts about similarity which marks them out as a

particularly theoretically important. To this end, Lewis argues that at least some facts

of genuine similarity are ’Moorean’. This is a particular status which Lewis attributes to

facts which are beyond philosophers’ ability to sensibly deny. As I will demonstrate in

§4.4, facts can be both subjectively and objectively Moorean. Subjective Moorean facts

are beyond a person’s ability to dispute just in case they have access to a certain

information. The Cogito is an example of such a fact. One’s own existence is impossible

to deny, but only given the experience of one’s own thoughts. Other minds who do not

have access to your mental life can sensibly deny your existence. Facts of genuine

similarity are meant to have Moorean status objectively. As Moorean facts are

indisputable, an account must be offered of them in a systematic metaphysics (see

§3.3).

The argument also relies on a number of assumptions about the nature of overall

similarity. As we saw in §3.6, facts of overall similarity must have a basis in the

properties that are shared amongst the overall similar objects. The only acceptable

accounts of facts of genuine similarity we should accept therefore are ones that take

these facts to be grounded in the aspectual similarities of the objects in question. In

addition, Goodman’s seventh stricture on similarity states that overall similarity cannot

be arrived at through an aggregation of all the properties shared between objects

(Goodman 1972 p443). This tells us that the group of properties which ground facts of

genuine similarity must be a minority of all the properties which the objects possess. I

will detail Goodman’s seventh stricture more fully in §4.3. These two assumptions

taken together this tells us that the account we give of facts of genuine similarity must

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make reference to a minority group of properties, the sharing of which accounts for

facts of genuine similarity. We can lay this argument out as follows:

1) Facts of overall similarity between particulars are grounded in the properties

they share or fail to share.

2) Certain facts of overall similarity (genuine similarities) have an objective basis

in reality.

3) Not every property shared by particulars can count towards the overall

similarity between them (Goodman’s seventh stricture).

Inference to the best explanation: There is an objective minority of properties

which make particulars more genuinely overall similar when shared, and more

overall dissimilar when divided by them.

The conclusion of the argument from genuine similarity is, in essence, the Similarity

role we introduced in §3.6.

The structure of this chapter will be as follows. §§4.2-4 will be directed towards giving

a detailed account of the three premises of the argument. §4.2 will be dedicated to an

understanding of facts of genuine similarity. In particular, I will outline what kinds of

facts of similarity genuine similarities actually are, the kinds of circumstances in which

they hold, and why it is not open to the supporters of privilege to simply stipulate that

genuine similarity is similarity in terms of privileged properties. The following section,

§4.3, will focus on premise three of the argument, and show how Goodman arrives at

his seventh stricture. Finally, in §4.4 I will explain exactly what is meant by the claim

that a fact is ‘Moorean’ in the sense that Lewis intends, and why a Moorean status for

facts of genuine similarity would commit us to an objective basis for facts of genuine

similarity.

I then move on to my own criticism of the argument from genuine similarity, and

beginning in §4.5 I will argue that the inference to best explanation is flawed. Facts of

genuine similarity which have Moorean status are relatively rare, but the supporters of

privilege assume that in addition to the indisputable Moorean facts of genuine

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similarity of which we are aware there are other, non-Moorean genuine similarities,

many of which we are completely unable to discern. In making this assumption the

explanandum of the argument changes from a relatively small group of facts of

similarity to a much broader one. This shift in explanandum favours the conclusion of

the Similarity role. If, on the other hand, facts of genuine similarity are indeed as rare

as they appear, the account in virtue of privileged properties is actually not very

satisfying, for this account suggests that there are facts of genuine similarity holding

between any objects which instance some privileged properties.

I propose an alternative account that not only does not assume there are more genuine

similarities than we have evidence for, but also explains why Moorean genuine

similarities have that special status. I argue that in any truly Moorean case of overall

similarity, there will be a ‘prevailing’ property. A prevailing property is any property

such that any two objects which share it cannot help but be more similar than any two

objects which are divided by it. We observe prevailing properties in all cases of

Moorean overall similarity. The existence of prevailing properties would account for

facts of genuine similarity without recourse to privileged properties, and actually

accord with our experience of genuine similarity better than a privileged properties

account. Establishing this will be the goal of §4.7.

I conclude that the prevailing property theory of genuine similarity is the superior one,

and in §4.8 I show that prevailing properties cannot be argued to be simply privileged

properties by another name, because they do not satisfy Supervenience. As such,

genuine similarity does not motivate the Similarity role introduced in §3.6.

Before beginning our investigation of facts of genuine similarity it should be noted that

in this chapter I have endeavoured to be as charitable to those who endorse the

argument from genuine similarity as possible. Lewis and Sider each pass over the

argument extremely quickly in their treatments, and as such I devote a great deal of

time in the following sections to reconstructing some of the tacit assumptions on which

the argument rests. Despite this, certain observations which are key to the strength of

the argument, such as the assumption that we have an indisputable privileged notion

of facts of genuine similarity as an objective phenomenon (see §4.4), may strike the

reader as extremely controversial even on their best possible reading. The reason I

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choose to devote so much time and effort to a scrutiny of this argument is not because

I think it is the most convincing argument that there is in favour of their being work for

privileged properties, but because the Similarity role is a huge part of the posit of

privilege (as we saw in chapter three), and this is the argument by which that role is

frequently justified. I believe it is possible to show that this argument fails to motivate

the Similarity role even whilst granting the existence of special, Moorean similarities

between particulars. If the supporters of privileged are unconvincing on this point then

so much the better for my own conclusion, which is that the Similarity role, in the form

in which it is co-satisfiable with Supervenience, is not work for privileged properties.

4.2 Facts of genuine similarity

The starting point for the argument from genuine similarity is the existence of a certain

class of facts. These facts are facts of overall similarity, but of a special kind. In this

section I will introduce genuine similarity as it is employed in the argument from

genuine similarity and note how this accords with the framework for overall similarity

I introduced in §3.6. I will also show why the goals of the supporter of genuine similarity

will not allow her to simply define genuine similarity in terms of the sharing of

privileged properties. I will conclude in this section that the argument from genuine

similarity requires some independent justification for the specialness of the genuine

similarity relations, and that this is the Moorean status such facts can be observed to

possess.

In §3.6 I defined overall similarity as a relation, admitting of degrees, which holds

between objects which are similar in one or more respects. The more respects in which

they are similar, and the fewer in which they are dissimilar, the more similar overall the

objects in question will be. ‘Similarity in a respect’ we call an aspectual similarity, and

the claim that a pair of objects are aspectually similar with respect to a property being

F is equivalent to the claim that those objects each instantiate the property of being F.

As such there are as many ways that objects can be aspectually similar as there are

properties for them to share, and there are as many properties as there are ways that

a particular can be (see §1.2). We have already seen that for any disparate group of

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objects it is possible to identify some property which unites them. In §1.3 I introduced

Florb, a property possessed by the Eiffel Tower, a particular pear that was picked and

subsequently eaten in the Summer of 1732, the left thumbnail of the Statue of Liberty

and nothing else. The Florb objects are aspectually similar in virtue of their shared

Florbness. We also established that there exist a range of overall similarity relations,

and that when individuals make judgements about overall similarity, they select an

appropriate relation based on context. Overall similarity relations vary with respect to

the importance they assign to individual aspects of similarity, and so not every

aspectual similarity between objects need count towards overall similarity to the same

extent in every case, or even at all. Even so, the infinity of aspectual similarities on offer

suggests that there is a basis for at least some degree of overall similarity holding

between any grouping of objects, at least according to one relation of overall similarity.

This account of overall similarity is compatible with there being no privileged

properties. According to Goodman’s seventh stricture, the degree of overall similarity

between two objects cannot depend on more than a fraction of the total number of

properties they share or fail to share (see §4.3). It is because of this that supporters of

the argument from genuine similarity believe that there must be a specifically

demarcated group of similarity-making properties to account for facts of genuine

similarity. On the above account overall similarity does not require a specifically

demarcated group of similarity-makers however. Any property can, in principle, be a

similarity-maker given the right context for assessing similarity. If, for instance, we had

some reason to be particularly interested in the three Florb objects, perhaps for the

purposes of some time-travelling scavenger hunt, then it would make perfect sense to

regard them as importantly similar to each other.

In order for Goodman’s seventh stricture to support the existence of privileged

properties, the argument’s supporters must be able to point to a kind of similarity for

which this simple account will not work. This is genuine similarity. In §3.3 we

established that a systematic metaphysics must give an account of every purported

fact. If there are indeed facts of genuine similarity, these will require that we give an

account of them. If there is something special about these facts that means they cannot

simply be seen as a kind of similarity on a par with the myriad relations which the simple

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account of overall similarity allows for, then a different account will be needed. A good

metaphysical posit is one which allows us to account for a great many different kinds

of fact using the same resources (see §1.4), so providing an account of genuine

similarity using the same group of properties that also satisfy the Supervenience role

would give us reason to believe in privilege. Now we must turn to the question of what

this supposedly special kind of similarity must be.

Genuine similarity is a much less promiscuous phenomenon than similarity simpliciter.

Not every fact of overall similarity is a fact of genuine similarity. The idea of what

separates genuine similarity from other similarity relations is meant to be fairly

intuitive. I will introduce this intuitive sense first, then go on to see how that initial

sense might be made more precise. Objects are genuinely similar to one another just

in case they, in Sider’s words, ‘go together’. Not just any property will make objects

which share it go together in this way, though (2011 p2). We can certainly speak of a

property such as Florb as making objects which share it similar, given the right context,

but Sider argues that there is something artificial about this kind of similarity. Objects

which share ‘genuine’ features by contrast do go together (2011 p3). There is

supposedly nothing artificial about the similarity between all members of the set of

electrons, for instance. Lewis too took it for granted that there was an intuitive

plausibility to the claim that only certain properties really made things similar when

shared.

Do not assume that just any respect of similarity you can think of must enter

into the balance of overall similarity with positive weight. The point is obvious

for some respects of similarity, if such they be. It contributes nothing to the

similarity of two gemstones that both are grue. (Lewis, 1979b p465)

At this point in time Lewis does not have the theory of natural properties in place to

justify the distinction between similiarity-making properties and non-similarity-making

properties, and so he leaves this observation at the level of a simply ‘obvious point’.

This brings up an interesting feature of the way Sider and the post-‘New Work for a

Theory of Universals’ Lewis introduce the notion of genuine similarity. The way Sider

introduces this idea of ‘going together’ relies on the notion of a ‘genuine feature’,

which is to say, a privileged property. The same is true for Lewis, who introduces the

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notion of a privileged property and then goes on to claim that privileged properties

alone ‘capture facts of resemblance’ amongst particulars (Lewis 1983 p192).

A difference between Lewis and Sider in how they introduce genuine similarity is that

Lewis is unwilling to acknowledge any kind of similarity besides genuine similarity at all.

In this chapter I am characterising genuine similarity as a particular, distinctive kind of

similarity. Lewis, by contrast, would claim that all similarity was genuine similarity, and

simply deny that any relation which was grounded in the sharing of non-privileged

properties deserved to be called a ‘similarity’ relation in the first place (Lewis 1983 192,

1979b p465). This terminological difference aside, both Lewis and Sider hold that there

is a relation of particular interest which holds between particulars which share

privileged properties: the relation of genuine similarity.

Nothing which Lewis or Sider claim about genuine similarity tells us anything about how

it fits in with what we already know about overall similarity. We already know that

there are myriad relations of overall similarity, each of which places a different

weighting on the various aspectual similarities between objects. According to

supporters of the argument there is an overall similarity phenomenon called ‘genuine

similarity’, but at this stage we do not know if genuine similarity is a single relation or

several. There may for instance only be one system of weights for properties that can

tell us the genuine similarity between objects, or there might be many. The Similarity

role as it is articulated by Dorr and Hawthorne seems to suggest the former, for it

specifies that more privileged properties will have higher weight (Dorr and Hawthorne

2013 p21). We rejected this simplistic approach in §3.6 though. The amended Similarity

role we came up with in chapter three functioned merely as a restriction on which

properties could ever be given positive weight in overall similarity relations. This at

least allows for the possibility that there are multiple different ways of weighting

properties even within genuine similarity itself. For the remainder of this chapter I will

therefore assume that when particulars are said to be genuinely similar this means that

they are overall similar in accordance with one or more of a particular group of overall

similarity relations, which Lewis and Sider identify as having some kind of intuitive

specialness.

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There is something additional we can note about instances of genuine similarity. In

truth, we see something similar with respect to all overall similarities, but the issue is

more obvious with genuine similarity. Overall similarities come in degrees, as we know,

so a pair of objects a and b can be overall similar to a greater degree than a and c. In

all but a few cases, however, it is very difficult to say what those degrees of similarity

actually are, and what the difference is between them. Suppose for instance we

correctly say that sheep are more similar to goats than sheep are similar to cows. This

seems plausible, and we may even be able to point to various aspectual similarities

which ground the difference in similarity. We cannot however say with any degree of

certainty how much more similar sheep and goats are than cows. We cannot even guess

at what kind of scale degrees of similarity should be calculated according to.

Should it for instance be the case that two particulars can be assessed as more or less

similar on a scale from zero to one hundred percent? Or do particulars start out at zero

and gain or lose points from an absolute score depending on the properties they do or

do not share? In very simple, artificial examples we can sometimes arrive at satisfying

accounts of degrees of similarity. Suppose for instance that a, b and c only have two

properties between them, F and G, and that a and b instance both F and G and c

instances G only. In this case it seems plausible to assert that a and b have twice the

similarity that a and c have. The problem is that when we try and apply these standards

to real life examples, our intuitions are nowhere near as clear. Sheep, goats and cows

have millions of properties each, and even if we could identify each and every one of

them it would still be a near-impossible task to calculate a weighting for them all.

It is interesting to note that this does not appear to be a barrier to our being able to

discern patterns of similarity between complex objects like sheep, goats and cows. This

suggests that our ability to observe overall similarity is not directly dependent on our

ability to calculate the degrees of similarity which hold between particulars. It seems

that we can judge overall similarities to be greater or lesser than each other in the same

way that we can judge piles of sand to be larger or smaller than each other without

knowing how many grains is in each one.

I noted that this issue is of particular importance for investigating genuine similarity,

and that is because all of the cases of genuine similarity which have Moorean status

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are comparative rather than absolute. We can certainly judge that Sider’s two electrons

‘go together’, to use his terminology, in a way that the two electrons with the addition

of a cow do not, but what we cannot seem to do, at least not with the same degree of

ease that characterises Moorean facts, is say how much greater the similarity between

the electrons is than the similarity between one of those electrons and the cow. To

make such a judgement would require that we had some idea of the similarity between

the two electrons independent of any similarity with the cow. It doesn’t appear that

we do in such cases.

If for the sake of argument we assume that these two electrons were in identical states

at the time at which the judgement was made, then it appears as though we could

make an absolute judgement about their similarity along the lines of ‘electron one is

maximally similar to electron two’. In fact, this is a comparative judgement as well,

since what we are actually claiming is that no two objects can be similar to a higher

degree than these two electrons.

For this reason I will restrict myself in this investigation to talking about comparative

overall similarity rather than absolute overall similarity. This is not to say that there is

no such thing as facts of absolute overall similarity, only that we have far less

experience of such facts than we do of comparative overall similarity, and that

furthermore all facts of genuine similarity that we take to have Moorean status tend to

be of the comparative kind. All the facts of genuine similarity that I will offer as

examples from this point on will take the form ‘the similarity between a and b is

greater/smaller than the similarity between a and c’.

With a reasonable understanding of what genuine similarity actually is now in place,

we can begin to understand why such facts require a special, Moorean status for them

to play a role in the argument from genuine similarity. If the goal is to defend privilege

on the basis of its ability to account for genuine similarity, then we cannot rely solely

on Lewis and Sider’s definition of genuine similarity outlined earlier in this section. We

noted then that supporters of privilege often cannot help but define genuine similarity

in terms of the sharing of privileged properties, but privileged properties are

themselves partly defined as the properties which make for genuine similarity. If the

only account we have of genuine similarity is as the relation that holds between objects

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which share privileged properties, then the Similarity role cannot be defined without

circularity. The claim that a group of properties are genuine similarity-makers reduces

to the claim that objects sharing privileged properties accounts for their sharing of

privileged properties. The inclusion of such a role amongst the various features of

privileged properties cannot possibly present an additional reason to believe in them.

A denial of privileged properties would make facts of genuine similarity disappear, so

it should not count in favour of privilege that it provides an account of them.

In order for the argument from genuine similarity to work as a motivation for privilege,

there would need to be some additional, independent reason for believing that there

were facts of genuine similarity that require accounting for. In addition, we require a

reason to suppose that these facts of genuine similarity require a different account be

given of them than is given of non-genuine similarity relations. Our general purpose

approach to overall similarity is that there are as many different kinds of overall

similarity as there are ways of weighting all the different aspectual similarities between

objects, and the one we use at any given time is determined by contextual factors, such

as who we are and what our goals are. If the argument from genuine similarity is going

to work, we need to know why the relation or relations which supporters of privilege

latch on to are similarity relations we should care about in particular. This is where the

Moorean status of facts of genuine similarity becomes crucial. Understanding this term

and the role it plays in the argument from genuine similarity will be the topic of §4.4.

4.3 Goodman’s seventh stricture on similarity

In this section I will detail premise three of the argument from genuine similarity and

argue for its truth. This premise invokes the last of Goodman’s ‘seven strictures on

similarity’: that ‘similarity cannot be equated with, or measured in terms of, possession

of common characteristics’ (Goodman 1972 p443). To see why this is, first of all

suppose an abundant view of properties according to which properties exist in one-to-

one correspondence with predicates. Goodman himself was sceptical about the

existence of properties, at least in the sense according to which they are universals. In

this context where he uses the word ‘property’ he intends the word to be merely a

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placeholder term for more careful formulations in terms of predicates alone. The

predicates in question designate repetitions of qualia associated with individuals, so it

is not disingenuous for him to speak of properties in this way (1972 p443, see also

Schottenkirk 2009 p42, Cohnitz and Rossberg 2006 p52). This view of Goodman’s on

the nature of properties is informed by his Carnap-inspired approach to empiricism and

ontology. Goodman takes qualia to be the basic elements of his system where Carnap

employs ‘elementary experiences’ (Cohnitz and Rossberg 2006 p114). This differs from

the specific kind of scientific realist approach to reality we have argued is distinctive of

mainstream privileged theorists, according to which the basic elements are those of

fundamental physics. Recall that we began by assuming the existence of properties

according to an abundant conception in §1.2, without assuming any particular ontology

for properties themselves. If properties are abundant, it follows that for any two

objects x and y, there will be infinitely many such abundant properties that are

possessed by both x and y, and equally many properties that are possessed by one of

the pairing but not the other. Consequently, if we take the degree of overall similarity

between two particulars to be an aggregation of all the shared properties between

them compared with all the unshared properties, then the similarity between any two

particulars will be ∞:∞. This means that any pair of objects will be equally similar to

one another, regardless of how they appear to us (Goodman, 1972, pp443-444).

We must modify Goodman’s stricture here, as his articulation of it does not take into

account the fact that properties can be differently weighted with respect to the extent

they contribute towards overall similarity. Certain systems for weighting properties

would allow for pairs of objects to differ with respect to overall similarity, even if every

property was given at least some positive weight. For example, suppose that property

F is given a weighting of one, that property G is given a weighting of one half, property

H is given a weighting of one quarter, and so on. Continue the series until all the

infinitely many properties have been assigned a positive weighting which is exactly half

that assigned to the preceding property in the series. Two objects which are alike with

respect to property F would then always be more overall similar than two objects which

are not alike with respect to F. The total value of all the properties shared by objects

with F in common would always be greater than one, whereas the total value of all the

properties shared by objects without F in common would always be less than one.

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There is however a way of understanding Goodman’s stricture according to which cases

like this one do not present a true counterexample. In cases like this one where the

weights assigned to individual properties decrease exponentially, the only property

which ever really counts towards overall similarity is the highest weighted property

which the particulars in question are divided by.

Suppose that an object a instantiates every property there is, beginning with F and

continuing down the series into infinity. Now suppose that object b instantiates every

property there is bar H, which has a weighting of one quarter, twice as much as I and

half as much as G. Object c meanwhile instantiates only three properties, F, G and H.

Given what we know about how these properties are weighted, in this case a will be

more similar to c than b, because the total value of the weighting of F, G and H is greater

than the total value of all the other properties which a and b share. These properties

are nominally assigned positive weight in this example, but in actual fact they make no

difference whatsoever to the overall similarity between a, b and c. The sharing of any

property with a weight of less than G might as well have a weighting of zero, for all the

ability they have to make for overall similarity between the particulars which share

them.

I propose that we should not distinguish between cases where certain properties of

particulars have zero weight or merely negligible weight. If we read Goodman’s seventh

stricture as simply claiming that if every property has the capacity to make a material

difference to the overall degree of similarity between particulars, then all particulars

will be overall similar to the same degree, then the point still holds.

Obviously, the conclusion that all particulars have the same degree of overall similarity

to one another will not do for a theory of overall similarity that accords with our

everyday experience. In the ordinary course of events we observe objects to be similar

to others to differing degrees. Overall similarity is discriminatory. If, as Lewis claims,

some of these discriminatory judgements have special Moorean status and are

therefore indisputable, Goodman’s seventh stricture rules out every single abundant

property contributing to overall similarity at once.

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The inference to best explanation that the supporters of the argument from genuine

similarity draw is that due to the restriction on overall similarity discovered by

Goodman, facts of genuine similarity can only be grounded in the sharing of an elite

group of properties. This is not the lesson that Goodman himself drew from his

observation about overall similarity, however. Instead, he believes that there are many

equally good ways of measuring similarity, none of which is privileged over any others.

The claims we make about objects being more or less alike with one another are so

prone to variation between persons that no such measure is ‘peculiarly and exclusively

validated by our highly unstable ordinary judgements of similarity’ (1972 p422).

Goodman’s own view therefore aligns with the simple account of overall similarity laid

out in the previous section, according to which there are many equally good ways of

calculating similarity. In fact there is one crucial difference in how Goodman and Lewis

view similarity. The kind of similarity that Goodman has in mind when he presents his

seven strictures is similarity in appearance, which we introduced in §3.6. This is

evidenced by his discussion of objects being alike with respect to their ability to make

for perceptual similarity (Goodman, 1966 pp267-340, see also 1972 pp423-436), which

accords with his assumption of qualia as basic elements of his system. Furthermore,

Goodman denied even that similarity in appearance was necessarily objective. He

denied that we could assume that human sensory faculties divide the world up in the

same way. Judgements of similarity, even similarity between qualia are constructed

phenomena for Goodman, relative to particular ways of engaging with reality

(Schottenkirk 2009 p106).

It is also worth noting that Goodman, unlike Lewis and the other supporters of

privilege, was not committed to a scientific realist worldview, even one which took

qualia rather than fundamental physics as basic. By 1978, Goodman’s position had

solidified into the view that different ways of describing the world, including those

systems described by the natural sciences, were no more than versions of reality, none

of which could claim to be the way the world really was, in a way that was privileged

over the other versions (1978 pp2-5). Goodman’s relativism about similarity can

therefore be read as an outgrowth of his instrumentalist tendencies towards science.

