Universals Central Problems of Philosophy

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J. P. MorelandUniversals

CentralProblems ofPhilosophyGeneral EditorJohn Shand


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Universals


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Central Problems of PhilosophySeries Editor: John Shand

This series of books presents concise, clear, and rigorous analysesof the core problems that preoccupy philosophers across allapproaches to the discipline. Each book encapsulates the essentialarguments and debates, providing an authoritative guide to thesubject while also introducing original perspectives. This series ofbooks by an international team of authors aims to cover thosefundamental topics that, taken together, constitute the full breadthof philosophy.

Published titles

Free WillGraham McFee

Forthcoming titles

Action ParadoxRowland Stout Doris Olin

Analysis PerceptionMichael Beaney Barry Maund

Artificial Intelligence RelativismMatthew Elton & Michael Wheeler Paul OGrady

Causation and Explanation RightsStathis Psillos Jonathan Gorman

Knowledge ScepticismMichael Welbourne Neil Gascoigne

Meaning TruthDavid Cooper Pascal Engel

Modality ValueJoseph Melia Chris Cherry

OntologyDale Jacquette


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Universals

J. P. Moreland


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J. P. Moreland, 2001

This book is copyright under the Berne Convention.No reproduction without permission.

All rights reserved.

First published in 2001 by Acumen

Acumen Publishing Limited15a Lewins Yard

East StreetCheshamBucks HP5 1HQwww.acumenpublishing.co.uk

ISBN: 1-902683-22-6 (hardcover)ISBN: 1-902683-23-4 (paperback)

British Library Cataloguing-in-Publication DataA catalogue record for this book is available fromthe British Library.

Designed and typeset by Kate Williams, Abergavenny.Printed and bound by Biddles Ltd., Guildford and Kings Lynn.


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Preface and acknowledgements vii

1 The problem(s) of universals 1

2 Extreme nominalism and properties 23

3 Moderate nominalism and properties 50

4 Minimalist realism: Wolterstorffs kinds andArmstrongs properties 74

5 Traditional realism: properties are abstract objects 97

6 Traditional realism: issues and objections 114

7 The individuation of particulars 140

Notes 158Bibliography 170Index 181

Contents


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Preface and

acknowledgements

This book is a study in analytic ontology with a focus on issues andoptions at the core of the problem of universals. The problem ofuniversals is actually a cluster of related issues central to debatesamong extreme nominalists, moderate nominalists and advocatesof various forms of realism about the ontological status of proper-

ties. The book is intended to be an introduction to the topic and Ihave aimed the level of exposition at upper level undergraduates,graduate students and professional philosophers, and I believe thebook should be of value to all three groups. Given the intendedaudience, the book is an introduction, not in the sense of beingaimed at beginning students in philosophy, but in the sense of seek-ing to focus on the most important issues central to the subjectmatter. Because of this focus and space limitations, I have of neces-

sity refrained from addressing certain topics in the study ofuniversals that have been prominent in the past ten years, specifi-cally: the relationship between higher and lower order universals;the relationship between universals and causation, laws of natureand scientific explanation; the use of moderate (especially trope)nominalism to do work in various areas of philosophy. As interest-ing as these topics may be, those who study them bring to theirreflections positions on the more fundamental topics aboutuniversals. And, often, philosophers who discuss these currentissues seem unfamiliar with or inadequately appraised of importantdistinctions and arguments at the core of those more fundamentaltopics. For these reasons, I have chosen to focus in this book onthose subjects that have been of perennial importance to the study


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v i i i U N I V E RS A L S

of universals. There is a gap in the recent literature in these areas onwhich I focus, and I have tried to make a contribution to fillingthat gap.

Several people have been instrumental in helping me with thisproject. I want to thank Dan Yim and Joshua Blander for theirencouragement to undertake the book. I am grateful to Paul Copanfor informing me about the series to which my book contributes,and I have been helped greatly in the manuscript preparation byLisa Vasquez and Robert Garcia. My two editors, John Shand andSteven Gerrard, have been an absolute delight to work with.Finally, my philosophical mentor, Dallas Willard, and my

colleagues in philosophy at Biola University have played a specialrole in my own philosophical development, and it is a joy for me toacknowledge them in this way.

J. P. Moreland


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11111 The problem(s) of universals

Along with the metaphysics of substance, the problem of universalsis the paradigm case of a perennial issue in the history of philoso-phy. The problem of universals is actually a set of related issuesinvolving the ontological status of properties. Prima facie, it wouldseem that properties exist. Indeed, one of the most obvious facts

about the world is that it consists of individual things that haveproperties and that stand in relations to other things.1 It would alsoseem that several objects can have the same property; for example,several things can possess the same shade of red. But both the exist-ence and nature of properties have long been a matter of disputeand the problem of universals is the name for the issues central tothis debate.

Those who accept the existence of universals have appealed to a

number of phenomena to make their case (e.g. the meaningfulnessof language, the lawlike nature of causation, the inter-subjectivityof thinking, our ability to classify and recognize new entities,gradation and the need for perfect standards or ideal paradigms).However, historically, the problem of universals has been mainlyabout the One and Many (a.k.a. One over Many, One inMany), which involves giving an account of the unity of naturalclasses. To illustrate, consider the following words: RED, RED,BLUE. How many words are in the sequence? Two answers seempossible: either two or three words. There would seem to be twoword types and three word tokens, where a type is a kind of wordthat can be instanced in different places and a token is a specificinstance of a type. If we form a set containing the first two tokens,


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2 U N I V E R S A L S

the unity of the set would seem to be grounded in the fact that bothtokens have the same word type in common. Similarly, if we hadseven red and three blue balls, there would be a sense in which we

would have two different colours and another sense in which wewould have ten different colours. There would be two kinds ofcolours red and blue and ten instances of colour. A set contain-ing the seven red balls seems to exhibit a natural unity in that eachball has something in common not possessed by any of the blueballs; namely, the colour red. Issues and options regarding the Oneand Many have formed the core of the problem of universals sincethe time of Plato. What are we to make of sameness of type? What

distinguishes a class of tokens that mark off a real natural class froma contrived artificial class?2 What grounds class membership innatural classes?

However, since the problem of universals is about the ontologi-cal status of properties, it goes beyond the One and Many andincludes these questions:

Do properties exist? If properties exist, are they universals or particulars? If properties are universals, are they abstract objects? What is the relationship between a property and the thing that

has it? Is the property in what has it and, if so, what sort of inis this (spatial, non-spatial)?

If properties exist, can they exist even if no particulars exem-plify them?

In addition to properties and concrete particulars (roughly,individual things like balls and baboons), are there property-instances? If so, are they simple or complex entities?

If properties are universals, what account can be given of theindividuation of two entities that have all their pure propertiesin common?3

The chapters to follow take up each of these questions along withother topics central to debates about universals. The remainder ofthis chapter highlights central issues and distinctions relevant todebates about properties.


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T HE PR OB LE M( S) O F U NI VE RS AL S 3

Issues and options regarding the ontological status ofproperties

Attribute-agreement and extreme nominalism, moderatenominalism and realismThe issues and options in the debate about exemplification can beclarified by an example of what is called attribute-agreement.4 Sup-pose we have before us two round red spots. Suppose further thateach spot has the same shade of red and the same roundness.5 Letus call the two spots Socrates and Plato. Let us also use red

1and

red2

to stand for the redness of Socrates and the redness of Plato,

respectively.Attribute-agreement can be interpreted in three general ways.

First, there is an interpretation called extreme nominalism. Thereare several varieties of extreme nominalism, but they all excludeattributes as they are construed by the realists or nominalists. Theextreme nominalist offers this reductive analysis:

a has the attribute F, if and only if, Q.

Different versions of extreme nominalism will spell out Q in differ-ent ways.6 A predicate extreme nominalist parses Q as the predi-cate F is true ofa; a class extreme nominalist as a is a member ofthe class of F-things; and a concept extreme nominalist as a fallsunder the concept F. The fundamental feature of this account ofattribute-agreement and exemplification is its denial that attributes

form an additional category of being distinct from the things thathave them (unless, of course, a new category other than that ofproperty is introduced, to which properties are reduced, e.g. predi-cates, classes, concepts, etc.). Rudolf Carnap, Nelson Goodman, W.V. O. Quine, Wilfrid Sellars and Anthony Quinton are importantextreme nominalists.