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The seventh stricture tells us that any measure of overall similarity which accords with

our everyday experience of the phenomenon must involve restricting the domain of

properties whose sharing can make a difference to overall similarity. The remaining,

second premise of the argument from genuine similarity aims to show that certain facts

of similarity are indeed ‘peculiarly and exclusively validated’. According to the structure

of the argument the existence of such facts of similarity would require a basis in some

objective feature of reality. As Goodman has already shown us that this basis must be

a minority of all properties, the privileged properties would appear to make for an

attractive explanation of these facts.

4.4 Moorean similarities

In this section I will detail the importance of the idea of a Moorean fact to the argument

from genuine similarity. Goodman’s stricture alone is not enough to suggest privileged

properties as similarity-makers, and in §4.2 I established that an independent

justification for facts of genuine similarity is required. Moorean status for facts of

genuine similarity completes the argument by both justifying a belief in facts of genuine

similarity and indicating their specialness. I will introduce the notion of a Moorean fact

as Lewis in particular employs the term, and distinguish between two ways in which a

fact can be Moorean: objectively and subjectively. I will then show how objective

Moorean status for genuine similarity can generate the Similarity role for privileged

properties.

Goodman’s stricture tells us that not every property can make a difference to overall

similarity at the same time, so if objects a and b are more genuinely similar than a and

c, then this must be so in virtue of a minority of the properties shared by a and b. Facts

of genuine similarity must have a restricted range of similarity-makers, but privileged

properties are not required to account for them. The simple approach to overall

similarity we introduced in §4.2 is perfectly able to accommodate genuine similarity as

it stands. Recall that on this account we claimed that context would allow us to choose

a similarity relation which assigns zero or negligible weight to certain aspects of

resemblance. Genuine similarity could be accounted for simply as a range of overall

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similarity relations selected in particular contexts. There wouldn’t have to be anything

special about the properties this relation assigned weight to, because there are

relations which assign weight to all kinds of other properties as well. It’s simply the case

that these properties are weighted by the range of relations which Lewis and Sider

happen to be talking about. In order for the argument from genuine similarity to

generate work for the posit of privilege, there has to be something special about

genuine similarity itself, something which suggests that the properties which are

responsible for it are themselves special. Furthermore, as we noted in §4.2, this

specialness of similarity cannot be accounted for in terms of the specialness of the

properties that make it up. This is where the requirement of special Moorean status for

genuine similarity becomes important.

Although Lewis does not offer a completely canonical description of what he takes a

Moorean fact to be at any point, the guiding idea behind his use of the term is that of

a fact that we have no business as philosophers in denying (Nolan 2005, pp207-208).

Sider does not explicitly use the term ‘Moorean fact’ to describe similarity relations at

any point, but he would I think agree with much of what Lewis says about them. His

assumption of ‘knee-jerk’ realism, which I introduced in §1.4, contains within it a

commitment to an objective character of reality which privileges some ways of

characterising the world over others (2011 pp18-19), and elsewhere he makes the

point that there is a strongly intuitive plausibility to the claim that a set containing only

electrons will have members which ‘go together’ better than a set which contains both

electrons and cows (2011 p3). The special status he accords facts about ‘going together’

can play a similar role in the argument from genuine similarity as Moorean facts do.

Both ideas imply that the facts which have this special status are extremely credible as

facts, and that they must have a basis in a mind-independent reality. In both Lewis and

Sider’s cases, I believe we can trace their willingness to believe in the specialness of

genuine similarity back to their scientific realist worldview (see §1.4). Theorists of

privilege take the world to be more or less the way physical science describes it, and so

descriptions of the world employing the terms and categories of physical science are

better according to some specialised metric than those made using different terms. It

isn’t hard to see how this would translate into a belief in the specialness of a similarity

relation which captured properties shared at this level of description. Supporters of the

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argument already have a reason to believe that there is a special kind of similarity,

reflecting something special about reality.

Although the term ‘Moorean fact’ is a reference to Moore’s famous defence of his

knowledge of his own hands (Moore 1939), Lewis means something slightly different

than Moore himself did. Moore attempted to rebut the radical sceptic who denied the

existence of any external world knowledge simply by insisting that his knowledge of his

own two hands was far more certain than any knowledge he had of the possibility of

sceptical scenarios. By a ‘Moorean fact’ Lewis simply means a fact that is not open to

dispute. Understanding this sense in which a fact can be ‘beyond dispute’ and how this

contributes to the argument from genuine similarity is the objective of this section.

First, we can discount one possible meaning: that of a fact’s holding necessarily.

Saying that a fact is Moorean is not the same as saying that it holds necessarily. Not

every necessary fact is impossible to deny. Mathematical theorems hold necessarily,

but that does not mean that someone unfamiliar with the proof of a theorem could not

sensibly question it. The ‘Moorean’ status Lewis proposes for certain facts is distinct

from necessity. Consider the following example of a statement expressing a purported

fact about overall similarity:

‘All badgers are more similar to each other than any particular badger is similar

to a snake.’

At first glance this certainly seems to be true. Badgers are quadrupedal mammals,

snakes are legless reptiles. It is hard to imagine that the degree of dissimilarity between

even the most dissimilar badgers could ever equal the dissimilarity between a snake

and the most snake-like badger. We could try to deny this claim by stipulating a certain

weighting of properties that elevates the importance of properties shared by some

snakes and merely some badgers, and ignoring many others. For instance, the property

of being housed in a zoo is one that at least one badger and at least one snake share,

but since not all badgers live in zoos, a similarity relation which only took living

arrangements into consideration would hold in such a way that a snake and a badger

would be more similar than all badgers to each other. This is not a denial of the original

statement though, because in order to make our denial work we have had to replace

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the similarity relation in the original statement with another. We have only succeeded

in denying a separate claim of our own devising.

In fact, it seems that the only way we could deny that all badgers are more similar to

each other than badgers and snakes are would be to have a fundamentally different

idea of the meanings of some of the terms involved. We could argue that pythons are

not in fact snakes, but badgers, or that overall similarity is not grounded in the sharing

of properties after all, and so the many shared properties amongst badgers do not

serve to make it so that all badgers are highly similar to one another. We could do this,

and in doing so deny that the statement expresses a fact, but the question is whether

we should. To make any of these moves would be to depart significantly from what the

words ‘badger’, ‘snake’ and ‘similar’ ordinarily mean, to the point that it is not really

clear that we are still talking about the same thing. Denying a statement expressing a

supposedly Moorean fact would require almost everything we know about the world

to be wrong. Taking certain things for granted, such as our ability to comprehend the

nature of similarity, is simply a precondition for engaging with the world. That, I

propose, is the best possible understanding we can give to the idea of a fact’s being

‘beyond dispute’.

The existence of Moorean facts of overall similarity would indeed place a demand on

philosophers to ‘make a place’ for them in their system, as denying that they are indeed

facts is not an option, if they really are Moorean (Lewis, 1983 p198). We can grant that

examples like the badger/snake case are indeed Moorean in the sense we require, but

the problem with genuine similarity as it was introduced in §4.1 was that it

presupposed privileged properties, and so could not be used to justify privileged

properties on pain of circularity. Whilst it is true that Moorean facts of genuine

similarity must be accounted for regardless of whether we believe in privileged

properties or not, they could still be accounted for by means of the simple overall

similarity account we already have in place. It still has to be shown that genuine

similarity is special. This specialness is a feature of the manner in which they are

Moorean.

We may distinguish two types of Moorean fact, those which are objectively Moorean

and those which are merely subjectively Moorean. A subjectively Moorean fact would

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be one which is beyond dispute, but only for a select group of persons. For example,

when a person experiences pain it is impossible for them to sensibly deny that they are

having an experience of pain. Arguably, one cannot be mistaken about the character of

one’s own sensations. An external observer lacking their viewpoint could well doubt

their claim to be in pain, though. They might suppose that the sufferer is being

deceitful. The fact that a person is in pain is Moorean only from the perspective of the

person actually in pain. An objectively Moorean fact, on the other hand, is Moorean for

everyone sufficiently acquainted with the details of the case. It is this latter kind to

which Lewis takes facts of genuine similarity to belong. The fact that badgers have a

higher degree of mutual similarity than badgers have to snakes is indisputable for

everyone with a reasonable idea of what badgers are and what snakes are. The

difference between a subjective and objective Moorean fact is that the former relies

on some relevant data which not every observer can have access to. If the kind of

similarity we were interested in here was our tendency to judge things similar in virtue

of their striking our senses in a particular way, i.e. similarity of appearance, then

subjective Moorean status for facts of genuine similarity is the best we could hope for

from them. It is entirely possible that for one person, the similarity of appearance

between two members of the same family is utterly transparent, whereas another

might be completely unable to see it. This is because similarity of appearance depends

on cognition, which can vary from one person to the next.

The kind of similarity that supporters of privilege wish to claim sometimes has Moorean

status is overall similarity grounded in the sharing of properties, and since properties

and their instantiations are not mind-dependent (see §1.2), facts about their overall

similarity will likewise hold for all observers independently of variations in their

cognition. The Moorean status of facts of genuine similarity is therefore of the objective

kind, rather than the subjective kind.

So not only are facts of genuine similarity beyond dispute, but they also have that same

indisputable status for all well-informed observers. It cannot for instance be the case

that from the perspective of a Manchester-based observer the badger/snake case

expresses something both true and Moorean, but from the point of view of a York-

based observer the badger/snake case expresses something true, but not Moorean.

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Whatever grounds Moorean facts of genuine similarity has to be the same for every

observer, because every informed observer reaches the same conclusions about what

objectively Moorean facts there are.

There is one final component to the work which objectively Moorean status performs

for facts of genuine similarity. It must also be the case that observers who agree on the

Moorean status of facts of genuine similarity must also agree that these are facts about

the same category of similarity relations. Given the simple account of overall similarity,

we know that for any statement expressing a comparative overall similarity claim there

will be some system for weighting properties that will make the statement come out

true. Consider the following example of a similarity claim:

‘Blackpool Tower is more similar to the Arc de Triomphe than Blackpool tower

is similar to the Eiffel Tower’.

At first glance this would appear to be false. Blackpool Tower and the Eiffel Tower are

both structures made of steel girders of roughly the same shape, whereas the Arc de

Triomphe is made of masonry. There will however be some relation of similarity which

weights properties in such a way that the Arc de Triomphe and Blackpool tower come

out more similar. For instance, the relation that assigns a great deal of weight to the

property of being a monument with a letter ‘c’ in its full name and zero weight to any

other. As such, practically any comparative overall similarity claim can be considered

to express an objectively Moorean fact, because it is indisputable that the claim will be

true with respect to some overall similarity relation.

This will not do for the kind of objectively Moorean status required by the argument

from genuine similarity. The argument requires not just that there is indisputably some

relation of similarity that holds in the case of Moorean facts of genuine similarity, but

that all of these Moorean facts of similarity are examples of the same kind of similarity,

if not precisely the same relation, then at least one of a small group of relations which

restrict the domain of similarity-makers in a similar way. We must therefore add the

requirement that Moorean facts of genuine similarity are also indisputably facts about

the same small family of overall similarity relations. In order for a fact to be Moorean

in the required way, an observer need not know precisely what relation she has

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selected for, or the precise weightings of all properties according to that relation, but

it seems that she must be at least roughly aware of the limits of the similarity relation

she has selected for. She must for instance be able to tell when the overall similarity

relation in question is not one of the obscure ones that weights a property like being a

monument with a letter ‘c’ in its full name.

The inclusion of objective Moorean status for some facts of genuine similarity

completes the argument from genuine similarity. We know that because genuine

similarity is a relation of overall similarity (or several such relations) that it must be

grounded in the sharing of a restricted domain of properties. The fact that genuine

similarities are in some cases objectively Moorean means that the basis for these facts

must be one which is independent of any observer-specific factors, such as habits of

thought or language, or interests and goals. The supporters of the argument from

genuine similarity then infer to what they consider to be the best explanation: that

there is an objective group of properties which are the sole similarity-makers for this

specific class of similarity relations. This is the Similarity role.

4.5 Moorean and non-Moorean facts of genuine similarity

My claim is that the argument from genuine similarity rests on the faulty assumption

that there are more facts of genuine similarity than just those which have Moorean

status. If we abandon this assumption than an alternative account of facts of genuine

similarity is possible that better accords with our experience. This alternative account

can not only account for facts of genuine similarity, but also accounts for their peculiar

Moorean force. The privileged properties account of genuine similarity cannot do this.

If such an alternative account is on offer, there is no reason to suppose that there is

work for privileged properties in satisfying the Similarity role.

The alternative account I wish to introduce in §4.7 is based on the presence of

prevailing properties. A prevailing property, as defined in §4.1, is a property which

ensures that any two objects which share it will be more similar to one another than

either is to any object which lacks it. If prevailing properties are an elite minority of

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properties, we can demonstrate that prevailing properties do not align with those

properties which satisfy Supervenience.

In this section I will show how the supporters of the argument perpetrate a shift in

explanandum from a relatively small range of facts with Moorean status to a much

larger domain of purported facts, and how doing so makes the privileged properties

account of such facts seem more attractive than it actually is.

First of all, it must be appreciated how rare Moorean facts of genuine similarity actually

are. Consider the following list of overall similarity claims.

1. Where a and b are electrons and c is a park bench: a and b are more similar

than a and c.

2. Where a is Ronald Reagan, b is Margaret Thatcher and c is a cathedral: a and b

are more similar than a and c.

3. Where a is Ronald Reagan, b is Margaret Thatcher and c is Phil Silvers: a and b

are more similar than a and c.

4. Where a is a blue, square block, b is a red square block, and c is a blue, round

block: a and b are more similar than a and c.

As we established in §4.5, what it means for a similarity claim to express a Moorean

fact of genuine similarity is for it to be indisputably true according to at least one of the

small family of relations which are constitutive of all the other Moorean facts of

genuine similarity. Of these examples, only 1 and 2 have this kind of Moorean status.

Claim 1 is Moorean because it cannot be accepted that there are any park benches

which could be more electron-like than some electrons, nor can we accept that one

human being could be very cathedral-like whilst another fails to be. This is not to say

that 1 and 2 could not be false according to some obscure relation of overall similarity

which weighted properties in an unusual way.

Claims 3 and 4 may well be facts, but they do not have Moorean status. Ronald Reagan,

Margaret Thatcher and Phil Silvers are all human beings and as such their material

compositions will admit of far less variation than the objects described in statement 2.

Reagan and Thatcher share a number of important similarities, in that they had similar

political careers and convictions in roughly the same time period, and their lifespans

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were much closer in length than Reagan and Silvers’ (Reagan died at ninety-three,

Thatcher at eighty-eight and Silvers at seventy-four). On the other hand, Reagan and

Silvers were both male, born in the same year, and both had radio careers at roughly

the same time. Even if we suppose that 3 is correct and Reagan and Thatcher are indeed

more similar, this fact doesn’t strike us with the same force of indisputability that is

indicative of Moorean facts. There is scope for sensible disagreement about the relative

importance of the different properties shared by a, b and c. The fourth of our examples

is even less clear. According to 4, a and b are alike with respect to being square, but a

and c are alike with respect to colour. The trade-off between these respects of similarity

in terms of the contribution they make to overall similarity is not obvious. Even if 4 is a

fact, it does not have Moorean status. Recall that in §4.4 it was established that a

similarity claim being indisputably factual according to some relation was not enough

to make that similarity claim express a Moorean fact. It has to be the case that the fact

is Moorean according to some relation of which the observer is at least roughly aware

of the limits of.

Examples like these show that whilst there are many facts of overall similarity, only a

select few can claim to be Moorean facts of genuine similarity. The proposed

specialness of genuine similarity is justified on the basis that there are Moorean facts

about it. The problem is that the supporters of the argument from genuine similarity

do not restrict themselves just to the Moorean facts of genuine similarity. We might

only have indisputable evidence for the existence of a select few facts of genuine

similarity, but supporters of the argument take these few indisputable facts to indicate

the existence of an entire realm of facts of genuine similarity. By analogy, imagine a

zoologist in a previously uncharted jungle discovering a novel specimen of frog. Strictly

speaking, she only has direct and convincing evidence for the existence of this one

particular specimen, but she may extrapolate from the discovery of this one frog that

there is an entire community of this species found in the region. The supporters of the

argument make a similar extrapolation in this case. They consider the few Moorean

facts of genuine similarity to be just those rare, obvious cases of a phenomenon which

is much broader. In §4.6 I will show why I believe this extrapolation is unwarranted. In

the remainder of this section however, I will show what difference this move makes to

the project of accounting for overall similarity.

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As we know, the supporters of the argument from genuine similarity equate being

genuinely similar with the sharing of privileged properties (see §4.2), so we can

interpret them as claiming that genuine similarity is as broad a phenomenon as the

sharing of privileged properties. Any two objects alike with respect to at least one

privileged property will be genuinely similar, regardless of the epistemic access we have

to that fact, or whether or not it is Moorean. The supporters of the argument assume

that the domain of facts of genuine similarity to be accounted for extend to relations

between any particulars which instantiate any privileged properties whatsoever.

Now we can see why it would make perfect sense for the properties which make for

genuine similarity to be the same as those which are defined out of the minimal

supervenience basis for reality, as per the Supervenience role (see §3.4). It is proposed

that most, if not all, particulars feature in at least some fact of genuine similarity. The

only domain of properties broad enough to be instanced by that great a range of

particulars are those which comprise a minimal supervenience basis for reality, or those

which are definable out of them in the way that less-than-maximally privileged

properties are known to be definable out of the maximally privileged ones. Taking

genuine similarity to be such a broad phenomenon is precisely what makes the

identification of properties which fulfil the Similarity role with the properties which

fulfil the Supervenience role the best explanation of the phenomenon of genuine

similarity.

4.6 Against non-Moorean genuine similarity

I do not believe we have reason to take genuine similarity to be as broad a phenomenon

as the supporters of the argument from genuine similarity claim. In this section I will

show why this is, and then show that the broad conception of genuine similarity is

deficient as an explanation of genuine similarity in any case.

It cannot be stressed enough that the shift in explanandum from Moorean facts of

genuine similarity to an entire purported realm of non-Moorean facts of genuine

similarity cannot be justified independently of the commitment to genuine similarity

being accounted for in terms of privileged properties. Genuine similarity is a

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phenomenon with two supposedly defining features: being grounded in the sharing of

privileged properties and being the subject of certain objectively Moorean facts. The

former we cannot use to justify the existence of any facts of genuine similarity,

Moorean or otherwise, for the reason given in §4.2. If accounting for genuine similarity

is meant to function as work for privileged properties, then they cannot be defined

solely in terms of privileged properties themselves. The existence of genuine similarity

would then actually presuppose the very thing it was seeking to justify: privileged

properties. This is why privileged properties alone cannot be a guide to what facts of

genuine similarity there are. If on the other hand the only positive reason we have to

believe in the existence of this particular kind of similarity in the first place is the

existence of some Moorean facts of genuine similarity, then we have no reason to

suppose that there are any non-Moorean facts of genuine similarity at all. Suppose that

our zoologist goes on to find a few more specimens of her novel species of frog, all

living in the treetops. She would not be entitled to think that some frogs of this species

were ground-dwelling, having never seen any living on the ground. There is likewise no

reason why we should extrapolate from the few Moorean facts of similarity to a

broader conception of genuine similarity.

The broader conception of genuine similarity also raises a question of its own. In

particular, why should it be the case that some facts of genuine similarity are so obvious

that they should have Moorean status, while the vast majority are so unclear, even to

the point that we are completely insensible of them? It appears that the supporters of

the broad conception must hold that there is some kind of epistemic gap precluding us

from observing genuine similarity in these cases. It’s not that there are no facts of

genuine similarity that are non-Moorean, it’s just that our limited ability to

comprehend the world around us means that we can only discern these relations in a

minority of cases. On closer examination, however, this response is inadequate.

In the example with the three blocks of different colours and shapes (see §4.5) we had

all the relevant information about the properties of the blocks given to us, and we still

had no idea of which pairs (if any) were more similar. According to the broad

conception of genuine similarity, there is indeed some fact of the matter about the

comparative overall similarity between the three blocks. Either one pairing is more

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similar than the other, or both pairs are equally similar. I submit that not only do we

lack an intuition that one pair out of the three is more similar, but we don’t have an

intuition that the three blocks are all equally similar either.

Morreau (2010) makes use of a similar example to this one, borrowed from John

Maynard Keynes, who originally made the point about similarity as an analogy with

probability. Morreau uses the example to argue for the claim that there can be no facts

of overall similarity, on the basis that similarity in one respect cannot ‘make up for’

dissimilarity in some other respect. In Moreau’s example, blocks and shapes are

replaced by books with either morocco or calf bindings. A book bound in blue morocco

has some similarity with a book bound in red morocco, and this likeness can be

decreased by changing the binding of the first book from blue morocco to blue calf.

What Morreau claims we cannot do, however, is to regain the original degree of

similarity between the two books by changing the colour of the first book, currently

bound in blue calf, to red. The problem, claims Morreau, is not simply that the rate of

exchange between colour and types of leather in calculations of overall similarity is

vague, but that it is simply non-existent. We have no more idea of a rough rate of

exchange between the two than we have of a precise one (Morreau, 2010 pp 481-482).

Morreau comes to the strong conclusion that overall similarity is a faulty idea at root,

but our everyday experience of overall similarity, not to mention the existence of

Moorean facts of similarity, indicate otherwise. Morreau’s argument aims to show that

there is no good way of measuring overall similarity. In fact, it seems as though there

are many. As I established in §4.2, just because we don’t know how properties trade

off against one another with respect to similarity-making doesn’t mean that they do

not trade off. Recall the analogy of the two piles of sand. We can know that one pile is

bigger than the other without knowing how many grains of sand are in each.

Although Morreau is incorrect in his conclusions about overall similarity in general, his

proposal for how we should understand examples like those of the books and blocks is

attractive. Morreau shows us that the further away we get from the Moorean facts of

genuine similarity the harder it is to find any basis for relations of genuine similarity at

all. In cases like these where there seems to be no basis for ruling one way or another,

I suggest that there are no facts of the matter about genuine similarity.

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I am not claiming that our ignorance of any fact of genuine similarity concerning the

three books shows us that there isn’t one. Morreau’s examples do not preclude facts

of genuine similarity of which we are simply insensible. All I am claiming is that we have

no reason to insist that there are such facts, either. We are perfectly at liberty to devise

an account of genuine similarity which does not admit the existence of a fact of genuine

similarity holding between the three books, and it is just such an account I set out in

the next section.

I hold that my account, which does not assume that there are facts of genuine similarity

holding between all groups of objects, actually has an advantage that the privileged

properties account lacks. It can explain why the phenomenon of genuine similarity is

observed in some cases but not others, and why Moorean facts of the same have their

peculiar status.

4.7 Prevailing properties

The alternative account of genuine similarity I will argue for is based on ‘prevailing

properties’. As I have said, a prevailing property is one such that any two particulars

which share it will be more overall similar than a pair which is divided by it. Prevailing

properties, I contend, are present in all cases of Moorean genuine similarity. In this

section I will show that when we consider what all Moorean facts of genuine similarity

have in common, their Moorean status can best be explained by the presence of a

prevailing property. Prevailing properties can account for genuine similarity whilst still

satisfying all the known constraints on overall similarity relations. I will go on to show

that a prevailing properties account better accords with our experiences of genuine

similarity.