The second major interpretation of attribute-agreement is calledmoderate nominalism. A moderate nominalist acknowledges theexistence of qualities but denies that attribute-agreement is to beexplained along realist lines where qualities are universals. Themoderate nominalist denies that the redness of Socrates is numeri-cally identical to the redness of Plato. Socrates and Plato may bothhave a determinate shade of colour that is exactly alike. But the


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two do not share the same numerically identical quality. Platoand Socrates each has a particular entity that is not multiplyexemplifiable; a little red. Quality instances construed along

moderate nominalist lines have various labels: tropes,7

abstractparticulars,8 perfect particulars,9 cases,10 aspects,11 unitproperties,12 property instances13 and moments.14 G. F. Stout,D. C. Williams, C. B. Martin, and Keith Campbell are four impor-tant contemporary nominalists.

Finally, there are realist treatments of attribute-agreement.There are different varieties of realism. For example, Aristotelianrealists disagree with Platonic realists over the question of the exist-

ence of uninstantiated universals. Traditional realists like Rein-hardt Grossmann hold universals to be non-spatio-temporalabstract entities and realists like D. M. Armstrong take them to bemultiply spatialized entities, located at the various places where thethings exemplifying them exist. But realists are agreed in holdingthat when attribute-agreement obtains, it is to be explained by anappeal to universals. The realist will argue that Socrates and Plato

both partake of, exemplify or instantiate a single attribute:redness. Thus, properties are universals that are multiply-exemplifiable, and attribute-agreement involves various particularshaving literally the same property. Recent important realists areEdmund Husserl, Gustav Bergmann, Reinhardt Grossmann,Nicholas Wolterstorff, Michael Loux and D. M. Armstrong.

Three important phenomena relevant to the debate aboutpropertiesAs mentioned above, from the time of Plato realists have offered awide variety of arguments in support of their views. However, threephenomena have been most important in the debate: predication,exact similarity and abstract reference.15 In each case, the realistappeals to what appear to be obvious facts, claims that they have astraightforward and powerful way of accounting for those facts andchallenges the extreme nominalist and moderate nominalist to comeup with an equally plausible analysis. In this way, the realist believesthat the burden of proof is on the other two schools of thought.

To probe the dialectic more deeply and relate these threephenomena to the traditional problem of universals (the unity of


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natural classes), let us begin with predication by considering thefollowing true statements:

(1) Socrates is red.(2) Plato is red.

Realists have a very powerful, direct way of explaining the truth ofsentences like (1) and (2): Socrates and Plato, have a property redness and the exemplification of redness by Socrates and Plato,respectively, is what grounds the truth of (1) and (2). Moreover, inrelation to the One and Many, the redness of Socrates is identical to

the redness of Plato and, more generally, redness is what groundsthe unity of the natural class of red entities. Entities like Socratesand Plato are members of this (non-arbitrary) class because eachhas the same property which grounds class membership. A bluespot is not a member of this class because it fails to exemplify therelevant property. In light of the realist analysis of sentences like (1)and (2), the realist challenges the extreme and moderate nominalist

to come up with alternative accounts that are adequate to explainthe truth of sentences of this sort.The second argument for realism focuses on certain obvious

facts about resemblance. Many particulars in the world exactlyresemble other particulars in various ways and these various waysconstitute the respects of resemblance that obtain between oramong the particulars. For example, Socrates and Plato are exactlysimilar to each other in being red. Moreover, the exact similarity

between two objects can be made the object of an intuitive act; theresemblance itself can be made an object of direct awareness, it canbe concretely distinguished, talked about and known. The realistwill explain these facts by grounding exact similarity in a propertyexemplified by the two resembling entities that constitutes theirrespect of resemblance. Thus, the resemblance between Socratesand Plato mentioned above is grounded in the fact that both Socra-tes and Plato share the very same property, redness, and redness isthe respect in which they exactly resemble each other. Related tothe One and Many, the unity of a class of exactly resembling redobjects is grounded in a numerically identical property redness exemplified by each class member while failing to be exemplifiedby objects excluded from class membership and that constitutes the


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respect in which all members of the class resemble each other. Therealist challenges the extreme and moderate nominalist to offer abetter explanation of exact similarity.

The third argument for realism involves the phenomenon ofabstract reference or, to state it non-linguistically, the fact thatproperties themselves have properties and stand in relations toother properties. Moreover, these facts appear to be necessary,unchanging ones in that they run throughout possible worlds. Forexample, consider the following sentences:

(3) Red resembles orange more than it resembles blue.

(4) Red is a colour.

The realist has a straightforward, powerful explanation for thetruth of sentences (3) and (4) and the states of affairs they describe.They can claim that the key terms in (3) and (4), e.g. the subjectterm in (4), are abstract singular terms that refer to universals. Thiscan be made explicit by the following paraphrases:

(3a) Redness resembles orangeness more that it resemblesblueness.

(4a) Redness is a colour.

The realist also has a way of explaining the de re necessity that,prima facie, appears to characterize the relations among redness,orangeness and blueness expressed in (3a) and redness and coloured-ness in (4a). In (3a), the relations are internal relations (see below)

among universals in the same quality-order and in (4a), the relationis a determinable/determinate predication relation between a secondand first order universal. Historically, the phenomenon of abstractreference has not been an explicit aspect of debates about the Oneand Many to the degree that predication and exact resemblancehave. Still, abstract reference is related to the One and Many in atleast this way: redness, blueness, etc., are all entities in their ownright, they form a natural class of colours (and are not members ofthe class, say, of tastes) in that redness et al. have the property ofbeing coloured that grounds their membership in the class. Putdifferently, they are all determinates of the determinable coloured-ness. The realist challenges the extreme nominalist and nominalist tooffer a better account of the truth of sentences like (3) and (4).


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Three important issues in the exemplification of propertiesExtreme nominalists deny that properties exist and in Chapter 2 wewill analyse and evaluate alternative forms of extreme nominalism.

Moderate nominalists and realists agree that properties exist butthey give very different treatments of the nature and exemplifica-tion of properties. Morever, there are differences on these issueswithin the moderate nominalist and realist camps and Chapters35 will examine these differences in detail. For now, it will behelpful to introduce a taxonomy of the main versions of moderatenominalism and realism regarding three important issues in analys-ing properties and exemplification. For clarity, I shall focus our

discussion on the fact that Socrates is red. These three issues are:

the nature of the universal redness; the relationship between redness and the quality-instance red

1,

which is a constituent of Socrates; the problem of giving an assay of the quality-instance itself.

Let us consider these in order.

The Nature of the UniversalThere are two major views realist and moderate nominalist ofthe universal redness, with important varieties of each. First,there is the realist position with four main versions. The first two(allegedly) realist versions hold that the universal does not enterinto the being of its instances and, thus, is a one-over-many. One

example of this version is model/copy realism according to whichproperties are abstract entities that exist outside space and time anddo not enter into the particulars that supposedly have them.Instead, each particular has a copy of that property.

The model/copy view is not widely held because of the difficul-ties that have been raised against it. One such difficulty has beencalled the Third Man Argument. This argument points out that themodel/copy view of properties and exemplification makes twoassumptions that, taken together, lead to a vicious infinite regress:

TheNon-identity assumption: F things are F in virtue of someother thing, F-ness, which makes them F.

The Self-predication assumption: F-ness is itself F.


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The non-identity assumption asserts that, for example, severalred things (Socrates, Plato, a brick) are red in virtue of some otherentity, redness itself, which is copied in each red thing. The self-

predication assumption implies that not only are individual redthings red, but redness itself is red.

Many realists accept the second assumption but reject the firstone. They argue that the non-identity assumption only applies toparticulars and not universals; for example, it is true that all redparticulars are red in virtue of some other entity (redness), butredness itself is red and not in virtue of something else. But themain point here is that the model/copy view implies both of these

assumptions and, taken together, they lead to a vicious infiniteregress, which can be seen as follows. If we ask of a set of severalred things (Socrates, Plato, a brick) what it is that accounts for thembeing red, the non-identity assumption will tell us that this is due tosome other entity besides the red things, redness itself, that makesthem red by being copied in them. So Set 1, composed of threethings (Socrates, Plato, a brick), is a set of red things because of

redness.But now, the self-predication assumption assures us that not onlyare Socrates, Plato and a brick red, but redness itself is red. Thismeans that we can now puzzle over what it is that accounts for theredness of all the items in a new set, Set 2, composed of Socrates,Plato, a brick and redness itself. The non-identity assumption willdemand that our answer must appeal to some otherentity, call itredness

2, possessed by all the members of Set 2. But now we can

form a new set, Set 3, composed of Socrates, Plato, a brick, rednessand redness

2, and ask what it is that accounts for the fact that all

members of this new set are red. The answer will appeal to redness3,

copied by all members in Set 3. This procedure generates a viciousinfinite regress and, thus, the model/copy view should be rejected.

Another One over Many approach that is purportedly realisttakes the universal to be a kind. Advocates of this position usuallyaccept the existence of both universals and abstract particulars.Adherents of this view have been J. R. Jones,16 the NicholasWolterstorff ofOn Universals,17 Michael Loux for universals in thecategory of substance18 and many others.19 Some would addHusserl to the list as well.20 Wolterstorff, for example, tells us thata kind has two similarities and two differences when it is compared


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to a set,21 where set is defined in the standard way, viz. as a collec-tion of members and such that Set A and Set B are identical if andonly if they have all their members in common. Kinds are like sets

in that examples of a kind are membersof that kind. Kinds areuniversals to which instances belong.Thus, red

1is a token of the

kind redness. Secondly, there can be kinds of kinds, just as there canbe classes of classes.

Despite these similarities, there are two decisive differencesbetween sets and kinds. First, no set could have had differentmembers from those it does have, whereas many kinds can havehad different examples from those they do have. For example,

there might have been some current examples of the dodo,although it is now extinct. There are possible worlds where a kindhas fewer members and there are possible worlds in which a kind isextendible; where it has more members.22 Secondly, while sets areidentical just in case they have the same membership, kinds are not.Non-identical kinds may be coextensive in their members. Forexample, the dodo and the passenger pigeon are different kinds

that have the same number of current members, namely, zero. Ihave suggested that this position ispurportedto be a realist one byits advocates, but in Chapter 4 we will find reasons for taking it asa version of moderate nominalism. The moderate nominalist orien-tation of this position will become clear, I hope, when we turn tothe relationship between redness and red

1.

The next two versions of realism depict the universal as a One inMany. When Socrates is red, Socrates has the universal redness in

it. The universal is not some perfect particular over and aboveSocrates being red that is somehow copied in or otherwise relatedto Socrates. Redness is literally in Socrates as a constituent. Thefirst variety of One in Many realism can safely be called the tradi-tional view. It takes universals to be non-spatiotemporal abstractentities . Universals are literally in their instances, but they are notat the spatiotemporal location of those instances and the former arein the latter by means of a primitive non-spatiotemporal tie ofpredication. Gustav Bergmann,23 Reinhardt Grossmann24 andMichael Loux25 (in the categories of property and relation) repre-sent this view.26

A second version of One in Many realism is offered by D. M.Armstrong.27 Armstrong rejects the axiom of localization (no entity


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1 0 UN I V E R S A L S

can exist at different places or at interrupted time intervals) andclaims that universals are capable of being at several spatio-temporal locations at once. The universal redness is at the spatio-

temporal location where Socrates exists. If naturalism is the viewthat the spatiotemporal world is all there is, then we can make adistinction between pure naturalism (all entities have a single loca-tion) and impure naturalism (some entities have multiple location).Moderate nominalists are pure naturalists and Armstrong is animpure naturalist.

So much for varieties of realism. The second major view ofuniversals is a moderate nominalist one that comes in two main

forms. The first moderate nominalist position was advanced by G. F.Stout.28 He held that the universal redness is not a singleindivisible quality numerically the same in each red thing. Rather, itis a class of abstract particulars or quality-instances where these areto be understood as simple entities that can only occur at one pointin space at a given time. By simple Stout means basic or non-complex. An abstract particular is not itself a complex of more basic

entities. Each abstract particular in the class redness exactly resem-bles each other abstract particular in the class and there is nothingoutside the class that exactly resembles each member in the class;thus, redness is a class of abstract particulars or little reds whichstand to one another in the relationship of exact resemblance.

According to Stout, the unity of the class of reds is not to beexplained by their exact similarity to one another. Rather, exactresemblance is grounded in afundamentum relationis, the distribu-

tive unity of the class.29 On this view, a relation between twoentities presupposes a complex unity into which both entities andthe relation are combined. For example, consider two concreteparticularsa and b existing in the relation above and below. In thisview, this state of affairs presupposes a spatial complex in whichaand b exist in that specific relationship. This spatial complex is acomplex unity and is the fundamentum relationisof the spatialrelation above and below. Likewise, with regard to resemblingabstract particulars, the complex unity which is thefundamentumrelationisof this resemblance is the distributive unity of the class.This distributive unity is ultimate and cannot be analysed. Soabstract nouns like redness are not singular terms for Stout butgeneral terms. Redness refers to a class of reds that are exactly


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T HE P RO BL EM (S ) O F U NI VE RS AL S 1 1

alike and this resemblance is grounded in the distributive unity ofthe class.30

The second version of moderate nominalism has been advanced

by D. C. Williams31

and Keith Campbell:32

the universal rednessis a set of little reds called tropes. Tropes are qualities that are, atthe same time, particulars and not universals. The view differs fromStouts view in that now the unity of the set is grounded in therelation of exact similarity.33

Moderate nominalists differ in their analysis of exact similarity.Exact similarity is like identity in that it is transitive and symmetri-cal. It is hard to know what to say about reflexivity. One motive for

making exact similarity irreflexive would be the moderate nomi-nalists desire to ground the diversity between two exactly similartropes. If exact similarity were reflexive, then a given trope couldbe two instead of one. This is not a problem with identity, for eventhough it is reflexive, identity only holds between a thing and itselfand not anotherthing. This is not the case, however, with exactsimilarity. If exact similarity is reflexive, it can hold between trope

a and trope b, or between tropea and itself. A moderate nominalistmight find some other ground for whya is one and not two, or theymight leave it as a brute fact. But they could ground the diversity ofexactly resembling tropes by holding that this relation, unlike iden-tity, is irreflexive. So there is some presumption for taking it asirreflexive, but I do not think this is conclusive.

In addition to the formal features of exact similarity, there is theissue of whether to take it as an internal or external relation. D. C.

Williams took it as an internal relation. Gustav Bergmann went sofar as to say that Provided one rejects the Platonic alternative(separable universals), one cannot make an articulate case forperfect particulars without introducing an alleged internal relationof equality, or, as it is also called, exact similarity.34 Consider twoentities,a and b, standing in a relation R. There are two things trueof internal relations as they are normally construed. First, if the Rofa to b is internal toa, then anything which does not have that Rto b is not identical toa. If a relation is internal to some x, thenwhenx loses R, it ceases to exist. Put another way, two or moreentities are internally related if and only if there are properties ofthose entities that necessitate that the relation holds. Examples ofinternal relations would be is the capital of or is larger than.


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Secondly, internal relations are not primitive but, rather, aregrounded in the natures of the entities they connect. As GustavBergmann put it,

The ontological ground of an internal connection lies whollyin the two or more entities it connects. More precisely, it liesin their natures. The notion is so crucial that I reword it. Theontological ground of an internal connection is the natures ofthe entities it connects and nothing else. Still differently, aninternal connection has no ontological ground of its own.35

More recently, D. M. Armstrong has defined an internal relationas a relation which is logically determined by the nature of therelated terms.36 Armstrong goes on to point out that we can explainwhy internal relations are such that given two internally relatedentities a and b, there is no possible world in which the objectsremain unaltered but in which the internal relation fails to obtainby recognizing that internal relations are derived from and

grounded in the natures of the entities so related.

37

Ifa is largerthan b, then this state of affairs is grounded in the size ofa and thesize ofb. Another way of putting this is to say that an internal rela-tion is not a basic entity (which need not be grounded in a furtherentity) but is a derived one.