All Moorean facts of genuine similarity have two features in common. Firstly, they are

all extreme cases, where the degree of similarity between the more similar pair is much

greater than the degree of similarity between the less similar pair. Secondly, there is

always at least one aspectual similarity between the more similar pair which we

recognise as being largely or wholly responsible for its greater degree of similarity. This

is so even if we are unaware of all the aspectual similarities which contribute to the

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fact, and their weightings relative to one another. Recall similarity claims 2 and 3 from

§4.4. In the former case we have the Moorean fact that Ronald Reagan and Margaret

Thatcher have a higher degree of similarity than Ronald Reagan and a cathedral. In the

latter case we have the non-Moorean fact that Ronald Reagan and Margaret Thatcher

have a higher degree of similarity than Ronald Reagan and Phil Silvers. According to the

narrow conception of genuine similarity which I defended in the previous section, only

claim 2 is a fact of genuine similarity because only it is Moorean. The difference

between the two cases is readily apparent.

In the case of genuine similarity, the degree of similarity between Ronald Reagan and

the cathedral strikes us as being very low indeed compared with the degree of similarity

between Ronald Reagan and Margaret Thatcher. The cathedral is a building made of

inanimate stone, whereas Ronald Reagan is a flesh and blood life-form. The two objects

are dramatically different in practically every way we can think of. It is clear that the

only way Ronald Reagan could be more like a cathedral than Margaret Thatcher is if we

employ some very bizarre relation of similarity indeed. If, on the other hand, we are

using one of the small family of relations that facts of genuine similarity all have in

common, then it does indeed seem indisputable that Ronald Reagan and Margaret

Thatcher will be more similar to each other than Ronald Reagan and a cathedral. We

also find it very easy to pinpoint a property which is shared by the more similar pair

that is in large part responsible for their having a higher degree of similarity. Both

Ronald Reagan and Margaret Thatcher have the property of being human, whilst the

cathedral does not. If we imagine a different scenario where object c were replaced by

any other kind of non-human, be it a park bench, a blue morocco bound book, a gorilla,

an electron, it would still be the case that Ronald Reagan and Margaret Thatcher would

be more similar than Ronald Reagan and object c. The property of being human is a

prevailing property.

Contrast this with claim 3, where every particular has the property of being human. In

this case, the fact is not Moorean, because there is no prevailing property that

separates out Ronald Reagan and Margaret Thatcher from Phil Silvers. Although being

a politician is a property they both share, it is not a prevailing property because it is still

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possible for a politician and a non-politician to be at least as genuinely similar as

something else which is a politician.

My proposal is that genuine similarity is a family of overall similarity relations in which

prevailing properties are extremely highly weighted, whilst the remainder of properties

are assigned only negligible weight. The requirements that are set down for a theory

of any kind of overall similarity in the argument from genuine similarity are that facts

of overall similarity are grounded in the aspectual similarities between particulars (see

§4.1), and that at least some properties are assigned zero or negligible weight (see

§4.4). The prevailing properties account satisfies both of these conditions. The benefit

of the prevailing property account of overall similarity over the privileged property

account is that it provides us with an explanation of why facts of genuine similarity have

Moorean status and why they are relatively rare.

Facts of genuine similarity only hold where a pair of particulars is united by a prevailing

property, and their similarity is being compared with the similarity between a pair of

particulars that are not united by a prevailing property. There are no facts of genuine

similarity under any other circumstances. Where they do occur however, they have

special indisputable status because the prevailing property responsible for the fact’s

holding is readily identifiable. This does require that competent observers be

particularly attuned to when a property is a prevailing property, but this is certainly no

more problematic than the supporters of the argument from genuine similarity’s

analogous claim that competent observers are particularly attuned to the sharing of

privileged properties.

I conclude that we have reason to prefer the prevailing properties account over the

privileged properties account of genuine similarity. Privileged properties are not the

best explanation of the phenomenon of genuine similarity. In the final section of this

chapter I will show the consequences of these findings for the co-satisfiability of the

Similarity and Supervenience roles.

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4.8 Similarity and Supervenience

I have argued that the best account of genuine similarity is not one which takes facts

of genuine similarity to be grounded in privileged properties, but rather in a kind of

property which I have called ‘prevailing properties’. If privileged properties do not

account for facts of similarity, then we can strike off the Similarity role from the list of

work that privileged properties do. The posit of privilege is therefore not as

theoretically useful as its advocates suppose. However, before we can accept this

consequence of the prevailing property account, it must be shown that the group of

prevailing properties cannot be the same as the group of properties which satisfy the

Supervenience role.

Firstly, it should be noted that prevailing properties are not usually very joint-carving

properties themselves. Recall from §2.3 that a joint-carving property is one which

tracks distinctions that can be made out at the level of the maximally privileged

properties, i.e. those which comprise a minimal supervenience basis for reality. In fact,

many prevailing properties are instantiated by one and only one particular. The

property of being Ronald Reagan, for instance, is a prevailing property. It is an

indisputable (and hence Moorean) fact that any particulars which instantiate the

property of being Ronald Reagan will be more similar to one another than they are to

anything which is not Ronald Reagan. Properties with only one instance are not joint-

carving, because two particulars which are alike with respect to all their maximally

privileged properties will still be divided by such properties.

In addition, prevailing properties become more common the further away from the

maximally privileged properties one goes. Although even some maximally privileged

properties, such as being an electron will be prevailing properties, most relatively joint-

carving properties, such as being made of gold or having a temperature of one hundred

degrees Celsius are not prevailing. There are a great many relatively non-joint-carving

properties which are prevailing though, for instance being a three-legged mountain

goat with exactly five million hairs on its body and a striking resemblance to Ronald

Reagan. If one were able to find two such particulars which instantiate this property, it

is difficult to imagine what could be more similar to one of them without having the

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property of being a three-legged mountain goat with exactly five million hairs on its

body and a striking resemblance to Ronald Reagan.

If a property like this is close enough to the maximally privileged properties in terms of

its definability to still be considered a privileged property, we may as well simply allow

that practically all properties are privileged, the only exceptions being some which are

incalculably distant from the maximally privileged properties. However, in doing so we

run afoul of the restriction on the scope of the privileged properties that we established

in §2.4. If we allow all properties to be privileged, or even practically all properties, then

the posit of privilege itself becomes trivial. The fact that the ability of properties to

perform the special functions attributed to privileged properties does not decrease

with their degree of privilege means that if the domain of privilege is cast too wide then

it becomes no kind of restriction on the properties that can perform those jobs at all. If

properties as bizarre as being a three-legged mountain goat with exactly five million

hairs on its body and a striking resemblance to Ronald Reagan are privileged and can

fulfil the Similarity role, then in what sense is the Similarity role a restriction on

similarity-making at all?

For this reason I conclude that prevailing properties are not found only amongst the

privileged properties. They do not, therefore, comprise a group of properties which can

be identified with those which satisfy the Supervenience role. We should therefore

abandon the view that the Similarity role forms part of the work for which privileged

properties are suited.

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Chapter Five: Counterfactuals and Similarity

5.1 Possible worlds semantics for counterfactuals

In the previous chapter we established that the argument from genuine similarity does

not justify a belief in a group of properties which combine the Supervenience and

Similarity roles. In this chapter I present an independent argument for the separation

between properties that satisfy Supervenience and those which satisfy Similarity, based

on a particularly important application of the notion of overall similarity in

contemporary analytic philosophy. This is the possible worlds semantics for

counterfactuals associated with Robert Stalnaker (1968) and David Lewis (1968).19 In

this chapter I will show that the Lewisian version of a possible world semantics for

counterfactuals is incompatible with his later view that only privileged properties count

towards overall similarity between particulars.

Most of Lewis’ work on the counterfactual theory predates his development of natural

properties in the early eighties. However, there is evidence from his writings around

this period to suggest that he always intended the counterfactual theory to be

constrained with respect to the features which could count towards overall similarity.

In fact this restriction appears to be entailed by developments he makes to the

counterfactual theory (1979b). It appears as though Lewis viewed an understanding of

overall similarity limited to the sharing of privileged properties to be an unproblematic

addition to the counterfactual theory. In practice, the introduction of such a restriction

would serve only to explain some features of how individuals judge overall similarity in

the first place (Lewis 1973a p93, 1979b p465).

Regardless of Lewis’ actual intentions, there are consequences for the posit of privilege

if the possible worlds semantics for counterfactuals depends on similarity relations

which assign weight to properties which do not satisfy Supervenience (see §3.4).

Supporters of both privileged properties and possible worlds semantics for

counterfactuals are left with an uncomfortable trilemma. The first two options are to

19 See also Counterfactuals (1973), and ‘Counterfactual Dependence and Time’s Arrow’ (1979b), in which he further develops his possible worlds semantics for counterfactuals.

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abandon one of the roles for privileged properties, either Similarity or Supervenience.

In doing so, the theoretical virtue of privileged properties, which depends on their

ability to perform multiple functions simultaneously (see §1.4), is much diminished. In

losing one of these roles we would also lose all of the derived roles we saw to follow

from them in §3.5 and §3.6. The alternative is to refine the Similarity role so that it

applies only to a particular range of similarity relations, and to claim that the

counterfactual theory makes use of a more exotic form of similarity to which the

Similarity role does not apply. I will return to this possibility and show why it is no better

than simply abandoning Similarity in the first place in §5.8. Either way it would be better

for supporters of privilege if this influential theory of counterfactuals did not present a

counterexample to the co-satisfiability of the Similarity and Supervenience roles.

The semantics for counterfactual statements proposed can be summarised as follows.

For a counterfactual to be (non-vacuously) true, we need only require that the

consequent of the counterfactual conditional holds in the most similar world to the

actual world in which the antecedent is also true. For example, the counterfactual ‘If it

had rained, the wedding would have been ruined’ is true just in case the closest

possible world in which it rains is a world in which the wedding is ruined (1973a p13).

The role played by similarity in this counterfactual theory is twofold. In the first case,

overall similarity is the means by which counterparts of objects in worlds besides our

own are to be identified. Lewis denies that ordinary particulars can be present in more

than one world,20 and so rather than establishing the truth of the above counterfactual

on the basis of what happens to the wedding in some other world, instead we should

look to what is true of some other event which is appropriately similar to the wedding,

its counterpart. Secondly, similarity determines the ordering of worlds as closer to or

further away from the world in which a counterfactual judgement is made. In both of

these capacities, a conception of similarity grounded only in the sharing of properties

which satisfy the Supervenience role is inadequate.

20 Sets are an exception to this rule, as these are partly located wherever their members are. If there are universals then these are similarly not world bound, although they are not particulars (Lewis 1983 p190).

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In keeping with the account of ‘mainstream’ theories of privilege set down in §1.3 and

§§2.6-2.7, I will be assuming that the properties which satisfy the Supervenience role

are those of fundamental physics, with the addition of those which are ‘not too distant’

from them. This notion of ‘distance’ from the maximally privileged properties was

introduced in §2.2. For convenience, throughout this chapter when I speak of only

privileged properties satisfying the Similarity role, by ‘privileged properties’ I will mean

those properties which are privileged according to this mainstream, microphysical

view.

Broadly, the structure of this chapter will be as follows. §§5.2-5.5 will demonstrate the

pivotal importance of overall similarity to the possible worlds semantics for

counterfactuals, whilst §5.6 and §5.7 will show why a notion of similarity limited to

those properties which satisfy Supervenience is inadequate for these purposes. In §5.8

I show the consequences of my findings for theories of privilege. I will now outline the

goals of this chapter in detail. In §5.2 I will show that Lewis’ commitment to a particular

form of modal realism is not a prerequisite for acceptance of a possible worlds

semantics for counterfactuals. Possible worlds semantics is in fact compatible with a

number of forms of actualism (the belief that only the actual, rather than the possible

exists). §5.3 and §5.4 will detail the role of overall similarity in counterfactual

semantics, and in particular show the importance of context-sensitive notion of

similarity to the theory. In §5.5 I outline the development of Lewis’ thought regarding

privileged properties as a constraint on similarity, and show that the best possible

understanding of Lewis’ own position on the counterfactual theory includes the

requirement that similarity judgements be restricted to those which assign weight to

privileged properties only. I will then show the deficiency of this account which

combines both the counterfactual theory and the restricted notion of similarity, first

with respect to the counterpart relation, and then the ordering of worlds. These will be

the goals of §5.6 and §5.7 respectively. Finally, in §5.8 I conclude that the

counterfactual theory requires a notion of similarity which allows non-privileged

properties (by which I mean those which fail to satisfy the Supervenience role) to be

positively weighted. I will then show why we should take this to mean that Similarity

and Supervenience are not co-satisfiable roles, and that amending the Similarity role to

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exclude the kind of similarity needed for a possible worlds semantics for

counterfactuals will not help theorists of privilege.

5.2 Variants of the Lewisian possible worlds semantics for counterfactuals

Although I will be focusing on Lewis’ own views in this chapter, elements of his possible

worlds semantics for counterfactuals have found favour even amongst those who

disagree with some of his other theoretical commitments. Disagreements aside, it can

be shown that all of these variant theories must rely on a similar notion of similarity in

some capacity. This will be the goal of this section. The most common form of variation

on Lewis’ preferred theory are those who support the analysis of counterfactuals in

terms of possible worlds, but disagree with Lewis’ understanding of what these worlds

are.

It is difficult to give a theoretically neutral account of what a possible world is, however

in general terms we can imagine a possible world to be a complete way for things to

be. With such a theoretical tool to hand, we can interpret modal notions such as the

words ‘necessarily’ or ‘possibly’ as generalisations about such worlds (see Divers 2002

p5). Necessity is defined as truth at all possible worlds, whereas possibility is just truth

at some world. Lewis himself famously (or infamously) claimed that possible worlds

were entities of the same sort as the actual world, being a maximal accumulation of

spatiotemporally and causally connected particular objects (Lewis 1986a p2). According

to Lewis, our world is the actual world only in as much as it happens to be the world

we ourselves occupy. From the point of view of a being inhabiting a different world,

theirs is the actual world and ours is merely possible. Alternative interpretations of talk

of worlds are available, however, and those views which endorse the existence of

possible worlds, but as entities unlike the actual world can be classed as moderate

realists (Melia 2003 p123). Sider, for instance, another prominent believer in privilege

discussed in previous chapters (see §1.4), endorses both the Lewisian theory of

counterfactuals and the existence of possible worlds. However, Sider does not consider

the merely possible worlds to be entities like the actual world. Instead, he identifies

possible worlds with linguistic entities, a strategy which Lewis himself describes as

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linguistic ersatzism about worlds (Lewis 1986a p142). For Sider, there is a single

linguistic entity which represents the totality of possible worlds and individuals all at

once, the ‘ersatz pluriverse’, and all the descriptive power of possible worlds is

intended to be reducible to what is the case according to the pluriverse sentence (Sider

2002 pp286-288).21 Still others have sought to take advantage of the usefulness of

possible worlds talk whilst denying altogether the existence of non-actual worlds. This

‘modal fictionalism’ takes possible world semantics as a heuristic model for the

understanding of modal notions and nothing more, while the truth conditions of modal

statements are grounded in whatever happens to be true according to a particular

theory which posits the existence of possible worlds (Rosen 1990).

Such alternative interpretations of talk of worlds share those features of the Lewisian

theory that are interesting for our present purposes in that they rely on similarity in

much the same capacities as Lewis’ own approach, and as such the question of whether

or not the requisite measure of similarity is restricted to privileged properties remains

relevant.22

It should be noted that it is additionally a live option to deny counterpart theory while

endorsing Lewisian modal realism, and instead to believe in genuine trans-world

identity of actual and possible particulars (see Lewis 1986a 198-209, Teller 2001,

McDaniel 2004). Such a viewpoint would of course preclude the relevance of similarity

to counterfactual semantics with respect to the identification of counterparts.

21 Note that Sider’s ersatz pluriverse is not the only way that attempts have been made to reduce possible worlds to linguistic entities. More common is an ‘entity-for-entity’ identification of individual possible worlds with a set of sentences. See Melia (2001) for a recent discussion of these proposals as well as his responses to certain objections to the ersatzist project. 22 There is of course one major difference between how these similarity relations are to be thought of in the context of these alternative interpretations of worlds talk and Lewis’ own theory. As ersatz worlds are entities wholly unlike the actual world (and fictional worlds don’t exist), they cannot instantiate properties in the same way. Instead such interpretations of possible world semantics for counterfactuals draw on the similarity between features of the actual world and those features which possible worlds are represented as instantiating. Such proposals are controversial however. For instance, Merricks (2003) has argued against the viability of any attempt to endorse counterpart theory in the absence of Lewisian modal realism, on the basis that represented worlds cannot suffice for an analysis of the counterpart relation. A full discussion of the merits of these claims would unfortunately take us too far from the topic of this chapter however.

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Nonetheless, the more general claim that truth conditions of counterfactuals depend

on the most overall similar worlds could be retained.

5.3 Similarity and the analysis of counterfactual conditionals

In this section I will detail the importance of overall similarity to Lewis’ counterfactual

semantics. I will lay out the details of Lewis’ preferred analysis of counterfactual

statements, paying particular attention to the counterpart relation and the ordering of

worlds as more or less distant from the actual world. Both of these are to be

understood in terms of similarity, according to Lewis.

Counterfactuals are analysed by Lewis as variably strict conditionals. Traditionally,

counterfactual or ‘subjunctive’ conditionals are considered to be of a separate kind to

‘indicative’ conditionals (Edgington 1995 p236). Compare the following two examples.

1. ‘If the glass has been dropped, then it will be broken.’

2. ‘If the glass had been dropped, then it would have broken.’

The behaviour of these sentences is very different. According to Fregean logic, a

conditional is false in a world just in case its antecedent is true and its consequent false.

This seems to work adequately enough in the case of 1, the indicative conditional, but

not so with respect to 2, which is in the subjunctive mood. If we assume that all the

counterfactual claims that we care to make will involve antecedents which are false in

the actual world, then it appears as though all counterfactual claims will be true on this

Fregean analysis. This is not the result we intend in making counterfactual claims, so it

appears that an alternative analysis is required for counterfactual conditionals relative

to indicative ones (Goodman 1947 p10).

There are two parts to Lewis’ proposed alternative analysis. Firstly, counterfactuals are

to be interpreted as strict conditional statements, which is to say material conditionals

which hold necessarily (Lewis 1973a p4). Necessity is generally defined in terms of

possible worlds as the feature of holding at every possible world, but the second part

of Lewis’ analysis is to claim that the domain of worlds at which a statement must hold

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in order to be true necessarily is relative to the kind of modal claim under discussion,

what Lewis calls a restriction on the accessibility of worlds (Lewis 1973a p5).23

Suppose we wish to know if it is possible that England will win the next World Cup. In

such a case we are clearly not intending to ask whether such a thing would be logically

or even physically possible. When we talk about the possibility of England winning a

World Cup, it seems that the domain of worlds in which we are interested are those in

which most of the relevant features of the English World Cup squad are the same as in

the actual world, specifically the players on the team, their levels of fitness and

disposition. It might be that in some possible world in which players from any country

on Earth were deemed eligible to play for the English team, a squad selected from

amongst the most talented players in the world goes on to win the cup, but such a

world does not seem to be accessible from ours when we ask whether or not England

is in with a chance of bringing home the trophy. In this way, modal claims can be

understood as generalisations about a restricted domain of accessible worlds.

According to Lewis, we should understand the domain of accessible worlds

corresponding to a counterfactual conditional to be limited to those worlds which meet

a certain threshold of overall similarity to the actual world, with this threshold being

just low enough to allow at least one world in which the antecedent of the conditional

is true. That is to say, we should interpret the counterfactual conditional to be just strict

enough to avoid its being vacuously true (1973a p13).

Note that this only works as an analysis of the truth conditions of counterfactuals if

there is a maximum degree of similarity to the actual world that any world at which the

antecedent is true can achieve. Lewis calls this the Limit Assumption (1973a p19). If the

true-antecedent worlds are able to become more and more similar to the actual world

without ever reaching such a maximum, obviously there will be no closest true-

antecedent worlds to the actual world. In such cases Lewis advises that we take a

counterfactual to be true just in case there is a certain degree of similarity such that at

23 This is not the only option available for the interpretation of counterfactual conditionals. See Edgington (2008).

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all worlds more similar to the actual world than this are worlds where the conditional

holds (1973a pp19-20).

For worlds which obey the Limit Assumption, however, we can give a simplified

statement of the truth conditions of any counterfactual claim. For a counterfactual to

be (non-vacuously) true, we need only require that the consequent of the conditional

holds in the most similar world to the actual world in which the antecedent is also true.

If there are several true-antecedent worlds which are at least as similar to the actual

world as any others, for the counterfactual to be true the conditional must hold in each

of these worlds. For the sake of convenience I will generally speak simply of the need

to find a single most similar true-antecedent world. Cases in which there is no one

closest world to the actual world are however important to the criticism of Lewis’

theory that I present in §5.7.

Similarity, then, is the thing which makes worlds accessible.24 Bear in mind that as in

chapter four, the similarity relation we are interested in with respect to the ordering of

worlds is one of comparative overall similarity (Lewis 1973a p48). In order to be true, a

counterfactual conditional must hold in the true-antecedent world which is more

similar to the actual world than any other, whereas the worlds accessible from the

perspective of a single counterfactual are simply those which are at least as similar to

the actual world as the closest true-antecedent world or worlds. We began however by

claiming that there were two functions which similarity plays in the counterfactual

theory, and so far we have only established one of these. There is still the issue of Lewis’

counterpart theory.

We have already noted that Lewis denies that any objects can exist in more than one

world (1968 p115). If this is so, then how might England ever win the World Cup in

some other world, given that both England and the World Cup exist in one world and

one world only? The answer Lewis offers is that while these entities do not exist in any

24 Arregui (2009) has proposed that the model of world-ordering described here is actually insufficient as it stands and would serve to make inaccessible certain parts of worlds which appear intuitively relevant to the truth conditions of counterfactuals. Instead she proposes that rather than focusing on similarity of entire worlds, we should focus on similarity of local regions rather than entire worlds. The comments I come to make regarding the role of natural properties in similarity judgements are insensitive to this issue.

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world, entities which are qualitatively very much like them do. These are the

counterparts of these entities in that world, and when we say that in another possible

world, England wins the World Cup, what we mean is simply that a counterpart of

England has won a counterpart of the World Cup. Counterparts are determined by

overall similarity. Suppose that ‘I could have been taller than I actually am’ is true. It

follows that there will be some possible world in which a counterpart of mine is taller

than I am, but suppose we wanted to know if one (non-actual) world in particular was

one in which I had a taller counterpart. In this admittedly small and boring world there

are only two candidate individuals for being my counterpart, A and B. A is a human

being of slightly shorter height than I am, whereas B is a giraffe of average height for

that species. Neither of them is of course identical with me, as I inhabit one world and

one world only, that which from our perspective we call the actual world. The giraffe,

B, is certainly taller than I am, but it is also less similar to me overall than A the human

is. A would therefore by my counterpart in this world, for even if A was a human as

dissimilar to me as any two humans can be, A would still be more similar to me than a

giraffe. According to the Lewisian counterpart theory, this would not be a world in

which I had a counterpart taller than myself.

Usually, there will either be one distinguished candidate for the counterpart of an

object in a world or else nothing in that world will be sufficiently similar to it to be

plausibly considered its counterpart, but in some cases there may be multiple objects

in a world with equally good claims to be counterparts of the original. In such cases,

every such object in that world is a counterpart of the original. In order for a

counterfactual conditional involving counterparts of mine to hold at a world, it must

hold with respect to all my counterparts, not just some (Lewis 1973a p40).