By contrast, exact similarity may be taken as an underived,primitive relation external to the entities it connects. External rela-tions are those that are not internal. If two entities,a and b, stand in

external relations to each other, thena and b can cease to stand inthat relation and still exist. This may be the view of KeithCampbell, but as we shall see in Chapter 3, his writings are unclearin this regard and he has changed his position during the last fewyears.

The relationship between redness and the quality-instance red1Some philosophers reject the existence of quality-instances and

accept only properties and concrete particulars in their analysis ofproperties and exemplification. On this view, if one embraces qual-ity-instances, then one is a moderate nominalist. Thus, ReinhardtGrossmann says:


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A certain view about the nature of properties has had a grip onthe minds of many philosophers. According to this view, thewhiteness of billiard ball A is not the same thing as the white-

ness of billiard ball B. Each ball has its own whiteness, so thatwe must distinguish between whiteness

1and whiteness

2, white-

ness1

being the colour of A and whiteness2being the colour of

B.38

Grossman seems to think that if a philosopher uses definite descrip-tions like the F of A or the F of B to refer to non-identicalentities, then that philosopher is a moderate nominalist. In later

chapters we will evaluate this claim. For those who accept qualityinstances like red

1, there are four major treatments of the relation

between them and their associated universals. First, there is whatcan be called the traditional realist view, which assays a quality-instance as a complex entity consituted by three entities: the uni-versal, a non-spatiotemporal nexus of exemplification and anindividuator. The state of affairs of Socrates being red is to be ana-

lysed as follows: a complex entity a quality-instance, moment,etc. which is predicatively red, is a part of the whole, Socrates.In this view, then, redness is predicated of red

1. This relation

has been called a variety of names: type/token, genus/species, part/whole and the relation of instancing or exemplification. Threeimportant features of this relation should be mentioned. First, thispredication relation is one of essential predication. This is whysome philosophers call it a genus/species relation. The important

point here is that the universal covers the nature of the quality-instance. Redness is an essential constituent in red

1. There is no

possible world in which red1

exists and is not red.A second feature is a very crucial one. Regardless of how it is done,

if the position is to remain a realist one, both the universality and theparticularity of the abstract particular must be given an ontologicalground. For the realist, the quality-instance must be a complex entity.There have been a variety of grounds given for the individuation ofthe quality-instance, including bare particulars, coordinate qualities,relations like space and time, and Leibnizian qualities like beingidentical to red

1. We will explore problems of individuation in

Chapter 7. Advocates of this general viewpoint would be Husserl (onone interpretation), Bergmann and Armstrong.


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Finally, neither the universal nor the exemplification relation isspatiotemporal. When a particular exemplifies a universal, theresultant state of affairs the particular having the universal is

itself particular. This is sometimes called the victory of particular-ity. Similarly, on this first view, when a universal is exemplified by aquality-instance, the resultant state of affairs, for example red

1, is

spatiotemporal even though two of the entities that compose it (theuniversal, exemplification) are non-spatiotemporal.

An alternative realist view has been offered by D. M. Armstrongaccording to which a universal is in the thing that exemplifies it andboth the universal and the exemplification relation are spatio-

temporal entities. The universal is spatially in and, therefore,located at the same place as the entity possessing it. Aside from thisdifference, Armstrongs analysis is the same as version one above.

A third position on the relation between redness and red1

is amoderate nominalist one. The relation is often called type/token,genus/species or kind/case. This view assays red

1as a simple entity.

Unfortunately, it fails to ground adequately the individuation of the

quality-instance. This position is held by Loux in the category ofsubstance, and it can be found in Wolterstorff. As I mentionedearlier, it might seem surprising to identify this view as a moderatenominalist one, since both Loux and Wolterstorff claim to berealists. I am sure that both of them would disagree with my labeland we will probe this tension in Chapter 4. To state the main issuebriefly, since they hold that quality-instances are simple entities,neither of them adequately solves the problem of grounding

individuation and their positions fall into moderate nominalism.Since a quality-instance is simple, there appear to be two optionsabout the kind and the kind/case relation. First, the kind may be atype of set or collection of quality-instances (without the exten-sional aspects of sets) that stand to those instances in a relation verysimilar to the of set membership. Secondly, it may be a perfectparticular over and above the being of its instances and not aconstituent of them. Here the kind/case relation is some sort ofmodel/copy relation or a primitive that would seem to bear ananalogy to the model/copy relation. What makes this a moderatenominalist view regarding properties is the simplicity of qualityinstances and the rejection of a constituent ontology regardingthem. Properties as kinds could still be abstract objects like sets, but


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they are not true universals if such are taken to be multiplyexemplifiable entities that are constituents of their instances.

Position four is uncontroversially a moderate nominalist one.

This view clearly takes the relation between redness and red1 to bethe of set membership. To say that red

1manifests (Williamss

term) the universal redness is to simply assert that red1is a member

of the similarity set of exactly resembling red tropes. This view isheld by Williams and Campbell.

An assay of the quality-instance red1

Quality-instances have been assayed in a variety of ways, but fromwhat we have already seen, there are two crucially different assaysof them relevant to the realist/moderate nominalist debate: realiststake quality instances to be complex entities with their natures inthem as constituents and moderate nominalists take those instancesto be simples.

First, the F ofa can be assayed as a complex entity. Realists

like Gustav Bergmann would assay the redness of Socrates as theuniversal redness, the nexus of exemplification, and an individu-ator; in his case, a bare particular. The redness of Socrates is afact or state of affairs. Realists are concerned to ground both theuniversal nature (redness) and the particularity (red

1or this red-

ness) in a quality-instance.Second, the F ofa (e.g., the redness of Socrates) can be assayed as

a simple entity. J. R. Jones says it is the universal particularized;39

Wolterstorff says it is the type tokened;40 and Stout, Williams andCampbell say it is a member of the set or class of Fs. A trope in thisview is a simple entity that has no other constituent outside theinfimae speciesthat grounds its exact similarity with other tropes inthe same set. Thus, while the trope is simple, it sustains two func-tions: grounding exact similarity with other tropes in its similarity setand being individuated from them. This view is stated clearly byCampbell: we must construct an ontology which does not accordthe particularizing role to one sort of being while attributingsortedness(quality) to another. We require one item with both roles;the Williams system attempts this.41 Both these functions arecaptured by red and the subscript 1 in red

1. Likewise, both

functions are captured by a and red in a red. The nature and


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Figure 1.1

The nature of the universal

Four (supposedly)realist views Two moderatenominalist views

Universals not in instance(One over Many)

Universals in instance(One in Many)

Model/copy

realism

Kind/case

realism(moderate

nominalism?)

Traditional

realism(in not

spatiotemporal)

Armstrongs

realism (in isspatiotemporal)

Primitive unity

of class ofabstract

particulars(Stout)

Unity of class of

asbtract particularsgrounded in exact

similarity (Campbell,external relation?;Williams, internal

relation)

Relationship of universal (redness) to quality-instance (red1)

Quality-instances do notexist (only properties and

concrete particulars)

Quality-instances do exist

Two realist views Two moderatenominalist views

Traditionalrealism

(properties/exemplification

abstract)

Armstrongs realism(properties/

exemplificationspatiotemporal)

Kind/case relation(Wolterstorff)

(realism or moderatenominalism?)

Set membershiprelation

(Campbell,Williams, Stout)

Figure 1.2

Assay of the quality-instance

Complex state of affairs with property,exmplification, individuator as constituents

Simple entity with no constituents

Figure 1.3


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particularity of a trope differ by a mere distinction of reason andwhenever A and B differ by a distinction of reason, A is identical to B.

Our discussion of properties and exemplification may be

summarized as shown in Figures 1.11.3.

Universals and philosophical naturalismThe debate about properties can be related to the debate aboutphilosophical naturalism and abstract entities. Howard Robinsonhas claimed that materialist theories are incompatible with realisttheories of universals. The tie between nominalism and material-

ism is an ancient one;42 his remark is intended to apply to certainforms of contemporary philosophical naturalism. Along similarlines, Reinhardt Grossmann argues that naturalists are at war withwhat he calls ontologists.43 According to Grossmann, the universeis the spatiotemporal totality of physical entities and the worldincludes every existent whatever, including non-spatiotemporalabstract entities. Naturalists deny the world and only believe in the

universe; ontologists like Grossmann accept the world.These claims are controversial and not all philosophers wouldaccept them. At appropriate points in Chapters 27, we will inves-tigate more fully the relationship between philosophical naturalismand the existence of universals, but for now it will be helpful tointroduce this topic.

Following Grossmann, let us define the universe as the total spatio-temporal system of matter and (impersonal) energy; that is, as the sum

total of material objects, in some way accessible to the senses and toscientific investigation. Let us also define the world as the sum total ofeverything that exists including non-spatiotemporal abstract entities.

Various issues are involved in a complete analysis of the notionof abstract object, but for our purposes two different uses areimportant. The first is metaphysical: an abstract object is a realentity that is not in space or time. Something is in space (or time) ifit has spatial (or temporal): (1) duration (we can ask how big orhow long is it); and (some would say or) (2) location (we can askwhere or when is it). Abstract objects have neither spatial (nortemporal) location nor duration. For the naturalist under consid-eration, nothing exists that does not have spatial (or temporal)location and/or duration. A second sense of abstract object is


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epistemological: an abstract object is one that is placed before themind by an act of abstraction, by concentrating on that object anddisregarding other things in ones field of awareness. As a rule of

thumb, realists use the ontological sense of abstract object andextreme nominalists and nominalists employ the epistemologicalsense. The naturalist under consideration could accept abstractobjects in the epistemological sense. We will use the ontologicalnotion unless otherwise indicated.

How does the debate about naturalism and the world relate tothe debate about properties? First of all, naturalists are eitherextreme or moderate nominalists. Advocates of these views believe

only in the existence of spatiotemporal concrete or abstractparticulars. They deny that properties are universals. Secondly, allrealists agree that properties can be exemplified by many things atonce; for example, the very same redness can be predicated ofmany red things at the same time. Does this mean that all realistsbelieve that properties are abstract entities; that is, entities that arenot inside of space and time? Let us review three realist views of

properties and exemplification.There are three main ways that realists have understood thisrelationship. The first is the model/copy view, according to whichproperties are abstract entities that exist outside of space and time.Moreover, properties remain outside space and time and do notenter into the particulars that have them. Instead, each particularhas a copy of that property.

The next two realist views are advocated by impure realists and

pure realists. These two schools of thought differ over a principleknown as the axiom of localization:

No entity whatsoever can exist at different spatial locations atonce or at interrupted time intervals.

Focusing on spatial location, concrete particulars like Socrates areat only one spatial location at one time. They cannot be in morethan one place at the same time. Now, the axiom of localizationsays that nothing can be in more than one place at the same time.Impure realists like D. M. Armstrong deny the axiom of localiza-tion. For them, properties are spatially contained inside the thingsthat have them. Redness is at the very place Socrates is and redness


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is also at the very place Plato is. Thus, redness violates the axiom oflocalization. Impure realists are naturalists at heart. Why? Becausethey accept the fact that properties are universals; that is, as entities

that can be exemplified by more than one thing at once. But they donot want to deny naturalism and believe in abstract entities that areoutside space and time altogether. Thus, impure realists hold thatall entities are, indeed, inside space and time. But they embrace twodifferent kinds of spatial entities: concrete particulars (Socrates)that are in only one place at a time, and universals (properties likeredness) that are at different spatial locations at the very same time.For the impure realist, the exemplification relation is a spatial

containerrelation. Socrates exemplifies redness in that redness isspatially contained inside of or at the same place as Socrates.

Pure realists such as Grossmann hold to a non-spatial (andatemporal) view of exemplification. Redness is in Socrates in thesense that Socrates has or exemplifies redness within its very being.But neither redness nor the exemplification relation itself is spatial.Properties are not in the concrete particulars that have them like

sand is in a bucket. The nexus of exemplification is not a spatialcontainer type of relationship.Thus, the impure realist accepts properties as universals but

rejects them as abstract objects. The pure realist claims that the bestway of understanding what it means to say that properties areuniversals is to view them as abstract objects. Moderate nominalistsare pure naturalists because they accept the axiom of localization,impure realists are impure naturalists because they reject the axiom

of localization but accept the idea that everything is in space andtime is some sense, and pure realists reject naturalism altogetherand embrace abstract objects.

Our discussion about extreme nominalism, moderate nominal-ism, and different form of realism can be summarized in Figure 1.4.

Key philosophical distinctions relevant to the problem ofuniversalsIt will be helpful for the pages to follow to close this first chapterwith a brief description of two laws of identity and three meta-physical distinctions that surface regularly in discussions aboutuniversals.


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Figure 1.4

Do properties exist?

No

Extreme nominalist (Sellars)

Yes

Pure realist (Grossman); Model/copy realist;Impure realist/impure naturalist (Armstrong);Pure naturalist/moderate naturalist (MN) (Campbell)

Are properties abstract (outsidespace and time)?

NoPure naturalist/MN;Impure realist

YesPure and model/copy realist

Acceptance of axiom of localization?

NoImpure realist

YesMN; Pure and model/copy realist

Are properties universals?

NoExtreme nominalist; MN(Model/copy realist?)

YesPure realist; Impure realist(Model/copy realist?)

Are properties in concreteparticulars?

No YesImpure realistPure realist; MNModel/copy realist

Is this inspatial?

NoPure realist

YesMN; Impurerealist

Extreme

nominalist


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Two laws of identityThere are two general laws of identity relevant to the problem ofuniversals. The first is known as Leibnizs law of the indiscernibility

of identicals:

(x)(y)[(x = y) (P)(Px Py)]

This principle states that for any x (e.g. that person who is J. P.Moreland) and for anyy (that person who happens to be EileenSpieks youngest son), if they are identical to each other (theyare, in reality, the very same entity), then for any property P (being

5'8", being human), P will be true ofx (J. P. Moreland) if and onlyif P is true ofy (Eileen Spieks youngest son). In general, everythingis what it is and not something else. Everything is identical to itselfand, thus, shares all properties in common with itself. This impliesa test for non-identity or difference: if we can find one thing true ofx not true ofy or vice versa, thenx is not identical toy. Leibnizslaw of the indiscernibility of identicals is relatively uncontroversialin philosophy and from now on the law of identity shall be used

to express this principle.There is another, highly controversial law of identity that will be

an important part of the discussion in Chapter 7: Leibnizs law ofthe identity of indiscernibles:

(x)(y)[(P)(Px Py) (x = y)]

This says that, for allx andy, ifx andy have all and only the same

properties, then they are identical to each other. Many philoso-phers take this principle to be false because, among other things,they believe that there is more to a particular than its properties.For example, we could have two red and round discs that had thevery same colour, shape, size, and so forth. They could share all andonly the same properties but still be two discs and not one becausean individual thing like a disc is not exhausted by its properties. Butas we shall see in Chapter 7, not everyone agrees with these claims.

Three important distinctionsClosely related to the nature of identity is a set of distinctions thatwill be of critical importance for evaluating the arguments in later


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chapters. The best place to turn for help in this regard is a discus-sion of three important distinctions by the great medieval philoso-pher Francis Suarez in Disputation VII of the Disputationes

Metaphysicae. The first distinction Suarez mentions is the realdistinction. This consists in the fact that two entities, A and B (e.g.my chair and my desk), are not identical and can exist as independ-ent entities in separation from each other. The second majordistinction is the distinction of reason. This is a purely mentaldistinction that does not actually intervene between the entitiesdesignated as distinct, as they exist in themselves, but only as theyare distinguished in thought. According to Suarez, there are two

types of distinctions of reason. First, there is the distinction ofreasoning reason (distinctio rationis ratiocinantis) This has nofoundation in reality and arises exclusively from the temporalactivity of the process of thought. For example, we distinguishPeter from himself in referring to him twice when we say Peter isPeter. Second, there is the distinction of reasoned reason (distinc-tio rationis ratiocinatae). This distinction arises from an inadequate

conception by the mind of the object. Assuming with Suarez thatGod is a simple entity, an example here would be the distinctionbetween Gods mercy and justice. The key thing about any distinc-tion of reason is this: if A and B differ by a distinction of reason (ofeither type), then A is identical to B.