5.4 The role of context

The preceding discussion assumed that there was but one way of calculating overall

similarity, however we already know that there are many (see §3.6). Before examining

how privilege influences the counterfactual theory we must understand how context

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can affect which similarity relations a counterfactual statement relies on. This section

will detail the role of context to Lewis’ theory.

Lewis holds that from our everyday experience we can attest to the fact that

counterfactual statements appear to be ‘vague’, albeit in a quite well-understood way

(1973a p1). In describing counterfactuals as vague Lewis has something very specific in

mind that does not correspond to the more familiar understanding of vagueness as

Sorites-susceptibility. Vagueness, according to Lewis, is ‘semantic indecision’ between

the members of a range of equally good meanings for our terms (1986a p212). With

respect to counterfactual statements, the issue is not that their vagueness makes them

impossible to resolve but rather that we need some basis for resolving them in one way

rather than another. In basing counterfactuals in similarity we have a ready explanation

of what this vagueness is and where it comes from. Any indecision between meanings

for terms in counterfactual statements can be ascribed to indecision over which

similarity relation with its associated weightings of properties we are invoking (see

§3.6). As Lewis claims:

The essences of things are settled only to the extent that the counterpart

relation is, and the counterpart relation is not very settled at all. Like any

relation of comparative overall similarity, it is subject to a great deal of

indeterminacy … (Lewis 1986a p42)

Although the above remarks relate explicitly to the identification of counterparts, they

may also be extended to the relations of similarity which dictate the ordering of worlds.

The appropriate similarity relation for a counterfactual is determined by context (Lewis

1973a pp67-68). Depending on which means of calculating overall similarity is apt in

that context, similarity relations between objects will differ, and the counterfactuals

that we base on similarity will differ in different truth-value between contexts as a

consequence. This, claims Lewis, reflects our everyday experience regarding

counterfactuals. Consider for instance the following two modal claims concerning

Socrates.

‘Socrates could have been born in the United States of America.’

‘Socrates could have been born a woman.’

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Both of these claims appear to be plausibly true, but although we can identify contexts

which allow one or the other of these claims to be true, there does not seem to be any

one system for the weighting of properties which permits both to be true according to

the same relation.

The first of these two claims would be true just in case Socrates has some counterparts

born in a counterpart of our world’s United States of America. In the context of such a

claim we would most likely base our judgements as to Socrates’ counterparts on

physiological similarity with our Socrates, assigning the greatest weight to an object’s

being constituted by the same kinds of matter in as close to the same arrangement as

possible. Perhaps we might even require that certain neurological properties or

dispositions possessed by our Socrates, such as curiosity, or a belief in Athenian

supremacy were present in a putative counterpart. We would however assign less

weighting to similarity with respect to certain other features of our world’s Socrates.

For obvious reasons we would not require that all Socrates’ counterparts be born in

Athens, or born to counterparts of our Socrates’ parents. But, this same system of

weightings seems wholly inappropriate to judge the second of our two counterfactual

claims. If being a counterpart of Socrates were to require the same threshold of

physiological similarity to our world’s Socrates in this context, then there could be no

female counterparts of Socrates in any world. Instead, when assessing the truth of this

modal claim we would be more inclined to assign weight to features such as being born

to counterparts of our Socrates’ parents, being born at the same time and in the same

place as our Socrates, the very properties to which we assigned almost no weight

previously.25

25 According to Cross, what Lewis calls ‘the context’ of a counterfactual is but one element of the ‘background facts’ that determine the truth-value of a counterfactual claim (a phrase he takes from Brogaard and Salerno 2008). Although context determines the similarity relation by which worlds are ordered, Cross argues that the accessibility of worlds from the actual world is additionally limited with respect to certain facts which follow from the antecedent of the conditional. For instance, if we have a counterfactual claim which begins ‘Had J. Edgar Hoover been born in Russia’, our interest is in worlds where Hoover is a typical Russian with traits typical to Russians of that era, such as a belief in communism, and restrict our attention to worlds like this. These antecedent-relative background facts do not immediately follow from the context in which a counterfactual claim is made, but from the antecedent of the counterfactual itself, and as such is separable from the similarity ordering of worlds by context (Cross 2011 p6). In this chapter, however, I need focus only on the impact of background facts relevant to the similarity

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It is the variety of similarity relations available to us and the flexibility this gives us with

respect to the range of worlds accessible from the point of view of a given

counterfactual that allows the Lewisian theory to deliver us the appropriate truth

values for counterfactual claims. As we established in §3.6, there are as many different

similarity relations as there are ways of weighting individual aspects of similarity, but

Lewis does not intend for all of these relations to be acceptable contexts for

counterfactual statements. In his own words, ‘not anything goes’ (Lewis 1973a p93).

The Similarity role for privileged properties claims that only properties with a degree

of privilege greater than zero contribute to overall similarity. Lewis intended similarity

in the context of the counterfactual theory to be restricted to privileged properties, in

accordance with the Similarity role. In the following section I will demonstrate how his

remarks on the subject show us this.

5.5 Privilege constraints on the weightings of similarity judgements

In Counterfactuals Lewis does not explicitly endorse the claim that only natural

properties are relevant to the kind of similarity he has in mind. Instead he merely

suggests that most of the time our judgements will lean towards emphasising certain

respects of similarity over others, and that there may not be any clear dividing line

between what counts as an acceptable or ‘familiar’ similarity relation compared with

an ‘eccentric’ one. In the extensive modifications he makes to the theory in

‘Counterfactual Dependence and Time’s Arrow’ (1979b), we can see a hardening of this

position. In this paper he introduces some clarifications of the type of similarity he sees

as relevant to the ordering of worlds, and taken together the constraints he imposes

imply a focus on perfectly natural properties. Evidence from papers of his written

around the same time suggest that something like the doctrine of natural properties

that he would expound in ‘New work for a theory of universals’ (1983) was what he had

in mind in imposing these constraints. In this section I will show how Lewis’ responses

ordering of worlds, and may assume that if Cross is correct in his claim that there are additional non-context based background facts, that these remain fixed.

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to objections raised by Fine (1975) and Bennett (1974) indicate a commitment to

similarity relations holding between objects with respect to privileged properties only.

In Lewis’ book-length articulation of the possible world semantics for counterfactuals

he suggests that while there may be a wide range of similarity relations which we might

choose to employ in any given circumstances, we have a pretty clear intuition that only

some of these are ever appropriate to employ. He draws an analogy with the distinction

between colours. There may not be a clear dividing line between blue and green, but

this does not mean that we are never able to say definitively whether any shade is blue

or green. There are shades which are blue under some acceptable definition, and green

under others, but the delineation which would insist that the sky is green is not a

permissible one (1973a p93).

Consider the example of a man who denies that he would have fallen had he stepped

out of a high window, not on the basis of any incorrect information, but rather because

he makes use of a system of weighting outside of the usual range of variance. Of such

a man Lewis says that:

He is not entitled to give in to his inclination to deny this, at least not without

giving warning of his eccentric notions. If he denies it without warning he lies;

if he denies it with warning, he temporarily changes the conventional meanings

of his words. There is a rough consensus about the importances of respects of

comparison, and hence about comparative similarity. (Lewis 1973a pp93-94)

The claim Lewis makes here is that in speaking in this way the man who denies a

plausible counterfactual claim about what would happen if he steps outside of his

window is guilty of speaking in bad faith. According to our ordinary intuitions about

similarity, the closest world in which he steps out of the window is not one where he

fails to fall. There are many different relations of overall similarity, and in the previous

section we noted that the ability of counterfactuals to invoke different such relations

was amongst the strengths of the theory. In this case however, the similarity relation

that is chosen is not appropriate to the context. We might compare this case to one of

a person who uses the word ‘several’ to describe groups of objects numbering in the

millions. The word ‘several’ is vague in the Lewisian sense of indecision between a

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number of equally good semantic alternatives. There is no unambiguous, settled

demarcation between those groups whose members number ‘several’ and those that

cannot. The boundary may be drawn differently by different people, at different times.

Even so there is a general assumption that it cannot be appropriately used to

characterise groups of millions of objects. Someone who uses such a word in this way

is actually temporarily changing its meaning (Lewis 1973a p93). The crime this man is

guilty of is not one of being mistaken about a means of ordering worlds. The message

here seems to be that we may choose to order worlds in accordance with their

similarity to the actual world where the similarity relation in question is one which

weights properties eccentrically, but that this is an unusual and potentially misleading

thing to do in communication without clarifying those intentions beforehand. The

tendency to be more interested in certain specific relations of comparative overall

similarity rather than others is left unexplained.

In ‘Counterfactual Dependence and Time’s Arrow’, the message is stronger, as we are

told that not just any respect of similarity is able to count towards overall similarity: ‘it

contributes nothing to the similarity of two gemstones that both are grue’ (1979b p

466). Such properties have zero weight. By this point we have gone from a general

stricture against adopting eccentric systems of weighting properties in respect of

importance without prior disclosure to a stricture against any non-natural properties

counting towards similarity at all.26 Additionally, in this paper we discover that the

properties which Lewis claims we should be interested in when assessing worlds for

similarity are perfectly as opposed to merely somewhat natural. This suggests that the

kind of similarity he has in mind for the ordering of worlds is even more restrictive than

just what the Similarity role would require.

The constraint arises from an apparent asymmetry of our counterfactual judgements

with respect to time. Lewis notes that we rarely, if ever, speak of counterfactual

26 Lewis does not use the term ‘natural property’ in connection with these remarks. In ‘Attitudes De Dicto and De Se’ (1979a), however, published shortly before ‘Counterfactual Dependence and Time’s Arrow’ (1979b) he uses the term ‘natural’ to describe properties in contrast with ‘gruesome gerrymanders’. This indicates that even before his full articulation of the theory of naturalness in ‘New work for a theory of universals’ he was content to think of properties as divided according to privilege in this way (1979a p515). It seems perfectly acceptable to take him to be referring to the same distinction in ‘Counterfactual Dependence and Time’s Arrow’.

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conditionals as extending backwards into the past. In almost all cases, the consequent

of a counterfactual judgement relates to an event that occurs at a later point in time

than the antecedent. We are perfectly content to say that if the past or present had

been different, then the future would have been different to what we might justifiably

expect it to be in the actual world, but we are far less happy with the idea that a

difference in the present would have implied a different past. Lewis suggests that we

can in fact make sense of such ‘back-tracking’ counterfactuals, but our usual

counterfactual reasoning makes the assumption of a past that exists independently of

future events (Lewis 1979b p 457).27 The notion that past events cause future events

but not vice versa is strongly ingrained in our psychologies, and so we have reason to

deny back-tracking counterfactual claims (Lewis 1983 pp217-218).

With respect to Lewis’ previously established distinction between familiar and

eccentric contexts, we can read Lewis here as claiming that back-tracking

counterfactuals are eccentric, and require us to temporarily change the way we

understand counterfactual dependence to accommodate them.

For Lewis, the evidence of this asymmetry can tell us something about the kind of

similarity relation we should be employing in our counterfactual judgements, in

particular what importance we should assign to various respects of resemblance. The

following are the resulting criteria he suggests for the ordering of worlds.

(1) It is of the first importance to avoid big, widespread, diverse violations of

physical law.

(2) It is of the second importance to maximise the spatiotemporal region

throughout which perfect match of particular matters of fact prevails.

27 Lewis’ assumption here is that our intuitive understanding of the past as ‘closed’ and the future as ‘open’ derives from an asymmetry of our counterfactual reasoning rather than vice versa. This claim has been criticised by Pruss (2003), who argues that our pre-theoretical notion that past event cause future ones is what leads us to avoid making backtracking counterfactuals, rather than the other way around. Lewis’ proposed solution, claims Pruss, actually trades on the assumption that there is already an asymmetry in place between past and future, as evidenced by the fact that Lewis’ small, localised miracles occur before the antecedent event to bring them about.

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(3) It is of the third importance to avoid even small, localised, simple violations of

law.

(4) It is of little or no importance to secure approximate similarity of particular fact,

even in matters that concern us greatly. (Lewis 1979b p472)

The inclusion of these additional conditions is intended to account for counterfactual

asymmetry, but is also meant to save the counterfactual theory from apparent

counterexamples, particularly those based on an observation made independently by

both Kit Fine (1975) and Jonathan Bennett (1974), although Lewis notes that the

objection was first introduced to him by Michael Slote.

Those counterfactual conditionals whose consequents seem to require a massive

departure from the course of events in our world appear to be false on the Lewisian

analysis, even when plausibly true. For instance it appears true to say that if Nixon

pressed the red button then there would have been a nuclear holocaust, but since any

world in which a nuclear holocaust takes place are certain to be very different to our

own world, it appears that a world in which Nixon pressed the button, but then a small

miracle prevented the holocaust, would invariably be closer to our own world than

worlds which lacked such a miracle (Fine 1975 p452). Constraint (4) in particular is

introduced to remove properties such as being a world in which there is a nuclear

holocaust from consideration, whereas constraint (2) indicates the kinds of similarity

which we should be looking for instead. Although the above constraints appear to

deviate quite far from our ordinary means of judging similarity, Lewis’ substantive

thesis is merely that there is some measure of similarity capable of accounting for our

counterfactual judgements. Fine and Bennett’s objection rely on the assumption that

we employ an ‘ordinary’ relation of similarity in assessing similarity between worlds

(Bennett 1984 p61).

Constraints (1) and (3) give us more detail on the kinds of similarity we supposedly are

inclined to look for in ordinary circumstances. As it is only of the third importance to

avoid minor, isolated miracles, but of the second importance to ensure agreement with

the actual world across the largest possible spatiotemporal region, the closest worlds

to our own in which Nixon presses the red button are said to be those with causal

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histories identical with ours, but in which a small violation of physical law at a certain

point causes Nixon to press the button. Note that this implies that obedience to the

same physical laws should not be one of the things we assign a great deal of weight to

in ordering worlds.

Lewis’ response to the objection relies on the fact that a world like this one in which

another small miracle following the pressing of the button resulted in the avoidance of

the holocaust would not be closer to the actual world than the world in which there

was no second miracle. The reason for this is that the first miracle which occasions the

pressing of the button causes small but wide-ranging differences between worlds in

which such a miracle occurs and the actual world. After Nixon has pressed the button,

air molecules have been sent careering down different paths, Nixon himself has

memories of pressing the button that he didn’t have before, and his memoirs will

contain stories of pressing the button. The agreement with the actual world across a

wide spatiotemporal region has been broken, and it would take more than just another

small localised miracle to restore it. Instead what would be required would be quite a

wide-ranging series of violations of physical laws to erase all these little divergences

from history. Now any such world which permits such a widespread violation of the

laws of nature is disallowed from being closest to the actual world by (1), whereas the

world described in Fine’s objection is disallowed by its violation of (2). Of course, the

world in which a miracle causes Nixon to press the button and a nuclear holocaust does

ensue will not be in agreement with the actual world after the button-pressing either,

but at least such a world only involves one localised miracle rather than two, as Fine’s

world does (Lewis 1979b p470).28

Contained within this response is the solution to the problem of back-tracking

counterfactuals as well. In the above argument it was noted that even small localised

miracles cause diverse and wide-ranging effects in the future, but not in the past, like

28 The conclusion that a world in which the holocaust does take place will be closer according to the above means of measuring similarity than a world in which it does not, relies on two additional assumptions. Firstly, that causation is deterministic, and secondly, that the convergence miracle occurs after various disparate effects have had the time in which to propagate. Wassermann offers variants of Fine’s counterexample which show the inadequacies of the four constraints under these circumstances (Wassermann 2006).

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ripples surrounding a stone dropped into water (1979b p475). Since the above example

shows that it would take a far more wide-ranging series of miracles to undo the effects

of past events in the present than it would to change past events themselves, we have

an explanation in this of why we tend to assume that counterfactuals do not back-track.

It is the second and fourth of these constraints however that tell against all but the

perfectly natural properties counting toward overall similarity between worlds. Recall

that in §3.6 we noted that perfect match between two non-numerically identical

particulars, in this case regions of space-time, with respect to all properties (abundantly

conceived) is in principle impossible. When Lewis discusses ‘perfect match’, the only

thing he could have in mind here is the notion of duplication he introduces in ‘New

work for a theory of universals’, which is the condition of sharing all one’s perfectly

natural properties (1983 p202). Although duplicates are defined by Lewis as those

objects which share all perfectly natural properties, in doing so they will share all their

intrinsic properties, which include all less-than-perfectly natural properties (the role of

privileged properties in making for duplication was introduced in §3.6). This is because

the pattern of instantiation of less-than-maximally privileged properties in reality is

supervenient on the pattern of instantiation of the maximally privileged ones (see

§3.4). The only properties they might not share are those which fail to be privileged

altogether, such as the property of having been owned by Winston Churchill. The

objects which Winston Churchill owned are most probably very disparate, and likely

have few if any properties not too distant from the fundamental physical ones in

common. Additionally, it is an extrinsic property, and in §2.8 we established that

extrinsic properties cannot be privileged. Constraint (2) tells us that we should assign

the greatest weight to those properties which are shared between duplicates.

Furthermore, when we combine constraint (2) with constraint (4), we can see that even

amongst those properties shared by duplicates we should assign virtually all weight to

the instantiation of maximally privileged properties. What Lewis has in mind when he

speaks of ‘approximate similarity of particular fact’ is something like a world’s

instantiating the property of being a world in which there is a nuclear holocaust.

Nuclear holocausts are multiply realisable by fundamental physical states, and so

similarity with respect to the property of being a world in which there is a nuclear

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holocaust can only guarantee an approximate match between worlds which both

possess this property. Such worlds may differ dramatically in the particular matters of

fact that apply within spatiotemporal regions smaller than the world itself. The only

properties which guarantee a perfect match between space-time regions are the

maximally privileged properties instantiated in those regions. Lewis’ proposal of

Humean Supervenience has it that in worlds like ours29, all fundamental (i.e. perfectly

natural, or maximally privileged) properties are those instantiated by individual space-

time points, and that everything else that our world contains is built up out of these

properties of space-time points (Nolan 2005 p27-33, see also §2.7). Perfect match

across a spatiotemporal region relies on the duplication of these properties of the

smallest space-time points, which just are the maximally privileged properties

according to Humean Supervenience. Taken together, (2) and (4) tell us that with

respect to the ordering of worlds relevant to counterfactual claims, only privileged

properties are ever eligible to count towards overall similarity, and even then we

should assign little or no importance to the sharing of any but the maximally privileged

properties. For this reason, we should take the Lewisian version of the possible world

semantics to be committed to privileged properties only as similarity-makers, at least

with respect to the ordering of worlds, in accordance with Lewis’ thoughts on the

nature of overall similarity more generally (as we discussed in the previous chapter, in

particular see §4.2).

5.6 Privileged properties and the counterpart relation

There is a tension between two of Lewis’ ideas with respect to the counterfactual

theory. On the one hand there is his insistence on overall similarity holding only in

virtue of the sharing of maximally privileged properties (those that satisfy the

Supervenience role). On the other there is his formulation of the counterpart relation

as based in similarity. The highest possible degree of resemblance with respect to

privileged properties is the relation which Lewis calls duplication (1983 p202, see also

29 The caveat ‘in a world like ours’ is included because Humean Supervenience is held to be contingent rather than necessary thesis (see §2.5), although one Lewis cautiously believed was true of our own world (Lewis 1994 p474, see also Nolan 2005 p29).

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§3.6), but not all duplicates are counterparts of one another. In this section I offer two

examples which show why this is the case.

In Counterfactuals Lewis claims that counterparts must resemble the objects of which

they are counterparts with respect to both their intrinsic and extrinsic qualities (1973a

p39). As I will show in this section, if intrinsic qualities alone are taken as relevant to

establishing counterparts, then this leads to some objects having implausible

counterparts in some worlds. Those properties of objects which are extrinsic, however,

are not privileged. Lewis himself claims this (1983 p203), and we also showed this in

§2.8. It is likewise not a requirement of duplicates that they share any extrinsic

properties (1983 p202). The shift in Lewis’ thought from an overall similarity relation

that allows extrinsic properties to have some weight to one which does not is what

causes problems for his account.

Suppose that the counterparts of objects are to be chosen by a measure of similarity

which only ever assigns weight to privileged properties, which are all intrinsic.

Following Lewis’ preferred convention, let us refer to the actual world as ‘I’. Now

suppose that there is a possible world w which is virtually qualitatively identical to i

save for one difference. The star around which the Earth’s counterpart in w orbits is a

qualitative duplicate, not of our Sun, but of some other star in our world of similar size

and composition located in some distant galaxy. Let us call this other star ‘Shmun’.

Meanwhile, the star which occupies the position in w analogous to Shmun’s position in

i is a qualitative duplicate of our Sun. In effect, world w is exactly like our world but for

the Sun and Shmun having swapped positions.

In such a case as this it does not matter what weightings we give to similarity with

respect to individual intrinsic properties. The Sun and its spatially displaced duplicate

in w will be alike with respect to all of them. Duplicates are alike with respect to all their

intrinsic properties. When an object such as the Sun has a duplicate in another world,

then that object has at least as good a claim to being the Sun’s counterpart in that

world as any object which is not a duplicate of the Sun.

The view that privileged (and hence, intrinsic, microphysical) properties are the sole

contributors to overall similarity is capable of recognising some important difference

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between our own world and the world where stars are in flipped positions in space, but

only at the level of regions of space-time larger than the one occupied by the Sun in

our world. The counterpart of our world’s Solar system would be correctly identified as

the one in orbit around Shmun, assuming that the internal composition of the stars in

our world and the Shmun world were the only differences between the two. The

similarities between the Solar systems in question, the arrangements of planets plus

their speeds and orbital paths would in this case be intrinsic properties of the space-

time regions occupied by each system. We could therefore correctly identify that in

such a world a Shmun-like star was now the Earth’s host. Such features would be

extrinsic to the stars at the centre of these systems, though, so these differences

cannot affect which object in w is the counterpart of our Sun.

This cannot be right. It seems perfectly plausible that the star around which Earth’s

counterpart in w orbits is the counterpart of our Sun, at least given some not altogether

eccentric means of calculating similarity. But, the only way that this star can be our

Sun’s counterpart is if properties besides those shared by duplicates sometimes

contribute to the counterpart relation. This tells us that the view according to which

only intrinsic properties are relevant to two objects being counterparts is false. It is also

possible to see how duplication is not enough to guarantee that two objects are

counterparts of one another when we consider a modified form of Sun/Shmun case.

World x is like world w, except that in world x the stars occupying the locations

analogous to Sun and Shmun in i are both duplicates of our world’s Sun (and so are also

duplicates of one another). In this world, we must conclude that both stars are

counterparts of our Sun, as each is as similar overall to the Sun as it is possible to get.

If the Sun has any counterparts in this world, it must have two. But if this is so, then the

following counterfactual would be false:

‘If Shmun were qualitatively identical with the Sun, then the Sun would still be

part of the Milky Way’.

However we order worlds, the closest world to i in which the antecedent of this

conditional is true has to be x. This is when the problems begin. We have already noted

that when objects from our world have multiple equally good counterparts of objects

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in the closest possible world, the consequent of a conditional must be true of every

counterpart in that world in order for us to say that the conditional holds at that world.