Suarez goes on to argue that there is a third distinction thatoccupies a middle ground between the first two. This distinction isan actual one found in nature prior to any activity of the mind but

it is not as great as the real distinction between two separableentities. Suarez says the modal distinction intervenes between anentity and its mode. He illustrates this by saying that the modaldistinction obtains between the property known as quantity andthe-inherence-of-quantity-in-a-specific-substance. A mode is adependent, inseparable, genuinely distinct entity from that ofwhich it is a mode. If a modal distinction obtains between twoentities A and B (where B is a mode), there is non-identity betweenA and B and inseparability in this sense: A can exist without B butnot vice versa.

These three distinctions and the two laws of identity are impor-tant to remember while grappling with the issues in the chapters tofollow.


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Extreme nominalism and

2 properties

Realists claim to have a straightforward analysis of predication/exemplification, resemblance and abstract reference and they placea burden of proof on extreme and moderate nominalists to offerequally plausible accounts. Extreme nominalists deny the existenceof properties altogether and offer the following reductive analysis:

a is F Q

Different versions of extreme nominalism (EN) spell out Q indifferent ways. Five such versions are predominant. Predicateextreme nominalists analyse Q as a falls under F or F cor-rectly applies toa. Concept extreme nominalists take Q as a fallsunder the concept F or the concept F correctly applies to a.

Mereological or exploded object extreme nominalists understandQ as a is a part of the aggregate of F things. Class extreme nomi-nalists reduce Q to a is a member of the class of F things. Finally,resemblance extreme nominalists treat Q in one of two way: aappropriately resembles a paradigm case of an F thing or a is amember of the class of appropriately resembling F things.

After presenting three preliminary issues, the chapter analysesthese versions of EN in the context of predication/exemplification,resemblance and abstract reference. It is important to bear in mindthat resemblance may be either the phenomenon to be analysed orpart of the analysis of predication/exemplification. With this inmind, the first four versions of EN shall be presented in the contextof predication/exemplification. Resemblance EN will be discussed


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in connection with both the phenomenon of predication/exemplifi-cation and resemblance and, finally, abstract reference will beprobed as it relates to EN in general.

Preliminary issuesBefore investigating EN treatments of the three core issues, it isimportant to grasp certain relevant topics.

Infinite regresses

Infinite regress arguments figure prominently in debates aboutuniversals. An infinite regress argument tries to show that somethesis, task or state of affairs is defective because it involves aproblematic infinite regress. There are at least three forms ofinfinite regress arguments. Form one argues that a thesis is defec-tive because it generates an infinite series that, in fact, does notexist. Form two argues that a thesis is defective because it generates

an actual infinite (

0) number of entities (or tasks) and this isuneconomical.0

may be defined as a set that can be put into one-to-one correspondence with either the set of natural numbers orwith a proper subset of itself.

Form three involves claiming that a thesis generates a viciousinfinite regress. How should vicious be characterized here? Atleast three characterizations have been offered. Roderick Chisholmsays that One is confronted with a vicious infinite regress when one

attempts a task of the following sort: Every step needed to begin thetask requires a preliminary step.1 For example, if the only way to tietogether any two things whatever is to connect them with a rope,then one would have to use two ropes to tie the two things to theinitial connecting ropes, and use additional ropes to tie them to thesesubsequent ropes, and so on. According to Chisholm, this is a viciousinfinite regress because the task cannot be accomplished.

D. M. Armstrong claims that when a reductive analysis of some-thing contains a covert appeal to the very thing being analysed, itgenerates a vicious infinite regress because the analysis does notsolve anything, but merely postpones a solution.2 No advance hasbeen made. He says that this is like a man without funds who writescheques to cover his debts, and so on, forever.


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E XT RE ME N OM IN AL IS M AN D PR OP ER TI ES 2 5

Thomas Aquinas distinguishesper se andper accidens regressesand claims that the former are vicious, while the latter are not.3

According to Aquinas, there are two features of aper se regress:

It is not just a list of members, but an ordering of members inthe sequence.

The relationship among the members of the series is transitive.Ifa stands in R to b and b in R to c, thena stands in R to c, andso on.

Per accidens regresses may or may not fulfil the first condition but

they do not exhibit the second. Aquinas uses a series of efficientcauses as an example of aper se regress and a series generated by thefather of relation to illustrate aper accidens regress. According toAquinas, if there is not a first member in the series that simply hasthe relevant feature in itself, no other member of the series willhave that feature since each subsequent member can only pass onthat feature if it first receives it.

Other philosophers add to this that aper se regress is impossiblebecause it involves traversing an actual infinite and that cannot bedone. To illustrate, one cannot count from 1 to

0for no matter

how far one has counted, he will still have an infinite number ofitems to count. Such a task can begin, but it cannot be completed.Moreover, trying to count from

0to 0 can neither be completed

(it involves the same number of tasks as going from 1 to 0) nor

begun for the reasons given above by Chisholm: trying to reach any

number in the past will itself require an infinite traversal as apreliminary step. Now in aper se regress, the transitivity of therelation ordering the regress implies that the dependence amongmembers runs from the earlier to latter members. Thus, suchregresses are precisely like traversing from

0to 0.

When we examine predicate EN, we will look at the differencebetween object and relation regresses.

PrimitivesSome entities are derivative, that is, they may be analysed in termsof more fundamental constituents. A primitive is a entity (e.g.concept, thing) that cannot be further analysed. Virtually all


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metaphysical theories have primitives and it is always open to aphilosopher to claim that some entity or other is unanalysable. Forexample, some say that personal identity through change is primi-

tive; others reject this and analyse personal identity in more basicterms (e.g. continuity of memory, character, bodily resemblance).

When one philosopher claims an entity is primitive and anotherrejects this assertion, how should the dialectic proceed? There arethree things one can do in association with a claim that an entity isprimitive. First, one can point to the phenomenon itself and inviteothers to attend to it similarly in the hopes that their awareness ofthe phenomenon will persuade them that the entity is primitive.

Secondly, one can clarify the relations in which the primitive entitystands to other entities and thereby show the intellectual fruit oftaking the entity as primitive. Thirdly, one can highlight problemsthat follow from denying that the entity is primitive, includingrebutting proffered analyses of the entity. Generally speaking, sucha dialectic involves a costbenefit analysis of the different positionsand decisive refutation is usually hard to obtain.

The truth-maker principleD. M. Armstrong has advanced what he calls the truth-maker prin-ciple:

[F]or every contingent truth at least (and perhaps for all truthscontingent or necessary) there must be something in the world

that makes it true. The making is not causality, of course:Rather, it is that in the world in virtue of which the truth istrue.4

The truth-maker is the ontological ground that makes the proposi-tion true in the sense that it is the relevant intentional object (e.g.substance, property, state of affairs) the proposition is about and towhich it corresponds so as to be true. It is important to note that incases where a proposition is about dependent, say superveniententities, it is the supervenient entity itself, and not its subvenient base,that is the relevant truth-maker. Thus, on an epiphenomenal view ofmental states, the truth-maker for Jones is in pain is Jones being inpain, not the brain state on which this state of affairs depends.


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The truth-maker principle seems to be correct, although not allphilosophers accept it. In fact, certain versions of EN require itsrejection.

Arguments for ENThe remainder of the chapter will investigate EN treatments of thethree phenomena of central importance to the problem ofuniversals. To close out these preliminary remarks, it will be helpfulto list briefly three main arguments for EN:

The problems with moderate nominalism and realism aresevere and justify acceptance of EN. We will look at theseclaims in Chapters 3 and 5.

Philosophical naturalism is true and it either entails or else isbest explicated in terms of EN. Two responses have beenoffered to this claim. Some accept it and reject philosophicalnaturalism (see Chapter 6). Others reject the claim and attempt

to make room for either moderate nominalist or realist proper-ties within a naturalist framework. EN is justified in light of Ockhams (or Occams) Razor (a.k.a.

the principle of simplicity, parsimony, economy) and, therefore,should be preferred. In response, two different forms ofOckhams Razor should be distinguished. First, there is the epis-temological/methodological interpretation according to whichone should not make an assertion, assume the existence of some-

thing, or multiply explanations without adequate reason. Givena simpler and more complicated explanation of something (asmeasured by their relative number of entities or kinds of entities,axioms, principles), one should prefer the simpler if they areequally adequate explanations because the more complicatedone includes superfluous factors. Now this principle is hardlycontroversial and amounts to little more that the claim thatsomething should be justified if it is employed in an explanation,assertion, etc. So understood, it applies to all views of universals.Specifically, realists claim that they do have adequate reasons forembracing universals and that entities should not be subtractedwithout necessity. So while this first interpretation may place asmall burden of proof on the realist, it is negligible.