Only one of the Sun’s two counterparts, the one which is located in the Milky Way, is

going to satisfy that consequent, however. Again, this cannot be right, because the

above counterfactual strikes us as true. The only difference between x and our own

world is that a star in a far-off galaxy has the same intrinsic nature as the Sun, but why

would some fact about an object in a distant galaxy render it false that the Earth orbits

the Sun? If we want to preserve our sense that the above counterfactual is true, we

have to allow that duplicates are not always the best possible candidates for

counterparts.

There is an additional difficulty for Lewis in that including extrinsic qualities within

counterpart relations would be the only means of distinguishing duplicates of objects

in the same world from each other in terms of their similarity to the original. At one

point Lewis is keen to make explicit that objects have a single unique counterpart in

their own world, and that is the object itself (1978 p39), although there is evidence to

suggest that he was willing to relax this stricture in his later work, at least on some

occasions (1986a p214). Consider the claim: ‘This coin, which landed heads up the first

time it was ever flipped, could have landed tails side up’. It does seem relevant to the

truth of this counterfactual that duplicate coins minted in the past sometimes landed

tails side up when first flipped. Even so, it seems unlikely that Lewis would be willing to

commit to the idea that every particular object that stood in the relation of duplication

stood in the counterpart relation also, for the reasons discussed above.

In this section I have demonstrated that of the two roles performed by relations of

overall similarity in Lewisian semantics for counterfactuals, at least one of them is

incompatible with the combination of Supervenience and Similarity. Supervenience

requires that privileged properties are all intrinsic (see §2.8), but the kind of overall

similarity required for establishing counterparts in other worlds requires weight be

assigned to extrinsic properties. In the following section I will show that the Similarity

role constrained by privilege is also unsuitable for the ordering of worlds as closer to or

further away from the actual world.

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5.7 Privileged properties and the ordering of worlds

Focussing now on the ordering of worlds, which Lewis proposes is also a matter of

overall similarity, I propose that we can construct counterexamples to the view that

privileged properties are the only ones which make for similarity when shared. The

examples I have in mind are of counterfactual statements which strike us as being true

but which can only be true according to Lewis’ possible world semantics if non-

privileged properties influence the ordering of worlds. In this section I will first of all

outline briefly the feature of Lewis’ system for ordering worlds that permits such

counterexamples to be generated, and then I will develop my objection in detail by

focussing on one particular counterfactual statement which Lewis’ theory cannot

accommodate. After showing how Lewis’ theory fails to generate the right truth value

in this case, I will show how ordering worlds as closer to the actual world when they

share some not-very-privileged properties can give us the right truth values in cases

such as this.

We can summarise the ordering system we outlined in §5.5 as follows: a world is closer

to the actual world than another if it matches the actual world perfectly over a larger

region of space-time than the other (Lewis 1979b). It is a consequence of this account

that any two worlds which match the actual world perfectly up until time t, and then

subsequently diverge, will be equally similar to the actual world. This is true regardless

of how exactly these worlds subsequently diverge from the actual world. I argue that

given this scope for divergence amongst the closest possible worlds in which the

antecedent of a counterfactual conditional is true, certain plausible counterfactual

statements must be deemed false.

The supporter of privilege may attempt to overcome my objection by relaxing the

fourth of Lewis’ proposed constraints on the relevant similarity relation just enough to

allow some less-privileged properties to count towards overall similarity of worlds at

the expense of an answer to Fine’s future similarity objection, but this would not be

enough. Using the recipe for producing counterexamples that I propose, it is possible

to generate infinitely many variations on the same theme. Each variant would require

that the constraint on privilege be relaxed with respect to some other less-than-

maximally privileged properties. The only way to disallow all such counterexamples and

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to secure the appropriate ordering of worlds is to allow that the sharing of properties

with a very low degree of privilege sometimes counts towards overall similarity

between worlds.

The particular example of a counterfactual that I will be investigating in this section is

as follows. Let us assume that the world from the perspective of which it is to be

considered is world i.

C. ‘If Napoleon had given the order to attack at dawn, the French would have won at

Waterloo.’

We can suppose that this counterfactual is true, at least according to some not-

altogether-bizarre contexts. In addition, let us ignore for the moment the previously

discussed issues with the identification of counterparts and assume that counterparts

of Napoleon, the event of his giving the order to attack and the battle of Waterloo may

be suitably selected in all worlds of interest. In some worlds, it might be that the signal

to attack is a raised hand, in others it might be hand quickly descending, in still more it

might be a shouted ‘Allez!’ and so on. Let us simply presume that whatever weighting

system we employ for making judgements of similarity required for the identification

of counterparts, we have some means at our disposal of successfully identifying the

events and particulars which play the proper role in each world, and focus just on how

the worlds themselves are to be ordered as more or less close to i.

If, as I have claimed, we should assume that C is true in some not-altogether-bizarre

context, it follows that there will be some world or worlds in which Napoleon gave the

order to attack at dawn which are as similar to i as it is possible to get whilst still being

a world in which Napoleon gives the order to attack at dawn, and that in all of these

worlds, the French are victorious. We can establish whether or not this is the case using

Lewis’ system for ordering worlds which we detailed in §5.5.

The first step is to zero in on those worlds which match the causal history of i up until

the fateful day of the battle of Waterloo. Just as in the case of Nixon pushing the red

button, the closest worlds to i in which the order to attack is given at dawn will be those

in which a small miracle causes a localised violation of the laws of physics at a time just

before the moment of dawn, allowing the antecedent of the counterfactual C to be

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true in worlds which are otherwise in perfect agreement with i up until that point.

There will likely be a great many closest possible worlds according to such an ordering

scheme, for most worlds in which Napoleon orders the attack at dawn will differ from

one another only with respect to some relatively miniscule physical differences.

Perhaps in w1, a world in which Napoleon attacks at dawn, particles of dust in the air

on that day are moving in a slightly different pattern to particles of dust in the air in

w2, another world in which Napoleon attacks at dawn. If this is the only difference

between w1 and w2, it seems reasonable to suggest that neither one of these worlds

is uniquely close to i. The simple fact that in w1 and w2 Napoleon has given the order

to attack at dawn rather than later in the day will be sufficient to break the

spatiotemporal agreement of these worlds with i.

In fact, it seems probable that the dust over the battlefield at i would behave

completely differently over the course of the day to any world in which the French

attacked at dawn. The laws of physics in all i-like worlds mean that disturbances in the

air and any particles suspended in it are going to be quite sensitive to the movements

of three large armies with horses and cannons. Given that no world in which Napoleon

orders the attack at dawn is going to be exactly similar to i with respect to all these

minor differences, it seems we must at least claim that in worlds where Napoleon

attacks at dawn which differ only with respect to such minor details, none can claim to

be uniquely similar to i. My point here is simply to suggest that amongst worlds which

differ only with respect to such minor details, there will likely not be one that stands

out as uniquely close to i. If the counterfactual is true, then in all of these most similar

worlds it must be the case that the French win the day.

Unfortunately, often extremely minor details can have widespread knock-on effects, as

Lewis himself notes (Lewis 1979b pp474-475). Let us suppose that in one of our worlds

in which Napoleon orders the attack at dawn, he makes a gesture. In this world

however, an errant particle of dust is disturbed by Napoleon’s making of this gesture

in such a way that it happens to catch the light from the sun in such a way as to

momentarily blind one of the general’s key officers, who as a result completely misses

the signal to attack. It does not matter that this would be a statistically improbable

event. As long as it is possible, it occurs in at least one world. An important point to

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note here is that statistical improbabilities are not miracles. We cannot immediately

locate such worlds as further away on the basis of their requiring further violations of

physical law to realise. Extremely improbable events, when they are the outcomes of

indeterminist systems are described by Lewis as ‘quasi-miraculous’. Quasi-miracles are

held by Lewis to detract from similarity, not in virtue of their improbability, but rather

as a consequence of ‘the remarkable way in which the chance outcomes seem to

conspire to produce a pattern’ (Lewis 1986b p60). In this case, however, the movement

of the mote of dust into the officer’s eye need not be the result of some combination

of unlikely chance outcomes. The situation is comparable to a lottery draw. An outcome

where the winning numbers are one, two, three, four, five and six is astronomically

unlikely, but no more unlikely than any other possible result. There need be no greater

‘conspiracy’ to a pattern in this particular motion of the mote of dust than in a nearby

world where it lands on the officer’s jacket instead. Lewis is unable to use the notion

of a quasi-miracle to distance such worlds from i in this case.

As a result of this minor lapse, this officer’s troops do not advance with the rest of his

army until much later and after much confusion. As a result, the French advance is

disorganised and its soldiers unfocused, and victory in this world goes to Wellington.

We are told that approximate agreement of matters of particular fact is to be assigned

little or no importance in the ordering of worlds, so such a world appears to be at least

as close to i as the worlds in which the officer was not blinded and the French advanced

together. Unless we can find some means by which this world may be seen to be further

away from i than the other closest possible worlds, C would be found to be false. Even

a tiny difference in comparative overall similarity would suffice in this regard.

All the events in question in the above example occur after exact agreement in matters

of physical fact between i and the worlds where Napoleon attacks at dawn has been

irredeemably lost, as no world in which Napoleon attacks at dawn will have the same

motions of dust motes as occur in i. Nor would it be the case that, according to the

current weighting system, a world in which one side of the French army failed to

advance with the rest would be less similar to i overall than one in which they did.

Remember, in i the entirety of the French army stayed where it was until noon. In the

world where the officer gets blinded, a significant portion of the French remain in the

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same positions they were in at the corresponding time at i for a longer period of time

than they do in those worlds where they all advance together. Even if we are advised

by Lewis to ignore such features of approximate agreement, it seems as though such

worlds could only ever agree with i over larger regions of space-time than worlds where

the French advance together, never smaller. It could therefore be claimed that a world

in which some portion of the French army fails to heed the order to attack at dawn is,

if anything, closer to i than one in which the entire army attacks at dawn.

If the world in which the officer is momentarily blinded is to be further away from i

than worlds in which he is not, and the truth of C is to be preserved, then we must find

some other properties to assign greater weight to that are shared between i and the

worlds where no blinding happens, but not worlds where the blinding does happen.

Perhaps we can point to some property of this particular officer, such as that of not

being struck momentarily blind at this particular time on the morning of the battle, and

say that this is a property we attach some importance to. Such a property is already

less-privileged than some property concerning the motions of dust particles, but is still

relatively easily defined in terms of more fundamental notions. The chain of definitions

connecting this property to the maximally privileged properties is still quite short (1983

p192). Since this officer was not blinded in i, this would make a world in which he was

blinded further away from i than one in which he was. Of course, if we were to attempt

to save the truth of C in this way we would have to relax the stricture against assigning

weight to approximate agreement of matters of particular fact, which would

necessitate an alternative response to Fine’s objection from future dissimilarity. There

are other reasons we should be cautious about such a move though, as I will now show.

Although the weighting of such a property as relevant to similarity would perhaps save

the truth of C from the threat of the blinded officer world, there are countless other

similar worlds that are going to be just as problematic. In some other world, the officer

was not blinded, but the dust went up his nose and caused him to sneeze, so he missed

the order through some other means. In yet another world, the dust was sent in the

opposite direction and caused someone else to sneeze, momentarily distracting him.

There are going to be as many worlds where minor physical differences confound the

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truth of C as there are wildly improbable freak events that might transpire on the

morning of the battle.

If we respond to each of these confounding possibilities in the same way, by assigning

importance to some similarity to i with respect to the absence of the confounding

circumstances, then we run into problems. Even if we allow that it is perfectly

acceptable for the context of a counterfactual judgement to assign importance to a

billion different conditions of varying degrees of privilege, one for every confounding

world, and even if we allow that all of these saving conditions are indeed something

which is common to both the possible worlds in which the French are victorious after

attacking at dawn, and i, which is by no means certain, it seems that the inclusion of all

of these conditions as relevant to the similarity ordering of worlds does the very thing

which we were determined to avoid: it assigns more importance to the system of

ordering to less-privileged properties. Recall that in §2.4 we established that although

there was no generally accepted cut-off between privileged and non-privileged

properties, it was necessary for there to be at least some properties which are not at

all privileged. It seems reasonable to assume that wherever the line is to be drawn, we

will be able to point to confounding worlds which can only be distanced from the actual

world by appeal to non-privileged properties.

Consider all the properties to which we must assign importance to prevent some officer

failing to heed Napoleon’s command at dawn. It seems as though, taken together, they

reveal that we assign importance to a very un-privileged property of the French military

organisation on the day of the battle, specifically the property of having a functional

system of command. This property, it seems, is significantly more important to

closeness of worlds to i than any which correspond the lowest-level physical properties

of the battlefield that day. It is a very un-privileged property in that it covers an

incredibly disjunctive range of potential happenings. There are infinitely many ways

that the command system in the French army could have been broken on that day,

ranging from momentarily blindness amongst key personnel, to moments of

distraction, to plain disobedience, and infinitely many more ways that they could have

remained functional. This property of the Grande Armée’s command structure is not,

moreover, the only such non-privileged property which is going to be important to the

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context of C. Morale is a very difficult thing to define in physical terms, especially when

one assesses the morale of a diverse accumulation of beings such as the one which

Napoleon commanded at Waterloo, and yet this is one of the properties that is of

importance when ascertaining the truth of C, because morale is one of those factors

with a disproportionate effect on the outcome of battles. Now, the neurological activity

in the brains of the French soldiers in a world where the French are ordered to attack

at dawn is likely to vary considerably over the course of the day from a world in which

the French are ordered to attack at noon. Such differences only become relevant to the

context of C as and when they contribute to a lowering of the morale of the army as a

whole. Plausibly, the context of C is such that worlds in which the dawn attack order is

given in such a way as to deplete the men’s morale are placed further away than ones

in which morale levels remain about the same as they do in i.

It will not do to respond that such properties as these are of but secondary importance

compared with maximally privileged properties. In the example we have considered,

the worlds in which the chain of command in the French Army was broken were

indistinguishable from worlds where it remained intact according to the system for

weighting properties proposed by Lewis. This was because only maximally privileged

properties were to be given weight under this system. A supporter of this system might

wish to acknowledge that sometimes less-than-maximally privileged properties do in

fact have weight, but only in cases where worlds are already indistinguishable with

respect to maximally privileged properties. Such properties might be said to break ties

and ensure that the officer-is-blinded worlds are slightly further away from i than

worlds in which no officers are blinded, although otherwise they do not affect the

ordering of worlds at all.

It would be unwise for the supporter of privilege to adopt such a response, not because

it would make too many plausibly true counterfactuals come out false as before, but

because it would make too many plausibly false counterfactuals come out true. In order

for a counterfactual to be true we established in §5.3 that it must be true in all the

worlds which are as similar overall as possible in all important respects to the world

from whose perspective the counterfactual is being assessed. The properties we have

just discussed are important respects, not just tie-breaking conditions with negligible

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importance in their own right. The following example illustrates why this is so. Once

again I will use C as an example, but this time I will suppose that attacking at dawn

would not have been enough to ensure French victory at Waterloo. Under such

circumstances Lewis’ ordering system could still generate the wrong truth value for C.

Suppose that there are several worlds in which Napoleon gives the order to attack at

dawn which are jointly the most similar worlds to i with respect to all of the relatively

un-privileged properties that are acknowledged to have some weight. In all of these

worlds factors of morale, military command structure and discipline are equally alike

with i. Now we must additionally suppose that only about half of these worlds are

worlds with French victories. If a system of weighting of properties for the ordering of

worlds were permitted to depend on non-privileged properties like these, then we

could end our analysis here and say that C is false. C’s consequent does not hold in all

the most similar worlds where C’s antecedent holds.

Let us now also suppose that one of these worlds is uniquely more similar to i, according

to Lewis’ canonical system for ordering worlds which only weights the fundamental

physical properties of the field and combatants themselves. Perhaps in this world some

motes of dust in a particular part of the battlefield happen to move in the same ways

as their counterparts in i for a longer stretch of time after the order to attack is given

than in any of the other worlds. According to the Lewisian weighting system, this would

be just enough to push this particular world ahead of its rivals, making it the most

similar world overall to i in which the antecedent is true. If this is a world in which the

French are victorious, then C is true.

In fact, given what we know about the other worlds nearby it seems as though C is false

on these assumptions. In all nearby worlds which are like i with respect to matters of

military disposition and competence, ordering the attack at dawn does not ensure

French victory. The fact that the French are victorious in a world which is closer to ours

with respect to the motions of particles of dust does not seem like a good reason to

think of C as being true. In this case, the less-than-maximally privileged properties of

the battlefield and the armies fighting over it actually seem more important than the

maximally privileged properties. Systems which allow such properties to have greater

weight than maximally privileged therefore have another advantage, in that they

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accord better with our intuitions about what kinds of properties are relevant to the

ordering of worlds.

In this section I have shown that a system for ordering worlds which allows weighting

of non-privileged properties is superior to one that does not. In the following section I

detail the implications of the findings of this chapter for theories of privilege.

5.8 Conclusion

In this chapter I have established that a Lewis-inspired counterfactual semantics using

a notion of similarity which permits only microphysical properties to count towards

overall similarity cannot succeed. With respect to counterpart theory I showed that

extrinsic properties, which we showed to be non-privileged in §2.8, are sometimes

relevant to establishing the counterpart relation. Duplication, which is proposed to be

the relation which holds between objects which share all their privileged properties,

was insufficient to guarantee that objects are counterparts of each other. Additionally,

with respect to the system of weighting relevant to the ordering of worlds in virtue of

closeness to the actual world, sometimes the properties which seem most important

to an appropriate ordering of worlds are quite far removed from the microphysical

properties indeed.

If privileged properties satisfy the Supervenience role, then the maximally privileged

properties are all microphysical (assuming scientific realism), while the complete

domain of privileged properties consist of all those which are ‘not too distant’ from

them. The fact that the notion of similarity required for the influential counterfactual

theory dealt with in this chapter cannot be restricted to the same group of properties

which satisfy Supervenience leads us to conclude that there is a tension between

Supervenience, Similarity, and possible worlds semantics for counterfactuals. There are

three options for resolving this tension, none of which are especially palatable for a

believer in privileged properties.

The first is to allow that there are extrinsic privileged properties. I will not repeat the

arguments I gave against adopting this possibility in §2.8, but it should also be noted

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that if we permit extrinsic privileged properties then we can no longer appeal to

privileged properties in defining duplication and all of its derivative notions, as Lewis

does (see §3.6). Furthermore, this would only resolve the tension with respect to the

counterpart relation, as discussed in §5.6. The problem of the ordering of worlds I

showed in §5.7 would remain. Alternatively we may deny one of the roles of privileged

properties, Supervenience or Similarity. If we deny Supervenience, then privileged

properties may be as distant from the microphysical properties as we need them to be

in order to ensure that the counterfactual theory gives us the right results. By

abandoning Supervenience, we would also remove the objections we had to extrinsic

privileged properties in §2.8, particularly that they would be superfluous. If maximally

privileged properties do not have to comprise a minimal supervenience basis then

there would be no reason to reject superfluous maximally privileged properties. If on

the other hand we deny Similarity, then we can assign weight to whatever properties

will give us the correct results for counterfactual statements. In either case though, the

‘work’ for privileged properties is greatly reduced. As I made clear in §1.4, the posit of

privilege is to be justified by its ability to combine various kinds of work using the same

theoretical resources. In chapter three I showed that there were three ‘keystone’ roles

for privileged properties from which all the available work derived. Without the

combination of Supervenience and Similarity, we may well question whether this

mainstream version of privilege is still worthwhile. I will reserve judgement on this issue

until chapter seven.

The final possibility is that we retain both Similarity and Supervenience, but amend the

Similarity role to only apply to certain kinds of similarity. We could then claim that the

‘similarity’ required by the counterfactual theory referred to a range of relations not

covered by the Similarity role. The Similarity role amended in such a way would be

toothless, though. The Similarity role we established in §3.6 held that non-privileged

properties never contribute to overall similarity. The amended version we are

considering would amount to the claim that non-privileged properties don’t always

count towards overall similarity, but we already knew that there are many ways of

calculating similarity which assign weight to different properties (see §3.6). A version

of the Similarity role amended in this way would not succeed in telling us anything

interesting about the phenomenon of similarity. To see why this is, consider the fact

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that it would not count in favour of the belief in privileged properties that each and

every privileged property is identical with some privileged property. In the same way,

it should not count in favour of the belief in privileged properties that they are the only

properties relevant to those kinds of similarity which rely only on privileged properties.

Once we accept that there are kinds of similarity to which the Similarity role and its

restrictions does not apply, we may as well abandon it altogether. There is no easy way

out of this tension. Supervenience and Similarity are not co-satisfiable.

In the previous chapter we looked at the plausibility of the Similarity role with respect

to accounting for our everyday experiences of the phenomenon of overall similarity,

whereas in this chapter we have been mainly concerned with a particular application

of overall similarity in metaphysics. In both cases our findings were the same: there is

no work for a posit that combines Supervenience and Similarity. In chapter six, I will

turn to the co-satisfiability of Supervenience with the third ‘keystone’ role for

privileged properties: that of Magnetism.

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Chapter Six: Reference Magnetism

6.1 Privilege and indeterminacy of semantic content

The conclusion to be argued for in this chapter is that the Supervenience and

Magnetism roles introduced in §3.4 and §3.7 are not performed by the same group of

properties. If it is indeed useful for some properties to fulfil the Magnetism role, then

we can identify better candidate properties than those which also satisfy

Supervenience.

The Magnetism role is posited as a response to a problem which affects certain theories

of intentionality, which I will call interpretationism, following Williams (2010 p2).

Williams defines ‘interpretationist theories’ as those which hold that the correct

semantic theory for a language is just that which is ‘selected’ by the actual practices of

a linguistic community. The semantic contents that words and sentences of a language

possess is just that which is entailed by the selected theory. Lewis proposed that

privileged properties could act as a constraint on acceptable theories of content, as a

means of avoiding certain objections to metasemantic theories which adopt this

strategy (1983 p220, 1984).

A common objection to such accounts is that the actual practices of a linguistic

community can leave the appropriate theory for a language underdetermined (see for

instance Quine 1960 p27, Davidson 1979, Putnam 1981). This is especially problematic

as the candidate interpretations sometimes ascribe wildly implausible contents to a

language. Lewis argues that privileged properties offer a means of limiting this

indeterminacy sufficiently to exclude all bizarre ascriptions of content. This approach is

sometimes called ‘reference magnetism’ (e.g. Sider 2011 p23), although not by Lewis.

The proposal is to impose an additional constraint on an acceptable semantic theory

alongside satisfactory fit with the relevant facts about linguistic practices. Acceptable

semantic theories must ascribe more privileged contents wherever possible. Although

most commonly associated with Lewis, this attitude to privilege as playing a role in

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metasemantics has some additional supporters, notably from Sider (2009 pp29-30,

2011 pp23-28), Schwarz (2014) and Weatherson (2003, 2012).30

The structure of this chapter will be as follows. Firstly, in §6.2 and §6.3 I will outline

Lewis’ own interpretationist metasemantics with particular focus on a simplified

version of this, global descriptivism, which Lewis is fond of using as a stand-in for his

own more complicated theory when responding to philosophical objections to

interpretationism (1984 p222). As the details of Lewis’ preferred theory are not directly

relevant to the task at hand, this is the version I will focus on as well.

In §6.4 I will introduce the problem of indeterminacy and how the Magnetism role for

privileged properties is proposed to solve it. In §6.5 I consider Williams’ ‘new’

indeterminacy argument (2007) which seeks to offer a fresh challenge to the

Magnetism role. I show that Williams’ argument does not succeed in this, and so will

limit my attention to the more familiar form of the objection introduced in §6.4.

I then consider an alternative form of reference magnetism which takes language to

favour ascriptions of privileged content by virtue of a requirement to assign rational

content. Privileged categories are therefore magnetic in virtue of their making for more

rational ascriptions of contents. This interpretation is espoused by Schwarz (2014) and

Weatherson (2012). I conclude in §6.6 that the indirect, rationality-constrained form of

the Magnetism role is the more plausible of the two, as it succeeds in making the

reference relation explanatory in a way which the direct appeal does not.

In §6.7 I argue that the properties whose selection as meanings of words are most in

accordance with norms of rationality are not in every instance the most joint-carving

candidates. Given the successes of the indirect appeal so far, I propose that we

abandon the requirement that eligible properties are joint-carving altogether in favour

of a straightforward rationality-based account. Finally, in §6.8 I detail the consequences

30 Hirsch (1993) adopts a theory similar to reference magnetism, although his goal is different. Lewisian reference magnetism is intended to address indeterminacy in the meanings of words of a language. Hirsch’s project is to answer the question of why languages have the words they do, what he calls the ‘semantic primitives’ of the language (1993 p3). For example, in English, ‘green’ is a semantic primitive, but there is no single word for ‘green and circular’. Hirsch acknowledges that a constraint on language for semantic primitives to pick out privileged categories can be part of the explanation of this phenomena (1993 p53).

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of these observations for the posit of privileged properties. Specifically, indeterminacy

of semantic content gives us no special reason to believe that the properties which

satisfy the Supervenience role are magnetic. Privileged properties do not solve the

indeterminacy problem.

As in the previous chapter, I assume from this point on that the privileged properties

are microphysical (in accordance with the account of mainstream theories of privilege

given in §2.7), and hence it will be taken for granted that they satisfy the Supervenience

role. When I speak of the ability of privileged properties to constrain reference, I am

therefore using this as shorthand for the co-satisfiability of the Supervenience and

Magnetism roles by the same group of properties.

6.2 Lewisian interpretationism and convention

As with much else in privilege literature, the appeal to privileged properties to solve

the problem of indeterminacy of intentional content has its earliest and best-known

formulation in Lewis, which he discusses at the same time as he introduces his theory

of natural properties (1983, 1984). Lewis himself favoured an interpretationist account

of intentionality, which he first began to set out in the early part of his career (see Lewis

1969). Interpretationism, in the sense I will use the term, has its origins with Davidson

(1973), with influences from Tarski (1935/1983) and Quine (1960). In this section I will

sketch the interpretationist approach in general based on Williams’ remarks (2007),

then briefly outline the interpretationist theories of Davidson and Lewis, paying

particular attention to the latter.

Roughly, interpretationism is the view that the proper method for investigating

semantics is to interpret the meanings of words from the observable behaviour of

individuals in a linguistic community. This broad approach is summed up in a remark of

Quine’s:

In acquiring [language] we have to depend entirely on intersubjectively

available cues as to what to say and when. Hence there is no justification for

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collating linguistic meanings, unless in terms of men’s dispositions to respond

overtly to socially observable stimulations. (Quine 1960 pix)

On this basis, the meaning of any sentence in a language is simply that which would be

attributed to it by an interpretive theory of that language that meets a certain set of

standards for successful interpretation, which may vary between interpretationist

theories. Regardless of the precise criteria for successful interpretation employed,

Williams (2007 pp363-364) proposes that all versions of interpretationism make use of

a two-step process for selecting an appropriate theory of the meanings of words in a

language.

Firstly, one begins with a series of relevant facts about the world and outlines a process

by which sentences come to be matched up with semantic contents. What these

‘semantic contents’ might be depends on the precise version of the theory under

discussion. They may for instance be propositions, truth conditions, or even truth

values. For instance, we might observe that German speakers only ever utter ‘Es regnet’

when they have access to good evidence that suggests that it is raining outside. We

might then come to the conclusion that ‘Es regnet’ is true just in places and at times

when it is in fact raining (this example is from Davidson 1973 p125). Interpretationist

theories differ in terms of how they take sentences to be paired up with semantic

contents, as we will see.

The second step is the claim that any word in a language has a meaning P just in case it

would be assigned P by a theory of that language whose predictions about which

sentences have which contents agree with the actual correspondence of sentences to

contents obtained in the first step (Williams 2007 p363). To return to the above

example, it seems that the most plausible interpretation of why ‘Es regnet’ is true only

when it is in fact raining is to take the word ‘Regnet’ to mean raining.

It is possible to identify two threads to Davidson’s interpretationist approach to

metasemantics. Firstly, he argues that a semantic theory for a language need not

consist of a pairing up words and sentences with entities which are the meanings of

those sentences. According to Davidson, whilst it is necessary to give an account of

what words and sentences in a language mean, nothing is gained by the postulating of

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such things as meanings (Davidson 1967b p21). Instead he proposes that we produce

a theory of a language which deals with meaning extensionally (1967b p23). For

Davidson, a theory succeeds in giving the meaning of words and sentences in a

language just in case that theory is capable of generating, for every sentence of that

language, a theorem that specifies the truth conditions of that sentence. As natural

languages are capable of producing infinitely many sentences and our cognitive

capacities are finite, the theory must be capable of generating infinitely many theorems

from only a finite set of axioms. It is for this reason that the theory of a natural language

must take the semantics of that language to be compositional, with the meanings of

whole sentences depending on the meanings of the parts or ‘aspects’, as Davidson calls

them, of those sentences (Davidson 1967b pp23-24, 1970a p56, see also Malpas 2014).

This is an application of Tarski’s work on defining truth in formalised languages (Tarski

1935/1983). Lewis follows Davidson in viewing the task of the linguist as finding a

theory of the truth conditions of sentences in a language. Despite the common

tendency to refer to the eligibility constraint as ‘reference magnetism’, Lewis himself is

reluctant to claim that the meanings of sentences can be reduced to the task of finding

the things referred to. Instead he prefers to use the more neutral term ‘semantic value’

to pick out meanings for linguistic entities over ‘reference’. As we shall see in §6.3,

however, when responding to objections to eligibility of content Lewis is often happier

to locate his own ideas within the framework which his opponents assume, and so is

sometimes content to speak of the goal of metasemantics as one of finding the

‘references’ of terms (Lewis 1984 p222).

The second thread of Davidson’s approach is that of radical interpretation. This name

is intended to emphasise the connection to Quine’s account of radical translation

(Quine 1960 p26). Quine tells us that in most cases of translation of sentences from an

unknown language to a known one there will be some form of shared basis between

the two, for instance a similarity of grammar or a word in the unknown language which

is similar to one in the known language. When there is no shared basis, this is what he

calls radical translation. In radical translation, one must connect the utterances of a

speaker of the unknown language to observable and verifiable states of affairs (Quine

1960 p29). Consider again our previous example, where we come to hypothesise that

‘Es regnet’ has the same meaning as ‘It is raining’ due to the fact that this phrase only

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ever seems to be uttered when it is raining. On successive occasions we might put our

hypothesis about the meaning of this utterance to the test, and revise our

interpretation as required.

Davidson’s ‘radical interpretation’ retains the Quinean idea of coming to an

interpretation of the meanings of sentences from evidence plausibly available to

individual, but unlike Quine, Davidson does not assume that the speaker must already

have a known language that they are translating the unknown sentences into. For

Davidson, there is just as much of a problem for someone coming to understand

utterances in their first language, or even to know that another person is speaking the

same language as they are, as there is in translating between languages (Davidson 1973

p125). The Lewisian version of interpretationism builds on this approach by identifying

what Lewis calls linguistic conventions, and using these to assign truth-conditions to

sentences.

A ‘convention’ in the sense Lewis employs it is a habit of behaviour amongst members

of a community which develops, often in the absence of explicit agreement, as an

attempt to settle problems of coordination amongst members of that community

(Lewis, 1969 pp5-8). More often than not it is beneficial for members of a community

acting in their own self-interest to adapt their own behaviour based on the behaviour

of others around them. A classic example concerns navigation on roads. Motorists have

a vested interest in keeping out of the way of traffic heading in the opposite direction

so as to minimise the possibility of collisions occurring, but doing this effectively

requires some reasonable expectations as to how other drivers will behave. If however

there is a known regularity of behaviour amongst almost all motorists of driving on one

particular side of the road, then provided there is sufficient reason for individual

motorists to think that this convention will be generally adhered to this generates an

expectation as to how others on the road will behave (Lewis 1969 p25). This ability to

anticipate behaviour from knowledge of a convention enables coordination problems

to be solved more easily.

It will not be necessary for our purposes to reconstruct completely Lewis’ account of

the ways conventions come about or how they come to create expectations, or the

various features that he takes conventions to have. What is most important for our

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purposes is that Lewis takes speakers of a shared language to share a series of

conventions for the purpose of communicating meanings by certain sounds or

inscriptions (Nolan 2005 p163).

Consider a function from sentences of a language to truth conditions, for instance one

that pairs ‘Es regnet’ with the set of worlds in which it is raining in the vicinity of the

speaker. This pairing alone is what many logicians are content to call a language,

although for Lewis a language is this pairing plus something further: an interpretation

of the sentences of that language. The pairing of sentences with truth conditions alone

is not a complete interpretation, as at present it says nothing about the meanings of

individual words used by the community, nor their use of grammar. As such there are

for Lewis no such things as multiple interpretations of the same language, although

there are multiple languages with the same sentences (Lewis 1969 p162). I will use the

term ‘uninterpreted language’ to mean only the pairings of sentences with truth

conditions, prior to any interpretation. For Lewis, an uninterpreted language is the one

which a community speaks just in case there is a convention within that community to

be both truthful and trusting with respect to it. For a community to be truthful with

respect to an uninterpreted language means that in most cases the members of this

community seek to avoid uttering sentences which they believe to be false or at least

have good evidence to doubt the truth of, whereas to be trusting means imputing

truthfulness to other members of the community, and to taking their utterances to be

a good guide to what beliefs one should hold (1975 pp6-7). In this way, Lewis

accomplishes the first step in his interpretationist metasemantics.

In characterising conventions of truthfulness and trust Lewis appeals to belief, which is

itself an intentional notion. It is however important to bear in mind that Lewis did not

take language to come about and acquire meaning independently of the meanings

already attached to mental states. Rather, the meanings of languages rely on an

established domain of facts about mental contents, an approach which has been

referred to as his ‘head-first’ rather that ‘word-first’ methodology (Nolan 2005 p164).

Lewis is a materialist about the mind and has a broadly functionalist view of mental

contents in that he equates contentful states with the property of being disposed to

behave as though one was in such a state, although he himself was cagey about

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describing his view as a form of functionalism (Lewis 1994a). Once again, it is not of

great importance to the project at hand to understand exactly what Lewis takes states

such as beliefs and desires to be, as our concern is with the indeterminacy objections

raised with respect to interpretationism concerning language rather than thought.31

The salient point to note however is that the conventions relevant to establishing what

uninterpreted language members of a community actually speak are permitted to

include regularities in the beliefs members of that community have and how they come

to revise them.

The truth conditions of sentences uttered by a community thus identified, the

remaining task is to develop a theory of the intentional content of the language which

would serve to accurately predict the pairing of sentences with truth conditions. A

theory which fits the truth conditions of sentences in an uninterpreted language in

which a community has conventions of truthfulness and trust can be called an

interpretation of their language. The interpretation of any language like the ones used

by human beings must contain more than just a function from sentences to truth

conditions. All natural languages of which we are aware are infinitely generative, which

is to say that the actual sentences uttered by speakers of that language will be but a

tiny fraction of the total range of meaningful sentences within it. Interpretations of all

such languages must also say something about the grammar of the language, which

Lewis suggests consist of a lexicon, a generative component and a representing

component.

The lexicon is the vocabulary of the language, consisting of all the individual words and

sometimes morphemes of the language, divided up into grammatical categories. The

generative component meanwhile is simply a series of rules for combining lexical terms

to build larger compounds, while the representing component is the systematic process

for linking words and sentences with the strings of letters or sounds used to represent

them. For instance, in the English language there is a certain pattern of marks which

can be made on a surface which represent the word ‘fish’. Like Davidson, Lewis assumes

31 However, see (Lewis 1979) for Lewis’ account of propositional attitudes as sets of possible worlds the believer represents themselves as inhabiting (or the desirer seeks to inhabit), and (Lewis, 1994) for more on Lewis’ preferred method for individuating mental states. Nolan (2005, chapters 5-6) gives a clear summary of these issues.

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that words have meanings only as abstractions from sentences. Words therefore

acquire their meanings from the sentences of the language of which they may be

constituents (1984 p22). The representing component of the language consists of the

rules for representing semantic content by means of these marks or patterns of sounds

in speech (Lewis 1969 pp167-168). It is by the introduction of grammar that we gain

fine-grained truth conditions for sentences.

Although this is Lewis’ preferred interpretationist metasemantics, in discussing

Putnam’s permutation argument for indeterminacy of language he adopts a simpler

theory than this, global descriptivism (Lewis 1984, p222). In the following section I will

set out this alternative theory in detail.

6.3 Global Descriptivism

It does not appear as though Lewis intended to endorse the version of

interpretationism he calls global descriptivism. Instead he employs it only as a

reconstruction of Putnam’s account of the ‘standard’ metasemantic approach

(Williams 2007 p366). Global descriptivism is used by Lewis as a toy theory, suitable for

addressing Putnam’s objections in his own terms. In more modern debate on the

subject of reference magnetism it is still common to assume such a descriptivist theory

for illustrative purposes (see for instance Sider 2011 p24). Global descriptivism makes

for an adequate stand-in for the more sophisticated interpretationist system, the

details of which are often not directly relevant to the issues under discussion, so in the

remainder of this chapter I will follow convention and assume this simpler theory,

unless otherwise noted. The purpose of this section will be to set out the global

descriptivist version of interpretationism.

Global descriptivism, as the term is used by Lewis, is a strategy for arriving at a theory

of meaning for a language similar to the one he proposes as a means of translating

between individual scientific theories (1970). This approach was outlined in §3.3, and I

will not repeat the details of it here. Global Descriptivism is an application of this

method to natural language rather than the technical terms of a scientific theory. In

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this case, the ‘novel terms’ to be defined are just the words of that language, whilst the

axioms of the theory are all the true sentences of a community’s linguistic practice.

In accordance with the process described in §3.3, we obtain the Ramsey sentence of

the language by replacing all novel terms within its expanded postulate with new

bound variables. Words in the language denote those entities which uniquely realise its

Ramsey sentence. If the Ramsey sentence is not realised, or is multiply realised, words

in the language fail to denote anything (Lewis 1970 pp430-431). In §6.4 we will see how

natural languages are in practice realisable by multiple collections of objects. It is this

which necessitates the appeal to privilege to constrain available interpretations.

Note that this is a departure from the more sophisticated account found in Convention,

which paired sentences up with truth conditions, rather than truth values. A suitable

interpretation that gives us the language of that community is therefore just a model

of that theory which makes the term-introducing theory true, rather than one which

predicts the correct pairing of sentences with truth values, on this simplified theory

(Lewis 1984 p224).

In the following section I will show that both forms of Lewisian interpretationist theory,

the simplified global descriptivism and his more nuanced position, are subject to

objections from the indeterminacy of semantic content.

6.4 Permutation arguments and the appeal to privilege

If the only constraint on a suitable interpretation of a total theory is that it must make

that theory true (assuming to global descriptivism), then this implies considerable

indeterminacy with respect to what language communities actually speak. In this

section I will show what this indeterminacy consists in and why it is problematic for

interpretationism.

An example of Sider’s illustrates this indeterminacy. First of all, let us follow Lewis in

describing the most plausible, familiar interpretation of a language as the ‘intended

interpretation’ (1983 p221). Based purely on the observable facts about how the word

‘pig’ is used by speakers of English, this string of letters fits equally well with a range of

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extensions, not just the one ascribed to it by the intended interpretation. The word

‘pig’ could just as easily mean pigs-that-I’ve-personally-encountered, pigs-in-my-

immediate-vicinity or pigs-before-t-and-cows-thereafter (Sider 2011 p23). This strikes

us as wrong, and yet it is perfectly possible that a model for our total folk theory which

attributed such bizarre meanings to the word ‘pig’ could achieve the right truth values

for sentences just as well as a more plausible interpretation.

The point can be generalised to show that for any language, there is a bizarre

interpretation possible which in fact gives all the same truth values for individual

sentences as the intended interpretation. If we assume that the language we are

working with contains only logical expressions, names, and predicates, then any

assignments of bizarre reference to names can be cancelled out by an equally bizarre

assignment of extensions to predicates (see Putnam 1981, Williams 2007). Suppose

that given the conventions of a community, we take it that the sentence ‘Bill is bald’ is

true just in case a certain entity, Bill, is bald. Furthermore let us suppose that Bill is

indeed bald, so the sentence is true. Clearly the intended interpretation here is for ‘Bill’

to pick out Bill, and for ‘is bald’ to apply to all and only those entities which are bald.

Now consider another interpretation of this community’s language, under which ‘Bill’

picks out a completely different entity, the Eiffel Tower. If that were the only deviation

made by this alternative interpretation then the sentence ‘Bill is bald’ would be false

according to this model, and so the intended interpretation would be a better fit. Now

let us introduce a new concept for the purposes of our deviant interpretation, that of

an entity’s being the image of another, and stipulate that the image of Bill is the Eiffel

Tower. We may then assign a new extension to the predicate ‘is bald’: the set of entities

which are the image of something bald. The Eiffel Tower falls under the application of

this predicate, because the Eiffel Tower is Bill’s image, and Bill is bald. Similar

permutations for all names and all predicates are available, and so even radically

deviant interpretations of the total theory can be made to match the truth values for

sentences generated by the intended interpretation.

It is in response to this argument that we see the appeal to privilege. In order to escape

these criticisms, Lewis (1983 p219) proposes an additional constraint on a semantic

theory for a language, based on a suggestion he attributes to Merrill (1980). Certain

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categories, Lewis claims, are simply better candidates to be the meanings of words than

others. Whilst not abandoning the requirement an interpretation must fit with the

actual usage of words by a community as far as possible, an adequate semantics must

also seek to ensure that the most eligible categories are picked out as the references

of words. Lewis’ proposal for these eligible candidates, the semantic ‘magnets’, are the

natural properties. As he puts it:

Reference consists in part of what we do in language or thought when we refer,

but in part it consists in eligibility of the referent. And this eligibility to be

referred to is a matter of natural properties. (Lewis 1983 p219)

Requiring that acceptable interpretations of languages maximise eligibility as well as fit

with use would avoid the problems raised by the permutation argument, as all of the

bizarre assignments of meaning are less natural than the meanings assigned by the

intended interpretation.

Two further features of Lewis’ view must be borne in mind. Firstly, the constraint of fit

with facts of use (which in the global descriptivist version of interpretationism amounts

to making the total theory come out true) and the eligibility constraint are intended to

trade off against one another. By relaxing the constraint on fit with usage and

decreasing the extent to which an acceptable interpretation must make utterances true

we can achieve greater overall eligibility of reference, whilst the more of our theory we

insist on making true, the more gruesome meanings start to creep into a language

(Lewis, 1984 p228). No one constraint dominates the other, the best interpretation of

a language is simply the one which achieves the best equilibrium between them,

although Lewis does not offer much detail on what that equilibrium between the two

might be.

There is evidence to suggest that it would not be advantageous to insist that a selected

for theory should make all utterances in a language come out true, for communities

can be prone to systematic error in how they describe the world. Thales believed that

all things were ultimately made from water, and we can imagine a community where

this belief came to be commonly held. It would be among the platitudes that made for

this community’s total theory that everything is ultimately composed of water. Given

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that everything is not in fact made of water, the only way to make this part of the theory

come out as true would be to assign an extension to their word ‘water’ that included

not just all H2O, but also every quark and every lepton. In this case, it appears that it

would be better to take the extension of ‘water’ to simply be H2O, and to take these

supporters of Thales to simply be mistaken when they claim that all things are made

from water. The eligibility constraint enables such interpretations, because H2O is a far

more natural meaning for ‘water’ than H2O or a quark or a lepton.

The second important feature of Lewis’ view is that whilst properties are the only kinds

of things which can be privileged, eligibility is not a constraint only on terms which

occur in predicate position within an interpretation of a language. The instantiation of

natural properties in regions of space-time is supposed to give us some idea of eligibility

of objects as well. Lewis gives the example of his cat Bruce, which is a very eligible thing

to be referred to because Bruce’s boundary is well demarcated by differences in the

instantiation of highly natural properties in neighbouring regions. The same cannot be

said for the cat-shaped region of space-time which always follows a few steps behind

Bruce (Lewis 1983 p221).

6.5 Henkin constructions as a new indeterminacy argument

The above permutation argument and Lewis’ response to it rest on the assumption that

the permuted interpretations will always be less joint-carving than the intended one,

as these bizarre interpretations begin with the intended interpretation and skew them

into new configurations which preserve the truth values assigned to sentences.

However, as Williams illustrates, not all bizarre interpretations will be parasitic on the

original in this way (2007). I contend that Williams’ modified indeterminacy argument

does not succeed in presenting a fresh challenge to the eligibility constraint, because

his conclusion relies on some unjustified assumptions about how degrees of privilege

are to be measured. I initially introduced some of these difficulties with measuring

degrees of privilege in §2.2.

In this section I will introduce the notion of a ‘Henkin construction’, on which Williams’

argument is based, and show how Williams uses such constructions to generate non-

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parasitic interpretations of languages that can in certain circumstances be better

candidates for a semantics of a language than the intended interpretation. I then go on

to show that although Williams succeeds in showing that these non-parasitic

interpretations exist this conclusion relies on a very specific conception of how the

overall eligibility of an interpretation must be assessed. Lewis does not tell us how

exactly we should do this, but Williams assumes that at the very least, a lower bound

on the overall eligibility of an interpretation can be given simply by counting the

numbers of connectives that appear in a ‘brute’ specification of that interpretation

(2007 p388). In §2.2 I showed that measures of this kind can function only as a rough

guide to a property’s degree of privilege at best.

My response to Williams in this section is that rather than showing that the

indeterminacy argument still holds despite the appeal to eligibility, Williams’ results

only provide another argument for why this one simplified strategy for assessing

eligibility in particular does not succeed. Recall that in §2.2 we were unable to suggest

a systematic theory for how degrees of privilege might be measured, if simply

measuring connectives would not suffice. If no such theory is forthcoming then this is

certainly bad news for supporters of privileged properties, but it should not lead us to

accept an argument that relies on ‘brute’ specifications of degrees of privilege in terms

of length of definition. I now turn to a detailed account of the mathematical

constructions which underlie Williams’ new indeterminacy argument.

In the middle of the twentieth century Leon Henkin developed a mathematical proof

of the following: any syntactically consistent theory T will have a model, that is, an

interpretation which makes all the statements of T true (1949, 1950). According to the

process Henkin employs constructing these models, the domain of the resulting Henkin

construction is a set of equivalence classes of constants, but these equivalence classes

can be mapped on to any suitably abundant domain of objects whatsoever. This is the

basis for Williams’ alternative indeterminacy argument. Suppose that T is the total

theory of a community’s linguistic practices. If the domain chosen for the Henkin model

for T contains only highly natural objects, then under certain circumstances this

arbitrarily chosen domain might actually score better than the intended interpretation

for eligibility (Williams 2007 p385).