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There is a second, ontological interpretation according to whichreality itself is simply and, thus, a simpler ontology is a moreaccurate representation of reality than a less simple one. There are

at least two problems with this interpretation. First, it is not clearlytrue and actually seems false in some cases. For example, thefamous ideal gas equation,PV= nRT, is much simpler than the VanDer Waals equation, (P+a/V2)(V b) = nRT, but the latter is a moreaccurate representation of reality. Secondly, it is not easy to decidewhat criterion of simplicity should be employed. For example, oneontology may be simpler than its rival in the number of kinds ofentities while the rival contains fewer entities overall. It is hard to

come up with a non-question-begging way to decide which issimpler in the honorific sense. It would seem, then, that OckhamsRazor is best construed in the epistemological sense. So under-stood, it applies to all views, it places a slight burden on the realistto justify belief in universals, and the issue then becomes thestrength and weaknesses of the different views regarding predica-tion/exemplification, resemblance, abstract reference and other

phenomena. With this in mind, let us turn to EN treatments ofpredication/exemplification.

Predication/exemplification

The realist challengeRecall from Chapter 1 our two qualitatively indistinguishable red,

round spots, Socrates and Plato. Realists claim that, linguistically,sentences such as Socrates is red employ the predicate termred that in some way or another picks out a universal, redness,that all and only red things possess. Put in a directly ontologicalway, realists claim that when one attends to Socrates and Plato,one can see that: Socrates redness is not identical either to Socra-tes or to any other feature of Socrates; and the redness in Socratesappears to be identical to the redness of Plato. These claims arebest explained by saying that Socrates and Plato have the sameentity, redness, in them and this way of being in is properlycalled the nexus of exemplification. The realist challengesextreme nominalists to provide alternative analyses of predica-tion/exemplification.


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Predicate, concept, and mereological extreme nominalismPredicate, concept, and mereological EN have enough features incommon to allow us to analyse them together. Arguably, these are

the weakest versions of EN and at least two criticisms have beenwidely taken to be successful against them. For expositionpurposes, I shall focus on predicate EN, the view that a is F is tobe analysed as a falls under F or F correctly applies toa.

First, linguistic predicates are neither necessary nor sufficientfor specifying a property. They are not sufficient for there arecontrived predicates that express no properties. For example, sup-pose we introduce the predicate Rzim to stand for being the

Empire State Building, being the square root of minus one, andbeing the 1995 Super Bowl. Clearly, Rzim is a predicate but itdetermines no property whatsoever. Neither are predicates neces-sary. Socrates would still be red in a world bereft of language. Thesimple fact is that properties are far more numerous than are thepredicates in human language. Moreover, on reflection, it is obvi-ous to most people that properties are what make our predicates

correctly apply to reality not vice versa. Put differently,

(1) Red correctly applies to Socrates.

is not primitive as predicate EN implies, but rather capable ofanalysis:

(1) Socrates is red and red correctly applies to Socrates red-

ness.

A predicate EN could respond by appealing to possible predicates.In a world without language and where Socrates is red, he could saythat there is a possible world where the predicate red does applyto Socrates. It is beyond the scope of our discussion to enter a dia-logue about possible worlds. Suffice it to say that the ground for thepossible applicability of red to Socrates seems to be the redness ofSocrates, not vice versa.

D. M. Armstrong has raised a second objection to predicateEN:5 it is involved in two vicious infinite regresses, an object and arelation regress. First lets consider the the object regress. Accord-ing to predicate EN, each red thing is red because it falls under the


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predicate red. Consider this famous statement made by DavidHume (my italics):

When we have found a resemblance among several objects,that often occur to us, we apply the same name to all of them,. . . After we have acquired a custom of this kind, the hearingof that name revives the idea of one of those objects andmakes the imagination conceive it with all its particularcircumstances.6

As the italicized words bring out, predicate EN analyses one type (a

property) in terms of another type (the predicate). The redness ofred things is constituted by their relations to tokens of the wordtype red, all tokens of this word type are so in virtue of fallingunder a second order word type, and so on to infinity. This regressis both uneconomical and vicious since it merely postpones butdoes not solve the problem of removing types from the EN frame-work.

Secondly, the relation regress. Consider all pairs of red thingsand predicate tokens of red. In each pair, the red thing stands inthe falling under relation to its word token, and this relation is itselfa type of relation. The predicate EN may leave the falling underrelation unanalysed, in which case they are stuck with a type or mayclaim that each first order falling under token is of the same typebecause a second order relational predicate correctly applies to it.But this generates both a new object regress (the second order

predicate falling under itself, and so on) and the regress relationwithin our purview (since each first order falling under relationstands in the same type of relation a first or second order fallingunder relation with respect to the second order predicate, and soon). Either way, a type is part of the analysans and the regress isvicious.

These two objections have convinced most philosophers toreject predicate (concept, mereological) EN.7

Class extreme nominalismA class is a collection of entities called members. Two classes areidentical just in case they share all and only the same members.


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Class EN is the view that some object a has the property of being Fjust in casea is a member of the class of F things. Moreover, on thisview it is a brute fact that classes have the members they do and

class inclusion/exclusion is not grounded in something more basic,e.g. resemblance between members. Socrates being red turns outto be the fact that Socrates is a member of the class of red things.

At least five objections have been raised against class EN. First, adistinct class is not a necessary condition for there being a distinctproperty. This can be seen by what is known as the companionshipdifficulty, where there is a possible world with co-extensive proper-ties that, contrary to class EN, are distinct. Consider a possible

world with only three green sticky objects in it. Letting gand sstand for being green and being sticky, respectively, we can form theclass of these three objects as follows: {gs,gs,gs}. Now class ENimplies that there is only one property here since there is only oneclass, but clearly being green is a distinct property from being stickyin spite of the fact that there are not two distinct classes. Again, theproperties of being a unicorn and of being a griffin are distinct,

even though the class of griffins is identical to the null set as is theclass of unicorns and, therefore, identical to each other.A class EN could invoke a framework of possible worlds to solve

this problem. It could be argued that the class of griffins andunicorns and the class of green objects and sticky ones will bedifferent classes and, thus, different properties if we let the classesrange throughout all possible worlds. But this response seems inad-equate. In addition to problems with taking all possible worlds as

being equally real with each other and with the actual world, thereare properties that are necessarily coextensive (e.g. being trilateraland being triangular) and necessarily unexemplifiable (e.g. being asquare circle and being a red taste). In these cases, the classes areidentical, and, therefore, class EN implies that the properties areidentical but, in fact, they are distinct. It will do no good to claimthat in these cases the properties are really identical because clearlythey are not; for example, being triangular has, but being trialateralfails to have, the property of being an angle.

Secondly, a distinct class of particulars is not a sufficient condi-tion for there being a distinct property, as can be seen in the famousimperfect community argument. Consider a world with only thesethree objects in it: a red wooden thing (rw), a square wooden thing


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(sw), and a red square thing, Even though this is a legitimate class indeed, it is one in which each member exactly resembles all othermembers in the class it is a contrived class for which there is no

property. In general, contrived classes fail to have correspondingproperties as class EN would seem to imply.

Thirdly, class membership does not determine a property; its theother way around. Socrates being red is an intrinsic feature ofSocrates; one can decide its truth by inspecting Socrates alone. ButSocrates being a member of a set of other objects is a function ofSocrates standing in relation to other things and one cannot decidewhether or not this is the case by examining Socrates alone. More-

over, at least typical properties form what are called unrestrictedclasses; they can have a variable, potentially infinite number ofexemplifications that form variable classes. Now the property itselfdoes not change depending on how many times it is exemplified. Butthe identity conditions for a class imply that when classes changemembers they lose their identity. The class of red things might haveturned out differently, but redness itself could not have turned out to

be something else. Again, a framework of possible worlds could beinvoked to solve this problem but the projection of a class of entitiesinto a possible world seems to depend on which particulars have therelevant property in that world, and not vice versa.