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Consider the following worked example offered by Williams showing how a model can

be generated according to Henkin’s proof (Williams 2007 pp382-385). Consider a toy

theory T which contains only a single non-logical predicate ‘Dog’ and no constants. First

we obtain a theory θ which extends T and possesses some useful qualities, such as

being negation complete. This means that for every formula of θ, S, either S is a

theorem of θ or ¬S is a theorem of θ. As θ is an extension of T, any model of θ will be a

model of T also. The theory θ will contain just two sentences:

∃x Dog x

∃x ¬Dog x

Additionally, θ contains ‘witnessing’ statements for all its existential claims, such that

for every statement of the form ∃x φx, there will be some statement of the form φc,

where c is some constant. In the above example, we can introduce constants ‘Fido’ and

‘Betsy’ for the purposes of witnessing existentials to obtain the following extended

theory θ:

∃x Dog x

Dog (Fido)

∃x ¬Dog x

¬Dog (Betsy)

If required we must then extend θ once again to ensure that it remains negation

complete following the introduction of witnessing statements, such that for any

sentence containing the new constants, the extended theory must contain either that

statement or its negation. Provided we do not introduce any new inconsistencies into

the theory, we can extend it in this way more or less arbitrarily. The theory θ will still

be an extension of T regardless of the new sentences we introduce, as long as they

don’t contradict T, and so any model of θ will still be a model of T.

Once we have this extended theory, we can build a model for it by establishing a

domain and extensions for predicates which make the theory as a whole come out true.

The domain of the model is just the set of all the equivalence classes of constant

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symbols in the extended theory θ. In our example there will be two equivalence classes,

f = {‘Fido’} and b = {‘Betsy’}. We replace constants in θ with equivalence classes just

when those constants are members of that equivalence class. For example, any time

that the constant ‘Fido’ occurs in θ it would be replaced with the equivalence class f, as

‘Fido’ is a member of f. The following statement in θ:

Dog (Fido)

would therefore become:

Dog (f)

Similarly, any occurrence of ‘Betsy’ would be assigned b. The extension of any predicate

‘F’ in θ can then be said to include any equivalence class γ just in case there is any

statement in θ to the effect that a member of γ is F. Since ‘Fido’ satisfies the predicate

‘Dog’ in our example and nothing else does, and ‘Fido’ is a member of f, then the

extension of ‘Dog’ will be f. Such an interpretation would make θ, and therefore T, true.

By mapping a domain of objects onto the equivalence classes of constants in a Henkin

construction we have the beginnings of what Williams considers a new argument for

the indeterminacy of language. Any objects whatsoever can be chosen as the domain

of the Henkin model, and Williams suggests that we might take an initial segment of

the natural numbers to be that domain, something he calls the arithmetical model of

the total theory (2007 p386). This is proposed as a problem for privilege as a constraint

on eligibility because, as the model is no longer parasitic on the intended

interpretation, it may no longer simply be assumed that the intended interpretation

will be the best fit between adherence with facts of usage and eligibility. Furthermore,

Williams argues that there will be possible worlds in which the arithmetical model is

actually more eligible than the intended interpretation, which he calls Pythagorean

worlds.

Williams’ Pythagorean worlds are imagined as follows. It is not too difficult to suppose

that there is a class of possible worlds like ours in most respects, but differing with

respect to the most fundamental particles. In the actual world, let us suppose, there is

nothing more fundamental than quarks and leptons. However, in the kind of world

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Williams imagines, these particles are in fact composed of still more fundamental sub-

particles. In both our world and the worlds Williams is interested in, global folk theory

is the same. Everything as far down as the level of quarks functions in exactly the same

way, but in the class of worlds Williams is interested in, the movements of quarks and

leptons are simply patterns of instantiation of more fundamental properties, whereas

in the actual world they are themselves fundamental.

Firstly, we can suppose that the eligibility of the arithmetical model does not vary from

world to world. If we assume that mathematical vocabulary is itself determinately

natural, then, since numbers must exist in all worlds, their definition is independent of

what particles are fundamental in each particular world. Williams suggests that

mathematical vocabulary might even be perfectly natural, although his argument is not

committed to this (2007 p388). An interpretation of total theory which takes as its

domain arrangements of quarks and leptons on the other hand, will vary in its eligibility

from world to world. It will be more eligible in worlds in which quarks and leptons are

fundamental than in worlds in which they are not. A Pythagorean world is one in which

the complexity which exists below the level of quarks and leptons is so great, with each

new tier of particles being subdivided into smaller and smaller such particles, that the

eligibility of the interpretation in terms of quarks and leptons is actually less than that

of the arithmetical model. In Pythagorean worlds, which at the level of macroscopic

objects are completely indistinguishable from our own, the words of its inhabitants pick

out numbers rather than tables and chairs. Even if our own world is not in fact

Pythagorean, the possibility of it being so is a non-sceptical epistemic possibility

(Williams 2007 p392).

Williams’ argument shows that provided we choose a domain for a Henkin construction

with a degree of privilege that is unlikely to vary between worlds, there will be worlds

in which this interpretation will be more eligible than the intended interpretation. His

argument does not succeed in presenting a fresh challenge to reference magnetism,

however. In the remainder of this section I will consider two objections to Williams’

argument. The first can be easily surmounted, but the second exposes a weakness in

the idea of Henkin constructions as a new argument against the Magnetism role.

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Timothy Bays notes that in taking the domain of the Henkin construction to be an initial

segment of the natural numbers we are committed to the existence of an infinite

system: the natural numbers. One of Williams’ assumptions was that the total theory

of the world be finitely specifiable, however. A commitment to an infinite series of

natural numbers implies that total theory is not finitely specifiable (Bays 2007 p412).

Bays offers a number of strategies for overcoming this apparent tension. On the one

hand, he outlines a way in which we might develop a Henkin construction compatible

with an infinite number of predicates, whilst on the other hand he suggests it might be

possible to restate the constraint on total theory as requiring only that there are finitely

many physical things. In my opinion there is a far simpler option, however. Bays’

objection and his subsequent modifications to the Henkin construction strategy

originate from the use of natural numbers as the domain for the model of total theory.

If we can find a suitably abundant domain that does not commit us to infinitely many

natural numbers we needn’t bother modifying Williams approach.

I propose that we find such a domain in a set of objects whose elements are

fundamental physical particles, drawn from every possible world. If quarks are

fundamental in a world, then quarks may form part of this domain, however if in some

other world some other exotic particles are fundamental, they too may form part of

this domain. Quarks vary in eligibility between worlds because across modal space not

all members of the set of quarks are perfectly natural. Every member of the set of

perfectly natural properties on the other hand is perfectly natural when viewed from

any world whatsoever. There are enough possible worlds containing enough possible

fundamental particles to supply a suitably abundant domain for a total theory of one

particular world, and at the same time we are committed to no infinity of things within

that world, so the concerns with the arithmetical model no longer apply.

The second objection is more problematic for Williams. Although it may be true that

the entities which make up the domain of some Henkin interpretations are indeed very

or even perfectly natural, the semantic values ascribed to predicates in this model will

generally be quite unnatural. According to global descriptivism the meaning of a

predicate is its extension, but it seems as though the extensions assigned to predicates

by the arithmetical model will in most cases be quite far from any natural categories.

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Under the intended interpretation, the predicate ‘is green’ picks out all the objects

which reflect and absorb light in certain similar ways, whereas it seems unlikely that

there will be any such unity amongst the set of natural numbers which is given as the

extension of ‘is green’ under the arithmetical model. Even if there are certain

predicates which pick out natural properties of sets of numbers according to the

arithmetical model, for instance if a certain predicate picks out all the multiples of three

within a certain range, or a span of consecutive numbers, the vast majority of

predicates will have arbitrary extensions. The intended interpretation, on the other

hand, appears to do reasonably well with respect to both the naturalness of the entities

picked out and the naturalness of the extensions assigned to predicates. Lewis does

not give us much detail about how we should assess interpretations of a total theory

with respect to their overall eligibility, but it seems plausible that we should prefer an

interpretation which picks out reasonably joint-carving meanings for both predicates

and objects over one which secures maximal naturalness for objects at the expense of

predicates. If, for instance, we formulated the eligibility constraint as a stricture against

systematic attributions of completely non-joint-carving meanings, then it seems that

even in the Pythagorean worlds the intended interpretations would fare better with

respect to eligibility of the semantic values it assigned. The extensions assigned to

predicates by the intended interpretation would for the most part be somewhat joint-

carving, whereas a great many of the extensions assigned by the arithmetical model

would be not-at-all joint-carving.

To see why this would be the case, recall the definition of joint-carving given in §2.3.

Under that account, a category carves at the joints just in case there is some unity

amongst the entities belonging to it in terms of privileged properties (or the perfectly

natural properties, if we take privilege to be a matter of degree) which serves to

distinguish them from the entities that do not belong to that category. So, for instance,

the category of mammals is somewhat joint-carving because there are certain

physiological features shared by its members that are not shared by non-mammals.

The category of canines is even more joint-carving a category than the category of

mammals, because there are a greater number of physiological features which unify its

members and distinguish them from the non-canine mammals. The category of being

this-or-that fundamental physical particle on the other hand is not an especially joint-

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carving category, despite the fact that the property of being a fundamental physical

particle has to be a privileged one. This is because there is no property of the members

of this category which unifies them and distinguishes them from those things which do

not belong to that category.

The category of being-any-fundamental-particle-whatsoever would be an extremely

joint-carving category, but the category of just these two such particles and no others,

not so much. According to this account, which I think is the best one available, joint-

carving is not simply a matter of being a category which has the shortest definition in

terms of perfectly natural properties. The semantic values of predicates in the

arithmetical model are not highly joint-carving simply in virtue of the fact that they

extend only over entities which share the very natural property of being numbers. If

we allowed that this was all that was required for predicates to have extensions which

are joint-carving, then it seems there is a far greater problem for the eligibility

constraint on meaning than the one suggested by Williams.

Williams acknowledges difficulties of this sort for his account, and acknowledges that

the arithmetical model is unlikely to assign very many joint-carving extensions to

predicates. This is what forces him to rely on the notion of ‘brute’ specification of

predicates by extension. We can at the very least specify the extension of a predicate

simply by enumerating the items in the domain which fall under it, provided that the

total theory is compatible with there being only finitely many things (Williams 2007

p388). We can then in principle calculate the total number of connectives in a

specification of the entire theory to arrive at an assessment of the lower bound of its

overall eligibility. Any particularly joint-carving categories of numbers (if there are any

such thing) that it then happened to assign as extensions for predicates would then

raise this benchmark degree of eligibility slightly. The crucial point is that as long and

gerrymandered as this ‘brute’ interpretation would be, in Pythagorean worlds it would

still be more eligible than the intended interpretation. As previously noted, this

assumption that brute specification provides a benchmark level of privilege cannot be

supported.

The cornerstone of this argument is that the overall eligibility of an interpretation of a

language cannot be less than the benchmark provided by counting the connectives

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required to specify the extension of each predicate within it, and the fewer connectives

included in the specification of the extension of some predicate the more joint-carving

it is presumed to be. Note that this assessment of the relative merits of differing

interpretations is based on the connection Williams makes between eligibility and

theoretical simplicity. On Williams’ understanding, the best interpretation of a

language is the one which is simpler overall. Williams characterises Lewisian reference

magnetism as the view that this simplicity amounts to eligibility, which is grounded in

naturalness (2007 p389). Limiting the total number of connectives in a specification

would be one means of assessing theoretical simplicity. If we take this view of eligibility

however we are led to some unwelcome conclusions.

For one thing, it implies that the predicate which picks out all dogs but one is more

joint-carving than the predicate which picks out all dogs. No two dogs are ever exact

duplicates of one another, so it is not possible to specify the extension of the predicate

‘is a dog’ in terms of perfectly natural properties by outlining some pattern of

instantiation of natural properties that all dogs share. Instead, all the different ways of

being a dog must be enumerated disjunctively, just as the predicates of the arithmetical

model must be. One way to shave a vast number of connectives off the specification of

‘dog’ therefore is to interpret that predicate as picking out all dogs save one particular

one. This interpretation would still fit adequately well with our usage, as the cases

where this dog were described as being a ‘dog’ would be infrequent enough to be

explained away as simple error. It is not plausible that the category of all dogs save this

particular one is more joint-carving than the category of all dogs, but if simply counting

connectives gave us a means of assessing how joint-carving the extension of a predicate

was, this would appear to follow.

If these bizarre consequences follow from this method of measuring privilege then the

supporter of privilege has no reason to accept it. As I noted in §2.2, in the absence of a

superior analysis of degrees of privilege it remains a live option for its supporters to

take degrees of privilege to simply be primitive and not further analysable. In addition,

there does not seem to be any good reason why we must take the eligibility constraint

itself to be as simple as the version Williams assumes in his discussion.

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Although presented as a single constraint the need to maximise eligibility might itself

take into account several different factors. The total number of connectives involved in

the specification of a theory might be one such factor, but it seems just as relevant to

take into account the upper and lower bounds of the degrees of eligibility assigned to

words across the interpretation, or the median eligibility of the theory. If the eligibility

constraint were complex in this way then the arithmetical model, with its very natural

referents for objects and its very unnatural extensions for predicates would likely fare

worse than an interpretation which manages to achieve a relatively high minimum

standard for eligibility across the board, as one would expect the intended

interpretation to do. As it would rule out such deviant interpretations as the

arithmetical model, I suggest that this more complex form of the eligibility constraint

is the more plausible one to attribute to the supporter of the Magnetism role.

For these reasons I conclude that Williams does not succeed in presenting a new

challenge to reference magnetism. Nonetheless, I maintain that the privileged

properties are not those which perform the Magnetism role. In the following section I

lay out two different approaches to Magnetism and argue that the more compelling of

the two is that which takes the eligibility constraint to only track privileged properties

indirectly. There is indeed a compelling challenge that can be made to Magnetism as it

is generally conceived, but this challenge arises when we consider why the indirect

form of the appeal to eligibility is the superior account.

6.6 Direct and indirect appeals

It is possible to distinguish between two different approaches to the eligibility

constraint on meaning, both of which have their supporters. The ‘direct’ form of the

appeal is the one we have assumed until this point. The direct appeal simply says that

a good interpretation of a language must favour joint-carving categories. According to

the indirect form of the appeal a good interpretation of a language will indeed favour

joint-carving categories, but only because joint-carving categories tend to have some

feature which we have independent reason to look for when selecting an

interpretation. This apparent division in forms of the appeal appears to be a

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consequence of Lewis’ use of global descriptivism to illustrate the indeterminacy

problem, as opposed to his preferred metasemantics. Global descriptivism says nothing

about why we should prefer that meanings track specifically joint-carving categories,

unlike the more sophisticated version. In this section I will argue that it is far more

plausible to adopt the indirect form of the appeal to eligibility based on the reasons

given by Schwarz (2014) and Weatherson (2012). In brief, I argue that a good semantics

for a language should make the behaviour of that community intelligible, and this is

best accounted for by the indirect form of the appeal.

The direct or orthodox approach derives from the most popular means of

understanding Lewis on the Magnetism role (1983, 1984). According to the orthodox

view, the eligibility constraint and the constraint on fit with usage are both constraints

on the interpretation of a total theory for a community. This line of thought has been

notably picked up by Williams (2007 and 2010) and Sider (2011). By contrast, Schwarz

(2014) and Weatherson (2012) have each argued for an alternative approach according

to which eligibility only constrains interpretations of a language indirectly, by first being

constitutive of rationality. Rationality acts as a constraint on the beliefs we can ascribe

to individuals in accordance with principles of charity (Lewis 1983 p224, see also

Davidson 1967b p27), and the first step of Lewis’ interpretationism pairs up truth

conditions with sentences based on speakers’ beliefs. The eligibility constraint is

therefore a constraint on mental content rather than language, which is more in

keeping with the ‘head-first’ methodology employed by Lewis in Convention (Nolan

2005 p164).

The global descriptivism-based approach according to which certain contents ‘attract’

reference purely in virtue of what they are would therefore be nothing more than

heuristic device employed by Lewis. Furthermore, Weatherson claims that if the

eligibility constraint were viewed as indirectly leading to more privileged contents in

this way, this would give us an additional reason to reject Williams’ new argument for

the indeterminacy of language. Arithmetical models for natural languages would not

make the behaviour of a community rational (Weatherson 2012 p1).

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Schwarz notes that for Lewis to endorse the direct form of the appeal would have

required him to abandon one of his key beliefs about the nature and purpose of

semantics:

At the core of Lewis’ philosophy of language is the idea that semantics should

be part of a more comprehensive theory of human interactions. The point of

semantics is not simply to record or systematise intuitions about meaning,

truth and reference, any more than the point of genetics is to systematise

people’s intuitions about genes and inheritance. Rather, the semantical pairing

of sentences with truth conditions reflects interesting patterns in the social

interactions among the members of a linguistic community. (Schwarz 2012

p30)

It might suffice as a means of systematising our intuitions concerning language to

observe that the meanings of our words track privileged categories, and that would

make sense of the constraint on language that it must make out joint-carving

distinctions. On the other hand, Schwarz argues that this would not be sufficient for

Lewis’ purposes. Schwarz would, I think, agree with Sider’s insistence that the

phenomenon of reference is intended to be an explanatory relation, in that it tells us

something important about how and why humans make the utterances they do (Sider

2011 p28). When members of a community are able to successfully use language as a

means of solving coordination problems of the type discussed by Lewis, this must be

because of some shared associations between the sentences uttered and some

possible states of affairs (Schwarz pp30-31). Accounting for these associations is the

goal of semantics. Reference relations that do not track eligibility are not explanatory

in the requisite way, but neither are reference relations that posit a brute force of

attraction between words and meanings.

Consider again Williams’ arithmetical models, or alternatively the possible fundamental

particles variant I suggest. Given certain assumptions about the way overall eligibility

of an interpretation of a total theory is to be calculated, such deviant interpretations

can score quite well with respect to both criteria for a successful interpretation. Even

so, they are deviant because they do not succeed in explaining the actual practices of

a linguistic community. To use an example of McGee’s which Sider draws attention to,

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when a teacher makes certain marks on a blackboard corresponding to the English

word ‘maiasaur’, the fact that those marks mean maiasaur must be part of the

explanation of her coming to make them (McGee 2005 pp83-85, Sider 2011 p28). A

theory of intentionality is supposed to account for these practices. According to the

indirect form of the appeal such deviant interpretations can be ruled out. The fact that

a series of chalk marks refer to some natural number goes no way towards explaining

why this teacher came to make those precise chalk marks at this precise time.

For Lewis, the beliefs that it is acceptable to consider individuals to hold are constrained

by principles of charity, alternatively principles of humanity (Lewis 1983 p224, see also

Davidson 1967b p27 Quine 1960 p59). Although he at no point gives a canonical

account of what these principles of humanity actually are,32 by the early eighties he had

come to believe that such principles will lead to assignments of eligible (privileged)

content for beliefs over ineligible content. In his own words:

It is here that we need natural properties. The principles of charity will impute

a bias towards believing that things are green rather than grue, toward having

a basic desire for a long life rather than for a long-life-unless-one-was born-on

Monday-and-in-that-case-life-for-an-even-number-of-weeks. In short, they

will impute eligible content, where ineligibility consists in severe unnaturalness

of the properties the subject supposedly believes or desires or intends himself

to have. (Lewis 1983 p224)

As noted earlier in this chapter, the assignment of contents to beliefs influence the

assignment of contents to language via the conventions of truthfulness and trust which

members of a community are assumed to follow when they speak a language.

Specifically, competent speakers of a language generally only make utterances in it

when they have a corresponding belief in the truth of what they are saying. If speakers

have predominantly joint-carving beliefs, then they will predominantly refer to joint-

carving categories in the way they speak.

32 See Nolan (2005 pp153-155) for a useful summary of how Lewis’ thoughts on this matter develop over time.

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Commenting on some earlier remarks of Schwarz’s, Weatherson (2012) aims to spell

out in more detail how we can view the principles of humanity as leading to more

assignments of privileged contents. At least at one point in his thought at least, Lewis

appeared to follow Davidson in claiming that, ceteris paribus, we should prefer to

assign beliefs to agents which were compatible with their being rational agents (Lewis

1974). Weatherson’s suggestion is that with respect to beliefs of the form ‘All Fs are

Gs’, this bias toward natural properties is easy to account for, as generally speaking,

beliefs about joint-carving properties require less evidence to rationally hold than

beliefs about properties which are not joint-carving (Weatherson 2012 p3).

Suppose that a miner has seen a lot of green emeralds. It just so happens that in

addition to being green, all emeralds are grue (that is, they are green if first observed

before 3000AD and blue if first observed thereafter). Having seen a lot of green

emeralds is good evidence for believing that all emeralds are green, however it is not

good evidence for believing that all emeralds are grue. In order to have equally good

evidence for believing that all emeralds are grue, the miner would not only need to

have seen a lot of green emeralds, but would also need to have some evidence that

either all emeralds will be first observed before 3000AD or that any emeralds first

observed after 3000AD will be blue, neither of which she has. In this case, it is rational

for the miner to believe that all emeralds are green but not for her to believe that all

emeralds are grue. A bias towards the attribution of rational beliefs appears to bias the

attribution of beliefs concerning joint-carving properties (Weatherson 2012 p2).

In §6.7 I show that in cases where the requirement to ascribe rational contents (as per

the indirect appeal) deviate from those categories which are joint-carving, it is

invariably the more rational contents which make for better meanings of words. From

this we can conclude that the properties which are indeed eligible contents for

language are not the same as those which satisfy the Supervenience role.

6.7 Parochial eligibility as a better alternative to eligibility as naturalness

In this section I will show that according to the most plausible account of the eligibility

constraint on meaning, that outlined by Schwarz and Weatherson, privileged

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properties are neither necessary nor sufficient to secure the intended interpretation of

language. Their approach would be just as successful even if it there are no privileged

properties at all. Williams calls eligibility without a basis in privilege ‘parochial

eligibility’, and I will argue that this is the most promising candidate for a constraint on

interpretationist metasemantics (2010 p15). Parochial eligibility is an umbrella term

Williams employs to describe those theories which endorse some form of the eligibility

constraint on interpretation, but reject the claim that more eligible content is more

privileged content. The argument from the indeterminacy of language makes some

form of eligibility constraint desirable, but as I intend to show it is not plausible to claim

that eligibility of content is nothing more than the degree to which that content is joint-

carving. It might perhaps be true to say that our language tends to avoid massively non

joint-carving meanings, but this does not by itself mean that the best interpretation of

our language is the most joint-carving one that fits with how our language is used. As

to what might replace joint-carving, Weatherson has already given us a plausible

answer.