This last remark suggests a fourth criticism: Some classes arenatural and some are clearly contrived with nothing in commonamong their members except class membership. Now the realistgrounds the difference in the fact that all the members of natural

classes have a property in common while all the members of con-trived classes fail to one. Obviously, this move in unavailable to anadvocate of class EN since it implies that: properties just are classesof particulars; and there is nothing prior to class membership todistinguish natural from contrived classes.

Two responses have been offered to this argument. Some claimthat all classes do, in fact, count for a property so that there is noreal distinction between natural and contrived classes, but thisseems clearly false. The class of red objects is natural; the classlisted above in connection with the imperfect community is not.Others argue that it is just a brute fact that some classes are naturaland others are not and there is no metaphysical ground for thisbrute fact. But this appears to be a mere assertion and, in light of


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the arguments listed above, it is more plausible to hold that there is,indeed, a ground for the difference. It may not be the one realistsoffer (e.g. resemblance EN implies it is the relation of exact similar-

ity among all and only members of a natural class) but that such aground exists seems hard to deny.

Finally, class EN seems to generate both the object and relationregresses. Regarding the object regress, class EN says thata has theproperty F if and only ifa is a member of the class of F things. Butnow the class of F things must be taken to exist and it seems to havethe property of being a class or, more precisely, classhood. Now aclass EN could respond that the fact that the class of F things has

the property of being a class may be analysed in terms of the class ofF things itself being a member of the unit class whose sole memberwas the class of F things. Still, it seems reasonable to ask of this newclass just what it is that makes it a class. After all, it is a type of thing.

Moreover, whatever it is that makes it a class must be intrinsic toit and not some external relation it sustains to something else (e.g.membership in a higher class). And it would seem to be the case

that it is the property of classhood that makes this second orderclass a class. If so, then the object regress is generated. This is avicious regress because at each stage the analysans has a propertyand this is precisely the target of reductive analysis, so no advancehas been made.

If a class EN denies that it is the property of classhood, then theyare still committed to an actual infinite number of ascending ordersof classes. At the very least, this is uneconomical, a value EN advo-

cates embrace. Moreover, this regress seems vicious. Why? Let theclass of F things be level 0, the unit class containing the class of Fthings be level 1, and so on. Now a class at level n cannot havemembers if it does not exist and it cannot exist if it doesnt have theproper nature to be a class. Yet this classs nature at level nconsists in its being a member of a class at level n + 1. If a thingontologically depends on its nature (however it is analysed) to existin the sense that its nature could exist if it did not but not vice versa(e.g. being human could exist without Quine existing but not viceversa), then there appears to be the kind of ontological dependencyfrom higher to lower entities in the series of classes that constitutesthe per se type regress. If so, then on this alternative, there is avicious object regress.


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Less controversially, class EN seems to generate the relationregress. According to class ENa is F if and only ifa is a member ofthe class of F things. Now this means thata stands in the membership

relation () to that class. Since this is a typeof relation (it has severaltokens, it differs from, say, various spatial relations), the analysansstill has a type in it (i.e. universality, kindedness) and this is just whatthe analysis sought to avoid. It will do no good to analyse all the firstorder tokens of in terms of ordered pairs; for example, to say thatSocrates is a member of the class of red things is to say the orderedpair is a member () of the classof all ordered pairs standing in the class membership relation.

This analysis explicitly employs e as a kind of relation because is a member () of . . . meansthat stands in the relation (a kindof relation) to the relevant set and, thus, it fails to eliminate referenceto a kind. Therefore, it falls victim to the relation regress.

Resemblance as a phenomenon and a solution to predicationResemblance may be taken as either a phenomenon for metaphysi-cal analysis or as part of the correct analysis to the phenomenon ofpredication. Taken as a phenomenon, cases wherea resembles bcan be analysed in terms of predication, e.g. red or the conceptred is true of botha and b (predicate/concept EN),a and b are bothparts of the relevant aggregate (mereological EN) or co-membersof the same natural class (class EN).

None of the versions of EN studied so far leaves resemblance aspart of its analysis of predication. In this way, resemblance EN isdifferent and it may be understood as either an analysis of predica-tion or the phenomenon of resemblance. In the former case, resem-blance EN amounts to the view thata has the property F if and onlyif eithera suitably resembles a paradigm case(s) of F things ora is amember of the class of all and only suitably resembling F things.Each disjunct spells out a slightly different variant of resemblanceEN. In the latter case, the fact thata resembles b is analysed interms ofa and b suitably resembling an appropriate paradigm caseor cases ora and b being co-members of the relevant similarityclass. In what follows, we will examine resemblance EN as asolution to the phenomenon of predication, since many of our


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observations are relevant to resemblance as a phenomenon or asolution to predication. And while resemblance comes in degrees,we will focus our discussion on cases of exact similarity. In Chapter

3, we shall look at some additional issues regarding resemblance asa phenomenon in association with nominalism. Some of our obser-vations there are relevant to EN.

Resemblance EN is clearly superior to class EN in its ability tojustify the distinction between natural and unnatural classes, sincethe former offers a clear ground for natural classes, viz. resem-blance among all and only members of the class. For the realist,cases of exact similarity where a exactly resembles b are cases

where there is some respect of resemblance, F, such thata and bboth exemplify F. Thus, realists claim that exact similarity can bereduced to an identity of universal which constitutes the respect ofresemblance. Socrates and Plato are exactly similar in, say, beingred since each exemplifies the very same property, redness. Resem-blance EN proponents deny that exact similarity can be analysed interms of identity of property and take exact similarity (and resem-

blance generally) to be a primitive, dyadic, internal relation that issymmetrical, transitive and, for some, reflexive.8 Resemblance EN,as well as the other versions of EN, are what has been called a blobtheory: while ordinary concrete particulars may be composed ofseparable parts, those particulars (and their parts, for that matter)are metaphysically structureless, undifferentiated wholes that, as aprimitive fact, exactly resemble other such wholes.

Several objections have been raised against resemblance EN. For

one thing, it suffers from certain forms of the companionship andimperfect community difficulties. The companionship difficultyarises when you have a possible world with co-extensive proper-ties, which, contrary to resemblance EN are distinct (or cases ofnecessarily co-exemplified properties such as being triangular andbeing trilateral). Lettinggands stand for being green and beingsticky, respectively, given a possible world with only three greensticky objects in it, we can form the class of these three objects asfollows: {gs,gs,gs}. Now resemblance EN implies there is only oneproperty here since there is only one class with objects that exactlyresemble each other and only each other, but clearly being green isa property different from being sticky in spite of the fact that thereare not two distinct classes.


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Moreover, there is a different contribution that being green andbeing sticky make to the resemblances between the various pairs ofthese three particulars. The realist can bring this out by saying that

they resemble each other in two respects, being green and beingsticky, and these are properties each object has. But the resem-blance EN, armed merely with a primitive exact similarity relation,cannot account for these different respects of resemblance. Theymight try to appeal to different paradigms a green one and asticky one and claim that the three particulars resemble each. Butthis wont work because the EN proponent must specify how thegreen paradigm is to be used in the analysis, but it is not clear how

this is to be done without making appeal to one being green and theother being sticky.

Alternatively, one might try to introduce two primitive predi-cates: green-resembles and sticky-resembles. But these appear to becontrived primitives. Why? Note that among the myriad of types ofexact resemblances in the word, the resemblance EN must nowintroduce a new primitive for each. Now given a new case of exact

resemblance, how are we to recognize the new primitive based onexperience of past cases of resemblance since the new case is acompletely new primitive? The realist does not face this problem.On their view, there is a pattern to all this. Each pair of exactlyresembling particulars has a respect of resemblance such that it is aproperty identical in each member of the pair. Thus, each newresembling pair does not involve a new primitive; rather, itinvolved the identity relation and a new property. By contrast, the

resemblance EN account not only seems contrived, it is uneco-nomical on two accounts: it multiplies primitives; and it has twoprimitive relations identity and exact similarity while realismhas only identity. EN attempts to avoid this last point by reducingidentity to exact similarity are highly counter-intuitive, since itseems obvious that the identity relation is a primitive metaphysicalentity.

The imperfect community argument shows that a distinct classof exactly resembling particulars is not a sufficient condition forthere being a distinct property. In a world with only these threeobjects in it, a red wooden thing (rw), a square wooden thing (sw),and a red s

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