Recall that Schwarz and Weatherson’s formulation of the eligibility constraint was

rooted in the need for the reference relation to be explanatory (Schwarz 2014 pp30-

31, see also §6.6 above). It makes sense to attribute more joint-carving beliefs to agents

because such beliefs make the behaviour of agents intelligible. An emerald miner’s use

of the word ‘green’ might fit equally well with an interpretation of that word as

meaning green or grue, but only the former would make her behaviour sensible. This

is the sense of rationality that Weatherson appears to attribute to Lewis. Although

Weatherson wishes to account for Lewis’ assertion that the principle of humanity in

assigning beliefs will lead to more joint-carving content, it is not his object to show that

such beliefs are more rational because they are more joint-carving, nor does he wish to

argue that the ease of forming beliefs about properties increases with the degree to

which that property is joint-carving. In fact, an objection he presents against Williams’

new indeterminacy argument relies on this being false. Weatherson’s claim is that

although Williams’ arithmetical model would make for a more privileged interpretation

of a language than the intended interpretation, it would classify as deviant simply

because it would not be rational for speakers of a language to have the beliefs about

natural numbers implied by such a model (Weatherson 2012 p2). We must assign

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rational beliefs to individuals where possible, but the rationality of holding a belief is

not simply a matter of being joint-carving. It is therefore possible for an interpretation

of a word in a language to fit with the facts of how that word is used, to be more

privileged than some competing interpretation, and still fail the test of rationality.

Joint-carving alone is not sufficient for rationality.

If it were the case that beliefs with more joint-carving content were always easier to

hold rationally than beliefs with less joint-carving content then, assuming that

privileged properties satisfy the Supervenience role (see §6.1), it follows that the easiest

things to rationally hold beliefs about would be fundamental particles too small to be

observed, but in fact these are some of the hardest properties in nature to investigate.

Consider again the emerald miner who asserts that ‘All emeralds are green’. Emeralds

are in fact pieces of beryl crystal containing trace elements of chromium or vanadium,

which gives them their characteristic green colour (Hurlbut and Kammerling 1991

p203). Greenness is a fairly joint-carving property, but much less joint-carving than the

property of containing a certain proportion of chromium or vanadium atoms. A

definition of greenness in terms of perfectly natural properties things will be far longer

than a definition of the property of containing either chromium or vanadium. It would

seem that we can then attribute to our miner a far more joint-carving belief than the

belief that all emeralds are green, namely the belief that all emeralds contain atoms of

chromium or vanadium. Furthermore, an interpretation of her word ‘green’ that

assigned it the meaning contains some atoms of chromium or vanadium would do just

as well in making her assertion ‘All emeralds are green’ come out true whilst doing

better than the intended interpretation with respect to the eligibility of the content it

assigns. Even so, this assignment of meaning is clearly deviant.

In addition we can note that the argument for the rationality of believing that all

emeralds are green does not hold for the belief that all emeralds contain either

chromium or vanadium. Even if it happens to be true that all emeralds contain traces

of either of these two elements, the miner’s extensive visual experience of emeralds is

insufficient for her to rationally form any beliefs about their microscopic structure. It is

rational for her to believe that all emeralds are green on the basis of her available

evidence simply because her eyes are capable of identifying green objects with relative

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ease. In order to form rational beliefs about the microscopic structure of emeralds, she

would require more evidence from the results of scientific tests. Just because the belief

that all emeralds contain chromium or vanadium is more joint-carving does not,

therefore make it more charitable to ascribe such a belief to her. If the best

interpretation of the miner’s word ‘green’ is that it picks out all and only the green

things, this cannot simply be because green is a joint-carving category.

Although we have shown that the fact of a property’s being joint-carving alone does

not make it rational to form beliefs about that property, the supporter of reference

magnetism may nonetheless insist that our beliefs will tend towards joint-carving

properties overall. Even if privilege is not the sole constituent of eligibility, it might still

be the case that being privilege makes properties more eligible, ceteris paribus.

Perhaps joint-carving is one of a range of factors that serves to make properties eligible

to be referred to. In the remainder of this section I will show that this view is

unsupported by available evidence.

Recall that Weatherson’s claim that non joint-carving beliefs generally require more

evidence to be rationally held, as was briefly mentioned earlier, only applies to beliefs

of the form ‘All Fs are Gs’. Every time the miner observes a green emerald prior to

3000AD, this is sufficient evidence for forming both the belief that this particular

emerald is green and the belief that this particular emerald is grue. Also, assuming that

all the emeralds she has observed in the past are likewise green, every new green

emerald she observes provides good evidence for beliefs about both the greenness and

grueness of emeralds she has hitherto observed. This causes problems for

Weatherson’s account of the rationality of joint-carving contents. Consider an

interpretation of the miner’s language which paired up the sentence ‘All emeralds are

green’ with the meaning all the emeralds I have seen are grue. This interpretation

would generate the right pairing of the sentence with a set of truth conditions, but

more importantly by Weatherson’s account it would be a more rational belief to hold

than all emeralds are green. If we take it to be among the aims of believers to aim at

truth and avoid believing false things, beliefs about categories whose members the

believer has personally observed will be more likely to be true than beliefs about

categories whose members she has not observed, even when the belief concerns a

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relatively gerrymandered property like grueness. In these cases, assigning beliefs to an

individual with more joint-carving contents like greenness will make that individual no

more rational overall than assigning them beliefs about grueness.

We should therefore conclude that when a belief requires more evidence to rationally

hold and this is correlated with its involving less joint-carving properties, that this is

more easily explained by it simply being a belief of a type that requires quite a lot of

evidence, rather than the fact that it involves properties which are not joint-carving.

The examples outlined above show that a property’s being joint-carving makes little

difference on its own to the rationality of forming beliefs involving it.

6.8 Magnetism as work for privileged properties

The conclusion we drew in the previous section has implications for theories of

privilege. According to the (by now, familiar) formula by which theoretical posits are to

be assessed, privileged properties are useful additions to an ontology just in case they

do some needed work. A posit is theoretically virtuous if it is able to perform a variety

of different kinds of work (see §1.4). The question which this chapter set out to answer

was whether or not the group of properties which satisfy the Supervenience role can

perform needed philosophical work by also fulfilling the Magnetism role introduced in

§3.7. As I have shown, they cannot. The most explanatory version of the Magnetism

role is one which relies on an indirect form of the appeal (see §6.6). The properties

which are needed to satisfy Magnetism are not the same as those which are joint-

carving (see §6.7). Furthermore, even when joint-carving properties do make for a

sensible restriction on intentional content we find that another explanation of why they

play this role is available which does not depend on the notion of privileged properties.

The account of rationality as a constraint on acceptable interpretations of a language

given by Schwarz and Weatherson is compatible with there being no distinction

between privileged and non-privileged properties whatsoever. According to their

indirect form of the appeal to eligibility, it is never the fact that certain properties are

privileged that makes them eligible contents. The property of being green would be a

good candidate for the content of the miner’s belief about emeralds even if properties

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were not divisible in this way, simply because greenness is a property which lends itself

well to having inductive judgements made involving it. Assigning this content would

make the miner’s behaviour and communication with others intelligible in a way that

wildly non joint-carving or overly joint-carving contents simply would not. The miner

has observed the greenness of emeralds and formed a belief about the nature of

emeralds on the basis of that observation. If indeed there is a distinction between

privileged and non-privileged properties which may be justified by some other means,

then it would no doubt be an interesting observation to note that a principle of

attributing rational beliefs to individuals produces more attributions of content that is

at least somewhat joint-carving than content which is not at all joint-carving, but this

cannot by itself amount to an independent justification of the posit of privilege. If the

posit did add some unity and intelligibility to our thinking about metasemantics it

would do so only to the extent that joint-carving content was more rational to have

beliefs about but as we have seen this is so only in a minority of cases. There is no work

being done here by the concept of privilege. Rationality is in this case bearing the

weight of the eligibility constraint. In emphasising rationality over and above joint-

carving, we can secure a response to the indeterminacy argument that does a better

job of unifying the available data without the theoretical commitments of privilege.

I conclude that Magnetism should not be counted as work for privileged properties,

just as chapters four and five showed that there was no work for privileged properties

in satisfying the Similarity role. The Magnetism role is better satisfied by properties

which do not also fulfil the Supervenience role. If the properties which satisfy

Supervenience are not also Magnetic, there is no gain in theoretical virtue for the posit

of privilege associated with the combination of these roles.

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Chapter Seven: Implications for Theories of

Privilege

7.1 Summary of findings

In this thesis I have argued that the central claim made by privilege theorists is

incorrect, and that the roles which privileged properties are supposed to perform are

not fulfilled by one and the same group of properties. In this final chapter I aim to

summarise my findings thus far, too say a little about what this means for theories of

privilege, and consider some objections to the possibility that we might do without

privileged properties altogether.

In the chapter one I identified a class of metaphysical theories originating in the final

decades of the twentieth century, which I termed ‘theories of privileged properties’.

The central claim of all theories of privilege is that there is an elite group of properties

which are solely responsible for performing a number of specialised roles in

combination. Although there is a great deal of variety amongst theories of privilege, I

showed that we could identify scientific realism as a particularly important

commitment of the majority of privilege theorists, in particular Armstrong (1978b pxiii),

Lewis (1983 p203) and Sider (2011 p19). All three of these theorists are committed to

producing metaphysical worldviews which respect the astonishing success of scientific

inquiry and take the subject matter of scientific theories to represent a privileged

window on reality (see §1.3). This enables us to separate out a category of theories of

privilege as representing the mainstream philosophical approach to privilege. For these

mainstream theorists of privilege the belief in an elite minority of properties is justified

by the work they do. The more roles of philosophical significance that can be performed

by the privileged properties, the more justified we are in assenting to their existence

(see §1.4).

In chapter three I showed that three roles for privileged properties were of particular

importance. After Dorr and Hawthorne’s terminology, I called these roles

Supervenience, Similarity and Magnetism (Dorr and Hawthorne 2013). In chapters four,

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five and six I argued against the co-satisfiability of the Supervenience role with Similarity

and with Magnetism. In chapter four, I showed that Lewis’ argument for taking

Similarity to be among the roles of privileged properties is unsuccessful, and that there

are better accounts of ‘genuine similarity’ available which avoid commitment to

privileged properties altogether. In chapter five I went on to show that a theory of

privileged properties which combines both Supervenience and Similarity is

incompatible with the Lewisian theory of the semantics of counterfactuals. Finally, in

chapter six I showed that the properties which satisfy the Magnetism role and the

properties which satisfy Supervenience are not the same in our ordinary experience. I

proposed instead that we take norms of rationality to be a guide to those properties to

which our words tend to refer. Doing so resolves problems of indeterminacy in

metasemantics in a more explanatory way, and does so without any commitment to

privileged properties.

These observations present serious problems for supporters of mainstream versions of

privilege. If the posit is to be deemed good or bad based on its ability to accomplish a

range of useful theoretical roles, anything which diminishes the work for which

privileged properties are proposed will make the posit as a whole less attractive. I have

shown that the three keystone roles of mainstream theories of privilege are not

performed by the same group of properties. Supporters of non-mainstream theories of

privilege which do not seek to combine Similarity or Magnetism with Supervenience are

unaffected by these observations. An example of such a theorist that I have already

mentioned is Schaffer (2004, see also 2010). In the following section I discuss what my

findings mean for our attempts to construct a systematic metaphysics. I consider

whether we should persist in a belief in privileged properties or abandon them, and

conclude that while this is a decision which will depend on further research beyond the

scope of this thesis to engage in, the prospects for egalitarianism about properties are

better than supporters of privilege consider them to be. In §7.3 I will show that

egalitarianism does not necessarily conflict with scientific realism.

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7.2 Implications for support for privileged properties

The argument of this thesis has been that mainstream theories of privilege do not work

as advertised, but the question remains as to what lesson we should draw from this.

There are two options available to us. On the one hand, we can abandon outright the

idea that there are privileged properties according to the mainstream view of them, or

we can propose solutions for the objections I raise in this thesis in the hope of

developing an account of privileged properties which preserves as much of the

usefulness of the mainstream approach as possible. This question is important, and to

provide a satisfactory answer to it would require another investigation as long as the

present one. In this section I propose only to sketch out some of the prospects for these

two options. I conclude that the more attractive option would be to do without

privileged properties, and in §7.3 I will say a little more about what taking this horn of

the dilemma would involve.

Amongst other things, privileged properties promise to answer our questions about

which regularities are laws of nature, play an important role in possible worlds

semantics for counterfactuals, and act as a constraint on meaning in a language, all

whilst conforming with our intuitions about scientific realism. We might sensibly

conclude that the potential value of privileged properties in terms of the simplicity and

explanatory power they lend a systematic metaphysics is sufficiently great that we

should persist in believing them in spite of the objections I have raised in this thesis. It

is not inconceivable that a supporter of privilege would argue that the potential

benefits outweigh the inconvenience of finding solutions to the problems highlighted

over the last three chapters.

Let us call a theory of privilege which succeeds in finding solutions to my objections

whilst retaining much of the mainstream account a theory of super-privilege. The

question of this section is whether it would be better to persist in the belief in privileged

properties or whether we should abandon that belief. The answer we give will depend

on our assessment of the prospects for a theory of super-privilege. In order for an

account of privileged properties to qualify as a theory of super-privilege, it would have

to retain at least two out of the three keystone roles for privilege: Supervenience,

Similarity and Magnetism. As I demonstrated in chapter three, there is nothing

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particularly explanatory or interesting about proposing a group of properties that fulfils

only one of these roles. There will always be a group of properties which satisfies

Supervenience. Even if it turns out that there is no neat minority of properties on which

all reality supervenes, the group which contains all properties would be a minimal

supervenience basis in the absence of anything smaller. We know this because

everything supervenes on itself (see §3.4). With respect to Similarity and Magnetism,

if we take it for granted that these roles are in fact satisfied by some properties, we

gain nothing by identifying those properties which satisfy a single one of these roles

with the privileged properties. A theory of super-privilege would have to work with a

different conception of the three roles themselves. In §5.8 I suggested some ways that

we could modify the Similarity role in order to avoid the conclusion of that chapter:

that the sharing of privileged properties cannot underlie possible worlds semantics for

counterfactuals. I also showed that none of them were attractive. Nonetheless, it is

some manoeuvre in this vein that a theory of super-privilege would require.

Our other option is to forgo the numerous benefits of the mainstream conception of

privilege. We would then be faced with a further choice between adopting some non-

mainstream form of privilege or outright egalitarianism about properties. Mainstream

theories of privilege we characterised as committed to a range of roles, in particular

Supervenience, Similarity and Magnetism, but there could still be some merit in

adopting a version of privilege that invokes a different combination of roles. This would

of course depend on whether there was any useful theoretical work for an atypical

theory of privilege to perform. Schaffer, for instance, constructs a theory of privilege

around the combination of the Similarity and Laws roles whilst ignoring Supervenience.

It should, however, be noted that Schaffer’s account of a law of nature is broader than

the one we considered in §3.5 in that he allows for laws of higher-order sciences such

as chemistry and biology rather than physics alone (Schaffer 2004 p92). We might

reasonably suppose that an approach which focuses on a combination of different roles

would not appeal to supporters of mainstream privilege, however. The abandonment

of the Supervenience role is a significant departure from the kind of properties

envisioned by Armstrong, Lewis and Sider. That being said, supporters of privilege

would likely be even less amenable to the alternative, which is doing without any sort

of privileged properties whatsoever. In §7.3 I consider what would be involved in

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making such a break, and argue that the consequences would not be so dire as might

initially be supposed.

7.3 Prospects for egalitarianism

Sider notably calls a commitment to privilege part of an instinctive, ‘knee-jerk’ realism

(Sider 2011 p18, see also §1.4). Although his thoughts echo those of a number of other

privilege theorists, Sider is more explicit about privilege being in accord with a certain

worldview. For this reason I will focus predominantly on remarks of Sider’s in this

section. My goal in this thesis has not been to attack the assumption that privileged

properties accord with our pre-theoretical notions about how the world works, but I

did note that privilege derives much of its appeal from its intuitive merit (see §1.3). If

we are to consider doing without privileged properties then this will require us to

rethink some elements of our worldview. In this section I consider how two challenges

to egalitarianism may be overcome. The first is making sense of our intuitive tendency

to view certain properties as more genuine or natural than others, which would

otherwise be explained in terms of privilege. The second is the problem of holding on

to scientific realism if we cannot hold the categories proposed by scientific theories to

be privileged. I conclude that both these objections can be overcome, and so

egalitarianism about properties remains a live option.

We can imagine the supporter of privileged properties issuing a challenge along the

following lines: if there are no privileged properties, why do we intuitively think of some

properties as more genuine or natural than others? I would respond that in this case,

the burden of proof lies not with the believer in egalitarianism, but in the supporter of

privilege. Before the egalitarian must take seriously the challenge to make a place for

‘genuineness’ or ‘naturalness’, whatever the feature is that is being attributed to the

property of being green but not the property of being grue, the supporter of privilege

must first explain what this feature is, and whether or not anything actually has it.

The most obvious strategy for defining this feature which greenness has but grueness

does not is to tell us what the difference is between the properties which have it and

those which do not. One such strategy for doing so has been the preoccupation of this

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very thesis. In listing the roles and functions of privileged properties we get a sense of

how they are distinct from the non-privileged properties. Of course, we determined

that the attempts made by mainstream theorists of privilege to do just this were

unsuccessful. Until a satisfactory account of privilege (super-privilege) is developed, the

egalitarian need not engage with the requirement to make a place for the supporter of

privilege’s intuitions. Otherwise, the supporter of privilege who issues this challenge

would be comparable to the theist who dismisses atheism on the basis that it does not

make a place for her intuitions about holiness.

A separate threat to egalitarianism about properties is the question of its compatibility

with scientific realism. In §1.3 I argued that a commitment to scientific realism was

among the key motivations of supporters of privilege. It would take us too far beyond

the topic of this thesis to question whether or not scientific realism is worth holding.

Suffice it to say, however, that if egalitarianism meant abandoning scientific realism

then this may well be seen by many as a good reason to hold out for a theory of super-

privilege instead. The apparent problem for egalitarianism then is that Sider and others

claim that realism about the outputs of scientific theories does in fact require a belief

in privilege (Sider 2011 pp18-20, see also Lewis 1983 p203, Armstrong 1997 p25). In

the remainder of this section I will sketch why I take this view to be mistaken.

As we have already established, scientific realism lacks a single clear definition (see

§1.3). Rather than a set of well-established doctrines, scientific realism is more of a

loose collection of ideas, characterised by a positive epistemic attitude to scientific

inquiry (Chakravartty 2011 §1.1, see also Smart 1963 chapter 3). Scientific theories aim

at accurate description of the world, and we have reason to believe in the literal truth

of our most successful scientific theories. This can be contrasted with the view that

scientific theories are merely useful tools, good for making predictions about the world

but by no means to be taken literally. According to the scientific realist, the repeated

success of the atomic theory in test after test gives us good epistemic reason to believe

in hydrogen atoms, and that these hydrogen atoms have the property of being orbited

by a single electron.

Let us for the moment assume that this is a good definition of scientific realism. If this

is all that scientific realism requires, then egalitarianism is indeed compatible with it. It

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is not a consequence of egalitarianism that there are no hydrogen atoms, or that

hydrogen atoms are not orbited by single electrons. The successes of the atomic theory

would still give us very good reason to believe in exactly that. The main difference

between egalitarianism and a theory of privilege is that the egalitarian believes that

hydrogen atoms also instantiate many other properties, such as being a hydrogen atom

or being a sheepdog, and that we can identify no specialised roles fulfilled only by a

small group of these properties.

It is important to note that the form of egalitarianism under discussion here extends

only to properties, and not to objects. In this thesis I have carefully avoided the question

of whether or not objects can be deemed as privileged or abundant in a manner

analogous to properties. Lewis and Sider engage with this question. Sider extends his

theory of structure ‘beyond the predicate’ to objects as well as properties (2011 p85),

and Lewis proposes that we demarcate natural objects by looking for changes in natural

properties from region to region (1993). I have no particular commitment to privilege

of objects either way, and so the form of egalitarianism I discuss is perfectly able to

allow scientific theories to have a special access to what objects there are in reality.

Science can for instance tell us that the process of combustion does not involve a

substance being consumed, as in the phlogiston theory, but involves a chemical

reaction between particles of a certain kind, all of which are preserved in different

molecular configurations. Nor do I deny that one of the functions of science is to

discover properties, as supporters of privilege claim (Lewis 1983 p203). The only claim

I make for egalitarianism is that the properties which scientific theories discover are

not the only properties which exist, and they do not perform the range of specialised

functions which mainstream theorists of privilege claim. I am, however, happy to allow

that physics in particular is concerned with the discovery of a minimal supervenience

basis for reality, and as such the properties which physics discovers will satisfy

Supervenience, and the roles which are implied by Supervenience such as Independence

and Laws (see §3.5). As I mentioned in §7.1, my objections only apply to those theorists

of privilege which endorse a combination of certain roles with Supervenience.

Egalitarianism, at least the kind that I have in mind, is simply the claim that properties

discovered through scientific inquiry do not belong to an elite minority of properties

which perform specialised functions. That said, there is a sense in which both

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scientifically discovered properties such as being an electron and ‘gruesome’ properties

such as Florb (see §1.3) will have a special status relative to properties which lack any

instances at all, such as the property of being phlogiston.33

Supporters of privilege reject egalitarianism of this form, though. For these privilege

theorists, Sider in particular, being a realist about scientific theories means describing

the world ‘in its own terms’ (Sider 2011 p8). It isn’t enough that scientific theories

identify real features of real objects, but that these features which are identified are,

in some way yet to be explained, the right features in which to describe the world.

Unless this ‘rightness’ is just a matter of fulfilling the Supervenience role alone,

egalitarian properties cannot make a distinction between those features which are the

right ones by which to describe the world and those features which are less right. If this

extra requirement is indeed something that scientific realists should insist on, then

egalitarianism will not be compatible with scientific realism.

We noted that scientific realism is not a set of well-established doctrines, so whether

or not Sider’s extra requirement should be accepted depends on whether or not we

gain anything of value from accepting it. It is not apparent that we do. We already

established in this section that words like ‘rightness’, ‘genuineness’ or ‘naturalness’ do

not by themselves present a challenge to an egalitarian unless they can be defined, and

I have shown that the definition in terms of roles given by mainstream theorists of

privilege is unsuccessful. It would beg the question to reject the definition of scientific

realism I gave earlier on the basis that it fails to make a place for how the properties

discovered by science are special.

It is sadly beyond the scope of this thesis for me to say anything more substantial about

the prospects for a systematic metaphysics which does without privilege. Along with

an investigation into the privileging of objects rather than properties, and the prospects

for a theory of super-privilege, this must remain a topic for further research. My goal

33 There is no phlogiston in the actual world, at least. In §1.2 I made it clear that I was going to make no presuppositions about the ontological nature of properties themselves. On some accounts there may be an uninstantiated property of being phlogiston in the actual world. We might still be inclined to say that properties with instances in this world are indeed special compared with properties whose only instances are in other worlds. The same can be said of properties with no instances in any world, if there are any.

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in this thesis has not been to argue for either one of these options, but only to highlight

some serious problems with mainstream theories of privilege. The worldview according

to which there are privileged properties has become increasingly popular over the last

few decades, to the point where it threatens to become philosophical orthodoxy. As I

have made clear in this chapter, this may be no bad thing. Theories of privilege promise

much and ask relatively little in return. Even when movement in the direction of

consensus is good and inevitable, however, any such movement must be rigorously

scrutinised. The window on reality provided by modern science is a towering

achievement, but bear in mind that it is the role of scientists and not metaphysicians

to stand on the shoulders of giants. Our task, no less important, is to take any

opportunity to bite their kneecaps.

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The Metaphysics of Privileged Properties · 2018-12-28 · perform certain jobs, such as featuring in laws of nature, or grounding similarity between objects. Metaphysical posits